Bishop-Kirtman perturbation theory

Corresponding CASSCF contributions calculated using the Bishop-Kirtman perturbation theory (BKPT) are also listed. All contributions were computed at the optimized bond length ropt for the given method. All values are in a.u. 

The treatment of the vibrational NLO properties in the previous sections employed either the Bishop-Kirtman perturbational theory (BKPT) or the finite field-nuclear relaxation (FF-NR) approach. These approaches may fail for molecules containing large amplitude anharmonic motions, as indeed was suspected to happen in Li C6o-In such cases a more recently proposed variational method, based on analytical response theory [78, 79], would in principle be applicable, but is computationally extremely expensive, as it requires an accurate numerical description of the potential energy surface (PES), at least if the anharmonicity is so large that a power series expansion of the PES is inadequate [80]. 

Nunes and Gonze [153] have recently extended DFPT to static responses of insulating ciystals for any order of perturbation theory by combining the variation perturbation approach with the modern theory of polarization [154]. There are evident similarities between this formalism and (a) the developments of Sipe and collaborators [117,121,123] within the independent particle approximation and (b) the recent work of Bishop, Gu and Kirtman [24, 155,156] at the time-dependent Hartree Fock level for one-dimensional periodic systems. 

Kirtman, Gu, and Bishop [155] have derived a fuUy self-consistent procedure by using a noncanonical form of perturbation theory. Following Genkin and Mednis [120], they employed the vector potential and replaced the quasimomentum k by... 

For the evaluation of the vibrational polarizability, Eq. (8.8), one needs to calculate the vibrational energies,, as well as vibrational transition moments, ( 1° l/Lta 1 , ), of the electric dipole moment. Both can be obtained by a perturbation theory treatment similar to the one used here for the evaluation of the ZPVC to electronic polarizability (Bishop and Kirtman, 1991). 

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