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Linear response formalism for the Douglas–Kroll–Hess approach to the Dirac–Kohn–Sham problem: First‐ and second‐order nuclear displacement derivatives of the energy
Author(s) -
Matveev Alexei V.,
Nasluzov Vladimir A.,
Rösch Notker
Publication year - 2007
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21501
Subject(s) - hamiltonian (control theory) , uranyl , quantum mechanics , dirac equation , physics , decoupling (probability) , quadratic equation , chemistry , mathematical physics , coupled cluster , mathematics , molecule , ion , mathematical optimization , geometry , control engineering , engineering
Starting from a matrix representation of the modified Dirac equation, we offer an alternative approach to the Douglas–Kroll–Hess (DKH) protocol, specifically for the popular decoupling of electronic and positronic degrees of freedom to second‐order in the potential. Then we use that approach for a convenient analysis of response properties. We discuss details of the linear and quadratic response of the DKH Hamiltonian to a geometric distortion encountered in calculations of first‐ and second‐order derivatives of the energy. We present an implementation of analytic force constants in a quasi‐relativistic (scalar) model constructed by the commonly used DKH transformation of second order in the nuclear potential only. We demonstrate the performance of the method by a comparison to the effective core potential method, using two isomers of the cluster Ir 4 and aqua complexes of the uranyl dication, UO 2 2+ (H 2 O) n ( n = 3,…6) as examples. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007