Self-consistent Held

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

It is simpler to consider the electric field produced by the distribution of an electron in an orbital or, in effect, a time-averaged potential. Adophng this point of view, each electron moves as if in a static potential produced by the nucleus and the hme-averaged distibutions of the other electrons. As each electron moves in the field of the other electrons, it creates by its own distribution a held affecting the mohons of each of the others. Thus the motions of all the electrons are coupled delicately the term self-consistent held indicates the requirement that all the individual electron distribuhons must produce the proper potenhals for one another s motion. 

S-S Sip Sop SALC SCF SO SOMO T tds tdt tfd TP UV xo 9m 9l 9 P Dithiolene or dithiolate chelate In-plane dithiolene S p orbital Out-of-plane dithiolene S p orbital Symmetry adapted linear combination Self-consistent held Sulfite oxidase Singly occupied molecular orbital Tesla (Trihuoromethyl)ethylenediselenato Toluene-2,3-dithiolate Bis(trihuoromethyl)-1,2-dithiete Trigonal prismatic Ultraviolet Xanthine oxidase Metal-based function Ligand-based function Symmetric in-plane dithiolene molecular orbital... 

Equation 4.7 has the form of a self-consistency problem. The solution to the equation is rffj(fi), but the exact form of the equation is determined by (/ y(/r) itself. It must be solved by an iterative procedure (called the self-consistent held, or SCF approach), in which convergence is taken to occur at the step where both sj and (/ y(/r) do not differ appreciably from the prior step. 

N.H. March, Self-consistent helds in atoms Hartree and Thomas-Fermi atoms, Pergamon, Oxford, 1975. 

In this contribution, we revisit the so-called Fenske-HaH molecular orbital (MO) method, an approximate self-consistent-held (SCF) ab initio method that contains no empirical parameters, which began almost 40 years ago in the research group of Richard... 

As often happens in self-consistent Held calculations (e.g., in the Har-tree theory of atoms) the two errors (i) and (ii) cancel each other to a large extent. Many post-Flory attempts, which tried to improve on one term, (i) or (ii), leaving the other unaltered, led to results that were power than eq. (1.39). 

Fig. 3.7. (a) Ab initio self-consistent Held calculated electron deformation density distribution of trans [(it -CjHslFelCOljlj in the plane containing the iron-iron axis and the bridging carbonyl ligand. The contour interval is -200e/nm and the dashed contours correspond to negative deformation and the solid contours correspond to zero and positive deformation density (b) experimental electron deformation density distribution derived from X-N calculations. The contour interval is — lOOe/nm . (From Bbnard, 1982.)... 

J. C. Slater, The Self-Consistent Held for Molecules and Solids, McGraw-Hill, New York, 1974. 

The self-consistent held theory is based on a lattice model [23-26]. Each chain is subdivided into segments with ranking number s = 1,2,3,..., N and these segments can take only discrete positions with respect to the surface in lattice layers numbered z = 1, 2, 3,... [23]. The spacing, I, between the lattice layers is equal to the bond length a. The length a is the invariant indifference lattice and I is not, so its value should be adjusted to 2 according 1 =... 

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