Self-consistent Field SCF Method

A method of molecular-orbital calculations, also referred to as the self-consistent field method (SCF), to characterize the bonding in unsaturated and aromatic molecules while neglecting electron-electron repulsion. The method has been extended to all valence electrons. 

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)). 

Looking at the history of correlation from the fifties to the seventies, one may be led to ask whether correlation has been a scientific fashion or a real problem. Twenty years ago, almost everybody seemed to accept the idea that the simple molecular orbital method (MO) must be completed by configuration interaction (Cl), in order to obtain reliable prediction for the physical properties of atoms and molecules. Ten years ago, electron correlation was considered as the central problem of Quantum Chemistry (7). Nowadays, about 90% of the quantum-mechanical calculations on molecules are performed by the self-consistent-field method (SCF) using more or less extended sets of basis functions, without any consideration of the possible effects of correlation. 

Figure 4-2. Computed potential energy surface from (A) ab initio valence-bond self-consistent field (VB-SCF) and (B) the effective Hamiltonian molecular-orbital and valence-bond (EH-MOVB) methods for the S 2 reaction between HS- and CH3CI...

The Hartree-Fock orbitals are expanded in an infinite series of known basis functions. For instance, in diatomic molecules, certain two-center functions of elliptic coordinates are employed. In practice, a limited number of appropriate atomic orbitals (AO) is adopted as the basis. Such an approach has been developed by Roothaan 10>. In this case the Hartree-Fock differential equations are replaced by a set of nonlinear simultaneous equations in which the limited number of AO coefficients in the linear combinations are unknown variables. The orbital energies and the AO coefficients are obtained by solving the Fock-Roothaan secular equations by an iterative method. This is the procedure of the Roothaan LCAO (linear-combination-of-atomic-orbitals) SCF (self-consistent-field) method. 

Semiempirical (CNDO, MNDO, ZINDO, AMI, PM3, PM3(tm) and others) methods based on the Hartree-Fock self-consistent field (HF-SCF) model, which treats valence electrons only and contains approximations to simplify (and shorten the time of) calculations. Semiempirical methods are parameterized to fit experimental results, and the PM3(tm) method treats transition metals. Treats systems of up to 200 atoms. 

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],... 

The set of molecular orbitals leading to the lowest energy are obtained by a process referred to as a self-consistent-field or SCF procedure. The archetypal SCF procedure is the Hartree-Fock procedure, but SCF methods also include density functional procedures. All SCF procedures lead to equations of the form. 

Leading references to the self-consistent field method employed here are cited by Pople, J. A., /. Phys. Chem. 61, 6 (1957). Calculations of the Hiickel and SCF orbitals were executed on an IBM-7090 computer using an entirely automatic program written by Dr. Bessis of the Centre de Mecanique Ondulatoire Appliqufee, Paris, France. 

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. 

J. H. van Lenthe, G. G. Balint-Kurti, J. Chem. Phys. 78, 5699 (1983). The Valence-Bond Self-Consistent Field Method (VB-SCF) Theory and Test Calculations. 

In order to make up for those imperfections one needs to turn to post-Hartree-Fock methods. Two variational techniques are worth discussing due to their popularity the configuration-interaction (SCF Cl) method and the multiconfiguration self-consistent-field (MC SCF) method. 

The MC SCF method usually takes into account a minimum number of configurations capable of assuring some fundamental requirements, this step being followed by the optimization of the basis functions using the self-consistent-field method. For example, in order to describe accurately the dissociation of ground-state H2 it is only necessary to consider the two-configuration wave function... 

The methods under the category of nonempirical fall into two subclasses. The first consists of the well known Hartree-Fock-Roothaan [7, 8] LCAO-MO-SCF (self-consistent field) methods. The second is an even more rigorous... 

Complete multiconfiguration-self consistent-field (CMC-SCF) technique designates the method where a given occupied molecular orbital of the set is excited to all unoccupied molecular orbitals. If an occupied orbital is excited to one or more, but not all, of the unoccupied orbitals, the technique is described as incomplete MC-SCF (IMC-SCF). The reader is referred to refs. 13 and 14 for details of the derivation. The CMC-SCF formalism differs from most many body techniques presented to date insofar as the Hartree-Fock energy is not assumed to be the zero order energy. 

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