AFCRL 681 THE UNIVERSITY OF MICHIGAN COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Physics Technical Report STARK EFFECTS IN THE NEAR INFRARED SPECTRA OF SIMPLE POLYATOMIC MOLECULES P, D. Maker ORA Project 03640 under contract with: AIR FORCE COMMAND AND CONTROL DEVELOPMENT DIVISION AIR RESEARCH AND DEVELOPNENT COMMAND CONTRACT NO. AF 19(604).6125 LAURENCE Go HANSCOM FIELD BEDFORD, MASSACHUSETTS administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR May 1961

This report was also a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1961.

ERRATA STARK EFFECTS IN THE NEAR-INFRARED SPECTRA OF SIMPLE POLYATOMIC MOLECULES Paul Donne Maker ORA Report 03640-1-T Page 42 line 8 read "(20)" for "(30)" Page 43 last line of Table VI read "TA" for,,Ci, B AtPage 47 line 3 read EXACT AM JM Page 54 line 12 read P(2) for P(1) 2 2 Page 95 line 14 read "2~ _" and "~ = 20 KV/cm", A+C Page 98 line 6 read "1.O" for "10"l Page 102 line 24 read "Edmonds" for "Edwards" Page 102 line 31 add ref. 21b: Peter and Strandberg, MIT Research Laboratory of Electronics Technical Report 336 (1957)

TABLE OF CONTENTS Page LIST OF FIGURES v LIST OF TABLES vii ABSTRACT ix I. INTRODUCTION 1 II. OUTLINE OF THE WORK 1 IIIo EXPERIMENTAL ARRANGEMENT 4 IV, THEORY OF THE STARK EFFECT OF POLAR SYMMETRIC TOP MOLECULES 23 V, OBSERVED STARK EFFECTS AND THEIR INTERPRETATION 49 5.1 Hydrogen Cyanide 49 5.2 Methyl Fluoride 64 5.3 Methyl Iodide 76 5o4 Ammonia 79 5o5 Water 90 VI SUMMARY 99 BIBLIOGRAPHY 102 iii

LIST OF FIGURES Fig. Page 1 High Field Stark Cell 9 2 Cell Breakdown Voltage as a Function of Sample Pressure 10 3 Diagram of Spectrometer and Auxiliary Optics 15 4 Diagram of Dual Detector Mount 22 5 Energies of a Linear Molecule in an Electric Field 39 6 Orientation of the Poynting Vector Relative to Space Fixed Axes 46 7 Stark Effects near the v3 Band Center of Hydrogen Cyanide 51 8 High Field Stark Effects in Hydrogen Cyanide 53 9 Stark Effect of P(1) in Hydrogen Cyanide Using Polarized Radiation 55 10 High Resolution Stark Spectrum of P(2) in Hydrogen Cyanide 56 11 Spectra Used in Computing the Dipole Mount of Hydrogen Cyanide in its v3 Vibrational State 62 ~R 12 Observed and Calculated Stark Spectrum of RR(6)3 in the v4 Band of Methyl Fluoride 67 13 Predicted Splitting and Difference Spectrum of the Line QR(3)2 in the 2v5 Band of Methyl Fluoride 68 14 Stark Effects Near RQ(J) of the v4 Fundamental of Methyl Fluoride 70 15 Stark Effects in the v4 Fundamental of Methyl Fluoride from RQ(J)2 to RQ(J) 7 72 16 Stark Effects in the v4 Fundamental of Methyl Fluoride from RQ() 7 to RQ(J) 13 74 17 Stark Effects in the v4 Fundamental of Methyl Fluoride under High Resolution 75 v

LIST OF FIGURES (Concluded) Fig. Page 18 Stark Effects near RQ(J) o f the v4 Fundamental of Methyl Iodide 77 19 Stark Effects in Methyl Iodide near RQ(J)3 of the v4 Fundamental 78 20 The vl Band Center of Methyl Iodide 80 21 DC Field Stark Effects in the vl Fundamental of Methyl Iodide 81 22 Energy Level Diagram for the R(1) Transition in the v1 Fundamental of Ammonia 85 23 Stark Effects of R(1) in the vl Fundamental of Ammonia 86 24 Stark Effect of R(3) in the vl Fundamental of Ammonia 88 25 Energy Levels for the R(3) Transition in the vl Fundamental of Ammonia 89 26 High DC Field Stark Effect of R(3) in the vl Fundamental of Ammonia 91 27 Stark Effects in Water near 3870 cm. 92 vi

LIST OF TABLES No. Page I Summary of the Optical and Electrical Characteristics of the Various Stark Cells. 12 II Comparison of the Spacing Between Rotational Lines in v3 HCN as Measured on the Michigan Ebert Spectrometer and as Reported by Rank. 20 III Nonvanishing Matrix Elements of DO DI Di+ and DI1 30 00 ~1 0 +1+1 ~11'750 IV Summary of Molecular Constants Pertinent: to a Perturbation Calculation of the Stark Effect. 34 V Polynomial Expansions for cJM( t) to Fit Data of Kusch and Hughes. 40 VI Perturbation Calculation to Fourth Order for the Stark Effect of a Symmetric Top Molecule. 43 VII Wave Functions for a Linear Molecule in an Electric Field. 47 VIII Relative Intensities of the Stark Shifted M Components of a Linear Molecule. 50 IX Summary of Observed and. Calculated Splittings and Intensities for the P(1) Line of the v3 HCN Fundamental. 57 X Summary of Data Used in Calculation for K1 for HCN. 61 XI Summary of Stark Effects Observed in the Spectrum of Water. 93 XII Coefficients in the Perturbation Calculation of the Stark Effect in Asymmetric Rotors. 96 XIII Summary of Nearly Degenerate Eigen States Having Connecting Dipole Moment Matrix Elements for the Water Molecule. 98 vii

ABSTRACT A survey has been made of Stark effects in the vibration-rotation spectra of simple polyatomic molecules. Employing a light guide type Stark absorption cell 90 cm long having front surfaced mirrors as parallel plate electrodes, fields of 120 kV/cm could be obtained with sample pressures below 1/4 mm Hgo The electrode spacing of 0.2 to 0.5 mm was evaluated by examining the fringe systems produced upon passing light through the cell perpendicular to its optical axis. For this purpose, partially transparent mirror electrodes were used. The gap was held to +~i(+ 2,5 microns), An Ebert-Fastie spectrometer of three meter focal length and equipped with a 300 line/mm grating 200 mm long afforded a resolving power in excess of 75,000 when used double passedo Liquid air cooled PbS detectors and synchronous amplifiers were used. Measurable frequency shifts were observed in the v3 fundamental of hydrogen cyanide. Its large dipole moment and simple spectrum made possible the resolution and identification of all the'M' components for the lines R(2) through P(3). Careful measurement (with a relative accuracy of ~ 5005 cm l) of the splittings yielded a value of 3.001 +.007 debye for the dipole moment of hydrogen cyanide in its v3 vibrational state. The identification of Stark components in the spectra of methyl fluoride and methyl iodide was made impossible by their dense zero field spectra. The low field Stark difference spectra did, however, show line intensities differing in a predictable way from the normal spectra. This intensity variation eliminated up to 70% of the normally observed absorption lines and could be used to advantage in making ix

assignments in the zero field spectrum. The Stark effects observed in the v1 fundamental of NlH resulted from field produced mixing of the wave functions describing adjacent inversion states and consequent vitiation of the a -aa, s-s selection rule. Near degeneracies which interacted in the presence of an electric field were found to account for the bulk of the Stark signals observed in the v1 and v3 fundamentals of water vapor. Stark effect techniques, at present difficult and applicable to only a few molecules, would become valuable new infrared. tools if a significant increase in resolving power (as might be obtained by using a Fabry Perot interferometer) were available, x

I. INTRODUCTION An electric dipole placed in a uniform electric field is acted upon by forces tending to orient it in that field. Classically, the dipole would align itself parallel to the field. Quantum mechanicallyy only certain angular orientations, each with its own energy of interaction, are allowed. Such effects were first observed in 1913 by Stark (1) in atomic spectra with electric fields of the order of hundreds of thousands of volts/cm. Stark effects in the pure rotational spectra of molecules having permanent dipole moments are extensively used in the microwave region (2) where fields of several hundred volts/cm produce sufficient separation of the components. Certain molecular beam experiments also depend upon the Stark effect (3). Stark effects in the vibration-rotation spectra of polar molecules were recently noted for 1NH3 and H110 by Terhune (4)0 The results, although not directly interpretable due to the large spectral line widths produced by the high gas pressures needed to prevent electrical breakdown, indicated that infrared Stark effect studies could be made provided that an absorption cell could be operated with low sample pressures and high electric fields (of the order of tens of thousands of volts/cm), II. OUTLIE OF THEE WORK The current investigation began with construction of such an absorption cell. It was learned (5) that fie of seeral hundred of thousands of volts/cm had been obtained at low gas pressures with closely spaced parallel plate electrodes under conditions of extreme cleanliness. The relation between these parameters is conveniently displayed by the Paschen curves (6). Here, breakdown voltage is plotted versus te product of sample pressure I

-2and electrode spacing, and it is indicated that for a pressure gap product less than about 2mm x lmm Hg depending upon the gas used, the breakdown voltage rises sharply to a limit imposed by field emission at the electrodes. Thus, the necessary conditions on the proposed Stark cell were that the electrode gap be fractions of a millimetery the length to be sufficient to produce 10% - 50% infrared absorption, with a sample pressure of about 1mm Hg, and that the cell could be incorporatedld into the foreoptics of a high resolution grating spectrometer. The final design of the Stark cell had front-surface mirror electrodes spaced 1/5 to 1/3mm apart some 90 cm long by 4 cm high. Electric fields up to 120,000 volts/cm were obtained at minimu gas pressures (1/2mm Hg or less), but higher pressures (and consequently lower fields) were necessary to obtain adequate absorption strengths for many transitions. Using the Michigan 3-meter double-passed Ebert-Fastie Spectrometer (7,8), observations in the three micron spectral region were made upon f mentals of GINI CH 3F CH3I' NI3H ad H200 Because of its very favorable dipole moment and moment of inertia, and its simple infrared spectrums HCN yielded to quantitative Stark effect measurementse, Spectral line shifts of as much as 1 cm were seen, and measurements of the shifts allowed a determination of the excited3 V vibrational state dipole moment. H3F cad H3I because of their less fPavorable molecular constants and ~3 Ol5I much more complicated spectra, did not demonstrate quantitatively measurable Stark effects, Hoever, their Stark effect spectra, when recorded as the differenee signal between absorption with electric field on and absorption with electrie field off, wre cons$iderably simpler and mch more easily

-3interpreted than their normal infrared spectra. In fact, with the aid of the Stark difference spectrum rotational assignments in the v4 fundamentals can readily and reliably be given, a task which otherwise would require extensive labor. The Stark spectrum of NH3 arises primarily from the inversion duality of the moulcule. The spacing between adjacent inversion level s s much smaller than that between adjacent rotational levels, and, consequently, the principal interaction with the electric field is through neighboring inversion levels. These facts imply that the wave functions describing adjacent inversion states will mix strongly in the presence of an electric field, allowing transitions otherwise forbidden~ Thus, the Stark spectrum shows not only large line shifts but also new, field produced absorptions, Observed Stark effects in the spectrum of H2O were in the main found due to the interaction of nearly degenerate energy levels in the presence of the applied field. Small shifts were also seen for lines arising from transitions between states of low rotational energy. Analysis of the Stark spectrum was complicated by the moderately strong absorpt;ion of traces of water vapor remaini in the spectrometer foreoptics. even after dry-nitrogen flushingo The effects encountered were fully explained on the basis of perturbation calculations except for the case of HCNo Here e small field approxiation was unsatisfactory and an exact solution of the Schroedinger equation including the electric field term s needed to account for the observed shifts and intensities' The Stark shifts produced in the present work are of the order of hundredths of a cml, excepting those due to the near degeneracies occurring in 1Ho3 and H2O and those found in the first few rotational lines of the HCN

spectrum.. The best resolution attaMinable was aebout 0o04 cm n so that auantitative measuraeents were all but impossible save in the few cases mentioned. IIIo. EPET ARRNGM A the expected Stark shifts were of the order of5 or in many ases smaller than the resolution availableg it was absolutely nery a to operate the spectrometer at peak resolutions This meant that sample pressures must be kept low enought to limit pressue broadening to a few hundredtEL of a cm" Thus having fixed the pressure (for most gases less thSn 3mm g ) the length of the Stark cell $t be sufficient to give adequate absorption0 However, the transmission efficiency of the cell ust also be consid ered in determin its optimm lengtho Consideration of the Pascn curves (6) indicated that at the pressures cQntemplated the electrode sepacing must be limited to fractions of a millimeter, and f her that the maX-lmm field applicable wold increase inversely as the second power of the electrode separationo The value of a small gap in this respect had to be balanced against the reduced transmission efficiency of the cell as the spacing decreased. It was decided to fix the cell lenth at 90 cm and spaci ng raned from 0t to O0., An appreciable transmission efficiency for such a long, narro cell could only be ahieved by sing it as a light gideo In this arrangement an image is formed at =he entrance to the cell and the r &iation emerging after a muti-reflection traversal is collected to form a iage of the exit aperture of the cell onto the entrance slit of the spectrometero The incident beam amst be confined to as narrow a cone as possible,, an the cell walls mlst be extremely flat and highly reflecting. Sine a mniW cell

-5'width of 0,2m was anticipated, and thie slit width of the spectrometer at maximum resolution was 0O04mm, a demagnification of 4X was indicated. The slit height was 1 cm, so that a cell height of 4 cm was necessary. The spectrometer operated at f/15, the cell at f/60. At this aperture, the extreme rays of the beam would strike the electrode at an angle of about 0.5~ from grazing incidence, a condition which seemed suitable. Calculations based on the optical constants of freshly deposited aluminum surfaces (9) ndiicated that a 90 cm Stark cell with a gap of 0,25mm operated at f/60 would have a theoretical efficiency of 90% for 3 micron' radiation polarized with its electric vector perpendicular to the plane of incidence, and 43% for the parallel polarization. These figures are extremely sensitive to the reflectivities used and severe downgrading of them is to be expected in practice where the reflecting surfaces are anything but'freshly deposited' and plane parallels With these requirements for the Stark cell firmly in mind, the most promising electrode seemed to be a front surface mirror, Thus the original Stark cells Model'IAt employed strips of 1/4" thick plate glass 36" long by 2-1/2" wide, selected for flatness, and aluminized in an especially constructed vacuum evaporator. There remained the problems of setting the gap uniformly over the length of the cell consistent with good electrical insulation, ane aking electrical contact to the film without disrupting either the flatness of the plates, their reflectivity the uniformity of the gap, or the electrical insulation. The first solution to these problemst which met with reasonable success$ used two 1/2" by 36" strips of 0oo08" Ltkin feeler gauge stock rnning lengthwise of the cell, one at the top and one at the bottom, to establish the gape The aluminizsed electrode ara extended

-6to within 1/4" of the ends of the cell, and to within 1/8# of the steel spacers.o Sall holes were bored through the glass electrodes at their centers, the electrical leads brought through these holes and soldered into place with indium Each hole was carefully filled with the solder and pared smooth at the surface to be aluminized. The pair of plates, separated by the spacers, was pressed together between the rails of two pieces of surface-ground 2-1/4t channel iron and cemented along the top and bottom edges with Araldite epoxy resin. Pressure supplied by a host of C-clamps over the spacers was uniformly distributed by inserting a strip of rubber between rail and glass. Once the resin set, the clamps were removed and the unit was secured in place inside a vacum-tight shell made of a piece of brass S-band waveguide having removable end plates with glyptal sealed rock salt windowso One electrode lead was internally attached to the vacuum shell which was grounded while the other was brought directly into the atmosphere through a vacuum seal to the glass electrode plate. The gas sample was admitted, and its pressure measured via a glass tubing system incorporating a differential oil manometer which was Araldited. directly to the vacuum shell. The manometer could be read to about + 30 microns Hg and had a range of 0 - 5mm Hg above the reference vacuum. This housing with its attachments was used without modification throughout the experiment. This cell allowed fields up to 70 kV/cm to be applied to several mm Hg of gas, enough to produce a O.7 cm shift of a 50-60% absorption line in the spectrum of HCNo The breakdown voltage versus pressure-gap characteristics of this and subsequent cells fell far short of that expected from consideration of the available Paschen curves. It was felt that dust specks between the electrodes initiated the discharge in the cells. Indeed, attempts

-7to produce dust-free cells by washing and assembling them in an air-tight dry box did yield slightly improved performance. Co C Costain (5) recognized this as the limiting factor and was able to attain fields of 500 kV/cm only after removing all traces of dust by immersion-washing his entire cell in purified liquids just prior to use. Considering the size and complexity of our cells, these operations were not feasible, and it seemed that dust specks would remain the field-limiting factor. The estimated transmission efficiency of this cell was 15 - 20% with a polarization ratio of about 61. The cell soon failed when intermittent sparking along the length of the electrodes caused immense current densities at the periphery of the solder spot which eventually melted down the thin alaminmm film, isolating the high voltage lead from the electrodes This weakss was corrected in later designs by using the spacer itself (or a narrow strip of OOl01" feeler gauge stock placed between spacer and electrode for those cells having insulating spacers) to conduct current into the film. The plates of Model'B' cells were aluminized to within 2mm of the ends and one edge was masked off to prevent electrical continuity through the steel spacer, a gap of about 1mm being left between the aluminum film of one electrode and the spacer-lead of the opposing electrode. The high voltage lead-out, a piece of enameled magnet wire, was soldered directly to the spacer,the joint sealed in epoxy and Apiezon W-10 0, and the lead brought out through a lucite observation port in the side of the vacuum shell. The enamel coating alone sufficed to prevent discharge from the lead in the space between electrode and shell wall at all vacuums and voltages encountered, This type of cell invariably failed due to intense sparking originating along the edge of the aluminum paralleling

-8the spacer. This led to the final electrode configuration, Model'C', shown in Figure 1. The steel spacers, at some sacrifice in gap uniformity, were replaced with ones made of Dupont Mylar, permitting the aluminized area to extend up to and beneath both spacers, eliminating the troublesome source of breakdown and at the same time minimizing electric field fringing effects. The strips were prepared by tightly winding an 8" x 96" piece of Mylar around a 2" spindle chucked in a lithe, facing one end of the bundle and slicing off the required width with a razor blade cutoff tool. This'produced a straight, square, and extremely smooth edge, necessary since the spaceredge serves also to reflect the vertically divergent light beams within the absoption cell, Having established a satisfactory design for the Stark cell, it remained to determine the optimum gap and electrode film material. It was found that the breakdown voltage was inversely proportional to the sample pressure (for small enough pressures and moderate fields) as would be predicted from the Paschen curves* Figure 2 shows the variation of breakdown voltage with pressure for a typical case. The upper voltage limit is evidently determined by the state of cleanliness of the electrodes but does show a distinct dependence upon the cell gap, varying approximately as the reciprocal of the electrode separation. Thias data was not particularly dependable as it involved a series of cells with different gaps, but there was no way to insure that the cells would all have equally clean (dirty) electrodes. Transmission measurements revealed efficiencies well below the theoretical maximum. As previously concluded, the chief reason for this discrepancy is undoubtedly due to the fact that the calculated value was based upon the optical constants for'freshly deposited', clean, unoxidized films. Even the vanishingly thin oxide film present on all aluminum surfaces exposed to

0.010 inch'MYLAR' F~igure^^ ^^^^^^-~0.001inch LUFKIN feeler gauge stock L.O.FI'MIRRO-PANE' 2.5 x36 x 0.25 inches Figure I HIGH FIELD STARK CELL

-10I I I 0 I 0 CELL GAP 0.011 in, ELECTRODE, CHROMIUM GAS' AMMONIA 0n 0 ^-\-^ \o~~~~~~~ o 0l~~~~~~~~~~ \ Lu~~~~~~r~ ~ ~ ~ ~ ~ ~ _J _ 0 \ I I 4 5 6 Od 0.._ C" 00 I 2 3 4 5 6 7 PRESSURE mm Hg Figure 2 CELL BREAKDOWN VERSUS SAMPLE PRESSURE

-llthe air will sharply reduce the calculated efficiency by refracting the light so as to increase its angle of incidence at the actual metallic surface, This does not inrease N, the total number of reflections sffered upon traversal of the cell lengths but does lower the reflectivity, R, which decreases linearly as the angle of incidence increases from grazing (for small enough departures from grazing)~ The transmission efficiency depends upon NI and since N is typically 30, even a small decrease in R will have a large net effects Aside from using idealized optical constants,' the calculated value failed to include losses due to reflections from either the unsilvered portions of the light guide or from the Mylar surfaces* Also not taken into account was the fact that slightly nonflat plates would increase the number of reflectionso The possibility of improving cell performance in both transmission and voltage characteristics by the film material was investigated, The only substance having optical constants materially superior to aluminm in the three micron region is goldo A cell was made having evaporated gold surfaced electrodes, and a slight increase in transmission over aluminum vas noted, However, the gold films seemed to be destroyed much more readily by the action of random breakdown sparking with resultant poor electrical characteristics and short operating life* Chromium was known to have superior characteristics as a high voltage electrode material (10) Although it was difficult to produce good uniform chromium films in our equipment because of the high temperatures needed in evaporation, a high quality front surface chromium mirror was available from Libbey-Owena-Ford under the te t name Mirro-pa.ne Tests with Mirro-pane cells revealed somewhat lower transmission efficiencies than for alumi-num

-12but generally improved electrical properties. Microscopic examination of the surface of an electrode in the neighborhood of a point at which a discharge had occurred revealed a dendritical pattern etched through the metallic flm accompanied by random globular deposits, evidently the remains of the detached filml With chrominum electrodes, the dendrites seemed shorter and the damage wrought by a single discharge seemed less that with aluminum films; perhaps due to the fact that chromium adhere o gs to g s orders of magnitude better than does aluminumo Thus, with regard to both cell life and to maximm bre akdown voltage, the Mirro-pane cells out-performed the aluminum ones. It was concluded that in spite of their somewhat lower transmission efficiency, the chromium cells were to be preferred, and the majority of the Stark measurements were made using these cells. Table I stummarizes the voltage and transmission characteristics of the various cells testedo TABLE I ummary of the Optical and Electrical Characteristics of the Various Stark Cells Coating Model Gap Max, Fielda Transo Polq Lifetime a Q Aluminum A.008" 80kV/cm 20% 6:1 poor B 00o8 80kV/cm 20% 6: poor C.oOl 60kV/cm 25% 4: 1 fair Chromium C o0085 120kV/cm 12% 10:1 good C 011 9ikV/cm 15% 5 1 good C.016 60kv/cm 20% 3:1 good Gold C o016 4OkV/cm 35%? poor a Measured with cell pressure less than one micron b Ratio of"Tj/T,,

-13Moreover, the Mirro-pane was about 10% transparent to visible lighto interference fringes of excellent definition could be seen upon looking through the cell parallel to the field direction into a monochromatic light source. The appearance (or disappearance) of a fringe upon scanning the cell across the line of vision heralded a decrease (or increase) in the gap of one-half the wavelength of the light employed. Thas a relief map of the spacing, in half-wavelength units, could be drawn for the entire cell area. Further, spectroscopic analysis of the light transmitted in this sense through the cell from an incandescent source revealed so-called'channel' fringes; that is, transmission maxima occurring when the gap is an integral number of half wavelengthso Measurement of these fringes yielded a determination of the electrode separation to one part in fifty thousand at a single point. Using this point as a reference, the relief map could then be employed to establish the mean gap and its tolerance. Using the above method, it was determined that with due care Stark cells could be constructed with a tolerance equaling either the thickness tolerance of the spacer or the flatness tolerance of the glass used, whichever happened to be larger. Thus, the cells having Iafkin No. 140 feeler gauge stock as their spacer had a tolerance of 2 fringes of sodium D light (1/4% of a 0o010" gap), a limit set by the plate glass. With Mylar spacers, the nonuniformity ranged upward to 2%, but at times was as good as 3/4%, depending upon the care exercised in selecting the spacers The bulk supply of Mylar seemed good to about 2/10,00".o Occasionally the Mirro-pane slabs as supplied were found unsatisfactory and had to be rejected, The electric field strength also depends upon the applied voltage, which must then be measured and maintained with an accuracy commensurate with that

-1iof the gape This was accomplished by using a Baird Atomic Model 318 regulated 0-2500 vDC power supply monitored by a Leeds and Northrup type K-2 potentiometer coupled to the supply through a thermally regulated precision calibrated voltage dividing network (203808 ~0,2:1) made of wire wound resistorso A Rubicon galvanometer with a sensitivity of 5 x 10 ua/mm allowed the voltage to be set to,05%. Regulation proved better than +.1% during a given run0 For operation with a 90 cps square wave Stark field, a negative-going 90 cps square wave signal from a Hewlett-Packard generator synchronized to the 60 cps line frequency was applied to the grid of a 6CU6 whose plate was connected directly to the Stark cell's hot electrode and also, through a 1/2 megohm 30-watt resistors to a 0-3000 V1C I amp unregulated power supply. In operation, the supply was set to its maximum voltage and the amplitude of the trigger signal adjusted to provide the desired cell voltage# This arrangement minimized rise and decay times, for the Stark cell discharged through the conducting 6CU6 and charged through the 3/2 megohm resistor toward the full B+ voltage until reaching the preset point at which the tube began to conducts Rise times of about 0O3 milliseconds and decay times of about OO01 milliseconds, compared to the ton' time of 5.5 milliseconds, were achieved at voltages up to 2000vDCo No precision voltage measurements were necessary in this mode of operation and the described tsquare' wave was found suitablei The spectrometer used is that described by Church (11), namely an EbertFastie Spectrometer (7a8) writh three meter focal length, double passed, having a 300 line/mm 6" x 8' Bausch and Lomb grating. The source (labeled IS' in Figure 3) was a 1-1/2" Nerset glower surrounded by a water-cooled vacuum

Ml, mf i - Mlo M,9 -T-G3 ~~~~~~~~~~~~~~~~~Mi~ M1mMo n m~~~~~~~~~ D w2| MaI / S.,I, a 5 G1 /J —,?~-G2, SP 13 M3 M4 F-,M2 ml~~~~~~~~~~~I s STARK CELL L Figure 3 DIAGRAM OF SPECTROMETER AND AUXILIARY OPTICS

tight jacket and operated from a Sorenson regulated Variac delivering one amp, An image of the source was formed on the entrance of the Stark cell by a KBr lens (L) set in a vacuum tight connecting tube. The exit slit 4 the Stark cell was imaged by a spherical mirror (M1), demagnified by three, at the surface of a small mirror ( 2) set at 450 to the beam. 4 was cut from a spectacle lens having the proper radius of curvature. to produce a curved image of the straight exit slit of the Stark cell at the curved entrance slit of the spectrometer, The alignment of the mirror had to be done carefully since the image on the spectrometer slits was not much wider than the 40 micron slit width. The mirror adjustments were cemented with epoxy resin, but building vibrations often interfered with the operation of the instrument. Leaving the small diagonal, the beam was filtered (F) using antireflection coated germanium (>75% transparent for the regions scanned) and chopped (C), all in vacuum tight brass enclosures, before passing into the spectrometer vacuum chamber through its sapphire window (W1). The foreoptics thus far described were dry-nitrogen flushed, which removed all atmospheric absorption except in the immediate vicinity of strong water vapor lines. Upon entering the spectrometer, the beam is reflected from a flat (M5) to a sphere (M4) demagnifying by 4/3 to another flat (DM) and finally to the entrance slit (Sn) In practice, the image was scarcely wide enough to fill the entrance slit and minute movements of any of the foreoptics after and including the Stark cell had the effect of scanning the image across the slit, causing disasterous signal fluctuations, Sturdy mirror mounts were designed and employed throughout this section of the optical path, ease of adjustment being generously traded for increased

-17vibrational stability. Once adjusted, the mirrors were cemented in place with epoxy resin (M1 excepted). This source of noise, except during huge building vibrations, was finally redced below that of the detector, It remained necessary to refocus (via M1) on the entrance slit before each run. The entire foreoptics as found to image 80% of the energy passing through a 200 micron slit set at the Stark cell exit, after 4X demagnification and image curvtagthrough a 50 micron entrance slit, The spectrometer proper had a theoretical resolving power, double passed, of 120,000 corresponding to a maximum resolultion of 0,036 cmg at three microns, Extensive efforts failed to produce spectra exhibiting resolution better than about 0o045 cm"1. Examination of the knife edge pattern produced when scanning the grating through either its central image or through a fifth order sodium line indicated that the cause of this discrepancy was nonflatness in the grating. Attempts to utilize the spectrometer in four-pass configuration thus gave only modest improvements in resolution and not the theoretically expected factor of two, at a sacrifice of about four in energy. A resolution of 0o040 cmn was observed in four pass with twice the theoretical minam slit widths and a signal about egqal to that obtained at mini mu slits when tWo-passed. Unfortunately, this mode of operation was not practical since the image of the Stark cell exit was mot wide enough to fill the expanded slits needed. This mltiple passing was accomplished by a set of flat mirrors (M7 and M8) aligned to intercept the beam in front of the exit slit, pass it across in front of the grating and send it through the collimator and dispersion paths again, this time at a slightly different elevation. To prove that imperfections in the grating did limit the resolving power, an optical flt was sublstituted for the grating and the central image scanned

with the instrment four passed. The test produced a central image line width only 5% greater than theoretically predicted. In attempting accurate wavelength measurements of the HCN spectra, it became evident that the rotational motion of the grating (G1) was not always continuous, eog,% on occasion the recorder trace of an absorption line would actually show a discontinuity. The drive chain, consisting ofs a) one of a choice of four drive motors, b) one of a set of four interchangeable spur gear pairs, c) a drive shaft extending through the spectrometer vacuum wall, d) a 128:1 precision lapped worm gear, e) a hand crafted nut and screw assembly 1-1/2' diameter 40 threads per inch 10" long and of extremely high precision, f) a steel tape, advanced by the nut, wound about a flat faced lO0i diameter ground pulley integral to the grating table, around a second identical pulley mounted on an idler shaft back onto itself, as completely disassembled, inspected, cleaned and carefully reassembled, t was also decided to apply a 3-1/2 pound gravitational load to the grating table so that screw and nut would be held forcibly in contact, rather than relying upon friction in the tape system The erratic motion of the grating, thus far detectable only if it occdrred while an absorption line was being traced, could only be investigated if a continuous accurate monitoring of the scan were availableo To do thisa a transmission grating (G2) 1/4" x 1" with 133 lines per inch was mounted with its lines parallel to the slit in the plane of the entrance slit (after re. / flection from a flat mirror, M13)o A similar grid (G3) this time 3" long by 1" high was mounted in a reflectfion (M) of the exit slit plane, and

-19an optically flat front surfaced mirror (M12) 2-1/2" square wvas mounted on a swivel table attached atop the grating supports With the optical flat in proper adjustment, a high quality image of the entrance slit grid was formed. by the spectrometer's collimator mirror (M6) at the exit slit grid. This grid was then adjusted so that its lines were exactly parallel to those of the image. The light transmitted by this system with the first grid uniformly illuminated from the back as modulated, in intensity by successive superposition of line upon line and line upon aperture as the grating table rotated, The output of a phototube placed to receive this radiation, wlen amplified, synchronously rectified and retcorded provided the desired monitoring, If the grating advanced discontinuously at any time during a run, the fringe record would also exhibit a discontinuity. Moreover, since many lines were being averaged in the superposition process, the grids could be considered'perfect and the spacing of the fringes used as a calibration device of greater reliability than the'counter numbers' (unit rotations at the low-torque end of the drive train) usually used for this purpose, Actual fringe traces demonstrated, in addition to occasional lurches in the grating rotation, random ripple attributa'ble to the ulttimate precision of the drive mechanism. Consideration of this ripple indicated that the grating angle was determinable to 8 x 10 7 radian corresponding to a linear motion of the drive tape of * 4 x 106 inches, a figure in keeping with the claimed precision of the nut-screw assembly. As a check on the scanning precision, the spectrum of HCN was run in the vicinity of its v3 band center and a dispersion relation established using the wavelengths reported by Rank (12) which have an absolute accuracy of i.003 ceL and a relative accuracy of o001 cm'l The grating drive uncertainty corresponded at

this wavelength to * *005 cm" o A dispersion relation based upon the counter numbers did aceoeunt for the observed relative line positiorns to within the above limits. Results of these measurements are given in Tble IIo' TABLE II Comparison of the Spacing Between Rotational Uines in v3 HC as Measured on the Michigan Ebert Spectrometer and as Reported by Rank et al (14) Line Freq (Rank) Av(Rank) C(Rank)a 1(b)b P(8) 3287~244 cm - P(7) 900345 3I0Q1 cm 12405 1243 O03 p(6) 93o425 3.080 12.306 12.31 P(5) 96.484 30059 12,194 12.19 P(4) 99~523 3.039 12.085 12.10 P(3) 3302.542 3.019 11 981 11o97 P(2) 05o540 2.998 11.874 lo88 P(l) 08.517 2.977 11 o767 11o74 R(O) 14,409 5.892 23o212 23016 R(1) 17,324 2.915 11.449 11.43 R(2) 20.217 2,893 11.348 11 37 a Based upon the gratig equation v = a3 b Average of three independent runs Upon passing throuh the exit slit (S ) the IR beam was reflected from a flat (l9) onto a spherical mirror (M) which formed a 2X demagnified image at a hole in the vaum enclosure, Coupled to the spectrometer at this hole via a bellows was the detector housing which contained an off-axis ellipsoidal mirror (M1,) vhich imaged at 5X demagnification upon the detector Do The recently introduled ICKodak tron Detectonrs, type F-2-Gold (lead sulphide) and type P-2-old (plumbide), becaue of their ability to withs8tand iBdefinite

-21cycling between room temperature and liquid air temperature, made it practical to mount the detector against the cold wall of a semipermanent glass dewar as shown in Figure 4. Two different detectors were mounted in the same dewar, and could be interchanged in the optical beam without destroying the spectrometer vacuum by removing the adaptor flange screws and rotating the dewar 1800 about its axis. This motion was facilitated by a shallow, well greased O-ring groove. The dewar vacuum chamber was accessible through a high-vacuum stopcock and once out-gassed held a satisfactory vacuum for ten days to two weeks, Freshly pumped, the system retained liquid nitrogen for twelve hours. Detector noise caused by bubbling of the nitrogen was eliminated by placing granular metal in the bottom of the dewar thus providing the necessary thermal mass* Care had to be taken to prevent accumulation of water within the metal ballast which could freeze, expand, and destroy the dewar, an. unpleasant experience which did occur, Some difficulty was also experienced when the detector resistance 8 gradually increased to 10 ohms presumably because of out-gassing4 Special precautions to eliminate pickup were necessary, shock mounting the preamplifier, and enclosing the detector dewar in aluminum foil being helpful. The detector output was amplified and synchronously rectified using lab-built electronics (lI) and recorded on a Leeds and Northrup strip chart recorder. Response times of up to one minute were used to obtain the lowest noise spectra. A fourth motor had to be added to the spectrometer drive unit in order to slow the scan enough to permit use of such long time constants. Many runs were made at a rate of 1-1/2 hours per wave number (corresponding to a grating speed of 9.2 years per revolutionS), The spectrometer vacuum chamber, including the detector housing could

-.22Glass Dewar Kovar Lead - Through Adaptor Flange Araldite Seal Beam from Ellipse.. ___ ~, -~-~~ — ~Li F Window 71~~/ Pb^^^PbS Detector Figure 4 DUAL DETECTOR MOUNT.

-23be evacuated to less than one micron Hg pressure by a Kinney model DVD 8810 mechanical pump and a CVC model KS-100 four-inch booster diffusion pump. The pressure built up to about 6mmi Hg overnight and the electronics were vibration sensitive enough to prohibit pumping during a runo As the optical path within the spectrometer tank was some 100 feet, difficulty in eliminating water absorption when scanning in the vicinity of a water band arose on this account. IVo THEORY OF THE SSARK EFET F POLAR SYMMETRIC TOP MOLECULES The quantum mechanical description of a rotating polar molecule in an externally applied electric field can be developed in a variety of wayso The method employed will ultimately depend upon the magnitude of the field, the molecular constants and upon the desired accuracyo The simplest approach is to assume the field small and employ conventional perturbation theory to find the corrected energy levels and wave functionsE In the opposite extreme, if the field is huge, one can drop those terms in the Hamiltonian that are relatively insignificant, and attempt some sort of approximation to the resultingly simplified problem0 Finally, one can attempt an exact solution of the unsimplified problems As the first and the last of the above mentioned approaches yields results directly applicable to the explanation of of observed Stark effects, they will be described in some detail0 For the sake of completeness, the second method will also be outlined. According to the prescriptions of perturbation theory, the first and second order corrections' l and a, respectively, to the n energy level ne given by (13) are given by a(13)

nE' -, n' 9 where1 is the contribution to the exact Hamiltonian due to the perturbation. It is equal, in the present case, to the potential energy due to the applied electric field, namely - F where / is the instantaneous molecular dipole moment and is the applied field. Similarly, the corrected wave functions t are given in terms of the unperturbed functions t, to second order by,J. - ~. T' \) \ -. 4" <urPmtA Ea v Thus, the pertur.bation solu..tion is available once the quantifties are determinedo Let us denote the wave functions for the rigid symmetric top by!K M(^ where, 8 and are the Buler angles (14), d being measured about the fig-ure axis, 8 about the line of nodes and about the vertical. These functions can be expressed analytically, and are given by (17) JK-M1 - r +3\<t+\(+9~tj =~CM~L /< t K d) (Sli (L\ K) Os where J is a positive integer or zero and is proportional to the molec'.ulets total angular momentum K is an integer such that IK1 J, and represents the projection of J on the figure axis, M is an integer with IMI 4 J and represents the projection of J on the vertical axis, and I equals K or M, whichever is larger. It is seen that the hypergeometric function always

-25terminates (as -J + I is a negative integer or zero) becoming simply a polynomial in (si.2. These functions represent solutions of the Schroedinger equation c4s[~.* cri?5 Y A& __ - - t > 16 t a t- [ ^ - El C; ^ - e C Ai zi E E F3 1(S1)4 (#ifBl)kz If the applied electric field is allowed to define the vertical axis and since because of synmaetry, the dipole moment of the molecule mast lie along its figure axis, we see that /,Att 1l1cOSc< pt os 6 We are now in a position to evaluate Lj =i-etU, by strictly analytic meanso The calculations were first made in this manner (15), but are extremely tedi-ous.,and require advanced techniques in function analysis. A more modern approach, using step-up and step-down opeators to derive expansions for cos 9. in terms of*'JKM has been developed (16).o The.most elegant means of doing this expansion- however, is to relate cos 9 and?IK to the eigenfanctions of total angular momentum and utilize our knowledge of how the product of two commuting angular momentum eilgenfunctions can be expressed as a sum of angular momentum eigenfunctions with appropriate coefficients, ie.,e of how angular moment, add. We will develop this last method using the formalism of Edwards (17)o Let D(Q3Y) denote that operator which when applied to a function of the Euler angles 9, 9, ead 1 simply rotates the frame of reference so as to increase t, 9 and ) by amounts a(, and^,g respectively. It is well known 2 that L the operation of total angular momentum, remains unchanged when the coordinate axes are rotated. hus, Our choeice of Elerangles and of phase factors also follow Edar (17),

-26lb(OAY) 0(+90 L~(4+04 9e,8 4trjY) N oL +t 4>+Y) If we replace F(t,4) by 4^(e ), the eigenfunctions of L2 with total angular momentum t and z component of angular momentum M, we get ^ ^ - v) ire = e Lli = ^9l\e(i.+) ) 41 rv Thus D ~L is an eigenfunction of L with total angular momentum. We may, therefore, write D(cAY) 6,(^^ =; D$,, (NoY) ^ (+, 4 9)> where D~, are the m1atrix elements of D. Next, noting that D(oioY) 9,,( = (+4d 64a 44r # (+@*) q^ ^^ Y)let us evaluate L, operating on D. I,T (q 4) L- (dr(y) D (4,f') ( (Ao/sy) - N+(l) (drct y (gmD(d) d(rr( *) = ^( t Dr,^ (\ BV), Thus the matrix elements of the finite rotation operator D are also eigenfunctions of total angular momentum. We can determine the explicit dependence of D,, on the angles +, @ and ) by first expressingB D, the operator of finite rotations, in terms of L, the operator of infinitesimal rotations. Thus,,8 12) (O OY) + (+ @ 4)) aay D(o-) i a(ooY){(e) = {( Ae c Y) -=(^^) ^ ^ )e^)

-27This operator equation has the solution D(ooY~ ='eLt4( ] k L where 4wi) (.; /Li) - nl.~ n -o Ntn Similarly, and ~: dB D(o(5o 4( @ a = D(l^ ^t'14(^ ^^ D(o0o$^ e / /3 L.3 Also, since by the way in which D(43Y) and the ialer angles were defined, D(oo= D (a00; we get D ((oo0 c-.c'"' P _ L( Since (D G( Y) = (X 0oo) D(o3 )D(ooY)> we- see that D( ( yl ii" L ^ ^1PiL;,4 - ^^44 Ly), where the constant multiplier is set equal to one to make D.unitaryo We may now partially evaluate D, (c03) as 0OA Y-) -K (c LQ44Y)) dt +(s L (i) e41 t p3 K Aeo e ) 4 - e T'^: (Gc7(y)" ^ ^ r^ Ot+ vY) d (r) Furthermore, we can show that -Jb is also an eigenf'nction of total angilar momen.tum. -has

-281 ST - (' P + E~ t Z- Pi - fl^o L^ G ZIi ZZTr;.E - But V6l^'T*+rfK E^/' - +KiL(Ktl t +.; it a Pa +AO (KV - = 1 Therefore, LL ^ z Jr {\ 3(3 -) Kw =.i:t _.( Ntt) Ym t Considering the above facts, we conclude that i3= *The constant can be determined via orthogonality relations (17) ~^ ^y II" - = ^^l bl9 -) ^ t (JM't, 1 c ^C., t~ = \( Also, since DJ (e49) represents a complete set of functions in +, @, and ), the direction cosines of the dipole moment can be expressed as sums of D's. In particular., cos (9) = D o Now let us expand products of the type D (c)) DK,(C ), d —=> CY. If U(J1 M1) U(J2 M2) is the product wave function of two comuting angular momenta in a representation diagonalizing Jl, J2, M, and M2, we may transform it, using'vector coupling coefficients' into a representation diagonalizing Jl' J2' J, M, ib.e. U(3'm\UO(^^ <S^M): >\ r(\,' W S\T),= MMZ. Applying a finite rotation of the coordinate axes to the left-hand side of this equation yields 0 3 U(O,~ U(JM -D \ Du t,\~

-29D{U ~IP3( 3 nU D 31 7BX t1 6 1 Applying the same rotation to the right hand side gives D z < l l>^(, ) Z <:,\t > b7' <J/n (f) T (Si - t T lVlt \ 8 S YL rsz - t <(A r e % t. \l (; Equating coefficients of U(J1M 1) U(J2 2) we obtain where o', o T 7' 114 < M ZI. < (s <K+\ I,> 0)(,<^ | Y M > The'vector coupling' or Clebsch-Gordan coefficients <JMIM1M2> may be replaced by the Wigner 3-J symbols, modifications which more clearly display their functional symmetries and are defined by (17) ( (A 1fv\J - (1 ((I)) <^^4^,> This then gives the relations Dtit Do, - t (-1) (2r~ J(M rt' -Y_ B) iN>' KitV c Y- 9- K Using the relation between KJK and DM, the matrix elements needed for the perturbation calculations are easily established, ioeo, Y~, v PoDK 3b i - Arj K j~ f 7 $ / \ - 1z2 -rtCt S(k s) -t) (oj 1 o y

-30whereby S Y11Mt CoS 0 I M + s =\' 1 (% IM S_ _ t I 3 It via the orthonormlity of the J Using the tabulated values of the 3-j symbols (17) we arrive at the final result, ts' ^ j =3(3t+)[1^^] < S I (11' ( K The nonzero matrix elements of Dl 1 D -D and D1 have also been computed and the results are given in Table II1o TABILE III 1 1 1 1 Nonvanishing Matrix Elements of D1 0, D,,l Dt < J+s K M i D I| 3 K M> = [-(2+)l )((l L (J+11)2J+(2J+3) Kl < JK h:I DO o I JK,> = 5 < J-1, K M - Do > = < J+1 K Mi1 l D1 0 I J K M> = [(j)K2(j~] <J K M~ I D+1 JKM> = K(. J~Ml -' iK J(+}..K..J~M+l}.) * J1 K1,11D0^ ^ J(KIM~

-31< J-+ K1 M~i I J K M >J K - <0J K 2J2 (2 J-1) (2J+31) I^ F^~~M({;(3PK)(J~K+1)) 1/2 < J KI M I DO1 I J K M > J < J+1 M | JK M> =.( J2) (jiC+2~)(a+i) ) 2_ 4(J++)'(2J+1)(2J+3) 1 _ (Ji;_ (_:K) (J~K+1))+ /2 -11 2 4J2(2J-1)(2J+1) <J+1 Kf llow ing Relati JK Pre > v 4 ( )4(J+0) (2J+) (2 J+3) < J K~F1 M~l I D:1+ I J K M > = ~E1/2 < J-1 K~l Ml1 I D1+ 1 J K M> = >1K)(J I) ) 1) 4J2(2J-1)(2J+1) J Up-er (Lo~er) sis mus, be Ised co~nsistenr 7 cos (z z) o= 2 O COS0 (o Z) s=i ( D1z X) - (D -1 Dio) The folowingRelatons Prvail

-32cos(y') D cos ( ) i l+o.1) (Y ) =.- (.D. 1 l i ) CO1y_+ 1 1 4+D1 l cos (x Y) = D (4 1-1-1 1 Knowing the matrix elements, the first and second order corrections to the energy levels can be computed and are given by At rK t aEe ~'' 2 U E: e: I D -D T^ ^(^ y ~> (1 CO~j (ylE)- 8tE 1 [ ( 1-7 I+t L The corrected wave functions are also readily calculateed rad the perturbation calculation is complete. For the case of linear molecules, we may put K = 0 getting only a second order effect; namely d E -+) " llt^^^j~ pecial'care is needed in handling the case J = M = 0. The result obtained by first putting M J and J = 0 may be shown to be correct, i.e., mer - th Of course, higher order corrections may be calculated according to standard tec hniques (13) but they wUi depend, upon nothing more than the maxtr ix elemtents already comaputed and thus are essentially solved forx. It will be noted

-33" that the energy levels now depend upon IMI and what was a single absorption line without an pplied field will now appear as a series of lines, one corresponding to each allowed M transition. This solution is applicable only when the perturbing Hamiltonian is * small compared to the unperturbed Hamiltonian; i.e., when the computed corrections of higher and higher order get progressively smaller and samllero It will be seen that, aside from factors of order unity in the limit J-o WC which depend upon the quantum numbers, successive approximations based on perturbation theory are proportional to A.Let us comr pute this'smallness parameter' for HCN. Since' 3 debye, Be 1.5 cm and8 = 0.016803 cm /debye-kV/cm. For a field E = 50 kV/cm we find that ~/T^ =I^^/J Thus only for J > 10 can the perturbation theory be expected to account satisfactorily for the observed shifts. Moreover, fo fields small enough to allow perturbation theory to holds the frequency shifts are smaller than the available spectral resolution (0,04 cm l) For instance, if /A / = o.1,' - 3kV/cm and the ground state (J = 0) shifts by only. - 025 cm. 68 It is of interest to compute the correction to the energy of the ground state for some typical linear and symmetric top molecules. Table IV gives the resuits for 5 = 50,000 V/cm together with the largest spectral shift calculated on the basis of second order perturbation theory. Note that HCN because of its favorable dipole moment, is somewhat unique in that it is the only linear molecule showing spectral shifts appreciably greater than the available spectrometer resolution, even at the highest fields attainable, To account for the Stark effects seen in HCeN a solution applicable for all field strengths muost be found. Since J 1, we cannot expect 3^a

-34TABIE IV Sumamr of Molecuar Constants Pertinent to a Perturbation Calculation of the Stark Effect Perturbation Largest Molecule /IAoL Correction to Spectral Molecule - - — 0 60 Ground Rot. Shift a a State a a HF 1.9 debye 20094cm.048 -.0081cm +.026cm1 H135 1.03 10.59 o081 -.0118 +.038 HBr 0.78 8.47.077 - 0083 +.027 HI 0.38 6.55 49 - 0026 +.oo008 HCN 2 98 1.48 1.690 -.711 +2.27 CO 0O10 1.96.043 oo6 +.0019 CH F 1.79 *850 1.76 -.439 - 626 3 CH( IC 1.87 443 3* 62 - 967 - 650 CHBr79 1.80.316 4.78 -1.205.630 CH3I 1.65.250 5.56 -1.289 -.576 3 CH CN 3.92.307 10.71 -5870 -1.37 CF H 164 345 4.oo -.921 -.575 CCi: 5& 1.2.110 9.17 -1.541.420 a for = 50,000 V/cm b J'M' T 10 JM' = 0.0 for linear molecules J'K.Mf = 210 J'"W = 11-1 for symetric top molecules that a high-field approximation would be helpful, although this calculation will be made later. Instead, the total Hamiltonian must be attacked. An exact solution is available, although it is not of a closed form, Including the Stark energy in the symaetric top Hamiltonian does not alter the Hamiltonian's cyclic dependence upon the variables and s, and K and M remain good quantum numbers. Also, although J is no longer a good quantum number, the levels of given K andM are unambigusously labeled by specifying

-35their J value in the limit of zero electric field, The wave functions in the exact case,.,JKM may be expressed in terms of the unperturbed wave functions,?JEM by I!^< _ E ^ ^ 3s'-Sf The sum' is taken from I = Im or IKI, whichever is larger. are ex-A pansion coefficients which we must determine. If _= "O +-1I' where O0 is the unperturbed symmetric top Hamiltoiian with energy EJK, and 1 = -p8 cos 9, we have to solve the equation: or 0M - Z A X,, A "VK M' -- --: L 3" — I Defining H#, = < J'l >, we have seen that HJt, 0 unless J" Jt+1 J' or J.-l. hus E R: t:,ES + H~5T^!t / AKr' E'Y'K ZK #+I ^^ ^ ^r^ KM \1 H. Shifting index, 91zj MEsE t M&3J^ + 1^I AJy sI HKM' fJKM A J. F AS ^ J ^,I-5 V.A T, - K':,, The first term of the third sum being identically zero because J < I, we get upon grouping the coefficients of IJ'KM A2 ~,,-,e. 4'- *. -rl 4T, kp 1- Et ILI'rA J+) 1:' KS'trn E,< 3 s:': t3'+- T H ", 37',,f-1 t T [A (Er E3eK+-l + A" F i,] \ - H, As the \JKM are orthonormal and complete, the coefficients must each be zero. Therefore, A;l3'- + A.".1 an

-36etting K MA Letti.ng.. - A t'M J/J. we see from the second equation that ii, - HIt' /Epe pETI( uS; jS'~t S and from the first that H,' - _ 0 Let us defigne t and - - h B- Bv Ee E3IK E 3 1 1K 3 or'1- J' (JoKM - E - (':J" A" I( K - - " - l B'('J) 0 With these abbreviations ul &3 C31 B 0| X ^'411 C- /lYU~ C.~, = B~,,~ -- =c %, -+ (32 Continming the expansion, we get i e ^,i(ct (C ^\ 3'+~ -( 5CS'+3-' Using the fact that'1S - " )r = - EsT. /4: - we obtain a cont inued ~raet ion re!ltio~ independent of f-, 7 namely B. - -C (c^ ) 0 (+ (CJ ) *_ C~~, ~ Fbtt ~> ~

-37Inverting both sides, this becomes o= Be<- r (C2) O (D In terms of molecular parameters and the electric field as defined by E = n - - (.) we get o= 6TKn - I(ti-) R~K < - ~ - L +s (ETr) (tIt+)(Ll+3) (TKi- (i-l)(l+% * R K1 t <I) r (T+Z)P-( ZLt3)(Zl. i5) (+ (R r)(r3) (i ______ ( [( ) I W) ^ t tL *3) This infinite continued fraction, corresponding to fixed K and M, may be inverted an infinite number of times to yield a polynomial of infinite deEe gree in the unknown E J KM = The smallest root will correspond to the.JKM J = I state, the next smallest to J = I+1, etc. This fact is assured because wave functions adjacent in energy have connecting matrix elements, and hence their energy levels may never cross. The continued fraction may be broken off after N terms by neglecting the term (CN+I) /BN+I compared to BI_ 1f If I is considered fixed, then

-38KM 2 2&~ ---- for large N (CI) and so that C I / a n the neglected term compares to the retained term as (1/N)4 Thus, the fraction submits readily to numerical solution~ Indeed, using the continued fraction, Shirley, (18) has recently machine calculated the symmetric top Stark energy levels for all states with J < 4 and for fields up to \ = 20~ Schlier (19) has also given curves for the Stark energies of symmetric top molecules for states up to J 2. Kusch and Hughes (20) have carried out similar calculations for the case of a linear molecule for all states with J < 4 A plot of their data is shown in Figure 5, and as a careful interpolation of their data for J ~ 2 was found necessary in treating the observed effects in HCN, coefficients in the expansions 63 = aOo t- t (7 Z) t +) (j -.2\L i-s' ~ )6s, = bT t (+-35 b, + (+ 3)tx (3-3)583+'9 were evaluated and are listed in Table V: As pointed out by Professor K. Hecht, use may be made of this continued fraction to compute higher order corrections to the Stark energies for the case of small The fraction may be rearranged by successive inversions to give Bi ~=- C1. C: 4 Br 6 *:. 5 1... t;t - CIL41 8 t - Cl ______. C1-_ tt^t- C3 *i.1 - C Te3:. 15: - ~ *;

-39J=3 IMI= I IMIO 12 IMI =2 IMI~~I = 3 10 8 - J=2 IMI= I IMI=0 IMI= 2 0 4 - "<,)~~~ { ~J=l IMI=0O ^^^-2^J= IMI=O -2 - -4 0 1 2 3 4 5 6 7 = p E/B Figure 5 Energies (W) of a Linear Molecule (rotational constant B, dipole moment i') in an Electric Field (E), from tables by Kusch and Hughes, Handbuch der Physik XXXVII/1,141.

-4o^ TABLE V Polynomial Expansions for jM( o) to fit Data of Kusch and Hughes (21) Let M() a + al(=-2) + a2(\-2)2 + a3(+ (2)3 + a(2)4 = bo + bl(X-3) + b2(3-3)2 + b3(?-3)3 + b4(N-3)4 a 1 a a3 a4 O00 - 85573 -.4813 -.0659.0138 -.0020 610 2,2872.2079 -.0005.0144.0002 6Ell 1,8051 -. 1900 -.0430.0018.0001 c20 66.0984. 106.0443.0004 -.0002 621 6.0426.0378.0051.0010 -.0001 22 5.9054 -.0939 -.0149.0000.0000 bo bl b2 b3 b4 600 -1.9027 - 5813 -.0795.0073 - 0014 E10 2.4780.1643 -.0352 -.0068.0017 11 1.5741 - 2696 -.0365.0021.0000 620 6.2278.1582 +.0324 -.0007 -.0003 621 6.0837.0468.0052 -.0036 - o0016 622 5.7890 -.1383.0221.0003 o 0001

i1. where we have dropped the superscripts K and M for the sake of neatnesso Here- Let us expand Ee/ as a series in?, i.e., let /5 =- \0l + \ \ e t RL@1 t v +' *- To t tehird order of approximation for example, Wo, Wl, W2 and W are retained on the left hand side of the continued fraction while since 2 2 C, the denominators of the right hand side need only be evaluated to the first order. Thus?K Since the right hand side of this exes is i f order two and higher, we obtain an expression good to first order by neglecti:ng it altogether, along with the term W and W3 giving O J(J + 1) ( - A/g)K2 T, + Using these values for and W we obtain * -'Y/ V(4'-l ) >. [(i3.i*'- K~L('P'. i l T^4 J I I (4- ))J Vl4t ^ (C I V (V)t

Equating coefficie0nts.of N. we tget _ (T - _t. (:) Equating coefficients of gives ^ ^^^^^t\t5+s2f~53)) \t34\ ) (^ I-I) The expressions for the first and second order te rs agree precisely with those previously calculated via the usual perturbation scheme. The fourth order term has also been worked out. together with the special cases J = = K = O and J M | = IK| l= Table VI semarizes these resultse As stated earlier, an approximation may also be made for the limiting case -, o E.o- B. Wilson, as quoted in reference 30, gives for the case of a linear rotor in this limit -WAE _ (+ — LA\ t jUE B & This result may be derived by expanding the'amiltonian including the Stark energy about @9 0O since for large X the potential energy -UI cos 0 has a deep minima very near 0 = O, The resulting Schroedinger equation may then be solved by expanding the ave fuactions as power series in Q, the eigenvalues being obtained by requiring the solutions to be polynomials miltiplied by their appropriate 9 -4 0 and 0 -,! limits. A somewhat more accurate formnla can be derived in a simpler manner by expanding the effective potential energy, after one-dimensionalizing the. amiltonianabout its minim rather than about Q9 0,^ an approximat ing it by a parabola. The.':xblem is then that e a harmonic oscillator, the energies being given by E- (nA^)k \/(^) where The exact Hlamiltokian is, for the case of a linear rotor, Since the normalization integra.is i + c s l~ d we may one-dimensionalize the probl em, thereby elLminating first derivative tes~ i' the

i43TABLE VI Perturbation Calculation to Fourth Order for the Stark Effect of a Symmetric Top Molecule J(J+) + ( - 1) r 14 1 -2 T/l T"'3V3( >J- - J~~+J J+~K2(.5J(.J+l + -(-jM) ~+~4 +X Fourth order Coef]. 2J (J+l) (J-1)(J+2)(2J-1) (2J+3) [Fourth Order Coefficient x [8(2J-1)3 -3)(2 J3)(2J+3)3(2J+5) 20J 4+ 20J + 33 -18( +2)(28+28J-5 + 9(M+K2)2 (68J4+36J3+125J2+57-45 ) 20J[ + 20J + 33 - +1 J ( J'J 1 ) J J+l_ 3(j,)3 ^^2M5K~ t 2052J6 + 6156J5 + 48854 - 490J3 - 292J2 - 3021 + 1710 2 2860J + 11440J + 19539J 2E (+ ) + 185775 - 92J - 17799J3 1 J2^(3t1Z -L 9522J2 + 576J + 2430 + (J-1)(+2)J3(J+1j) 3 5876J11 + 41132~ + 134009J9 (~J+ < )+ 27521J-J) + 355474J7 + 217100o J (J+L) (J+2) - 58250J5 - 194746 - 125274J3 =L~~- 8775J + 22140J + 8100 Except when 21 4 U 1 T 1J=IKI1I 11 e1+- K 2 3 3 KM 4 89 J!KI = MlI = I, - l +~- - ^A N^ + 32 -2, 6- oo

-44 Hamiltonian, by substituting \: s. Mak ing this substitution, one gets 2.1x, ( )h i ldi^^T t, - si^ which may be likened to where if \1 ts-LK, ther F- (CK\t{L/2) - (Y\tt/ X k. In our case, \/ef -,, [ - - ol must first be expanded about its minimuo. 9e is determined by setting the first derivative of Veff equal to zero. Thus Since \ is vary large, we make the approximationn <<. ~1 and;4'\1 L'iL ^\1) ^ ^ Evaluating the s ec ond derivative of Veffwe get and As" -6 i -(Z ^ ^ o- iu ^y

45. Thus, the energy is given by E': -'1N b Also, the state J with zero field corresponds uniquely to the state n = J - IMI with large field. This is true since for fixed M, adjacent J states have connecting. matrix elements and hence cannot cross as the field increases. Thus,. as the states are ordered by the integers J - IMI for zero field and by the integers n for large field, the correspondence n*J - IMI must hold. Thus in our approximation, This formula differs from the one given by Wilson, except for an additive constant, only to the extent of the term 1/4 indicated by the arrow. Our derivations it must be pointed out, is not valid for the case M = 0* At M = 0O the expansion must be made about Q o since Vff has no minimum for this value of M. A high field expansion has also been developed by Peter and Strandberg (21lb) The same calculations may be carried out for the case of a symmetric rotor, the result being given by where I M= 14 or IKI, whichever is the larger. Again, the case M - K must be treated separately by an expansion about 9 = 0 which.yields Once the energy levels are knowmthe wave functions can be obtained, 0G for we saw that if =, K AJ +IJ then Jl=1 42, A A:: [uE'3K- ESKCM + ~ th 3'4n1 4'.an-d that - and that /; E,- ~, If MA~1irir

For a linear molecule this reduces to A 3- *^t ^- z(~;x VT^^T^A Am-L for Jt > 11+ 1. This relation has been employed to detexmine exact wave functions for all the M sublevels for J up to two at fields corresponding to k = 1, 2, 3, and 6. The results appear in Table VII. Calculation of the expansion coefficients is a self-checking process as well as being an excellent test of the accuracy of the published energy values, for unless every detail of the calculation is absolutely correct the magnitude of successive coefficientsg instead of tending uniformly to zero, will explode violently. The intensities of the Stark absorptions may also be calculatedo If only the relative strengths of M components resulting from transitions between the same twro tJ states are desired it suffices to consider only the ratios of the esqared matrix elements of the dipole moment between the states involved. The dependence of the absorption strengths of these components upon population and frequency differences will be negligible in view of the accuracy of any intensity determinations. Choosing.:- axes a. in Figure 6 where the applied field defines the Z direc- tion, perpendicular to the Poynting vector' of the infrared radiation which in 7 turn makes an angle a with the space, fixed Y axis, Let n denote the direc- X tion perpendicular to both t and o Fg. 6 Orientation of Poting Vector S Relative to the SpaceThe inrared be-am is then to be thought Fixed Axes

TABLE VII Wave Functions for a Linear Molecule in an Electric Field Exact M MM M AJJ tM J M X AJ j AJ A3J A4J 0 0 1.000 0 0 0 0 0 1 o964.263.022.001 o000 o000 2.898 o 434 o069 006 000.000 3.840 0530 ol18 013 001 o.000 6 o726 642 o 235.011.001 o000 100 0 loOOO 0 O O O 1 - 264 o.956.127 007 0000.000 2 -.436.865.248 o026 o002.000 3 - 533 763 361.059 o005 o002 6 -.617 463 o601.203 ~ 024.008 1 1 0 1000 -0 0 0 0 1 0.994.111.007 o000.000 2 0.977 o213.020 o001.000 3 0.952 o 32.042.002.000 6 0.865 o486 o125 oOl..000 200 0 0 1.o000 0 0 0 1.012 - o128.988.084.003 000 2.048 -.253 o952 o166.012.000 3 o102 -.369 0891 o242 o027 o002 6.298 -.596.6il- 425.104.025 2 1 0 0 1 o00 0 0 0 O 1 0 -.110.991.079 -003 o000 2 0 -.213 ~964 o157 oOl.000 3 0 -.304.925.230 o024.002 6 0 -.o490 758.417.090 o.008 220 0 0 1,000 0 0 0 1 0 0.998 o063 o002.000 2 0 0.992.124.008 o000 3 0 0.983 0183 o016.000 6 0 0 940 o336 oo060.003

of as coiaposed of one component polarized in the Z direction and one in the n direction. Absorption of the Z polarization will be proportional to I where while absorption of n polarization is proportional to In where LA =I \ ^ ^Z (co^ -y,SlW ()(s A,\Z We see that Pr /P Cosi)'^ C MOD - o^. o - 5 MCS - i0 - Di + D,1)/ Thus w - S\ |OL Aieo spanding the exact ave functions in terms of the symmetric top functions, we get I - \ a ( EA 33 A anad L^ ia' +T\ KJ' foil boo oTWK^jr ln=; (e' 5'K' tWIOW%1 ( "C\ ^b^+i

,49The matrix elements of Do 01 D and D 1 have been computed and are given 1 in Table III. It is seen that for transitions involving AM = 0, only DO 0 has nonzero matrix elements and for XIM 1 l only D+ 0 contributes, Thus a AM = O line will be polarized in the z direction and have an intensity proportional to IO where A A4 = ~1 line will be polarized in the n direction and have an intensity proportional to I1~ where I T X =i AIr ( M at, o i<^p t The lengthy sums necessary for the computation of actual intensities have been carried out for certain field strengths for low J lines of a linear molecule. The results are tabulated in Table VIII. The most striking feature of the calculated intensity tables, perhaps is the appearance of weak Q (AJ=0), 0 (J=-2), and S (JT=+2) branches. Actually, since the exact wave unctions are composed of symmetric top functions of many different total angular momenta, nonzero intensities will exist for transitions of arbitrary AT. This is simply a statement of the fact that in the presence of an applied field the total angular momentum is no longer a constant of the motion and that J is therefore not a'good' quantum number. These "field induced' transitions for AJ > 2 are too weak to be detected in the present experiment but the Q branch is observed. V* OBE D E STA EK TS AID TEIR INTERPRETATION 5.1 Hydrogen Cyade Figure 7 shows the observed electric field effects in HCN near the band center of v3 (the C-H stretching vibration)* The normal absorption spectrum

50TABLE VIII Relative Intensities of the Stark-Shifted'Mt-Components of a Linear Molecule Branch Tr.asition Relative Intensity I0 (a) JM': -M-l A-0 xl= o = 2 3 6 = 6 Q(O) 00 00.0000 0O088 02e32 0*336 o.484 Q(1) 10 1o 0o00o 0.027 o0o43 o.o27 0o008 11 10 o 0 o00 0 0.0519 001 077 0o153 11 11 0.000 0.020 0.07 0.114 0,292 Q(2) 20 20 0,000 0,002 0,010 0,025 0,073 21 20 0000 0,000 0,002 0,006 0,038 21 21 0,000 0o001 0,003 0,003 0.000 22 21 0O000 0,002 0,009 0.018 00047 22 22 0.000 0,004 0,013 0,038 0.132 P(1) or R(O) 10 00 0. 333 0,270 0,182 0,128 0.062 11 00 O,333 0O327 0,281 0,255 0,212 P(2) or R(l) 20 10 0,267 0,266 0,265 0,263 0.213 21 10 0.200 0,199 0,201 0.208 0,300 20 u] 0o,67 0,064 o0,08 o,42 0o0o22 21 11 0,4o00 0,391 0 363 0 328 0 227 22 11 o0.400 0,399, 389 0,377 0.328 0(0) or S(O) 20 00 0,000 0,004 0.008 0,009 0,002 21 00 0.000 0.003 0,007 o0,008 0..6 (a) I' L = a I~ where i defined on Page 48 ad a = 1 if M a3 3 e 1 zero an^ a otherise if 4'1 an ".f are both zero and a == Z otherwise

ZERO FIELD P(2) P(I) I Q(J) MO I M *2-l M i- 0 M 0-0 M *1-0 J 1-1 J-J J 1-1 M*1-kl M0 O M O-l M-M M.il-O C 1I 1 3305 3309 cm' 3313 Figure 7 STARK EFFECTS NEAR THE V3 BAND CENTER OF HYDROGEN CYANIDE. A. Normal spectrum. B. Spectrum with 44.1 kv/cm DC -electric field. C. Predicted spectrum.

is at the top and the spectrum with an applied., DBC* electric field corresponding to A = 15, together with the theoretically predicted spectrum, below9, t 0 transitions only absorb radiation polarized in the z direction parallel to the electric field; AM = ~1 transitions only absorb the perpendicular polarization. The transmission of the eperpendi cular polarization through the. Stark cell was nearly three times greater than that for the parallel polarization. This factor has been included in the predicted spectrum. The induced absorption of the Q branch is apparent in Figure 7, with the stronger members labeledo The M components of lines P(l) and P(2) are partially resolved and are labeled, Lines marked with dots appearing in both spectra are due to srmll amounts of water vapor in the sample. The series of doublets in the normal trace which show Stark effects in the electric field trace are members of the combination band v + v2 -v2 Also present but barely discernible at the present sample pressure is the v fundamental of HC 3N. Though the v3 + v2 v2 band shows modest electric field effects in the trace of Figure 7, and would seem an interesting example of the Stark effect in a band having A-type doubling, the weak intensities of the low-J lines prohibit their measurement. Figure 8 is a section of a trace at a field of 120,000 volts/cm (7A4) showing the' lines' R(2), R(3) and R(4)o In order to obtain this extreme field, a cell with a gap of 0. 2m was used. Transmission of the rprendicular polarization in this case was less than 10%, while that of the parallel polarization as practically zero. Thus only the AM = ~l transitions can contribute to the spectrum. The M components of the'line' R(2) are completely resolved. The R(3) and R(4)'lines' show incomplete splitting

<~ R(4) r7^'R (3) ~"~ R(2) cu o ^n I I I I I I I~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~ _; CM~~~~ i o Flo 4 OJ~~~~~~~~~~~~J 3325 cm'' 3320 cm-' Figure 8 HIGH FIELD STARK EFFECTS IN HYDROGEN CYANIDE above = recorder trace of Stark spectrum with E= 125,000 volts/cm, p= 1/3mm hg. below predict,,ed spectrum assuming complete attenuation of the parallel (Am=0) polarization, m assignments given for R(2) only.

even at this maximum field. The polarization dependence of the M components is verified by the spectra of Figure 9~ Here the region of 5 P(1) with unpolarized radiation and zero field is shown in Figure 9a. The spectrum was then run with a field corresponding to - 1, using polarized radiation, Figure 9b is the result for the parallel polarization, Figure 9c for the perpendicular. It is seen that the spectrum is completely polarized, as predicted, In order to insert the silver chloride polarizer, a section of the brass tubing enclosing the beam had to be removed and the dry nitrogen flush of the foreoptics discontinued. The line marked (o) appearing in all three traces is due to atmospheric water vapor. An expanded, low noise, high resolution scan of the P(l) region of HC, v3, at a field of X = 2 is shown in Figure 10l The trace required six hours running time and represents the best resolution and signal to noise attained The observed frequency splittings and intensities for this case are shown on line one of Table IX, The values calculated from ground state molecular data given on line two of Table IX are only in fair agreement with observation, and indicate that the effects of the excited state upon the molecular constants mast be considered. Thus, the Stark spectrum is correctly predicted only by determining the rotational energy levels of each vibrational state separately, using the molecular constants of that state. For the fundamental vibrational state of HCN, the reciprocal moment of inertia is 1.467799 cm (12), as compared to 1.478219 cm (21) in the ground state (B1 and Bo, respectively). However, only the ground state dipole moment 0 ha been measured, the most recent determination being 2.985 ~.005 debye, from the microwave Stark effect (22).

-55P(I) 0 0 A 0 \ I o I B 0 ICI 1 0 Figure 9 STARK EFFECT OF P(I) HCN USING POLARIZED RADIATION. A. unpolarized, F = 0 B. polarized Erad. II Estark ~e = O to the right of the dashed line, e8 30kV/cm to the left of the dashed line. C.. polarized E 1 8, 8=0 on right, E = 30kV/cm on left.

0 oM 0 N 0 3305 cm' 3306 cm' Figure 10 HIGH DISPERSION TRACE OF THE P(2) LINE IN THE 3 FUNDAMENTAL OF HYDROGEN CYANID^ SHOWING COMPLETE ISOLATION AND IDENTIFICATION OF ALL FIVE'M' COMPONENTS =60kV/cm p"= 1/4mmhg

-57TABLE IX Summary of Observed and Calculated Splittings and Intensities for the P(1) Line of the v HCIC Fundamental with an Electric Field Strength Near 60 kV/cm Relative Position of the Mt' - M Component 0H0 14-0 0-1 1i-1 1Observed -.086cm1 -.825 0 -.743 -.538 CalculatedA -.083 -.802 0 -.716 -.513 Calculated3 -.083 -.831 0 -.7P8 -.540 Relative Intensity of theC Mt - Mt Component 0'OK 3-0 1- 11 1<2 Observed.26.21.70.32 1.00 CalculatedA.25.20.70.33 1.35 Calculated A Using 7 - 2.01 0 =?x B Using 0 = 2.01;, = 2.06 C Assuming T/T'" = 3.68

A58 The predicted spectrum of Table IX line 3 was obtained using L1 = 3.04 debye and the above values for BO, B1 and P0; it differs from the observed spectrum by less than the experimental error. Since it is necessary to include the effects of a changed excited state dipole moment to account for the observed spectrun, this change must be evaluated as carefully as possible. Moreover, the change is of fundamental interest, never before having been measured, There are many means of reducing the available data to determine l; two of the most direct methods will be describede Let Wl(?) l = BleJtM(?l) be the rotational energy of the excited vibrational state and WJ )M() that of the ground vibrational state * Since h s (IE/B,'l1/:1, 1 and B1/Bo 1, then a1 = 7\ A. o LB) 1B 0 B~ op B and 6jM(li) % ~'(Xo) + &A.* To a good approximation, we see that TeSaksiftmaoi b M 0 and ^ b)1 The same transition with zero field falls at the^"' " vited state 6S'si(ml- Orly gie(Dn - vp:r(I+U(^ttR - (3b4^YB. The Stark shift accordingly is given by it,( (t)|oitMo B~( e The Stark shift of the transition which proceeds between the same two rotational levels, but now from JT'W in the ground vibrational state to JWMI' in the excited state is similarly given by

dY.rc^i\ -RP(Lt,k" Y - rV(hs\)- t^^ r ( Vr A | Adding these two frequency shifts yields ^^y, c 4.:^ r d (t S mri( - 3I(JI3B(3I. Table VI may be used to obtain expressions for eJ'M' + eJ'M' for all levels up to J 2 as polynomials in (A -a) for a = 2 or 3. These expansions mar be differentiated and the results used in the above equation to determine the only unknown Ao To achieve the greatest accuracy in the determination of tp those levels most sensitive to changes in? should be measured at the highest possible field. Thus the levels J = 0, M= 0 and J= 1 M = were employed and the following expressions developed: 4- i = t A1.16 0&f\? >i2.(t-O~ ((-;Y)1 eoI-(? —V- 0Ioo1(7?-t)4 t t 0814 - oo(A-) — o18(- 93(- 0,0033 Differentiating: d)( 61\ f (O04 A- O, t1o8(1-L) -t114)8(;* 1 - dr,~ ~i o (- - os 5 8 0, 14o1- ( -o ~ o,ot)9 ( - ~ - O. b oo 5Z-(R. As a check on the range over which these expansions may be safely used, 4 (6e, t617 was evaluated using the first and then the second relations, yielding -0o7693 and -0,7694, respectively. It was concluded that the expansions were valid over the small regions encountered in the calculations (185 < A < 2,15). Thus, for example, with? = 2.00, we get

-6o0 5 3 + 3B - _ oousS _,7e- rv t L Many independent determinations of a/L were made for fields very close to = 2o0. The experimental procedure finally adopted involved scanning the spectrometer slowly through the line P(1)0l with a D.Co voltage applied to the Stark cell. Then both electrodes of the Stark cell were grounded and the scan continued without interruption through the zero-field position of P(1). The spectrometer was then advanced by hand to within thirty minutes running time of the unshifted R(0) line and it was scanned. The electric field was re-established and the scan continued without stop through R(0)1 <. The two splittings were then added algebraically (their magnitudes subtracted since )e0,,0*, is already negative). The results of seven runs are listed in Table X and a typical trace is shown in Figure 11. Also shown in Figure 11 is a recording of the fringes, mentioned earlier. Their lack of smoothness is attributed solely to erratic rotation of the grating, Drive train slack is responsible for the delay of the first fringes and necessitates a twenty to thirty minute'running in' prior to each scan. The precision of the measurements is obviously poor, being limited by the drive mechanism to about ~0.005 cm" on a single run. The final value obtained for ^ was 00126 F~00017, corresponding to Ap =+(0.0055 o 00017)o A4d M, A3,00 t.oo Cdehe. The above method affords a determination of the dipole moment change between ground and excited vibrational states and thuas will provide a more precise value fo'r than would a scheme of data reduction leading -directly

TABLE X Summary of Data Used in Calculation of i1, HCN Run AR(O)+l 0 AP(1)0 ~1 A a 1 1.87 0.484 cm -0.496 cm- 0.0109 2 1.94.521 -.542.0150 3 1*94 524 - 551.0182 4 2.01.549 -.563 0112 5 2.06.547 - 594.0265 6 2.07.581 -.6oo.0133 7 2.07.509 - 519 0oo86 = 0.0126 +.0017 (Neglecting Run #5) = o.0055.o00o17 a Using relation given on Page 59

-62A B A.FRINGE TRACE ACCOMPANYING B. aC Z b a| b C 5 7 D Figure II SPECTRA USED TO COMPUTE THE DIPOLE MOMENT OF H CN IN ITS V3 VIBRATIONAL STATE. A. FRINGE TRACE ACCOMPANYING B. B. P() aN ZERO FIELD b ES 2.06 (OkV/cm) M =FIDUO COMPOENT C. R(O) at ZERO FIELD b Xh =2.06, /M =0. D. FRINGE TRACE ACCOMPANYING C. LIKE NUMERALS DESIGNATE CORRESPONDING FIDUCIAL MARKS

63 - to a value for gl Such a method, somewhat simpler than the one just described, is to measure the difference of the splittings of two lines having one rotation-vibration level in common. The result will depend only upon the molecular constants of the second vibrational state. Thus, "Vr^+n^r^' -V5n.V,#\ - "~l&G,^.,(7d cr^^1 ^"^,l ) and V^:l -e^^^ y = 13ot6Sn (o - "'M (.4J The above relations can be used to calculate the field by determining?A BA O and with the known values for lo and B, then - - Conversely the field, either as Ikno from voltage and cell gap measurements, or as determined from a measurement of? o, may be considered as a known quantity and 1 evaluated. For this purpose, the following relation was derived from the data of Kusch and Hughes; (21); This expression proves to be accurate to ~0.1% and, therefore, allows a determination of p to the precision with which the field is known or to the precision of the wavelength measurements, whichever is larger. Using this method of measurement, A was evaluated with A - 2 o was thus determined to be (1,8 018 5)4 consistent in value with the previous result. The method can also be used to obtain gO The value from the present work is O = 2*.96 ~.04 debye, in agreement with the microwave determination, The possible influence of polarization effects of the electric field on the molecule has not been considered. Although no data are available on the polarizability components for WON, they are typically of the order of 1024 esu (ll) Thus,^ the induced dipole would be of the order of ~ x 10 4; at maximnm field strength about 120,000/300 x 10 or 0o0004 debyeo

-64This is negligible in comparison to the permanent dipole moment of HCN of 3 debye and the barely discernible change of dipole moment between ground and first excited vibrational state of 0.0165 debye. Consequently, one would not expect to see any such influences with the present apparatus. 5.2 Methyl Fluoride CH1F. Only symmetric top molecules will in general show linear Stark effects. Methyl fluoride was selected for study as a representative case because of its following properties: a. No isotopic species of fluorine to complicate its spectrum. be Fundamental vibrational frequencies within the wavelength range of good detectivity (23). c. Large dipole moment, 1.79 debye (24). d. Large value for B and (A-B) (25). Unfortunately, in none of its absorption bands does methyl fluoride absorb as strongly as does hydrogen cyanide in its V3 fundamental. Furthermore, the low J lines, which have the fewest M components and greatest M splitting in the presence of a field, are weaker in intensity relative to the strongest lines in the band for methyl fluoride than for hydrogen cyanide because of methyl fluoride's lower B value. In order to obtain sufficient percentage absorptions for these low J lines high sample pressures were needed, and only moderate electric field strengths could be used. Quantitatively measureable Stark patterns thus were difficult to produce. Even though chosen for its large B value and consequent widely spaced rotational structure, the great number of absorption lines in the methyl fluoride spectrum invariably afforded camouflage for the M components produced by the field. All attempts to identify Stark fine structure patterns in methyl fluoride were unsuccessful.

-65% A number of interesting effects were noticed in the Stark spectra of methyl fluoride, howevers particularly when using a modulated electric field~ Since the frequency splittings f e for we filds are comparable to the original line width (determined primarily by pressure broadening) the over-all effect of the electric field is to somewhat broaden the absorption lineo If the difference between absorption with field on and field off is recorded, with phase-sensitive electronics, a spectrum as illustrated in Figure 13c will result. The magnitude of the difference signal is determined by the amount of the line broadening together with the zero-field line strength; the spectra recorded in this manner show an intensity pattern markedly different from that of the normal tracee e calculation ofhe cacu of e linebroadening by the electric field for arbitrary values of J, K and M is laborious because of the large number of components and the integration over the line widths of the numerous transitionso By first order perturbation theory (Chapter IV), the components are shifted by an amount Yvav,LT ( *mt i ( t/ ])Kt - t (3~)( KA lS'i" K K or XA 1-A From the first. expression, the broadening is seen to be symmetric about the parent lineo It is also observed, by inspection of the second expression for the shifts, that for certain values of K", K' and J, the coefficient of' nvanisheso Thus forL LJ =+; AK +l(-1), K' = ( - 2 )(and for J+l J+l J = -1, K -1(+-1), K = — ( -— )) corresponding to the line R(J)J (PP(J)J+l), the M-splitting depends not upon M but only upon AM. The Stark 2

these circumstances, the first order line shifts are given by IAVs'ic'm' 3'"M =K -/ "A rA~5 For example, the line %(6)3 in the v4 fundamental of methyl fluoride, at a -1 field of 15 kV/cm, is made up of a component shifted -0oO317 cm-1 with a relative intensity of loO corresponding to Z~ = +l(-1)9 M = +l(-~l)~ a second corresponding to;K +l(-L) ~ = -1(+1) of the saintensity shifted by +00031T cm1 uand a third unshifted component of intensity 2.0 corresponding to 4M = 0. In computing these relative intensities' the 8Wave functions w ith f ield are assumed identical to those without field, (consistent with first order perturbation theory). The observed and calclated spectra are shown in Figures 12a and 12b The discrepancy between them is probably due to the the fact that the naturally occurring line %(6)3 is strong enogh to be in the nonlinear absorption region. Satisfactory agreement can be obtained as shown in Figure 12c, by assuming a 68% absorption for the zero field line (which is close to the measured value), As a further exmple9 the Stra spectm of the line QR(3)2 for 2v5 of methyl fluoride at a field of 10 kT/cm has been caleylated, as in Figure 13 The fine structure could only be resolved with a resolution of 0.01 clma only a broadened line will result with the actual resolution of 003 c lo Fdr an arbitrary line of high J value, the Stark broadening will vary roughly as K/J2 Therefore, the intensities of the rotational lines obserred. by using Stark difference-signal techniques will be modulated by this factor in addition to those present with no field, This accentuation of the high K low J lines cn be employed to great advantage in the analysis of the rotatonal stCtre of an absorption bandoeT technique has been applied

-67RR(LO) RR(6) RR(5) A B Figure 1 2 OBSERVED AND CALCULATED RR(6) IN THE V BNAND OF METHYL FLUORIDE A. Observed difference signal, 15kV/cm,, 0.03 cm-I resoltion. Positive signal implies greater absorption with field on B+ Calculated spectrum assuming linear absorption. Ed Caleulated spectrum assuming exponential absorption and 68% absorption for the zero field line.

-68A..... ______ I A-I / I. cmB Figure 13 PREDICTED SPLITTING AND DIFFERENCE SPECTRUM OF THE LINE R(3)2 IN THE 2J5 BAND OF METHYL FLUORIDE. A. Splittings and Relative Intensities Calculated to First Order for E=lOk\Vcm B. Difference Spectrum with a Spectral Resolution of 0.03 crm'

-69extensively, and successfully, to the V4 fundamental of methyl fluoride and several of the results will be presented. In Figure 14we see the region of the band center. As v4 derives its infrared activity from a dipole moment change perperpndicular to the figure axis, the selection rule in K is AK = ~lo Following the usual conventions, this change in K is denoted by a left superscript P (AKj = -1) or R (AjKl = +1) while the ground vibrational state IKI value is denoted by a right subscripto The J states involved are as usual denoted by P, Q, or R followed in parenthesis by the J value of the lower state. Thus, RQ(7) labels the transition J" 7, J' = 7, K" = 5 and K= 6. Returning to the figure, a normal spectrum of the region is shown above and no distinguishing structure is noted. Only careful measurements and a trained eye can establish the location of R(O)0, and positive identification of Q branches (only RQ(J)0 and. RQ(J) are shown here) is difficult. The fact that for K = 3n, n = 0, 1, 2... the Q-branch strength is greater because of nuclear statistics is of course helpful but three choices for the band center will remain, since PQ(J), RQ(J)0 and RQ(J)3 are approximately equal in strength. A quick glance at the Stark difference signal, shown in the lower half of Figure 14, is enough to convince one of its value. Here the entire sub-branch RR(J)0 can immediately be identifiedt the fct that the first line of the sub-branch occurs just 2B cm from the associated Q branch (where 2B is not calculated but simply measured as the distance between the successive rotational lines of what surely is a sub-band) proving the correctness of the assignment of Q(J)30 The first three members of the sub-branch RP(J)0 are identified, this assignment being somewhat more difficult since the sub-branches RP(J)K

-70R~o Ro0 R4 R5 Ro I |R6 Rz A P4 P3 PZ Ro RI R2 R3 R4 R5 R6 R7 K 0-1 Figure 14 STARK EFFECTS NEAR RQ(J)o OF THE V4 FUNDAMENTA.. OF METHYL FLUORIDE. A. Normal Spectrum. The R(J) subbranch of RQo is designated. B. Stark Difference Signal Spectrum. = 12kV/cm. Positive signal implies greater absorpton with field on.

-71r and.R(J)K are much weaker in intensity than are P and R sub-branches (26). The first two lines of RR(J)1 are also shown, where, as to be expected (0o)l is missing (because J must be greater than or eqal to KI ). That quantitative measurements of the Stark effect are hindered by the multitude of absorption lines is well illustrated by this spectrum. Although at 12 kV/cm (the field used for this run) the M components of R(l)0 are all certainly resolved, one from another, they are overlapped by other, stronger, transitions* The Stark spectrum here has been taken with the infrared signal and the electric field modulation phased so that absorption with no field is recorded down scale while absorption with field is recorded up scale. The net signal above the zero line indicates that the absorptions with zero field are of a nonlinear type as explained previously. Figure 15 shows the region from Q(J)2 to RQ(J)7 of v4 methyl fluoride, an extension of Figure 14. Again the sub-branches may be readily identifield with the help of the Stark spectrum of the lower half of the figure. Each line so identified has been labeled with its K" value. It is seen that the strong lines of the normal spectrum, aside from those of the Q branchy have all been assigned. The remaining weak lines may be either members of P R sub-branches or belong to'hot' bands. An interesting phenomena is seen to occur at R(J)4. This Q branch is extremely broad compared to RQ(J)3 and for RQ(J)5 and higher the Q branches are not split at all. The exact explanation of this anomaly is not proffered but it has been suggested (27) that it arises from a Corioli. resonance between the K = 5 levels of v4 and vl. Associated with this disturbance is an increase of the effective B value of the sub-branch %(J)4, an unmistakable fact in view of the Stark effect spectrum where no ambiguities exist in making the assignments. The lines

RQ7 ~I1 23 0i!, o 3 3L a lr0 j3 r'z^ ^ - 3 3 3 3 3I z z ~ I S 4 5 2 ~ 3 3 Figure 15 STARK EFFECTS IN THE ~4 FUNDAMENTAL OF METHYL FLUORIDE FROM RQ(J)z TO RQ(j)? Above: Normal spectrum. Below: Stark difference signal. 12kV/cm. Positive signal implies greater absorption wiih field on. Numerals designate the K value of RR(J)K subbranch members.:ii iiii r I i iiii~ i i ni~ \ ir iillI \ r, I i 2i3 3 i ivl C f. i;:ii~~~~~~~~~~~~~~~~~~~~~~~~~ ii ll 1ii~s jW iii iii uii/liiii~ir a r i E 1 I\ i iI iii 2 I I i i2 llii 2:~ 12 iILL

-73R(10)4 and RR(6)5 fall on top of one another while R(9)4 is to the left of an(5)5 and R(ll)4 is to the right of RR(7)5. Unraveling this sort of snarl would be quite a tedious task, whereas a positive identification of the lines can be made alost immediately via the Stark effect. Figure 16 shows the Stark difference spectrum of v4 of methyl fluoride from Q(J)7 to RQ(J)l a farther extension of Figures 14 and 15. The ability of the Stark effect to modulate the intensity pattern of the zero field spectrum is perhaps best illustrated here. The region of RQ(J)2 is dense with lines in the normal spectrum, whereas only the members of the sub-branch (J)9 appear in the Stark modulated spectrum. The abrupt termination of this branch near 3091 cm" in the Stark effect mode is unmistakable, and simple measurements indicate that 9 x (2B) to the left brings us exactly to ~(J)9. The sub-branches R(J)7 and R"(J)g are indicated, and little effort is required to identify several mores In, this figure we note the complete lack of negative going signals, indicating that, at the pressures employed, the normal absorptions approached 100% so that a negligible decrease in the mximum absorption occurred when the line was broadened by the Stark field. Figure 17 shows sections of a high-resolution, slow speed scan of V4 methyl fluoride in which as many assignments as possible have been made with the Stark effect. Some twenty five members of the RQ(J)3 branch are indicated on the normal spectrum, but the Stark effect provides no clue to their assignment, The region of RQ(J)4 is also shown where the complete disruption of the usually intense Q branch has already been noted. The change in spacing in the corresponding sub-branch is also illustrated by the section showing the crossing at %R(10)4 of the R(J)4 and ](J)5 sub-branches o

R \R0 A Q. IQ 10 Qs Q I 1, 7 810 I~~ 3080 cm'* 3100 EFFECTS IN THE V4 FUNDAMENTAL OF METHYL FLUORIDE FROM RQ(J)7 TO OQ(J)3. ctrum. Below: Stark difference signal spectrum. = 18kV/cm. Positive signal implies greater absorption with field on. Members of the RR(J)7 and RR(J)9 subbranches are indicated.

x A, I,,, I,, IRR8', "R61 PR51"R22 "RIlo RR7,1 R16,RR32 PR12o P R17, R42 RRI30 R91 "RR2 0 PRI81 b a I RR43 B I O RR33 RR82 RR62PRIs RM% RRI RR PR201 RRIRI2, R R 13,RR17, "R92 PR22, 3 R4 "RI229R "RIll "R4 " R20 3 I "RRIO R192 RRiR R 24R75 RRI4 "R202 " RR167o RR8 RQ( Figure 17 STARK EFFECTS IN THE V4 FUNDAMENTAL OF METHYL FLUORIDE UNDER HIGH RESOLUTION. A. Illustration of the RQ(J)3 region. Successive members of the Q branch are marked by x'. B. The RQ(J)4 region showing the degeneration of the Q branch. Successive members d both wings are marked by'x'. C. The region of RR(10)4 and RR(6)5 illustrating the increased effective B' value in the RR(J)4 subranch. a. Normal spectrum. 0.03cmn' spectral slit width. b. Stark difference signal. 15kV/cm field. Positive signal implies greater absorption with field on.

-765.3 Methyl Iodide, CH I To further illustrate the value of the Stark difference signal as a tool in unraveling the rotational structure of complex bands, a molecule having very closely spaced lines was sought, Methyl iodide was chosen as it has a single isotope, a fundamental vibration within range of lead sulfide detectors' sufficient vapor pressure, and a B-value of only 0,25 cm!i23). As in methyl fluoride, it was found that high sample pressures were needed for sufficient absorption so that fields of only about 10 kV/cm could be applied without breakdown. No quantitative measurements were attempted. Figure 18 shows the normal and Stark difference spectra of the v4 fundamental band center. The only recognizable features of the zero field trace are the strong Q branches identified as RQ(J)0 and PQ(J)lo The Stark difference signal trace, on the other hand, shows beautifully developed RR(J) and RP(J) sub-branches, as identified by O's on the figure. It is seen that the sub-branch lines reach maximum intensity for J` 30 in the normal spectrum, but for J a 5 in the Stark spectrum. Thus the Stark difference signal eliminates most of the high J transitions. This fact is strikingly demonstrated in Figure 19 which again comR pares normal and Stark spectra, this time in the region of RQ(J)3 Here a monotone of weak, unresolved, unassignable lines is found between the Q branches of the normal spectrum. In the Stark spectrum, only a half-dozen or so single, completely resolved lines appear, identified as the 3rd through 9th members of the sub-branch R(J)3 (lettered'J) and the fourth through seventh members of jR(J)2 A fuErther effect which proved useful in making assignments in parallel

-77RQo PQ 0 0 000 0 0 0 0 0 I,,I RQ PQi Figure 18 STARK EFFECTS NEAR RQ(J)o OF THE V4 FUNDAMENTAL OF METHYL IODIDE. Above: Normal spectrum. Members of RR(J)o and RP(J)o are dotted. Below: Stark difference signal spectrum. E=10 kV/cm. Numerals indicate the K value of members of RR(J)K subbranches. RP(J)o is alsoindicated.

-78A j NJJ \J vX j i \ J j I ~ I II h 3 5 1' ~ 4 Figure 19 STARK EFFECTS IN METHYL IODIDE NEAR RQ(J)3 OF THE V4 FUNDAMENTAL. A. Normal spectrum. B. Stork difference spectrum; 15kV/cm, negative signal implies greater absorption with field'on, members of the RR(J)3 subbranch arelabeled by their'J' value.

type bands (ones involved a vibrational dipole moment change parallel to the figure axis of the molecule and therefore requiring AK - 0) can also be demonstrated in methyl iodide. For low fields the first order perturbation treatment can be expect to apply; and since AK = 0, A^^^S'KnJ "^" 8g'KI\ 3" ^^ b ^ 5'(3,,2 For the case K = 0O no shifts occur. The spectrum of a parallel type band is complicated in general by the K' splitting of the individual R(J)K and (J)K lines. Thus each'(J)K'line' has J components (one for each value of KI ). Ideally, these components are degenerate, but centrifugal distortion and vibration-rotation interaction terms cause them to split somewhat, giving rise to structures varying from slightly broadened lines to actual'sub-branches*' The V, vibration of methyl iodide at 2970 cm is such a parallel band having rather large'K' splitting, as indicated in Figure 20. Here the assignments may be given to some extent by observation, a few being labeled. On applying a D.C. Stark field, the K components suffer symetric Stark broadening which simply'washes" out' their intensity the net result being destruction of the'line' spectrumo This does not occur, however, for K = 0, since there is no Stark shift for these lines. Figure 21 demonstrates this effect where we see the normal and Stark spectra (with a DeC. field of 10 kV/cm) and observe that only three'lines" persist in the R branch and must correspond to %(0)0, R(1()0 and $(2)0. With this help, the K components of the normal spectrum can be assigned with certainty. 5.4 ammonial, om It is well kno wn that the ammonia molecule, shaped as a pyramid, may suffer an inversion, the nitrogen atom crossifng through the triangle formed

-80-'I- I I 2y I cm' Figure 20 METHYL IODIDE 1) BAND CENTER NEAR 2970cm1'

Q LINES /R(2' a K.,,, R(O)o Figure 21 DC FIELD STARK EFFECTS IN THE'1 FUNDAMENTAL OF METHYL IODIDE Above: Normdc Spectrum. Below: Spectrum with IOkV/cm DC Electric Field.

-81by the three hydrogens at the rate of about 24 KMC (28). This phenomena leads to a doubling of all otherwise single rotational states. The energy separation of these inversion doublets is of the order of one wave number for the vibrational modes encountered in the present work. Adjacent inversion states have a connecting dipole moment matrix element. Since the next nearest interacting state is 2(J+1)B = 20(J+1) cm1 away, to a good approximation the inversion pair may be considered doubly degenerate and the presence of the other rotational states may be ignored. The wave functions properly describing inversion states change sign under an inversion of the molecule through its center of mass, The molecular dipole moment, behaving as a vector, also changes sign under this operation. Thus first order contributions of the electric field to the energy are zero, for: ICT ( <e mpe, t* |Kf vt P"n7 =-<TOFcm E\ TYMCg>v and the energy must be invariant with respect to symmetry operations. Second order effects do occur, however, and nonvanishing matrix elements for this case (developed in Chapter IV) and their corresponding energy denominators are: < 5 - tl sm ^|- KE ta> -LtY\ (ll- l /M(t(' \; +t~: _ (1h4LPe- Here,. is the energy separation of inversion doublets. The choice of sign (-l)K+?, for. the inversion contribution to the energy differences is not

-83arbitrary but depends upon the fact that the lowest level of an inversion doublet will have positive symmetry under R (a reflection in the plane through the center of mass and perpendicular to the figure axis). Since _ Y C _*\ RxytsutP un= (-70 P^^^tm?^, The second order corrections to the energy are then T_(Jt^l K'14(^)' RCrA where P - C^'P n ^ Ji The energy denominators in this expression for AW are approximately 2BJ~A for the first the third terms, but only A for the second term. Hence the second term will usually be dominant. (In certain vibrational modes involving v2, A can become large and the relative importance of the three terms will change. For example when (viv2v3 34 ) (o0), A 18.5 cm-1 (29) and 2B = 19o88 cm 1 so that 2BJ-A = 1= 43 cm k,) J -1 The exact solution to the problem of two interacting states is available (2) and may be given as: L.-E.O (^^\ E. Ea,(IL +1 41 SYN^TT -y^ ^^

-84where - - ~E and T is the state of lower energy. As in the case of the symmetric top molecules studied, many millimeters pressure of ammonia had to be used to produce reasonable absorption strengths for the low J (simple Stark pattern) lines. Consequently, fields were limited to the order of 30-50 kV/cm. For example, the state (JKMPcm) = (222 +) shifts by 0Ol117 cml under an applied field of 10,000 volts/cmo The change of frequency of a transition involving this state will be the difference between its shift and that of the other participant state, and will be equal to or greater than this amount. In spite of these large displacements, identification of individual Stark patterns was not possible with available resolution simply because of the great number of components which arose when a field was appliedo Ordinarily the selection rule P m -,* P, P C +Pc"m holds for the parallel vibrations of ammoniae We have seen, however, that application of a Stark field mixes states of different Pa and this rule is vitiated to the extent of the mixingo Figure 22 is aschematic level diagram illustrating the splitting of the J=1 level of the ground vibrational state and the J=2 level of the v fandamental vibrational state with a field of 20 kV/cm, The M splittings caused by application of the field and the inversion splitting are drawn to the same scale as indicated in the figureo Figure 23 shows a trace run under these conditions, using the modulated field technique, together with the regular spectrum and that predicted on the basis of the above theory, including the difference in transmission of the cell for the two polarizationso This last factor effectively eliminated radiation polarized parallel to the field so that only transitions involving AIMI=~l were observed, The two weak absorption peaks located symmetrically about

-852 I- _G___, - - IMI-0,1,2 + \ \ I' 0IMI~0 J= 2 o V = I d IN =0 IMI=0 = I /___ IMI=0 *~-I =2 =2 E 0) cr ro I + t - ~ — IMI =0 3+1 aS VO o0 + ~ - -IMI=0,1'- 0 = 0 E =20 kV/cm =0 E = 20 kV/cm =0 = 20 kV/cm IKI = IK= I IKI= 2 Figure 22 ENERGY LEVEL DIAGRAM FOR THE R(I) TRANSITIONS IN THE'Z FUNDAMENAL OF AMMONIA, WITH AND WITHOUT AN EXTERNALLY APPLIED ELECTRIC FIELD. Selection rules for allowed transitions: with field, AK=O, AM=0O,*, + —-, + —+, --—. without field, AK = O, AM = O, l,+ -, The K dependence of the energy is suppressed, only the aitference term between states of the same K being retained.

-86I I I I 3374 cmA' 3376 cm' 3374 cm-' 3376 cm'* Figure 23 STARK EFFECTS OF R(l) IN THE V, FUNDAMENTAL OF AMMONIA A. Normal absorption spectrum. B. Stark difference signal spectrum, 15 kV/cm. C. Predicted spectrum.

the center of gravity of the inversion doublet are the tinduced transitions resulting from the mixing of the wave functions by the fields Although in principle there are eight such induced absorptions, only two have appreciable intensity, namely the IMI = 1 to IMI = 2 transitions. (Two of the others'are weak due to the polarization effects of the Stark cell. The remaining four transitions involve M = 0 states which remain tpure' in the presence of a field and hence are not strongly'induced.') The frequency separation of this pair is dependent upon the field strengths On extrapolation of this separation to zero field (where the line intensities are zero), one obtains directly the frequency difference between the inversion splitting in the ground and excited vibrational states, Since the sum of these inversion splittings may be obtained directly from the frequency interval between the members of the normally active doublet, the individual splittings may be determinedo These inversion splittings have been thoroughly investigated in ammonia (29, 30, 31, 32) However, the spectra of the mixed isotopes NI2D and ND (which are asymmetric tops) are difficult to analyze by conventional methods, and it would appear that the Stark difference signal would be of aid in identifying the doublets and in determining their inversion splittings. Figure 24 shows the R(3) region of the 1 fundamental of ammonia with and without an A.Co field of 20 kV/cm. Identification of Stark components was hindered by the presence of small water vapor absorptions (marked with dots) which also showed Stark effects. In a supreme effort, and at the cost of one burned out Stark cell, the same region was run at a D.C. field of 50 kV/cm. Figure 25) is a level diagram for these conditions, the displacements being drawn to scale. The allowed transitions have not been indicated as there are 133 obeying the PS + -P" and 132 more, weaker ones, in cm cmI

-883416 3414cm' 3412 _, I, I A 2 3 3 1,0 3 3 2 2 B s a Figure 24 STARK EFFECT OF R(3) IN THE )1 FUNDAMENTAL OF AMMONIA. A. Normal spectrum. K values indicated. B. Stark difference signal. 20kV/cm. Negative signal implies greater absorption with field on.

— 4 -3 -4 ~2 — 2 -3 _ 4 -2 -o TT J=4 V I 0~~~~~~ V~~~~~~~~~~~~~~~~l~~~~~~ ~ ^ ^_____ 0~~~~~ -,_ +,. S ~~ ~~ — ~ ~ ~ —--'E'f'E~~~~~~~~~~ io~~~~~~~~~~~~~~~~~~~~~~~3 J=3' V=O PI: 0 X + -' —- 0,1,2,3 0 + *-3'- -1 -2 - ~-0 -3 -2 -3 E 0 eC50kV/cm E.0 E 50 kV/cm E =0 e=50kV/cm e=0 S=50kV/cm ~"0 e 5k0V/cm K=O KI=l K=2 K=3 K=4 Figure 25 ENERGY LEVELS FOR THE R(3) TRANSITIONS IN THE -, FUNDAMENTAL OF AMMONIA, WITH AND WITHOUT AN EXTERNALLY APPLIED ELECTRIC FIELD. IMl values ore indicated. + and - refer to symmetry under 1cm. K dependence of the energy is suppressed, only the difference term between states of the same K being retained.

-90violation of this rule due to mixing of states in the presence of the field. Figure 26 shows the results of the 50 kV/cm run, together with another zero field trace of the region at maxiumn resolution, No attempts were made to correlate spectrum and theoryt 5~5 Water 120 was selected as a representative case of an asymnetric top molecule in which to observe the Stark effect on the rotation-vibration spectrulm A section of the Stark spectrum of water, obtained using the difference signal technique is reproduced in Figure 2T. Table XI lists the prominent signals occurring in such a spectrum, giving both the relative intensities and the zero field transitions involved. It is seen that the largest Stark effects are not necessarily associated with states of low rotational energy, contrary to our previous experience. The two strongest signals arise from transitions involving rotational levels having J > 4 This implies the existence of closely spaced levels capable of interacting through an electric field perturbation. A detailed theory of the Stark effect of asymmetric molecules, to second order in the perturbing fields, has been given by Golden and Wilson (33). They show that first order effects vanish identically, ~nd are able to express the second order energy corrections as: [A;(Al t l ) ( di pP+

-91B 3 A I Iu~ I I11 I 3412 3414 cm'1 3416 Figure 26 HIGH DC FIELD STARK EFFECT OF R(3) IN THE 71 FUNDAMENTAL OF AMMONIA. A. Normal spectrum. K values indicated. B. Spectrum with 50kV/cmr DC field.

i!.,i' I$ 00,,,.,11l\, jla V i P 22 2''iII)iI I'- 65-, _ 5 I -, 4_3 5_3- 42 _. 5-174 7- 6 Figure 27 H20 NEAR 3870 cm' I cm. press. ABOVE STARK DIFFERENCE SIGNAL, 10 kV/cm BELOW NfORMAL SPECTRUM

-93SABIE XI uma of Stark Effects Observed in the Spectrum of 120 Frequency Parent Transition Rel. Stark Sig. Orig. of Stark Sig J'* Vib 3880.07 cm 511 v3 o105 B 3869067 6_5 54 v3 9.5 B 3863.48 22 1 3 4*3 C 3871.65 5 4_ v1 2.5 B -1 -3 3973-98 51 44 v3 2.4 B 11 0 v C 3779.41 3 2.3 5_1 5.2 v3 B 3892,80 31 22 v3 2.2 C 3711-09 2 1_L v1 2.2 C 3885.77 76 6_5 v 2.0 A 3696.22 5 5_3 v1 2.0 B 3629.53 4 33 V3 1.8 X 3904.22 62 5- v 1.7 A 395.11.3 3835.02 43 32 3 1.7 B 3746.23 21 1 v1 1.4 C 3874.53 5 4 v 1.3 B 3770.17 65 5_5 1 13 B 3759476 11 1.3 C 3738.31 21 20 v3 1.3 C 3637.99 1. 1 V1 1-2; C 36749 95 1l 11 1 1.2 C 2 21 v C 37091o 6 1 2 1.2 l l 22 v3 C -2 -2 3 3831!.68 3-1 20 3 1.0 C 3785.01 7 7 6 v 09 A 3823.09 5_3 54 v3 0.8 B 3749.49 21 22 v3 0.8 C

-94Table XI (Con't) 3819.88 3, 33 3 0.7 X 3815.96 3 2 2i1 V3 0.7 C 3750.84 44 2 l07 X 3843.68 64 65 3 0.6 A 3779.41 0 v3 o.6 C 5_1 5_2 3 B 3701.45 1 20 v3 0.6 C 3820.65 33 22 v3 0.5 a. Simply the peak-to-peak Stark signal and only a crde estimate of the Stark shifts. b. A Degenerate level in ground vibrational state B Degenerate level in excited vibrational state C Ordinary Stark shift of a strong transitions beteen low J(<2) levels. Independent of near degeneracies. X Unexplained by A, B, or C.

-95Here A and C are the respectively largest and smallest rotational constants, andxi. is the x. component of the molecular diople moment (x is defined as.1 the axis of least moment of inertia, z that of the largest). The quantities xi'i Aj and BT depend upon the quantum numbers and upon the molecular asymmetry A-C 2B-A-C parameters a = AC and K = A —--- A and B are listed in Table XII in terms of the quantum numbers, the state function expansion coefficients (34,35) using symmetric top eigenfunctions and the parity PX of the state function xiheri for a rotation by 1800 about x.O A and B have been numerically evalu1i t Jt ated by Golden and Wilson (33) for all levels between 0 J < 2, entries being given for values of a ranging from Ool to 0.9 and for K from -0.9 to 0.9, both in steps of 0.*2 Let us compute, using Golden's tables, the second order perturbation correction to the ground rotational state Woo for water. Here, a= 0.48 K = -.043 2= 18,4 cm and C = 0.023 cm at 20 kV/cm, The permanent dipole moment of water lies along its y axis and thus oooP 0t 0,03A / 0.004 CrAs in the case of linear and symmetric top molecules, the ground rotational state of asymmetric molecule s is strongly affected by Stark fieldso This computation then indicates that, barring accidental interacting degeneracies, field effects in H20 will be very weak and individual Stark components cannot at present be resolved. Golden and Wilson (33) have also considered the case of accidental doubly degenerate levels by first solving the double degenerate problem exactly, and then proceeding with the perturbation calculation as before. The dipole moment of water lies along the y axis and changes sign under 1800 rotation about either the x or z axes. The Stark perturbation, - got,

-96TABL XII Coefficients in the Perturbation Calculation for the Stark Effect of Asymmetric Rotors I~, ~),.~~~~~~~~~~~~~~~ * i^ _ k- " -^ ~s _, =^"^ ^ ^^~~ * %''~~~ I - 1- 4-~4-r r -I 4- -~~~~~~~~~~~~, I!~ ~- I-1 +I "^ ~~~ ~ ~~~~~ LL' ^ ^ ix \ ^^ 1f ^1 ^^ - 4- -1- OL-, ^ Si + f- Iu - h 4e /r~~~~~~~~~~~~~~~~~~~~~~~1NI —i' a -I — ^c r"J e5 ^ 0-, II 1 I,c ^ \ -I - t w ^ E )T - - - ~~ ~ ~?~ Z ^ ~ I____ I____ cr E: G "a~~ ^

____ \ (\t Pi P^ )i-^ 6Pi (e Lt I1K (zysy(Z li) 4 ^T^ - WJT~t -v 4~te~~~~~~~~~~~~~~~~~~~~~~4 A3?' - ^ -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\ P9~~~~~~~~~~~' (^1^ ^) \A^^ - ^^ Z I^^c ~I ~' W3,_rv^~- 4-\-M/ 1 rr t A+C C I~tfrr~)( i,J ~;It )1(z f,~) i Vi ^ P R )L^a^^a i] ______~3i (I +I rifh)& r \ (^-0 ^ ^ w^^-^Tm ^~~~~P

will have the same symetry properties Thus two state functions having opposite parity under both of the rotatiorsC2 and C2, and also satisfying IAJI 1, will interact in the presence of an applied electric field, Reference to the term values for water as given by Plyler (36) reveals that several pairs of states satisfying these conditions are degenerate to wiTth-1 in 10 cm 1 They are listed in Table XIII for the three vibrational states of interest (Vv2v3) = (000), (100), (001), TABLE XIII Summary of Nearly Degenerate Eigen States Having Connecting Dipole Moment Matrix Elements for the Water Molecale Higher State Lower State Energy Separation J Vib State J Vib State cmn 6g grnd 5- grnd 0.74 6_5 1 5_1 1 0.18 65 3 51 0 16 5 4 v1 4 3 v3 oo8 50 V1 5_3 v3 0.37 4 V 3 V o,9 41 1 32 v3 0.'42 1 31 3 0~92 The interpretation given the observed spectra is immediately confirmed. The closest interacting degeneracy gave rise to the strongest observed effect. Indeedy every entry (with one exception) to the list of strong bSark signals as given in Table XI can be traed to either a transition involving an interacting degenerate level or to one involving levels of very small rotational energy.

-99VIo SUMMARY A survey has been made of Stark effects in the vibration-rotation spectra of hydrogen cyanide, methyl fluoride, methyl iodide, ammonia and water. The experiment depended entirely upon construction of a Stark cell which would permit application of fields between 10 and 100 kV/cm to vapor samples at several mm pressure. A light guide type cell was employed which had chromium front surfaced mirrors as plane parallel electrodes, The electrode separation of 0,2 to 0.5mm was evaulated by employing partially transparent mirror electrodes and examining the fringe systems produced upon passing light through the cell perpendicular to its transmission axis. A mean cell gap and a gap tolerance could in this way be determined. The voltage was established to ~0.1% and the gap tolerance held to l1% so that the electric field was known to l~%I All of the observed field effects could be adequately explained on the basis of either perturbation theory, the theory of two interacting nearly degenerate states, or an exact solution to the problem of a symmetric top in an arbitrarily high electric field. Hydrogen cyanide was found ideally suited to Stark effect studies. Its intense infrared absorption permitted use of minimum sample pressures and therefore of maximum electric fields~ Its large dipole moment and reasonably small'Bt value gave rise to measurable frequency displacements. Its normal spectrum, that of a linear molecule and not seriously complicated by overlapping absorption bands, permitted identification of resolved Stark patternse Careful measurement of certain splittings yielded a value for the dipole.moment of hydrogen cyanide in its v3 vibrational state of 3.001 ~,007 debye

-100(as compared to 2.985 ~~005 in the ground state)o Isolation and identification of individual M components in the Stark effect patterns of methyl fluoride and methyl iodide was not possible because of the close spacing of lines in the normal spectra. Additionally, only modest fields could be applied since high sample pressures were needed to produce adequate absorption strengths. In the presence of a weak field, the individual absorption lines of a symmetric top molecule are broadened by an amount proportional to K/J2 The intensity of a Stark difference signal will be proportional to this as well as to the usual factors. The Stark difference spectrum proved useful as an aid to making assignments in the zero field spectrum due to this new intensity modulation. At optimum field, some 70% of the transitions observed in the normal spectrum of methyl iodide were of negligible intensity in the Stark difference signal spectrum, The inversion doubling of the ammonia molecule gave rise to interesting Stark effects in its spectrum. In the presence of an applied electric field, the wave functions describing adjacent inversion states mix and permit transitions previously forbidden in accordance with the selection rule s <- a, s — ii- s, a -lI a. When extrapolated to zero field, the frequency separation between the'st —y's' and'al la'-'field induced' absorptions equals the difference in the inversion splittings of the ground and excited vibrational states. These effects would prove helpful in understanding the spectra of the isotopic species IH2D and iHD2 Accidental degeneracies, characteristic of the energy levels of asymmetric top molecules, led to the bulk of observable signals in the Stark difference spectrum of water. In addition, slight displacements were detected for transitions involving low J energy levels.

-101With present resolution and. detectivity, observation of Stark effects in vibration-rotation spectroscopy remains limited to the spectra of carefully selected molecules. Increased luminosity of the source and a more sensitivity detector, as well as a Stark cell with higher transmission efficiency and higher Ireakdown voltage rating (conditions optimized as far as possible in the present experiments) would not greatly change this situation. A major improvement would result, however, from increased spectral resolution. With increased resolution, smaller frequency shifts could be detected and the lower sample pressures required to obtain adequate absorption strengths would enable higher electric fields to be applied without breakdown. In particular, the substantially greater resolving power of a Fabry Perot interferometer, if it could be incorporated into the experimental arrangement, would permit isolation and measurement of a great many Stark patterns which cannot currently be resolved,

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