Electronic Wavefunctions and Calculation of Matrix Elements

For most calculations of rotatory strengths to date, each of the APTs and AATs as well as the force field has been evaluated using SCF (uncorrelated) wavefunctions. However, the evaluation of the force field and the APTs has been well established at higher levels of theory, for instance MP2 theory, and some have been applied to VCD intensities. 

The first full MP2 VCD calculations, in which the AATs as well as the APTs and the force field are all calculated at the MP2 level of theory using the VCT method (VCT/MP2), appeared only very recently. In the VCT/MP2 approach, the electronic ground state, o, for all matrix element evaluations is approximated by the normalized MP2 wavefunction, i.e.. 

For the MFP approach, most calculations have used SCF wavefunctions. However, very recently, Bak et al. have implemented the MFP theoretical approach at the correlated multiconfigurational self-consistent-field level by using the complete active space wavefunctions (CASSCF) expressed over conventional and gauge invariant basis sets. 

Wavefunction derivatives involved in Eq. [12] and [17] comprise the major part of the evaluations of AATs. In earlier days, a finite difference method was used to obtain these derivatives. The implementation of analytical coupled perturbed Hartree-Fock (CPHF) methods 3- 6 has permitted these derivatives to be obtained more efficiently. In the MFP approach, two sets of CPHF calculations are required to obtain re- 

In an alternative approach, the APTs and AATs are calculated by the RPA method. In this method, the APT and AAT are converted from nuclear electromagnetic shielding tensors which are directly related to the APT and AAT.24.68 These nuclear shielding tensors are expressed as sums over states, which are evaluated by the SCF-RPA method. 

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