Augmented correlation consistent valence basis sets

Augmented Correlation Consistent Valence Basis Sets... 

Table 6 First Four Augmented Correlation Consistent Valence Basis Sets for Hydrogen, Helium, and the First-row Atoms Boron through Neon...

Stuttgart pseudopotential for Au with a uncontracted (lls/10p/7d/5f) valence basis set and a Dunning augmented correlation consistent valence triple-zeta sets (aug-cc-pVTZ) for both C and N, but with the most diffuse f function removed, was used. 

Correlation-consistent polarized basis sets are another popular choice, so called because they have been optimized using correlated (CISD) wavefunctions. These basis sets are labeled with the prefix cc-p before the valence zeta notation. They can then be augmented with diffuse functions, to give aug-cc-pVDZ, for... 

Dunning s augmented correlation-consistent valence double- basis set, aug-cc-pVDZ." " Of these approaches, CCSD(T) is considered the most sophisticated and reliable. 

G(d,p), both intermediate and TS geometries become more reliable, at least as judged from a comparison with the corresponding geometries achieved using the augmented correlation-consistent polarized valence triple-zeta (aug-cc-pVTZ) basis sets.32... 

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... 

The basis sets used in the reactions including F and Cl are the augmented correlation consistent polarized valence double zeta (aug-cc-pVDZ) sets [16]. In the reactions including Br and I, the relativistic effective core potential (ECP) due to Stevens et al. [17,18] and their associated basis sets were used for Br and I, and the cc-pVDZ set for H. The basis sets of Br and I were augmented by adding a d polarization function with an exponent of 0.389 (Br) / 0.266 (I) and sp diffuse functions with an exponent 0.03574 (Br) / 0.03007 (I). The diffuse p polarization function of the aug-cc-pVDZ set of H was omitted for consis-... 

FCI energies of the ground state and several excited states (3 12+, 2 ll, and 2 2A states) were obtained by Olsen et al. [66] in 1989 using a DZP basis set augmented with diffuse functions. These data have been used as tests for a wide variety of EOM/FR-CC methods, including CCSD [20, 24], CCSDT-la [44], CC3 [45], CCSDT-3 [46], and CCSDt [52], Later Hirata et al. [49] obtained FCI results with the 6-31G basis set. Shiozaki et al. [57] have obtained FCI results with the augmented correlation-consistent polarized valence double-zeta (cc-pVDZ) and valence triple-zeta (aug-cc-pVTZ) sets. 

Obviously, the first consideration one must address when performing population analysis is the reliability of the wavefunction at hand. Whereas this topic is well beyond the scope of this review, a quick scan of the populations reported in this chapter indicates that basis set size and elearon correlation play an important role in defining the electronic distribution. For most compounds, a split-valence basis set augmented with polarization functions on the heavy atoms is the smallest basis set that produces reasonably consistent populations, regardless of the population method employed. One should further keep in mind the effects of electron correlation. Generally correlation contracts the core electrons, lengthens bonds, and reduces the ionic component of bonds. 

The ionization potentials and electron affinities of the atoms H, C, N, O and F have been computed by means of coupled-cluster methods using doubly augmented correlation-consistent one-electron basis sets in conjunction with explicitly correlated Slater-type geminals. Excitations up to the level of connected quintuples have been accounted for, and all orbitals in the core and valence shells have been correlated. Relativistic effects (spin-orbit as well as scalar) and diagonal Born-Oppenheimer corrections have been included. 

Using DMBE IV potential, Meijer and coworkers carried out wavepacket calculations of the initial state selected total cross sections for the H + O2, including partial waves up to / = 35. All of the projections of J onto the intermolecular axis have been incorporated in the calculations. They found that the calculated cross sections are lower than the experiment, which indicated the deficiencies in the DMBE IV potentials. In 2005, Xu et al. constructed a new potential (XXZLG PES) for this reaction at the internally contracted multireference configuration interaction plus the Davidson correction level with the augmented correlation consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set. It has been shown that there is remarkable improvement over the previous DMBE IV potential. Based upon this new potential and using the recent developed RGB quantum wave packet method. Sun et al. calculated state-to-state DCS and ICS of the H + O2 reaction up to 1.5 eV. 

A series of basis sets developed in calculations which included electron correlation effects have been introduced by Dunning et al. " These basis sets are referred to as correlation-consistent polarized split-valence basis sets (cc-pVXZ, where X = D for double, T for triple, Q for quadruple, and 5 for quintuple-split). These basis sets have been systematically constructed to improve the description of the polarization space as the valence-space description is improved. They have also been augmented with diffuse functions (aug-cc-pVXZ), with a set of diffuse functions added for each value of the quantum number t which appears in the original basis set. (For example, the cc-pVTZ basis set has three sets of valence-space functions, two sets of functions in the first polarization space, and a single set of functions in the second polarization space. For a second-period element, this translates to a single s orbital for the inner shell, three sets of s and p orbitals in the valence shell, and two sets of d and a set of f orbitals in the polarization space. The aug-cc-pVTZ basis set includes an additional set of diffuse s, p, d, and f orbitals.) Because... 

The correlation-consistent basis sets described in Section 8.3.3 have been designed for one particular purpose the accurate calculation of valence-correlated wave functions of ground-state neutral systems. The cc-pVXZ basis sets therefore do not have the flexibility required either for the investigation of core correlation discussed in Section 8.3.1 or for the study of anions and excited states with diffuse electron distributions. For such applications, additional AOs must be introduced. In the present subsection, we shall first discuss the correlation-consistent polarized core—valence sets cc-pCVXZ [24], where the standard cc-pVXZ sets have been extended for additional flexibility in the core region, and next the augmented correlation-consistent basis sets aug-cc-pVXZ and aug-cc-pCVXZ [25], where diffuse functions have been added so as to improve the flexibility in the outer valence region. 

We now turn our attention to the outer, diffuse regions of the electronic system. The valence and core-valence basis sets considered so far are inadequate for the description of the difiuse electron distributions characteristic of anionic systems and excited states. In addition, these sets do not have the flexibility required for a proper description of interactions with external electric fields and hence the accurate calculation of dipole moments and polarizabilities. For such calculations, additional functions must be added in the outer valence region. Within the framework of correlation-consistent basis sets, we proceed by adding primitive functions to the standard cc-pVXZ sets, with exponents adjusted so as optimize the energy of atomic anions. Diffuse functions are added in groups, with one set of functions for each angular momentum present in the root set. This procedure leads to the augmented correlation-consistent polarized valence basis sets aug-cc-pVXZ [25], the composition and size of which are listed in Table 8.13. The number of functions in the aug-cc-pVXZ sets may be calculated as... 

The largest basis set was of triple-i plus polarization plus/functions (TZP + f) quality, which consisted of a TZP basis set flexibly contracted to Geil4sllp3dlfll0sSp3d f) This basis set was augmented with a set of d- and /-like polarization functions [a Ge) = 0.25 and ay(Ge) = 0.45 a (H) = 0.75]. Only the valence electrons were correlated the 14 lowest occupied molecular orbitals for GeH5 and GeH (Ge U, 2s, 2p, 3s, 3p, 3d) were frozen, and the six highest virtual molecular orbitals (Ge Is , 2s, 2p, 3s ) were deleted in the Cl and CC procedures. 

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