Electronic structure methods frozen core

The structural parameters and vibrational frequencies of three selected examples, namely, H2O, O2F2, and B2H6, are summarized in Tables 5.6.1 to 5.6.3, respectively. Experimental results are also included for easy comparison. In each table, the structural parameters are optimized at ten theoretical levels, ranging from the fairly routine HF/6-31G(d) to the relatively sophisticated QCISD(T)/6-31G(d). In passing, it is noted that, in the last six correlation methods employed, CISD(FC), CCSD(FC),..., QCISD(T)(FC), FC denotes the frozen core approximation. In this approximation, only the correlation energy associated with the valence electrons is calculated. In other words, excitations out of the inner shell (core) orbitals of the molecule are not considered. The basis of this approximation is that the most significant chemical changes occur in the valence orbitals and the core orbitals remain essentially intact. On... 

In the calculations based on effective potentials the core electrons are replaced by an effective potential that is fitted to the solution of atomic relativistic calculations and only valence electrons are explicitly handled in the quantum chemical calculation. This approach is in line with the chemist s view that mainly valence electrons of an element determine its chemical behaviour. Several libraries of relativistic Effective Core Potentials (ECP) using the frozen-core approximation with associated optimised valence basis sets are available nowadays to perform efficient electronic structure calculations on large molecular systems. Among them the pseudo-potential methods [13-20] handling valence node less pseudo-orbitals and the model potentials such as AIMP (ab initio Model Potential) [21-24] dealing with node-showing valence orbitals are very popular for transition metal calculations. This economical method is very efficient for the study of electronic spectroscopy in transition metal complexes [25, 26], especially in third-row transition metal complexes. 

One way to reduce the computational cost of DFT (or WFT) calculations is to recognize that the core electrons of an atom have only an indirect influence on the atom chemistry. It thus makes sense to look for ways to precompute the atomic cores, essentially factoring them out of the larger electronic structure problem. The simplest way to do this is to freeze the core electrons, or to not allow their density to vary from that of a reference atom. This frozen core approach is generally more computationally efficient. One class of frozen core methods is the pseudopotential (PP) approach. The pseudopotential replaces the core electrons with an effective atom-centered potential that represents their influence on valence electrons and allows relativistic effects important to the core electrons to be incorporated. The advent of ultrasoft pseudopotentials (US-PPs) [18] enabled the explosion in supercell DFT calculations we have seen over the last 15 years. The projector-augmented wave (PAW) [19] is a less empirical and more accurate and transferable approach to partitioning the relativistic core and valence electrons and is also widely used today. Both the PP and PAW approaches require careful parameterizations of each atom type. 

Abstract We summarize an ab-initio real-space approach to electronic structure calculations based on the finite-element method. This approach brings a new quality to solving Kohn Sham equations, calculating electronic states, total energy, Hellmann-Feynman forces and material properties particularly for non-crystalline, non-periodic structures. Precise, fully non-local, environment-reflecting real-space ab-initio pseudopotentials increase the efficiency by treating the core-electrons separately, without imposing any kind of frozen-core approximation. Contrary to the variety of well established k-space methods that are based on Bloch s theorem... 

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