Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?*
Dylan Jayatilaka A C , Kunal K. Jha B and Parthapratim Munshi B C
+ Author Affiliations
- Author Affiliations
A School of Chemistry and Biochemistry, University of Western Australia, 35 Stirling Highway, Nedlands, WA 6009, Australia.
B Chemistry Department, School of Natural Sciences, Shiv Nadar University, Tehsil Dadri, UP 201314, India.
C Corresponding authors. Email: dylan.jayatilaka@uwa.edu.au; parthapratim.munshi@snu.edu.in
Australian Journal of Chemistry 71(4) 295-306 https://doi.org/10.1071/CH17624
Submitted: 12 January 2018 Accepted: 23 March 2018 Published: 3 May 2018
Abstract
Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.
References
[1] Y. Fainman, J. Ma, S. Lee, Mater. Sci. Rep. 1993, 9, 53.| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK3sXlt1SmsLw%3D&md5=3493fc25bd4adf4927953baf33482a20CAS |
[2] D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey 2005 (Springer: New York, NY).
[3] H. Nalwa, S. Miyata, Nonlinear Optics of Organic Molecules and Polymeric Materials 1997 (CRC Press: Boca Raton, FL).
[4] C. Bosshard, J. Hulliger, M. Florsheimer, P. Gunter, Organic Nonlinear Optical Materials 1995 (Gordon and Breach: Basel).
[5] S. R. Marder, Chem. Commun. 2006, 0, 131.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD28XhtVehtrg%3D&md5=1dc375f50844b015b6fb833511a68c5fCAS |
[6] T.-C. Lin, J. Cole, A. Higginbotham, A. Edwards, R. Piltz, J. Perez-Moreno, J.-Y. Seo, S.-C. Lee, K. Clays, O.-P. Kwon, J. Phys. Chem. C 2013, 117, 9416.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3sXlvVyku7c%3D&md5=8d746474c3d4511317b844d5e5a23cb0CAS |
[7] A. P. Higginbotham, J. M. Cole, M. A. Blood-Forsythe, D. D. Hickstein, J. Appl. Phys. 2012, 111, 033512.
| Crossref | GoogleScholarGoogle Scholar |
[8] P. Hohenberg, W. Kohn, Phys. Rev. B 1964, 136, B864.
| Crossref | GoogleScholarGoogle Scholar |
[9] E. Runge, E. Gross, Phys. Rev. Lett. 1984, 52, 997.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL2cXhsVGit78%3D&md5=bcf50ea38c73e3eedddd7037c04094ebCAS |
[10] S. Trickey, A. Vela, J. Mex. Chem. Soc. 2013, 57, 105.
| 1:CAS:528:DC%2BC3sXhsFeqtr%2FO&md5=3570ff03271a8cf4e42329743952da23CAS |
[11] A. Whitten, D. Jayatilaka, M. Spackman, J. Chem. Phys. 2006, 125, 174505.
| Crossref | GoogleScholarGoogle Scholar |
[12] A. Unsöld, Z. Phys. 1927, 43, 563.
| Crossref | GoogleScholarGoogle Scholar |
[13] A. Willetts, J. Rice, D. Burland, D. Shelton, J. Chem. Phys. 1992, 97, 7590.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK3sXmslahsw%3D%3D&md5=38d110824f9eca19607aeb1adbe5e0f4CAS |
[14] R. McWeeny, Methods of Molecular Quantum Mechanics, 2nd edn 1992 (Academic Press: New York, NY).
[15] C. Huiszoon, Mol. Phys. 1986, 58, 865.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL28Xlt1Ggtrk%3D&md5=b273d64d8fcd1e5217b205938f871a57CAS |
[16] M. G. Sylvain, I. Csizmadia, Chem. Phys. Lett. 1987, 136, 575.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL2sXltVejtb0%3D&md5=2df09ac9bb79dd271cfc91f99c715d8dCAS |
[17] R. Fisher, J. Wishart, Proc. London Math. Soc. 1932, s2-33, 195.
| Crossref | GoogleScholarGoogle Scholar |
[18] M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, 9th edn 1970 (Dover Publications: New York, NY).
[19] M. Wolkenstein, C.R. Acad. Sci., U.R.S.S. 1941, 32, 185.
[20] D. A. Long, Proc. R. Soc. Lond. A 1953, 217, 203.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaG3sXltVCisQ%3D%3D&md5=68363cbddc68ea3e8ac47768d4095ad3CAS |
[21] A. Stone, The Theory of Intermolecular Forces, 2nd edn 2013 (Oxford University Press: Oxford).
[22] J. Oudar, D. Chemla, Opt. Commun. 1975, 13, 164.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaE2MXhslOqsrY%3D&md5=94fed05f5bc80a2cb2bd1e8fa9506596CAS |
[23] E. Fermi, E. Amaldi, Accad. Ital. Rome 1934, 6, 117.
[24] P. Nandi, N. Panja, T. Ghanty, J. Phys. Chem. A 2008, 112, 4844.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1cXlt1Slt7s%3D&md5=6b2dd982d0074d5d3b661b2363745639CAS |
[25] P. K. Nandi, N. Panja, T. K. Ghanty, T. Kar, J. Phys. Chem. A 2009, 113, 2623.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1MXhvFylsr4%3D&md5=8e6736971a86267fc93db5f1e6a488b0CAS |
[26] F. Robinson, Bell Syst. Tech. J. 1967, 46, 913.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaF2sXks1yqs7k%3D&md5=e4ddb3309303a5011bfec3e6d30a64c5CAS |
[27] J. Zyss, D. S. Chemla, in Nonlinear Optical Properties of Organic Molecules and Crystals (Eds D. S. Chemla, J. Zyss) 1987, Vol. 1, pp. 23–191 (Academic Press: New York, NY).
[28] S. Jha, N. Bloembergen, Phys. Rev. 1968, 171, 891.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaF1cXksVOhtb8%3D&md5=bbfccc93781642b82d8a5ad28cf4a74aCAS |
[29] J. Oudar, J. Chem. Phys. 1977, 67, 446.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaE2sXkvFars7o%3D&md5=9343bedfe1f433f035b02168100f0127CAS |
[30] M. G. Kuzyk, J. Pérez-Moreno, S. Shafei, Phys. Rep. 2013, 529, 297.
| Crossref | GoogleScholarGoogle Scholar |
[31] Y. He, J. Shi, G. Su, Acta Crystallogr. Sect. C 1994, 50, 804.
| Crossref | GoogleScholarGoogle Scholar |
[32] H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S.-T. Ho, E. Brown, M. Ratner, T. Marks, J. Am. Chem. Soc. 2007, 129, 3267.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2sXhvFKktbk%3D&md5=b2ec533d4d88d26ce206d14ae7d66c9eCAS |
[33] P. C. Hariharan, J. A. Pople, Theor. Chim. Acta 1973, 28, 213.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaE3sXhtFGnsL4%3D&md5=3ad08c3354a7048fb8548fd5d9a90680CAS |
[34] M. Francl, W. Petro, W. Hehre, J. Binkley, M. Gordon, D. DeFrees, J. Pople, J. Chem. Phys. 1982, 77, 3654.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL38XlsFSqt7g%3D&md5=457b181501a74df389b81ddfa0f07eaeCAS |
[35] F. Allen, Acta Crystallogr. B 2002, 58, 380.
| Crossref | GoogleScholarGoogle Scholar |
[36] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian 09, Revision D.01, 2009 (Gaussian, Inc.: Wallingford, CT).
[37] D. Jayatilaka, D. Grimwood, Comput. Sci. ICCS 2003, 2003, 142.
[38] P. Munshi, B. W. Skelton, J. J. McKinnon, M. A. Spackman, CrystEngComm 2008, 10, 197.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1cXhs1KjtLY%3D&md5=dd827da317326cf98d6093a3c7e1f396CAS |
[39] R. Vrcelj, E. Shepherd, C.-S. Yoon, J. Sherwood, A. Kennedy, Cryst. Growth Des. 2002, 2, 609.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD38XmslGns70%3D&md5=21d68962f7455af44347c4de63f9ad5dCAS |
[40] F. Kiuchi, X. Chen, Y. Tsuda, Chem. Pharm. Bull. 1990, 38, 1862.
| 1:CAS:528:DyaK3MXlvFCr&md5=e67d0f87b433d21865884c1b311103f6CAS |
[41] D. Jayatilaka, P. Munshi, M. Turner, J. Howard, M. Spackman, Phys. Chem. Chem. Phys. 2009, 11, 7209.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1MXpslelsb8%3D&md5=b6bbae4b4067ea1c92b686bde1bebc89CAS |
[42] D. Jayatilaka, in Modern Charge Density Analysis (Eds C. Gatti, P. Macchi) 2012, Ch. 6, pp. 213–258 (Springer Science & Business Media: Berlin).
[43] D. D. Hickstein, J. M. Cole, M. J. Turner, D. Jayatilaka, J. Chem. Phys. 2013, 139, 064108.
| Crossref | GoogleScholarGoogle Scholar |
[44] E. Brown, T. Marks, M. Ratner, J. Phys. Chem. B 2008, 112, 44.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2sXhsVehurzK&md5=de2ed983c10077798c3925c328c4852fCAS |
[45] R. G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules 1989 (Oxford University Press: Oxford).
[46] L. Cohen, C. Frishberg, Phys. Rev. A 1976, 13, 927.
| Crossref | GoogleScholarGoogle Scholar |
[47] H. Nakatsuji, Phys. Rev. A 1976, 14, 41.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaE28XltFaru7g%3D&md5=f386c8c79ee3954d2b54fcebb4090523CAS |
[48] D. A. Mazziotti, Phys. Rev. A 1998, 57, 4219.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK1cXjsFKktro%3D&md5=c34ff00c3be7851ab018cde1a8081fd9CAS |
[49] D. M. Bishop, J. Chem. Phys. 1994, 100, 6535.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK2cXjtVOqsL4%3D&md5=64f823b5a7c4dee2c2dbeac614057690CAS |
[50] J. Applequist, Chem. Phys. 1995, 190, 153.
| Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK2MXisFaqt7Y%3D&md5=3b405466a172b794bc292e28197b8708CAS |
[51] A. Buckingham, Adv. Chem. Phys. 1967, 12, 107.
| 1:CAS:528:DyaF1cXovF2gsw%3D%3D&md5=d9ad34736e7b29076b44fecce9387df4CAS |
