Polarized double zeta

Andzelm and Wimmer, 1992, published one of the first comprehensive studies on the performance of approximate density functional theory in which optimized molecular geometries were reported. These authors computed the geometries of several organic species containing the atoms C, N, O, H, and F at the local SVWN level, using a polarized double-zeta basis set optimized for LDA computations. Some trends have been discerned... 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

All methods employ a correlation-consistent polarized double-zeta basis set. 

In general, DFT calculations are known to converge fast with the size of the basis set. Although polarized double-zeta basis sets are a minimum requirement, polarized triple-zeta basis sets are... 

Experimental trends in Si shielding observed experimentally arise from variations in the coordination number (i.e. the number of atoms in the 1st coordination sphere), the extent of polymerization of the silicate tetrahedra, the degree of replacement of one net-work forming cation by another (e.g. coupled Na+, Al+3 for Si+4 substitution), the size of the rings of tetrahedra present and the Si-O-Si angles (1,2). Similar trends are seen in gas-phase molecules, species in aqueous solution and in both crystalline and amorphous solids. Polarized double-zeta basis set Hartree-Fock level calculations using small molecular cluster models reproduce these trends semiquantitatively, as we will show. 

The geometries of cyclopropanethione (1), methylenethiirane (3), cyclopropanethione S-oxide (24), methylenethiirane 1-oxide (31), cyclopropanethione S,5-dioxide (21) and methylenethiirane 7,/-dioxide (32) were optimized at the SCF level by the use of ah initio molecular orbital theory with a polarized double zeta basis set. The surprising difference in energy for each pair of isomers is 3 more stable than 1 by 6.4 kcal mol 24 more stable than 31 by 8.2 kcal mol 32 more stable than 21 by 0.2 kcal mol ... 

The corresponding reaction with methane has PESs that are rather similar to those described here, so it will not be discussed in detail. It should, however, be pointed out that the description of the MECP in this system appears to have been one of the first such reports for a transition metal system in the literature (77). The study used CASSCF calculations with four electrons in an eight-orbital active space, combined with polarized double-zeta basis sets (77). Dynamic correlation is not very important in this system, partly because Sc+ has only one d electron, so this level of theory produces rather good agreement with experiment for quantities such as the D <— excitation energy, the complexation energy... 

Atomization energies (in a.u.), bond lengths (in A), and force constants k of the breathing mode (in a.u.), from one-component SCF calculations using energy-consistent scalar-relativistic pseudopotentials (EC-PP), ab initio model potentials (AIMP) and valence basis sets of double zeta (DZ) and polarized double-zeta (DZP) quality, in comparison to all-electron (AE) relativistic SCF calculations. Numbers in parentheses are differences to corresponding non-relativistic results. 

An ab initio SCF calculation, using effective core potentials and polarized double-zeta basis sets, has been conducted o on the harmonic force fields of Me2M (M=Zn, Cd or Hg) good agreement was found with the experimental data. Laser induced fluorescence studies on [RZn] (R=Me, Et or Pr)2< > and [MeC5H4Zn] have been reported. oc... 

In Table 2 we show some results on the effect of polymerization on the Si shift, taken from Moravetski et al. (1996). These were obtained using the GIAO method with polarized triple zeta basis sets at polarized double zeta Hartree-Fock geometries. The experimental values are taken from Harris and Knight (1983). 

Calculation of the reaction paths for both reactions (6) and (7) have been reported by Harding Wagner (38). These calculations employed a polarized double zeta basis set and a four orbital - four electron CASSCF wavefunction. This wavefunction allows for the correlation of both CH bond pairs of formaldehyde and thus provides a qualitatively correct description of both reaction pathways. The angular dependence of the potential surface for a hydrogen atom moving in the field of a frozen formyl radical is shown in Figure 6. Two reactive channels are clearly seen in this plot. One, on the left side of the plot, leads to the addition product, formaldehyde, while the other, on the right side of the plot, leads directly to abstraction products, H2 + CO. From this plot it can be seen that there is no barrier for either reaction. 

One advantage of Ax is its relatively low cost. The cc-pVTZ basis set may still be out of reach for many practical problems, however, and therefore, the basis set dependence of the diagnostic is of interest. Table 3 lists correlation coefficients and deviation statistics (from near-basis-set-limit values with Jensen s pc-3 polarization consistent basis set [49-55]) for the LANL2DZ, 6-3IG, and 6-3IIG basis sets. It is shown there that > 0.98 for basis sets of at least polarized double-zeta quality, while > 0.995 can be reached for triple-zeta double polarization or better basis sets. Only for small double-zeta basis sets like LANL2DZ or SDD could basis set dependence potentially become an issue. 

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