Space frozen core approximation

HyperChem supports MP2 (second order Mdllcr-l Icsset) correlation energy calcu latiou s u sin g any available basis set. lu order to save main memory and disk space, the HyperChem MP2 electron correlation calculation normally uses a so called frozen-core approximation, i.e. th e in n er sh el I (core) orbitals are omitted. A sett in g in CHHM.IX I allows excitation s from th e core orbitals to be include if necessary (melted core). Only the single poin t calcula-tion is available for this option. 

The Self-Consistent (SfC) (G)RECP version [23, 19, 24, 27] allows one to minimize errors for energies of transitions with the change of the occupation numbers for the OuterMost Core (OMC) shells without extension of space of explicitly treated electrons. It allows one to take account of relaxation of those core shells, which are explicitly excluded from the GRECP calculations, thus going beyond the frozen core approximation. This method is most optimal for studying compounds of transition metals, lanthanides, and actinides. Features of constructing the self-consistent GRECP are ... 

The third change in the program was the implementation of a frozen core approximation. Unfortunately, this procedure does not save much computing time and space because during the first iteration - defining the frozen core part - all electrons must be taken into account to achieve orthogonal ization of the valence orbitals to the core orbitals. 

Note thaty(r) describes the change in electron density at point r in space with respect to the variation in the total number of electrons N, at constant external potential (i.e., at fixed molecular geometry). There are several approximate formulas to evaluate the condensed to atom Fukui function. A three-point finite difference approach is normally used [24, 61], albeit it may be also readily obtained by single-point calculations, using the frozen core approximation. The former approach will be used herein. Using the normalization to unity condition [57, 58] ... 

GPaw All-electron real-space code using projected augmented wave method and frozen core approximation. Available http //www.camd. dtu.dk/software.aspx. 

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... 

In electron correlation treatments, it is a common procedure to divide the orbital space into various subspaces orbitals with large binding energy (core), occupied orbitals with low-binding energy (valence), and unoccupied orbitals (virtual). One of the reasons for this subdivision is the possibility to freeze the core (i.e., to restrict excitations to the valence and virtual spaces). Consequently, all determinants in a configuration interaction (Cl) expansion share a set of frozen-core orbitals. For this approximation to be valid, one has to assume that excitation energies are not affected by correlation contributions of the inner shells. It is then sufficient to describe the interaction between core and valence electrons by some kind of mean-field expression. 

The volume contribution by the metallic 5f-5f and the covalent cation 5f-N2p bonds to a virial-theorem formulation of the equations of state of a series of light actinide nitrides was calculated in the self-consistent linear muffin tin orbital (LMTO), relativistic LMTO, and spin-polarized LMTO approximations [46]. The results for ThN give the same lattice spacing in all three approximations higher by ca. 3% than the experimental value, which discrepancy is attributed to the assumed frozen core ions [47]. 

However, if the valence spinors are modified to create pseudospinors—and this applies to both model potentials and pseudopotentials— the expectation of the valence wave function over the property operator is no longer the same as in the all-electron or the frozen-core case. For external fields, where the bulk of the contribution comes from the valence region of space, the deviation of the pseudospinor property integrals from their unmodified counterparts will be small. However, for nuclear fields, the approximation to the core part of the spinors will have serious consequences for the property. Pseudospinors used with pseudopotentials are designed to have vanishing amplitude at the nucleus, and therefore the property integrals will be much smaller than they should be. This means that properties such as NMR shielding constants calculated for the pseudopotential center will inevitably be erroneous. 

Several methods have been proposed to alleviate this problem. The first is to freeze the core orbitals for some suitable state, such as the isolated atom, and perform the calculation in the valence space only, where the gauge problem is not as serious because the eigenvalues are smaller (van Lenthe et al. 1994). Such restrictions may prove to be too limiting for widespread applications— but no less serious than those made in pseudopotential or model potential methods, where the core is frozen. The second is to freeze the potential that appears in the denominator. To do this some approximations must be made. Several criteria for a valid frozen potential have been proposed by van Wiillen (1998) which are that the potential (a) has the correct behavior near the nuclei, (b) does not depend on the orbitals, and (c) has no contribution from distant atoms or molecules. In addition, the potential must represent the real system fairly well or it will be of no value. Probably the most obvious choice are to take a superposition of atomic potentials or to construct the potential from a superposition of atomic densities. These two differ for a density functional method only in the exchange-correlation potential. A third approach is to add terms from neighboring atoms to the potential in the... 

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