13 If Truncated Wave Functions of Excited State Energy Saddle Points Are. . .
511
are standard subroutines of most of the common computational codes. The lower
lying approximants φ i < n need not be very accurate; it is sufficient to be crude but
reasonable. F n can be also used to identify a “flipped root,” a usual problem near
an avoided energy crossing in the variational parameter space. It can also be used
to immediately improve a ground state approximant if the 1st excited state is more
accurately known.
Acknowledgments The present work was supported in part by the project “Advanced Materials
and Devices” (MIS 5002409) implemented under the “Action for the Strategic Development on
the Research and Technological Sector,” funded by the Operational Programme “Competitiveness,
Entrepreneurship and Innovation” (NSRF 2014–2020) and co-financed by Greece and the European Union (European Regional Development Fund).
References
1. E.A. Hylleraas, B. Undheim, Z. Phys. 65, 759 (1930); J.K.L. McDonald, Phys. Rev. 43, 830
(1933)
2. N.C. Bacalis, Z. Xiong, J. Zang, D. Karaoulanis, AIP Conference Proceedings, 1790 UNSP
020007 (2016) https://doi.org/10.1063/1.4968633; N.C. Bacalis, Z. Xiong, Z.X. Wang, Int. J.
Quantum Chem (2017) (submitted)
3. J. Golab, D. Yeager, P. Jørgensen, Chem. Phys. 93, 83 (1985)
4. P. Jørgensen, J. Olsen, D. Yeager, J. Chem. Phys. 75, 5802 (1981)
5. M. Reed, B. Simon, Methods of Modern Mathematical Physics. Analysis of Operators, vol IV
(Academic, New York, 1978)
6. P. Jørgensen, P. Swanstrøm, D. Yeager, J. Chem. Phys. 78, 347 (1983)
7. H. Jensen, P. Jørgensen, J. Chem. Phys. 80, 1204 (1984)
8. H. Jensen, Electron correlation in molecules using direct second order MCSCF, in Relativistic
and Electron Correlation Effects in Molecules and Solids (Plenum, New York, 1994), pp. 179–
206
9. E. Cancès, H. Galicher, M. Lewin, J. Comput. Phys. 212, 73 (2006)
10. H. Nakatsuji, K. Hirao, J. Chem. Phys. 68, 2053 (1978)
11. D. Hegarthy, M.A. Robb, Mol. Phys. 38, 1795 (1979)
12. R.H.E. Eade, M.A. Robb, Chem. Phys. Lett. 83, 362 (1981)
13. O. Christiansen, H. Koch, P. Jørgensen, J. Chem. Phys. 103, 7429 (1995)
14. H. Koch, O. Christiansen, P. Jørgensen, T. Helgaker, A.S. de Meras, J. Chem. Phys. 106, 1808
(1997)
15. C. Haettig, F. Weigend, J. Chem. Phys. 113, 5154 (2000)
16. C. Haettig, Adv. Quantum Chem. 50, 37 (2005)
17. E.S. Nielsen, P. Jørgensen, J. Oddershede, J. Chem. Phys. 73, 6238 (1980)
18. S.P.A. Sauer, J. Phys. B 30, 3773 (1997)
19. J.J. Eriksen, S. Sauer, K.V. Mikkelsen, H.J.A. Jensen, J. Kongsted, J. Comput. Chem. 33, 2012
(2013)
20. J. Schirmer, Phys. Rev. A 26, 2395 (1982)
21. A.B. Trofimov, J. Schirmer, J. Phys. B 28, 2299 (1995)
22. J.H. Starcke, M. Wormit, A. Dreuw, J. Chem. Phys. 130, 024104 (2009)
23. M. Tassi, I. Theophilou, S. Thanos, Int. J. Quantum Chem. 113, 690 (2013)
24. D.H. Weinstein, Proc. Natl. Acad. Sci. U. S. A. 20, 529 (1934)
25. J.E. Subotnik, J. Chem. Phys. 135, 071104 (2011)
26. A. Dreuw, M. Head-Gordon, J. Am. Chem. Soc. 126, 4007 (2004)
511
are standard subroutines of most of the common computational codes. The lower
lying approximants φ i < n need not be very accurate; it is sufficient to be crude but
reasonable. F n can be also used to identify a “flipped root,” a usual problem near
an avoided energy crossing in the variational parameter space. It can also be used
to immediately improve a ground state approximant if the 1st excited state is more
accurately known.
Acknowledgments The present work was supported in part by the project “Advanced Materials
and Devices” (MIS 5002409) implemented under the “Action for the Strategic Development on
the Research and Technological Sector,” funded by the Operational Programme “Competitiveness,
Entrepreneurship and Innovation” (NSRF 2014–2020) and co-financed by Greece and the European Union (European Regional Development Fund).
References
1. E.A. Hylleraas, B. Undheim, Z. Phys. 65, 759 (1930); J.K.L. McDonald, Phys. Rev. 43, 830
(1933)
2. N.C. Bacalis, Z. Xiong, J. Zang, D. Karaoulanis, AIP Conference Proceedings, 1790 UNSP
020007 (2016) https://doi.org/10.1063/1.4968633; N.C. Bacalis, Z. Xiong, Z.X. Wang, Int. J.
Quantum Chem (2017) (submitted)
3. J. Golab, D. Yeager, P. Jørgensen, Chem. Phys. 93, 83 (1985)
4. P. Jørgensen, J. Olsen, D. Yeager, J. Chem. Phys. 75, 5802 (1981)
5. M. Reed, B. Simon, Methods of Modern Mathematical Physics. Analysis of Operators, vol IV
(Academic, New York, 1978)
6. P. Jørgensen, P. Swanstrøm, D. Yeager, J. Chem. Phys. 78, 347 (1983)
7. H. Jensen, P. Jørgensen, J. Chem. Phys. 80, 1204 (1984)
8. H. Jensen, Electron correlation in molecules using direct second order MCSCF, in Relativistic
and Electron Correlation Effects in Molecules and Solids (Plenum, New York, 1994), pp. 179–
206
9. E. Cancès, H. Galicher, M. Lewin, J. Comput. Phys. 212, 73 (2006)
10. H. Nakatsuji, K. Hirao, J. Chem. Phys. 68, 2053 (1978)
11. D. Hegarthy, M.A. Robb, Mol. Phys. 38, 1795 (1979)
12. R.H.E. Eade, M.A. Robb, Chem. Phys. Lett. 83, 362 (1981)
13. O. Christiansen, H. Koch, P. Jørgensen, J. Chem. Phys. 103, 7429 (1995)
14. H. Koch, O. Christiansen, P. Jørgensen, T. Helgaker, A.S. de Meras, J. Chem. Phys. 106, 1808
(1997)
15. C. Haettig, F. Weigend, J. Chem. Phys. 113, 5154 (2000)
16. C. Haettig, Adv. Quantum Chem. 50, 37 (2005)
17. E.S. Nielsen, P. Jørgensen, J. Oddershede, J. Chem. Phys. 73, 6238 (1980)
18. S.P.A. Sauer, J. Phys. B 30, 3773 (1997)
19. J.J. Eriksen, S. Sauer, K.V. Mikkelsen, H.J.A. Jensen, J. Kongsted, J. Comput. Chem. 33, 2012
(2013)
20. J. Schirmer, Phys. Rev. A 26, 2395 (1982)
21. A.B. Trofimov, J. Schirmer, J. Phys. B 28, 2299 (1995)
22. J.H. Starcke, M. Wormit, A. Dreuw, J. Chem. Phys. 130, 024104 (2009)
23. M. Tassi, I. Theophilou, S. Thanos, Int. J. Quantum Chem. 113, 690 (2013)
24. D.H. Weinstein, Proc. Natl. Acad. Sci. U. S. A. 20, 529 (1934)
25. J.E. Subotnik, J. Chem. Phys. 135, 071104 (2011)
26. A. Dreuw, M. Head-Gordon, J. Am. Chem. Soc. 126, 4007 (2004)