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Random Lattice Calculations on Frenkel Excitons in Disordered Molecular Crystals—1B2u Naphthalene
dc.contributor.authorHong, Hwei‐kwanen_US
dc.contributor.authorKopelman, Raoulen_US
dc.date.accessioned2010-05-06T20:52:06Z
dc.date.available2010-05-06T20:52:06Z
dc.date.issued1971-12-01en_US
dc.identifier.citationHong, Hwei‐Kwan; Kopelman, Raoul (1971). "Random Lattice Calculations on Frenkel Excitons in Disordered Molecular Crystals—1B2u Naphthalene." The Journal of Chemical Physics 55(11): 5380-5392. <http://hdl.handle.net/2027.42/69611>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/69611
dc.description.abstractUsing the recently acquired exciton dispersion relations for crystalline naphthalene, we have calculated the density‐of‐states functions for heavily doped isotopic binary mixed crystals of naphthalenes with arbitrary compositions and various energy separations (trap depths). This constitutes the first attempt to extend the negative factor counting (NFC) method, developed originally for lattice phonons, to a real physical system of three‐dimensional molecular excitons. In most calculations, a total of 1280 molecules were included. The exciton interactions, which included both the translationally equivalent and the interchange equivalent ones, involved all 16 neighbors. Calculations based on the coherent potential approximation (CPA) were also performed for comparison. It was concluded that these two sets of calculations compared very well except in the split‐band limit and at low concentrations. Under these conditions the cluster or conglomerate states become important and the computer‐simulated density‐of‐states functions revealed some fine structure, which was completely indiscernible in the density‐of‐states function based on CPA. This fine structure is experimentally significant. The relationship between the Green's function method and the moment trace method was investigated in the light of these new results. Particularly, some of the lower moments were calculated for the density‐of‐states functions and compared with those calculated from the exact expressions in our previous paper. It was shown numerically that the CPA results indeed agree with the exact moments up to the seventh order.en_US
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dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleRandom Lattice Calculations on Frenkel Excitons in Disordered Molecular Crystals—1B2u Naphthaleneen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Chemistry, University of Michigan, Ann Arbor, Michigan 48104en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/69611/2/JCPSA6-55-11-5380-1.pdf
dc.identifier.doi10.1063/1.1675683en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
dc.identifier.citedreferenceFor the theory and experiments on dilute mixed crystals see, for example, E. R. Bernstein, S. D. Colson, R. Kopelman, and G. W. Robinson, J. Chem. Phys. 48, 5596 (1968); D. M. Hanson, R. Kopelman, and G. W. Robinson, J. Chem. Phys. 51, 212 (1969); D. P. Craig and M. R. Philpott, Proc. Roy. Soc. (London) A290, 583, 602 (1966); A293, 213 (1966); B. S. Sommer and J. Jortner, J. Chem. Phys. 50, 187, 822 (1969). For heavily‐doped mixed crystals, see Refs. 16 and 18.en_US
dc.identifier.citedreferenceS. D. Colson, D. M. Hanson, R. Kopelman, and G. W. Robinson, J. Chem. Phys. 48, 2215 (1968).en_US
dc.identifier.citedreference(a) D. M. Hanson, J. Chem. Phys. 52, 3409 (1970); (b) H. K. Hong and R. Kopelman, Phys. Rev. Letters 25, 1030 (1970); (c) H. K. Hong and R. Kopelman, J. Chem. Phys. 55, 724 (1971).en_US
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dc.identifier.citedreferenceFor a review and bibliographies, see J. Hori, Spectral Properties of Disordered Chains and Lattices (Pergamon, Oxford, 1968).en_US
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dc.identifier.citedreferenceTo our knowledge, the only existing literature on the comparison between CPA and NFC results is Taylor’s paper (Ref. 10) on disordered phonons. The treatments of disordered phonons and excitons are similar but not identical. For further discussions see Sec. II.A.en_US
dc.identifier.citedreferenceH. K. Hong and R. Kopelman, J. Chem. Phys. 55, 3491 (1971).en_US
dc.identifier.citedreferenceJ. Frenkel, Phys. Rev. 37, 17, 1276 (1931); A. S. Davydov, Theory of Molecular Excitons (McGraw‐Hill, New York, 1962); A. S. Davydov, Usp. Fiz. Nauk 82, 393 (1964) [Sov. Phys. Usp. 7, 145 (1969)]; A. S. Davydov, Theory of Molecular Excitons (Plenum, New York, 1971).en_US
dc.identifier.citedreferenceE. R. Bernstein, S. D. Colson, R. Kopelman, and G. W. Robinson, J. Chem. Phys. 48, 5596 (1968).en_US
dc.identifier.citedreferenceHnn  =  ϵn∗+Σprime;mϵm0,Hnn=ϵn∗+Σprime;mϵm0, where ϵ∗ϵ∗ and ϵ∘ϵ∘ are the energies of excited and ground state molecules in the site, respectively. Subscripts refer to the site indices. We can rewrite Hnn  =  (ϵn∗−ϵn∘)+Σmϵm∘.Hnn=(ϵn∗−ϵn∘)+Σmϵm∘. Choosing the ground state of the crystal, which is Σmϵm∘,Σmϵm∘, as energy zero, we have HnnHnn equal to ϵn∗−ϵn∘,ϵn∗−ϵn∘, or the excitation energy.en_US
dc.identifier.citedreferenceThe following proof is an adaptation of the one given on p. 34 of Ref. 5, except that the latter contains some misprints.en_US
dc.identifier.citedreferenceJ. H. Wilkinson, Rounding Errors in Algebraic Processes (Her Majesty’s Stationery Office, London, 1963), Chap. 3.en_US
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dc.identifier.citedreferenceWhen the trial and error method is used, it is found that at the band edges, the real part of the Green’s function does not vary too much with either concentrations or trap depths. It always is roughly equal to the reciprocal of half the pure crystal bandwidth ( ≃ 0.02≃0.02 in our case)! Consequently, the real part of the self‐energy can be determined from the following equation [see Eq. (48) in Ref. 16, assuming b, d ≃ 0d≃0]: ±0.02=−c∕{c[(CB−CA)Δ+c]−CACBΔ2}. This value is used as the first trial value. A small imaginary part is then assigned to the self‐energy so that the iterations lead to a complex Green’s function.en_US
dc.identifier.citedreferenceD. M. Hanson, R. Kopelman, and G. W. Robinson, J. Chem. Phys. 51, 212 (1969); B. S. Sommer and J. Jortner, 50, 822 (1969).en_US
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dc.identifier.citedreferenceThis table can be prepared from Fig. 6 of Ref. 3(c).en_US
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dc.identifier.citedreferenceE. I. Rashba, Opt. Spektrosk. 2, 568 (1957).en_US
dc.identifier.citedreferenceSee also p. 177 of Ref. 5.en_US
dc.identifier.citedreferenceSee Footnote 23 in Ref. 21.en_US
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dc.identifier.citedreferenceG. Castro and G. W. Robinson, J. Chem. Phys. 50, 1159 (1969).en_US
dc.owningcollnamePhysics, Department of


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