Theor Chem Acc (2015) 134:125
1 3
We have evaluated these four different contributions
for a GCHF calculation on the H 2 O
+ cation. Note that we
used the IOTC relativistic Hamiltonian [ 36 ] so that the term
“spin contamination” is not really appropriate in this context, departure from the ROHF reference value being legitimate. However, the so-called spin contamination contribution has been found to dominate the noncollinearity and
perpendicularity ones. This could be made even more so,
by tilting the quantization axis to the optimal collinearity
direction.
Acknowledgments We acknowledge Dr. Lukáš Bu c ˇ inský for drawing our attention to the problem of the derivation of GCHF spin
contamination, and to the fact that S
2 does not commutes with the
“spin-same-orbit” coupling term, usually used in quantum chemistry.
The referees and the editor are acknowledged for suggesting many
improvements to the manuscript. This article is a tribute to Prof. P.
Surjàn and is also dedicated to the memory of the late Prof. Gaston
Berthier, who introduced to the author in the course of vivid discussions, many of the references listed below.
References
1. Hartree DR (1928) Proc Camb Philos Soc 24:89
2. Slater JC (1929) Phys Rev 34:1293
3. Fock V (1930) Physik 61:126
4. Berthier G (1964) In: Löwdin PO, Pullman B (eds) Molecular
orbitals in chemistry, physics and biology. Academic Press, New
York, p 57
5. Cassam-Chenaï P (1992) Algèbre fermionique et chimie quantique, Ph.D thesis, Université de Paris 6
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
7. Cassam-Chenaï P, Chandler GS (1993) Int J Quantum Chem
46:593–607
8. Amos AT, Hall GG (1961) Proc R Soc A 263:483
9. Löwdin PO (1962) J Appl Phys 33:251
10. Cassam-Chenaï P (1994) J Math Chem 15:303
11. Roothaan CCJ (1960) Rev Mod Phys 32:179
12. Andrews JS, Jayatilaka D, Bone RGA, Handy NC, Amos RD
(1991) Chem Phys Lett 183:423
13. Brändas E (1968) J Mol Spectrosc 27:236
14. Berthier G (1954) Comptes-Rendus de l’Acadmie des Sciences
238:91–93
15. Pople JA, Nesbet RK (1954) J Chem Phys 22:571
16. Bunge C (1967) Phys Rev 154:70
17. Lefebvre R, Smyers YG (1967) Int J Quantum Chem 1:403
18. Lunell S (1972) Chem Phys Lett 13:93
19. Löwdin PO (1955) Phys Rev 97:509
20. Hendeković J (1974) Int J Quantum Chem 8:799
21. Prat RE, Lefebvre R (1969) Int J Quantum Chem 3:503
22. Penney R (1968) Am J Phys 36:871
23. Jordan P, Neumann JV, Wigner E (1934) Ann Math 35:29–64
24. Solèr MP (1995) Commun Algebra 23:219
25. Holland SS (1995) Bull Am Math Soc 32:205
26. Mayer I, Löwdin PO (1993) Chem Phys Lett 202:1
27. Cassam-Chenaï P (2002) J Chem Phys 116:8677–8690
28. Cassam-Chenaï P, Jayatilaka D (2012) Chem Phys 137:064107
( And supplementary material )
29. Coey JMD (1987) Revue canadienne de physique 65:1210
30. Libby E, McCusker JK, Schmitt EA, Folting K, Hendrickson
DN, Christou G (1991) Inorg Chem 30:3486
31. Jayatilaka D (1998) J Chem Phys 108:7587
32. Small DW, Sundstrom EJ, Head-Gordon M (2015) J Chem Phys
142:094112
33. 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
34. Bu c ˇ inský L, Mal c ˇ ek M, Biskupi c ˇ S, Jayatilaka D, Vl Büchel GE,
Arion B (2015) Comput Theor Chem 1065:27
35. Dunning TH (1989) J Chem Phys 90:1007
36. Barysz M, Sadlej AJ (2001) J Mol Struct (THEOCHEM)
573:181
180
Reprinted from the journal
1 3
We have evaluated these four different contributions
for a GCHF calculation on the H 2 O
+ cation. Note that we
used the IOTC relativistic Hamiltonian [ 36 ] so that the term
“spin contamination” is not really appropriate in this context, departure from the ROHF reference value being legitimate. However, the so-called spin contamination contribution has been found to dominate the noncollinearity and
perpendicularity ones. This could be made even more so,
by tilting the quantization axis to the optimal collinearity
direction.
Acknowledgments We acknowledge Dr. Lukáš Bu c ˇ inský for drawing our attention to the problem of the derivation of GCHF spin
contamination, and to the fact that S
2 does not commutes with the
“spin-same-orbit” coupling term, usually used in quantum chemistry.
The referees and the editor are acknowledged for suggesting many
improvements to the manuscript. This article is a tribute to Prof. P.
Surjàn and is also dedicated to the memory of the late Prof. Gaston
Berthier, who introduced to the author in the course of vivid discussions, many of the references listed below.
References
1. Hartree DR (1928) Proc Camb Philos Soc 24:89
2. Slater JC (1929) Phys Rev 34:1293
3. Fock V (1930) Physik 61:126
4. Berthier G (1964) In: Löwdin PO, Pullman B (eds) Molecular
orbitals in chemistry, physics and biology. Academic Press, New
York, p 57
5. Cassam-Chenaï P (1992) Algèbre fermionique et chimie quantique, Ph.D thesis, Université de Paris 6
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
7. Cassam-Chenaï P, Chandler GS (1993) Int J Quantum Chem
46:593–607
8. Amos AT, Hall GG (1961) Proc R Soc A 263:483
9. Löwdin PO (1962) J Appl Phys 33:251
10. Cassam-Chenaï P (1994) J Math Chem 15:303
11. Roothaan CCJ (1960) Rev Mod Phys 32:179
12. Andrews JS, Jayatilaka D, Bone RGA, Handy NC, Amos RD
(1991) Chem Phys Lett 183:423
13. Brändas E (1968) J Mol Spectrosc 27:236
14. Berthier G (1954) Comptes-Rendus de l’Acadmie des Sciences
238:91–93
15. Pople JA, Nesbet RK (1954) J Chem Phys 22:571
16. Bunge C (1967) Phys Rev 154:70
17. Lefebvre R, Smyers YG (1967) Int J Quantum Chem 1:403
18. Lunell S (1972) Chem Phys Lett 13:93
19. Löwdin PO (1955) Phys Rev 97:509
20. Hendeković J (1974) Int J Quantum Chem 8:799
21. Prat RE, Lefebvre R (1969) Int J Quantum Chem 3:503
22. Penney R (1968) Am J Phys 36:871
23. Jordan P, Neumann JV, Wigner E (1934) Ann Math 35:29–64
24. Solèr MP (1995) Commun Algebra 23:219
25. Holland SS (1995) Bull Am Math Soc 32:205
26. Mayer I, Löwdin PO (1993) Chem Phys Lett 202:1
27. Cassam-Chenaï P (2002) J Chem Phys 116:8677–8690
28. Cassam-Chenaï P, Jayatilaka D (2012) Chem Phys 137:064107
( And supplementary material )
29. Coey JMD (1987) Revue canadienne de physique 65:1210
30. Libby E, McCusker JK, Schmitt EA, Folting K, Hendrickson
DN, Christou G (1991) Inorg Chem 30:3486
31. Jayatilaka D (1998) J Chem Phys 108:7587
32. Small DW, Sundstrom EJ, Head-Gordon M (2015) J Chem Phys
142:094112
33. 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
34. Bu c ˇ inský L, Mal c ˇ ek M, Biskupi c ˇ S, Jayatilaka D, Vl Büchel GE,
Arion B (2015) Comput Theor Chem 1065:27
35. Dunning TH (1989) J Chem Phys 90:1007
36. Barysz M, Sadlej AJ (2001) J Mol Struct (THEOCHEM)
573:181
180
Reprinted from the journal