Self-consistent charge and configuration

Korchowiec J, Uchimaru T (2000) New energy partitioning scheme based on the self-consistent charge and configuration method for subsystems application to water dimer system. J Chem Phys 112(4) 1623—1633... 

Partitioning Scheme Based on the Self-Consistent Charge and Configuration Method for Subsystems Application to Water Dimer System. 

Each VSIE is a function (empirically established) of charge and electronic configuration the latter is obtained by Mulliken s population analysis ° conducted on the molecular orbitals. Therefore an iterative method is required. Each secular determinant is solved in cycles until self-consistent charge distribution is obtained. Some relation between the output from one iteration and the input from the next is often necessary to ensure convergence... 

It is explained elsewhere in this Volume that the self-consistent charge density and ionic potential corresponding to a given configuration of atoms not only determine the system s total energy - but also provide the fo qe gacting on all atoms through the theorem of Hellmann-Feynman (HF). The details of application in the context of DF, and u jJ.n the concept of the pseudopotential, are discussed elsewhere it will be examined... 

The most consistent charge redistribution is given by ICONC. This is quite understandable in view of the iterative charge and configuration self-consistency (described by nine parameters for the metal nd(n+l)s(n+l)p atom and three parameters for each of the nsnp atoms) employed by this method. However ICONC does not contain direct geometry optimization. Therefore we chose to optimize the geometry by means of INDO/1, while the charge distribution and the DSC procedure were carried out by ICONC. 

The empirical (semiquantitative) methods are based on a one-electron effective Hamiltonian and may be considered as partly intuitive extended Hiickel theory (EHT) for molecules [204] and its counterpart for periodic systems - the tight-binding (TB) approximation. As, in these methods, the effective Hamiltonian is postulated there is no necessity to make iterative (self-consistent) calculations. Some modifications of the EHT method introduce the self-consistent charge-configuration calculations of the effective Hamiltonian and are known as the method of Mulliken-Rudenberg [209]. 

As we have seen, EHT is a nonself-consistent method but the self-consistency over charge and configuration is included in the MR approximation. The Ab-initio HE SCF method requires the self-consistent calculation of the density matrix (see Chap. 4). This feature of the HE approach is maintained in the semiempirical methods, based on the zero differential overlap (ZDO) approximation. This approximation is used to reduce the number of multicenter integrals appearing in HE LCAO calculations. 

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