Frozen-core

Frozen fish fingers and similar products are made from a mixture of different fish that arrive at the processing plant as frozen blocks of the average size 62.7 x 254 x 482 mm (thick x width x length). The frozen blocks are minced and the still frozen minced fish blocks are mixed and pressed into the desired shape, covered with batter and bread crumbs, baked on the outside (still with a frozen core), packed and stored in a deep freezer. 

Flere we distinguish between nuclear coordinates R and electronic coordinates r is the single-particle kinetic energy operator, and Vp is the total pseudopotential operator for the interaction between the valence electrons and the combined nucleus + frozen core electrons. The electron-electron and micleus-micleus Coulomb interactions are easily recognized, and the remaining tenu electronic exchange and correlation... 

HypcrChcrn sup )orLs MP2 (second order Mollcr-Plessct) correlation cn crgy calculation s tisin g ah initio rn cth ods with an y ava liable basis set. In order lo save mam memory and disk space, the Hyper-Chern MP2 electron correlation calculation normally uses a so called frozen -core" appro.xiniatioii, i.e. the in n er sh ell (core) orbitals are om it ted,. A sett in g in CHKM. INI allows excitation s from the core orbitals lo be included if necessary (melted core). Only the single poin t calcii lation is available for this option. ... 

There are several variations of this method. The PRDDO/M method is parameterized to reproduce electrostatic potentials. The PRDDO/M/FCP method uses frozen core potentials. PRDDO/M/NQ uses an approximation called not quite orthogonal orbitals in order to give efficient calculations on very large molecules. The results of these methods are fairly good overall, although bond lengths involving alkali metals tend to be somewhat in error. 

ADF uses a STO basis set along with STO fit functions to improve the efficiency of calculating multicenter integrals. It uses a fragment orbital approach. This is, in essence, a set of localized orbitals that have been symmetry-adapted. This approach is designed to make it possible to analyze molecular properties in terms of functional groups. Frozen core calculations can also be performed. 

Most of the scale factors in this table are from the recent paper of Wong. The HF/6-31G(d) and MP2(Full) scale factors are the traditional ones computed by Pople and coworkers and cited by Wong. Note that the MP2 scale factor used in this book is the one for MP2(Full) even though our jobs are run using the (defriultj frozen core approximation. Scott and Radom computed the MP2(FC) and HF/3-21G entries in the table, but this work came to our attention only just as this book was going to press. 

Gl theory also predales frozen core gradients, which is why the Full option is specified. 

It is usual to make the frozen core approximation in calculations of this type. This means that the seven inner shells are left frozen and not included in the Cl calculation. 

The HF-LCAO calculation follows the usual lines (Figure 11.10) and the frozen core approximation is invoked by default for the CISD calculation. CISD is iterative, and eventually we arrive at the improved ground-state energy and normalization coefficient (as given by equation 11.7) — Figure 11.11. 

The MP2 and CCSD(T) values in Tables 11.2 and 11.3 are for correlation of the valence electrons only, i.e. the frozen core approximation. In order to asses the effect of core-electron correlation, the basis set needs to be augmented with tight polarization functions. The corresponding MP2 results are shown in Table 11.4, where the A values refer to the change relative to the valence only MP2 with the same basis set. Essentially identical changes are found at the CCSD(T) level. 

The remarkably ordered behavior of N, 2)-nets derives principally from the appearance of a connected frozen core of sites, each element of which remains frozen in a fixed stattn This frozen core creates percolating walls of constancy that effectively partition the not into a dynamically static subset and (dynamically) isolated islands of sites that continue evolving but are incapable of communicating through the frozen core. 

We consider the expression of the lab frame photoelectron angular distribution for a randomly oriented molecular sample. The frozen core, electric dipole approximation for the differential cross-section for electron emission into a solid angle about a direction k can be written as... 

The localized basis function for the set 0 (Is) are usual frozen-core valence-shell Cl states all the bound states involved in the present calculations are also described at this level. 

AE First order (or Frozen Core) Second Order Fligher orders (8E)... 

In G3(MP2) theory, the MP2(fu)/G2Large calculation of G3 is replaced with a frozen core calculation with the G3MP2Large basis set [23] that does not contain the core polarization functions of the G3Large basis set. 

As Fig. 12 shows, the inner shell electrons of the alkaline ions behave classically like a polarizable spherical charge-density distribution. Therefore it seemed promising to apply a "frozen-core approximation in this case 194>. In this formalism all those orbitals which are not assumed to undergo larger changes in shape are not involved in the variational procedure. The orthogonality requirement is... 

Fig. 3. The effect of freezing the 3s,3p core electrons. Errors in computed excitation energies are shown (in eV). Solid lines CCSD(T) dashed lines CASPT2 (upper hues with frozen core in both cases).

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