We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the “surrounding” molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals.
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21 January 2012
Research Article|
January 17 2012
Higher order alchemical derivatives from coupled perturbed self-consistent field theory
Michał Lesiuk;
Michał Lesiuk
1Faculty of Chemistry,
Warsaw University of Technology
, Noakowskiego 3, 00-664 Warsaw, Poland
2
Institute of Physical Chemistry of Polish Academy of Sciences (PAS)
, Kasprzaka 44/52, 01-224 Warsaw, Poland
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Robert Balawender;
Robert Balawender
2
Institute of Physical Chemistry of Polish Academy of Sciences (PAS)
, Kasprzaka 44/52, 01-224 Warsaw, Poland
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Janusz Zachara
Janusz Zachara
a)
1Faculty of Chemistry,
Warsaw University of Technology
, Noakowskiego 3, 00-664 Warsaw, Poland
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a)
Author to whom correspondence should be addressed. Electronic mail: janzac@ch.pw.edu.pl.
J. Chem. Phys. 136, 034104 (2012)
Article history
Received:
August 24 2011
Accepted:
December 12 2011
Citation
Michał Lesiuk, Robert Balawender, Janusz Zachara; Higher order alchemical derivatives from coupled perturbed self-consistent field theory. J. Chem. Phys. 21 January 2012; 136 (3): 034104. https://doi.org/10.1063/1.3674163
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