Coupled-perturbed self-consistent field

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Another more successful MO approach, referred to as INDO (intermediate neglect of differential overlap), avoids the average electronic energy approximation [115]. Its concept is a self-consistent field perturbation calculation. The INDO approach permits computation of one-bond carbon-13 coupling constants. The results obtained for JCH agree well with the experimental data for hydrocarbons and molecules with — F, —OR,... 

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

In the INDO method, a perturbation corresponding to one of the three coupling mechanisms is introduced during the calculation of the self-consistent field (SCF) wavefunction for a given molecule. 

Purely quantum studies of the fully coupled anharmonic (and sometimes nonrigid) rovibrational state densities have also been obtained with a variety of methods. The simplest to implement are spectroscopic perturbation theory based studies [121, 122, 124]. Related semiclassical perturbation treatments have been described by Miller and coworkers [172-174]. Vibrational self-consistent field (SCF) plus configuration interaction (Cl) calculations [175, 176] provide another useful alternative, for which interesting illustrative results have been presented by Christoffel and Bowman for the H + CO2 reaction [123] and by Isaacson for the H2 + OH reaction [121]. The MULTIMODE code provides a general procedure for implementing such SCF-CI calculations [177]. Numerous studies of the state densities for triatomic molecules have also been presented. 

Another major point in which the theoretical methods differ is the quantum chemical approach to solve the operator equation of the Hamilton operator itself. The most important schemes are Hartree-Fock self consistent field (HF-SCF), density functional theory (DFT) and multi-body second order perturbation theory (MP2). Different combinations have been established, so for instance GIAO-SCF, GlAO-DI I, (,IA()-MI>2, or DF I-IGLO. Most precise measurements on small systems were done with coupled cluster methods, as for instance GIAO-CCSDT-n. ... 

Ochsenfeld C, Head-Gordon M. A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme. Chem Phys Lett 1997 270 399 405. 

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