Hartree-Fock theory, time-dependent coupled-perturbed

Quantum Chemistry (1992) which is entirely devoted to molecular non-linear optics. The foundations of time-dependent coupled-perturbed Hartree Fock theory, referred to in Section 3.1.2, are beautifully described in Sections 12.5-12.7 of Roy McWeeny s book [7]. 

The electronic contribution can be computed using two derivative schemes involving quantum mechanical calculations of the free energy or, alternar tively, of the dipole moment followed by derivatives with respect to the perturbing external field, computed at zero intensity. At Hartree-Fock (HF) or Density Functional Theory level both approaches lead to the use of the coupled HF or KS theory either in its time-independent (CHF, CKS) or time-dependent (TDCHF, TDDFT) version according to the case. 

Table 16 Results for hyperpolarizabilities (in a.u.) for N2- TDHF and MBPT(2) are results from time-dependent Hartree-Fock and perturbation-theory calculations, respectively, whereas CCSD and CCSD(T) are coupled-cluster results. Exp. denotes experimental results, and LDA, GGA, and LB94 are results from time-dependent density-functional calculations with different density functionals. For a description of the quantities, see the text. The results are from ref. 95...

Figrire 8 An overview of quantum chemical methods for excited states. Bold-italic entries indicate methods that are currently applicable to large molecules. Important abbreviations used Cl (configuration Interaction), TD (time-dependent), CC (coupled-cluster), HF (Hartree-Fock), CAS (complete active space), RAS (restricted active space), MP (Moller-Plesset perturbation theory), S (singles excitation), SD (singles and doubles excitation), MR (multireference). Geometry optimizations of excited states for larger molecules are now possible with CIS, CASSCF, CC2, and TDDFT methods. 

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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