Numerical Calculation of Adiabatic Corrections with the Born-Handy Method*
Institute of Physical and Theoretical Chemistry
Wrocław University of Technology
Wybrzeże Wyspiańskiego 27, 50–370 Wrocław, Poland
e-mail: strasbur@chkw386.ch.pwr.wroc.pl
Received:
Rec. June 12, 2006
DOI: 10.12921/cmst.2007.13.01.59-66
OAI: oai:lib.psnc.pl:632
Abstract:
A modified algorithm of the numerical calculation of adiabatic corrections is proposed. It is based on earlier approaches, introduced by Cencek and Kutzelnigg and by the present author. The adiabatic correction is approximated in terms of overlap integrals between electronic wave functions for a given geometry and for a single nucleus shifted by h. The leading term of error is proportional to the square of h in the original methods. The new approach, while requires the same wave functions as those methods, shrinks the error, so that it becomes proportional to h4 in atomic cases. Test calculations show, that similar behavior is retained also for two–atom molecules and additional stable decimal digit of the adiabatic correction can be obtained.
Key words:
adiabatic correction, Born-Handy method, explicitly correlated Gaussian function
References:
[1] J. Rychlewski, J. Komasa, in: Explicitly Correlated Wave Functions in Chemistry and Physics, Kluwer Academic Publishers 2003, pp. 91-137.
[2] R. D. Bardo, M. Wolfsberg, J. Chem. Phys. 68, 2686 (1978).
[3] H. Sellers, P. Pulay, Chem. Phys. Lett. 103, 463 (1984).
[4] N. C. Handy, Y. Yamaguchi, H. F. Schaefer III, J. Chem. Phys. 84, 4481 (1986).
[5] W. Kutzelnigg, Mol. Phys. 90, 909 (1997).
[6] J. Rychlewski, W. Cencek, in Explicitly Correlated Wave Functions in Chemistry and Physics, Kluwer Academic Publishers 2003, pp. 249-274.
[7] W. Cencek, W. Kutzelnigg, Chem. Phys. Lett. 266, 383 (1997).
[8] http://www.psicode.org and http://sourceforge.net/projects/psicode
[9] K. Strasburger, J. Phys. B 37, 4483 (2004).
[10] K. Strasburger, H. Chojnacki, A. Sokołowska, J. Phys. B38, 3091 (2005).
[11] H.-J. Glaeske, J. Reinhold, P. Volkmer, in Quantenchemie. Ein Lehrgang. Band 5. Ausgewählte mathematische Methoden der Chemie, VEB Deutscher Verlag der Wissenschaften, Berlin 1987, p. 567.
[12] K. Strasburger, CCP2 Workshop, Nottingham, 2-5.04.2006.
[13] J. Mitroy, Phys. Rev. A 70, 024502 (2004).
[14] J. Komasa, private communication.
[15] K. Strasburger, J. Chem. Phys. 111, 10555 (1999).
[16] W. Cencek, J. Komasa, K. Pachucki and K. Szalewicz, Phys. Rev. Lett 95, 233004 (2005).
[17] K. Strasburger, M. Wołcyrz, Mol. Phys., accepted for publication.
A modified algorithm of the numerical calculation of adiabatic corrections is proposed. It is based on earlier approaches, introduced by Cencek and Kutzelnigg and by the present author. The adiabatic correction is approximated in terms of overlap integrals between electronic wave functions for a given geometry and for a single nucleus shifted by h. The leading term of error is proportional to the square of h in the original methods. The new approach, while requires the same wave functions as those methods, shrinks the error, so that it becomes proportional to h4 in atomic cases. Test calculations show, that similar behavior is retained also for two–atom molecules and additional stable decimal digit of the adiabatic correction can be obtained.
Key words:
adiabatic correction, Born-Handy method, explicitly correlated Gaussian function
References:
[1] J. Rychlewski, J. Komasa, in: Explicitly Correlated Wave Functions in Chemistry and Physics, Kluwer Academic Publishers 2003, pp. 91-137.
[2] R. D. Bardo, M. Wolfsberg, J. Chem. Phys. 68, 2686 (1978).
[3] H. Sellers, P. Pulay, Chem. Phys. Lett. 103, 463 (1984).
[4] N. C. Handy, Y. Yamaguchi, H. F. Schaefer III, J. Chem. Phys. 84, 4481 (1986).
[5] W. Kutzelnigg, Mol. Phys. 90, 909 (1997).
[6] J. Rychlewski, W. Cencek, in Explicitly Correlated Wave Functions in Chemistry and Physics, Kluwer Academic Publishers 2003, pp. 249-274.
[7] W. Cencek, W. Kutzelnigg, Chem. Phys. Lett. 266, 383 (1997).
[8] http://www.psicode.org and http://sourceforge.net/projects/psicode
[9] K. Strasburger, J. Phys. B 37, 4483 (2004).
[10] K. Strasburger, H. Chojnacki, A. Sokołowska, J. Phys. B38, 3091 (2005).
[11] H.-J. Glaeske, J. Reinhold, P. Volkmer, in Quantenchemie. Ein Lehrgang. Band 5. Ausgewählte mathematische Methoden der Chemie, VEB Deutscher Verlag der Wissenschaften, Berlin 1987, p. 567.
[12] K. Strasburger, CCP2 Workshop, Nottingham, 2-5.04.2006.
[13] J. Mitroy, Phys. Rev. A 70, 024502 (2004).
[14] J. Komasa, private communication.
[15] K. Strasburger, J. Chem. Phys. 111, 10555 (1999).
[16] W. Cencek, J. Komasa, K. Pachucki and K. Szalewicz, Phys. Rev. Lett 95, 233004 (2005).
[17] K. Strasburger, M. Wołcyrz, Mol. Phys., accepted for publication.