Optimized Valence Basis Sets

The final step is to generate optimized basis sets for valence orbitals not replaced by the ECP. Returning to the lanthanide example, one can assemble the following orbitals for inclusion in the lanthanide valence basis set 5s, 5p, 4f, 5d, 6s, and 6p. The first two AOs are completely occupied in all chemically reasonable oxidation states for the lanthanides. The final three AOs are unoccupied in the prevalent -1-3 ion. The ground state for the -1-3 ion is f with n ranging from 1 (for Ce3+) to 14 (Lu +). Methods for optimizing valence basis sets (VBSs) are similar to those employed in traditional all-electron calcula-tions s and need not be discussed here. The lanthanide 4f AOs emphasize many salient features regarding the choice of valence basis sets for lanthanide and transition metals. 

The contraction exponents and coefficients of the d-type functions were optimized using five d-primitives (the first set of d-type functions) for the STO-NG basis sets and six d-primitives (the second set of d-type functions) for the split-valence basis sets. Thus, five d orbitals are recommended for the STO-NG basis sets and six d orbitals for the split-valence basis sets. 

A speculative proposal was made thirty years ago by Schmid and Krenmayr77, namely that a nitrosyl ion solvated, but not covalently bonded, by a water molecule may be involved in these systems. This hypothesis was investigated theoretically in 1984 by Nguyen and Hegarty78 who carried out ab initio SCF calculations of structure and properties employing the minimal STO-3G basis set, a split-valence basis set plus polarization functions. Optimized geometries of six planar and two nonplanar forms were studied for the nitrosoacidium ion. The lowest minimum of molecular electrostatic potential... 

The number No of occupied valence SCF orbitals in a molecule is typically less than the total number Nmb of orbitals in the minimal valence basis sets of all atoms. The full valence MCSCF wavefunction is the optimal expansion in terms of all configurations that can be generated from N b molecular orbitals. Closely related is the full MCSCF wavefunction of all configurations that can be generated from Ne orbitals, where Nc is the number of valence electrons, i.e. each occupied valence orbital has a correlating orbital, as first postulated by Boys (48) and also presumed in perfect pairing models (49,50), We shall call these two types of frill spaces FORS 1 and FORS 2. In both, the inner shell remains closed. 

The. totally symmetric operators M(r) are of the same form as the operators fi(r). The c s are atomic core orbitals expressed in the full all-electron basis set, and Fval are normal Fock operators defined in the valence space only. The valence orbitals v = cpXv are expressed in an appropriate valence basis set, determined through some optimization procedure, which is considerably smaller than the original all electron basis set. 

Valence basis set for Cs and Ba including the outermost 5s, 5p and 5d electrons. fcThe s and p valence basis sets were optimized for the contraction scheme 311. 

We treated only a / -methyl and /Mluoro substituent, 127 and 128, in both the E- and Z-constitution, with the resulting molecular heavy atom geometries presented in Table 11. Additional split-valence basis set optimizations with diffuse functions (3-21 + G) have been performed comparatively by Rivail and coworkers225 for / -push-pull sub-... 

The geometry optimizations have been carried out at the MP2 level of theory17 using effective core potentials (ECPs)18 for the heavier elements. Hydrogen and the first and second row elements B, C, N, O, Na, Mg, Al and Si were described by standard all electron 6-31G(d) basis sets.19 For tungsten we used the relativistic ECP developed by Hay and Wadt and the corresponding (441/2111/21) split-valence basis set.20 A pseudopotential with a (31/31/1) valence basis set was used for Cl, Ga, In and Tl.21 This basis set combination is our standard basis set II.22... 

The s and p valence basis sets were optimized for the contraction scheme 311. 

Our consecutive optimizations and findings have been based on applications of 3-21G, 6-31G and 6-3IG basis sets. These three basis sets have been selected for the following reasons The 3-21G basis set is the most economical split-valence basis set which allows comparison to similar systems the 6-31G basis set was used because this was statistically the best basis set for calculations of CC distances and the 6-3IG basis set was applied as a highly reliable and computationally still manageable basis set and because we found, in agreement with References 206 and 207, that polarization functions are needed to treat successfully the problem of pyramidality at nitrogen. 

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