Self-consistent field calculation definition

The PPP method is the first semiempirical method presented here where the Fock matrix does depend on the MO coefficients C [via the density matrix elements P, see Eq. (11)]. Therefore, the Roothaan equations (by definition due to the ZDO approximation) in the orthogonal basis, Eq. (13), have to be solved in an iterative process until self-convergence is achieved [self-consistent field (SCF) procedure]. As starting coefficients C°, usually the orbitals of an HMO calculation are used. 

Two terms in the sum, Jj(i) and /fj(i), correspond to the Coulomb interaction between electron i and all other electrons j, and the exchange interaction between electrons with the same spins, respectively. The calculations of the HF potential energy for electron i require prior knowledge of all other occupied MOs. We have to guess the initial form of the MOs, use them in the definition of the Coulomb and exchange operators, and solve the HF equations iteratively in a process known as the self-consistent field (SCF) procedure. 

Basis Sets Correlation Consistent Sets Circular Dichro-ism Electronic Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Density Functional Applications Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Electronic Diabatic States Definition, Computation, and Applications ESR Hyperfine Calculations Magnetic Circular Dichroism of rt Systems Non-adiabatic Derivative Couplings Relativistic Theory and Applications Structure Determination by Computer-based Spectrum Interpretation Valence Bond Curve Crossing Models. 

Equation (18) is a quantum mechanical expression for the force on a nucleus in a planar molecule due to a homogeneous electric field. The expression is accurate to first order (i.e., polarizability is neglected) and, in view of the definitions (equations 16 and 17) of atomic charge and charge flux, is nothing else than equation (2). The latter, as already stated, underlies the empirical force field calculations. This further demonstrates the self-consistency of the present approach. 

With respect to standard molecular-cluster techniques, this approach has some attractive features explicit reference is made to the HF LCAO periodic solution for the unperturbed (or perfect) host crystal. In particular, the self-embedding-consistent condition is satisfied, that is, in the absence of defects, the electronic structure in the cluster region coincides with that of the perfect host crystal there is no need to saturate dangling bonds the geometric constraints and the Madelung field of the environment are automatically included. With respect to the supercell technique, this approach does not present the problem of interaction between defects in different supercells, allows a more flexible definition of the cluster subspace, and permits the study of charged defects. The perturbed-cluster approach is implemented in the computer code EMBEDOl [703] and applied in the calculations of the point defects both in the bulk crystal, [704] and on the surface [705]. The difficulties of this approach are connected with the lattice-relaxation calculations. 

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