# Applications of the SCF-X_{α} Scattered-Wave Method to Molecular Crystals and Polymers

## Abstract

To facilitate the application of the self-consistent-field X scattered-wave (SCF-Xα-SW) method to certain types of molecular crystals and polymers, it is possible to introduce two modifications of the theory and computational procedure: (1) the use of overlapping atomic spheres and (2) the partitioning of the system into component interacting molecular units. The theoretical assumptions underlying the use of overlapping spheres are discussed first, and the theory is illustrated for molecular TCNQ, a component of highly conducting organic molecular crystals of the TTF-TCNQ type. The results obtained for TCNQ suggest that the SCF-Xα-SW method, in conjunction with overlapping atomic spheres, can be used to produce realistic electronic energy levels and charge distributions for large planar organic molecules. To calculate the electronic structure of a crystalline or polymeric array of interacting polyatomic molecules, it is possible to make use of some unique features of the SCF-Xα-SW method. The calculations are carried out on one part of the system at a time using overlapping atomic spheres and a local intersphere potential, iterating between interacting parts until self consistency is attained. By exploiting the local molecular symmetry of each component part, the calculations can be further simplified, and only moderate amounts of computer time are required. This method is not dependent on the assumption of molecular periodicity or Bloch’s theorem and therefore is applicable to disordered or amorphous polymers and molecular solids, where there is at most only short-range molecular order. Results for a water trimer are presented as a simple illustration of the computational procedure for a weakly coupled polymer. Extensions of this procedure to more complex systems, such as the molecular crystal TTF-TCNQ, are also discussed.

## Keywords

Molecular Crystal Outer Sphere Secular Equation Atomic Sphere Energy Level Structure## Preview

Unable to display preview. Download preview PDF.

## References

- 1.J.C. Slater and K.H. Johnson, Phys. Rev. B5, 844 (1972)ADSGoogle Scholar
- K.H. Johnson and F.C. Smith, Jr., Phys. Rev. B5, 831 (1972).ADSGoogle Scholar
- 2.K.H. Johnson, J. Chem. Phys. 45, 3085 (1966).ADSCrossRefGoogle Scholar
- 3.K.H. Johnson, in Advances in Quantum Chemistry, Vol. 7, edited by P.-O. Löwdin (Academic Press, New York, 1973), p. 143.Google Scholar
- 4.K.H. Johnson, J.G. Norman, Jr., and J.W.D. Connolly, in Computational Methods for Large Molecules and Localized States in Solids, edited by F. Herman, A.D. McLean, and R.K. Nesbet (Plenum Press, New York, 1973), p. 161.CrossRefGoogle Scholar
- 5.K.H. Johnson in Annual Review of Physical Chemistry, Vol. 26, edited by H. Eyring (Annual Reviews, Inc., Palo Alto, California, 1975), to be published.Google Scholar
- 6.J.C. Slater, in Advances in Quantum Chemistry, Vol. 6, edited by P.-O. Löwdin (Academic Press, New York, 1972), p. 1.Google Scholar
- 7.J.C. Slater, The Self-Consistent-Field for Molecules and Solids, Volume 4 of Quantum Theory of Molecules and Solids (McGraw-Hill Book Company, New York, 1974).Google Scholar
- 8.N. Rösch, W.G. Klemperer, and K.H. Johnson, Chem. Phys. Lett. 23, 149 (1973).ADSCrossRefGoogle Scholar
- 9.F. Herman, A.R. Williams, and K.H. Johnson, J. Chem. Phys., October 15, 1974 issue, in press (provides a theoretical justification for the use of overlapping spheres and a sketch of Models I through IV for molecular TCNQ).Google Scholar
- 10.J.G. Norman, Jr., J. Chem. Phys. (submitted for publication).Google Scholar
- 11.J.C. Slater, Intern. J. Quantum Chem. (in press).Google Scholar
- 12.J.C. Slater, J. Chem. Phys. (in press).Google Scholar
- 13.A.R. Williams, Intern. J. Quantum Chem. (in press).Google Scholar
- 14.N. Rösch and K.H. Johnson, Chem. Phys. Lett. 24, 179 (1974).ADSCrossRefGoogle Scholar
- 15.N. Rösch, R.P. Messmer, and K.H. Johnson, J. Amer. Chem. Soc. 96, 3855 (1974).CrossRefGoogle Scholar
- 16.R.C. Evans, An Introduction to Crystal Chemistry (Cambridge University Press, 1966), Second Edition.Google Scholar
- 17.R. Foster, Organic Charge-Transfer Complexes (Academic Press, London, 1969).Google Scholar
- F.H. Herbstein, in Perspectives in Structural Chemistry, eds. J.D. Dunitz and J.A. Ibers (John Wiley and Sons, New York, 1971), Vol. 4, p. 166.Google Scholar
- 18.I.F. Shchegolev, Phys. Status Solidi 12(a) 9 (1972).ADSGoogle Scholar
- 19.H.R. Zeiler, in Festkörperprobleme, ed. H.J. Queisser (Pergamon, New York, 1973), Vol. XIII.Google Scholar
- 20.A.J. Epstein, S. Etemad, A.F. Garito, and A.J. Heeger, Phys. Rev. B5, 952 (1972)ADSGoogle Scholar
- L.B. Coleman, J.J. Cohen, D.J. Sandman, F.G. Yamagishi, A.F. Garito, and A.J. Heeger, Solid State Commun. 12, 1125 (1973).ADSCrossRefGoogle Scholar
- 21.J. Ferraris, D.O. Cowan, V. Walatka, Jr., and J.H. Perlstein, J. Amer. Chem. Soc. 95, 948 (1973).CrossRefGoogle Scholar
- 22.L. Scheire and P. Phariseau, Chem. Phys. Letters 26, 149 (1974); Intern. J. Quantum Chem., in press; Physica, in press.ADSCrossRefGoogle Scholar
- 23.D.A. Liberman, unpublished.Google Scholar
- 24.J.C. Slater, Phys. Rev. 45, 794 (1934).ADSMATHCrossRefGoogle Scholar
- 25.F. Herman and I.P. Batra, Nuovo Cimento B, June, 1974 issue (Models I and III).Google Scholar
- 26.F. Herman and I.P. Batra, Phys. Rev. Letters 33, 94 (1974) (Models I and IV).ADSCrossRefGoogle Scholar
- 27.R.E. Long, R.A. Sparks, and K.N. Trueblood, Acta Cryst. 18, 932 (1965) (TCNQ crystal). The C-H bond distance was taken as 1.09 Å, a representative neutron scattering value. See alsoCrossRefGoogle Scholar
- A. Hoekstra, T. Spoelder, and A. Vos, Acta Cryst. B28, 14 (1972)Google Scholar
- T.J. Kistenmacher, T.E. Phillips, and D.O. Cowan, Acta Cryst. B30, 763 (1974).Google Scholar
- 28.F.A. Cotton, Group Theory with Chemical Applications (Wiley-Interscience, New York, 1971). Second edition.Google Scholar
- 29.K.H. Johnson and F.C. Smith, Jr., M.I.T. Scattered Wave Computer Programs, unpublished.Google Scholar
- 30.D.A. Liberman and I.P. Batra, IBM Research Report RJ 1224 (May, 1973), unpublished. This report documents a modified version of Ref. 29. The formalisms underlying Refs. 29 and 30 are identical.Google Scholar
- 31.The expressions used for the potential and kinetic energies reflect the approximations we are making, namely, spherically averaging potentials and charge densities in the atomic spheres and outside the outer sphere, and volume averaging these quantities in the intersphere region. These simplifications also affect the calculated virial ratio. Accordingly, this quantity should be regarded as a rough figure of merit rather than an exact one. For a detailed discussion of the virial theorem within the context if the statistical exchange approximation, see Ref. 7.Google Scholar
- 32.J.N.A. Ridyard, Perkin-Elmer Limited, private communication. Spectrum obtained with Perkin Elmer Model PS18. The authors are grateful to Dr. Ridyard for permission to reproduce his experimental spectrum for TCNQ vapor.Google Scholar
- 33.W.D. Grobman, R.A. Pollak, D.E. Eastman, E.T. Maas, Jr., and B.A. Scott, Phys. Rev. Letters 32, 534 (1974).ADSCrossRefGoogle Scholar
- 34.H.T. Jonkman and J. Kommandeur, Chem. Phys. Letters 15, 496 (1972).ADSCrossRefGoogle Scholar
- 35.F. Herman, W.E. Rudge, I.P. Batra, B.I. Bennett, and K.H. Johnson, to be published.Google Scholar
- 36.R.A. Pollak, private communication.Google Scholar
- 37.D.W. Turner, C. Baker, A.D. Baker, and C.R. Brundle, Molecular Photoelectron Spectroscopy (Willey-Interscience, London, 1970). Since the 2σ orbital for HCN is analogous to the lowest-lying bonding σ orbitals for TCNQ, the following information is relevant: The 2σ orbital energy for HCN has been found to lie between 33 and 37 eV, according to several orbital energy calculations which are summarized in Table 13.1 (p. 345) of this reference. Of course, these calculations neglect relaxation effects, which can amount to few eV.Google Scholar
- 38.R. Kjellander, to be published.Google Scholar
- 39.This section describes preliminary work published elsewhere. See R. Kjellander, Chem. Phys. Lett., submitted for publication.Google Scholar
- 40.This simple mixing formula probably suppresses some of the effects due to the neighboring units and is regarded as a preliminary one, which can be used to examine the legitimacy of the partial decoupling. A more elaborate mixing scheme, which is under development, includes the full contributions to the potential from the nearest neighboring units and takes care of teh main effects due to the delocalization of the orbitals over neighboring pairs of units when computing the total electron density.Google Scholar
- 41.R. Kjellander, to be published.Google Scholar