Spin contamination and noncollinearity in general complex Hartree–Fock wave functions

Theoretical Chemistry Accounts - Tập 134 - Trang 1-6 - 2015
Patrick Cassam-Chenaï1
1CNRS, LJAD, UMR 7351, University of Nice Sophia Antipolis, Nice, France

Tóm tắt

An expression for the square of the spin operator expectation value, $$\langle S^2 \rangle$$ , is obtained for a general complex Hartree–Fock wave function and decomposed into four contributions: the main one whose expression is formally identical to the restricted (open-shell) Hartree–Fock expression. A spin contamination one formally analogous to that found for spin unrestricted Hartree–Fock wave functions. A noncollinearity contribution related to the fact that the wave function is not an eigenfunction of the spin-S z operator. A perpendicularity contribution related to the fact that the spin density is not constrained to be zero in the xy-plane. All these contributions are evaluated and compared for the H2O+ system. The optimization of the collinearity axis is also considered.

Tài liệu tham khảo

Hartree DR (1928) Proc Camb Philos Soc 24:89 Slater JC (1929) Phys Rev 34:1293 Fock V (1930) Physik 61:126 Berthier G (1964) In: Löwdin PO, Pullman B (eds) Molecular orbitals in chemistry, physics and biology. Academic Press, New York, p 57 Cassam-Chenaï P (1992) Algèbre fermionique et chimie quantique, Ph.D thesis, Université de Paris 6 Cassam-Chenaï P, Chandler GS (1992) Sur les fonctions de Hartree–Fock sans contrainte. Comptes-rendus de l’académie des sciences série II 314:755–757 Cassam-Chenaï P, Chandler GS (1993) Int J Quantum Chem 46:593–607 Amos AT, Hall GG (1961) Proc R Soc A 263:483 Löwdin PO (1962) J Appl Phys 33:251 Cassam-Chenaï P (1994) J Math Chem 15:303 Roothaan CCJ (1960) Rev Mod Phys 32:179 Andrews JS, Jayatilaka D, Bone RGA, Handy NC, Amos RD (1991) Chem Phys Lett 183:423 Brändas E (1968) J Mol Spectrosc 27:236 Berthier G (1954) Comptes-Rendus de l’Acadmie des Sciences 238:91–93 Pople JA, Nesbet RK (1954) J Chem Phys 22:571 Bunge C (1967) Phys Rev 154:70 Lefebvre R, Smyers YG (1967) Int J Quantum Chem 1:403 Lunell S (1972) Chem Phys Lett 13:93 Löwdin PO (1955) Phys Rev 97:509 Hendeković J (1974) Int J Quantum Chem 8:799 Prat RE, Lefebvre R (1969) Int J Quantum Chem 3:503 Penney R (1968) Am J Phys 36:871 Jordan P, Neumann JV, Wigner E (1934) Ann Math 35:29–64 Solèr MP (1995) Commun Algebra 23:219 Holland SS (1995) Bull Am Math Soc 32:205 Mayer I, Löwdin PO (1993) Chem Phys Lett 202:1 Cassam-Chenaï P (2002) J Chem Phys 116:8677–8690 Cassam-Chenaï P, Jayatilaka D (2012) Chem Phys 137:064107 (And supplementary material) Coey JMD (1987) Revue canadienne de physique 65:1210 Libby E, McCusker JK, Schmitt EA, Folting K, Hendrickson DN, Christou G (1991) Inorg Chem 30:3486 Jayatilaka D (1998) J Chem Phys 108:7587 Small DW, Sundstrom EJ, Head-Gordon M (2015) J Chem Phys 142:094112 Jayatilaka D, Grimwood DJ (2003) In: Sloot P, Abramson D, Bogdanov A, Gorbachev Y, Dongarra J, Zomaya A (eds) Computational Science–ICCS 2003. Lectures notes in computer sciences, vol 2660. Springer, Berlin, pp 142–151 Bučinský L, Malček M, Biskupič S, Jayatilaka D, Vl Büchel GE, Arion B (2015) Comput Theor Chem 1065:27 Dunning TH (1989) J Chem Phys 90:1007 Barysz M, Sadlej AJ (2001) J Mol Struct (THEOCHEM) 573:181