Perturbation and Response Theory with Approximate Wavefunctions

Perturbation and Response Theory with Approximate Wavefunctions 

In this chapter we will follow now the second approach, which means that we will apply time-independent and time-dependent perturbation theory from Chapter 3 to approximate solutions of the unperturbed molecular Hamiltonian. In particular, we will illustrate this in the following for Hartree-Fock, MCSCF and coupled cluster wavefunctions. 

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For nonlinear (magneto-) optical properties, calculations of an accuracy close to that of modern gas phase experiments require - similar to what has also been found for other properties like structures [79, 109], reaction enthalpies [79, 110, 111], vibrational frequencies [112, 113], NMR chemical shifts [114], etc. - at least an approximate inclusion of connected triple excitations in the wavefunction. This has been known for years now from calculations of static hyperpolarizabilities with the CCSD(T) approximation [9-13]. CCSD(T) accounts rather efficiently for connected triples through a perturbative correction on top of CCSD. For the reasons pointed out in Section 2.1 CCSD(T) is, as a two-step approach, not suitable for the calculation of frequency-dependent properties. Therefore, the CC3 model has been proposed [56, 58] as an alternative to CCSD(T) especially designed for use in connection with response theory. CC3 is an approximation to CCSDT - alike CCSDT-la and related methods - where the triples equations are truncated such that the scaling of the computational efforts with system size is reduced to as for CCSD(T),... 

Molecular theory of the VCD by Stephens involves the determination of wave-function parameters perturbed with respect to the nuclear displacements and the magnetic perturbation. It means, it requires solution of 3V-I-3 response equations N is the number of atoms in the system). Theory of the VCD spectra is constructed within the following assumptions of (a) Born-Oppenheimer approximation (BO) (15.1), in which total wavefunction is a product of electronic and nuclear wave functions for an electronic reference state gO and vibrational state gl ... 

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