Polar valences, calculation

Dunning has developed a series of correlation-consistent polarized valence n-zeta basis sets (denoted cc-pVnZ ) in which polarization functions are systematically added to all atoms with each increase in n. (Corresponding diffuse sets are also added for each n if the prefix aug- is included.) These sets are optimized for use in correlated calculations and are chosen to insure a smooth and rapid (exponential-like) convergence pattern with increasing n. For example, the keyword label aug-cc-pVDZ denotes a valence double-zeta set with polarization and diffuse functions on all atoms (approximately equivalent to the 6-311++G set), whereas aug-cc-pVQZ is the corresponding quadruple-zeta basis which includes (3d2flg,2pld) polarization sets. 

The quality of quantum-chemical calculations depends not only on the chosen n-electron model but also critically on the flexibility of the one-electron basis set in terms of which the MOs are expanded. Obviously, it is possible to choose basis sets in many different ways. For highly accurate, systematic studies of molecular systems, it becomes important to have a well-defined procedure for generating a sequence of basis sets of increasing flexibility. A popular hierarchy of basis functions are the correlation-consistent basis sets of Dunning and coworkers [15-17], We shall use two varieties of these sets the cc-pVXZ (correlation-consistent polarized-valence X-tuple-zeta) and cc-pCVXZ (correlation-consistent polarized core-valence X-tuple-zeta) basis sets see Table 1.1. 

In the present work, correlation consistent basis sets have been developed for the transition metal atoms Y and Hg using small-core quasirelativistic PPs, i.e., the ns and (nA)d valence electrons as well as the outer-core (nA)sp electrons are explicitly included in the calculations. This can greatly reduce the errors due to the PP approximation, and in particular the pseudo-orbitals in the valence region retain some nodal structure. Series of basis sets from double-through quintuple-zeta have been developed and are denoted as cc-pVwZ-PP (correlation consistent polarized valence with pseudopotentials). The methodology used in this work is described in Sec. II, while molecular benchmark calculations on YC, HgH, and Hg2 are given in Sec. III. Lastly, the results are summarized in Sec. IV. 

A full valence calculation on CH4 gives 1764 standard tableaux functions, and all of these are involved in the 164 A1 sjmimetry functions. The second and fourth tableaux are also present in the principal constellation and, as with the earlier cases, these are not simple symmetry functions alone. The third tableau is ionic with the negative charge at the C atom. As before, this contributes to the relative polarity of the C—H bonds. 

The SCF, SCVB, full valence tv, and full valence tt + S results of using a 6-3IG basis on benzene are given in Table 15.6. The geometry used is that of the minimum SCF energy of the basis. In this case the SCVB energy is lower by 0.4 eV than the full valence it energy. This is principally due to the 3d polarization orbitals present in the SCVB orbital, but absent in the valence calculation. The SCVB orbital is... 

Examining the results given in these two tables, it is seen that, for this small molecule, very advanced calculations can be carried out. In the tables, all the methods employed have been introduced in the previous sections. For the basis sets, aug-cc-pVnZ stands for augmented correlation consistent polarized valence n zeta, with n = 2-5 referring to double, triple, quadruple, and quintuple, respectively. Clearly, these basis functions are specially designed for... 

Examine now the determination of exponents for polarization functions. Obviously, the atomic ground state calculations that are so useful in the optimization of valence shell exponents cannot help us. There is a possibility of performing calculations for excited states of atoms. This approach is, however, not appropriate. The role of polarization functions is to polarize valence orbitals in bonds so that the excited atomic orbitals are not very suitable for this purpose. Chemically, more well-founded polarization functions are obtained by direct exponent optimization in molecules. Actually, this was done for a series of small molecules in both Slater and Gaussian basis sets. Among the published papers, we cite. Since expo-... 

The valence-bond method has been used in an ab initio study of the potential surface for H4 186). The basis orbitals were linear combinations of gaussian functions with a polarization factor. Calculations were performed with and without inclusion of ionic structures, and with and... 

Fig. 3.8. Direct magnetoabsorption in germanium at RT. The polarization condition is usually referred as n polarization. The calculated peaks 1 and 2 correspond to transitions from spin-split levels of the Landau ladder of the heavy hole valence band and the 1+ and 2+ ones to corresponding transitions for light hole VIS. With the ordinate scale used, the indirect absorption is barely visible (after [13])...

We next carried out calculations with a larger basis set and active space to compare the calculated and experimental results. The splitting with Dunning s correlation consistent polarized valence triple zeta (cc-pVTZ) basis set is 10.1 kcal/mol, which is in good agreement with the experimental value of 9.4 kcal/mol [33]. In the calculations with CAS[6e,6o], even the reference CASSCF gives good results 12.8 (DZP) and 10.5 (cc-pVTZ) kcal/mol. The deviation from the full Cl and experimental values are only 0.8 and... 

Several points should be mentioned in this context. First, while we use QCISD(T) in our basic dehnition of G2 and G3 theories, analogous methods have been defined where the CCSD(T) method replaces QCISD(T). Both variations seem to yield very similar mean absolute deviations in most cases. However, in our most recent work on transition metal systems [78], it appears that CCSD(T) has a clear advantage over QCISD(T) and will thus become the preferred method. For the first- and second-row molecules, however, there is no clear preference. The key point to note is that the accuracy and predictive capability of these methods comes from the inherent accuracy of QCISD(T) or CCSD(T). Finally, this is one of the steps in the calculation and is likely to be rate-limiting if carried out with very large basis sets. Indeed, it is the bottleneck in CCSD(T) calculations with large correlation-consistent basis sets. In G2 theory, QCISD(T) calculations are carried out with a polarized valence triple-zeta basis set. This is a very modest basis set and this makes it possible to carry out G2 calculations on molecules of the size of naphthalene on small workstations. In our later work on G3 theory, we use even smaller 6-31G(d) calculations that makes these methods applicable for even larger molecules. 

With the advent of all-valence calculations in the 1960s, the o electrons were explicitly included and the effects such as charge transfer and polarization could be explained by an interplay of o and jr electrons. Needless to say that the approach, which separated 7t and o effects, had an enormous impact on the interpretation of molecular properties. 

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