Hartree-Fock self-consistent field response

In the self-consistent field linear response method [25,46,48] also known as random phase approximation (RPA) [49] or first order polarization propagator approximation [25,46], which is equivalent to the coupled Hartree-Fock theory [50], the reference state is approximated by the Hartree-Fock self-consistent field wavefunction < scf) and the set of operators /i j consists of single excitation and de-excitation operators with respect to orbital rotation operators [51],... 

Besides the elementary properties of index permutational symmetry considered in eq. (7), and intrinsic point group symmetry of a given tensor accounted for in eqs. (8)-(14), much more powerful group-theoretical tools [6] can be developed to speed up coupled Hartree-Fock (CHF) calculations [7-11] of hyperpolarizabilities, which are nowadays almost routinely periformed in a number of studies dealing with non linear response of molecular systems [12-35], in particular at the self-consistent-field (SCF) level of accuracy. 

In this section we will introduce some wavefunction-based methods to calculate photoabsorption spectra. The Hartree-Fock method itself is a wavefunction-based approach to solve the static Schrodinger equation. For excited states one has to account for time-dependent phenomena as in the density-based approaches. Therefore, we will start with a short review of time-dependent Hartree-Fock. Several more advanced methods are available as well, e.g. configuration interaction (Cl), multireference configuration interaction (MRCI), multireference Moller-Plesset (MRMP), or complete active space self-consistent field (CASSCF), to name only a few. Also flavours of the coupled-cluster approach (equations-of-motion CC and linear-response CQ are used to calculate excited states. However, all these methods are applicable only to fairly small molecules due to their high computational costs. These approaches are therefore discussed only in a more phenomenological way here, and many post-Hartree-Fock methods are explicitly not included. 

In order to appreeiate the general eoneepts that are involved, the linear response equations for a Self-Consistent Field (SCF) ground state will be sketehed below. This description is appropriate if the state of interest is well described by a HF (Hartree-Fock) or DFT single determinant ( 2.1). The ground state energy is... 

Reaction coordinate, 296, 314, 365, 368 Reaction Path (RP) methods, 390 Reaction surface, 390 Reaction volume, 390 Redundant variables, 34, 327 Relaxation time, in simulations, 380 Renormalized Davidson correction, 137 Resonance, resonance structures, 200 Response, wave function, 242 Restricted Active Space Self-Consistent Field (RASSCF) method, 119 Restricted Hartree-Fock (RHF) method, 70 Restricted Open-shell Hartree-Fock (ROHF) method, 70... 

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