Valence double zeta

Dunning valence double zeta Dunning (1975) Dunning and Hay (1976)... 

The chemical bonding occurs between valence orbitals. Doubling the 1 s-functions in for example carbon allows for a better description of the 1 s-electrons. However, the Is-orbital is essentially independent of the chemical environment, being very close to the atomic case. A variation of the DZ type basis only doubles the number of valence orbitals, producing a split valence basis. In actual calculations a doubling of tire core orbitals would rarely be considered, and the term DZ basis is also used for split valence basis sets (or sometimes VDZ, for valence double zeta). 

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. 

Related basis sets in common usage include the original Dunning full and valence double-zeta sets, denoted D95 and D95V, respectively (built from nine s-type and five p-type primitives). These sets may be augmented in the usual way with diffuse and/or polarization functions, as in the example D95++ (diffuse and first-polarization sets on all atoms). 

Although there is no strict relationship between the basis sets developed for, and used in, conventional ah initio calculations and those applicable in DFT, the basis sets employed in molecular DFT calculations are usually the same or highly similar to those. For most practical purposes, a standard valence double-zeta plus polarization basis set (e.g. the Pople basis set 6-31G(d,p) [29] and similar) provides sufficiently accurate geometries and energetics when employed in combination with one of the more accurate functionals (B3LYP, PBEO, PW91). A somewhat sweeping statement is that the accuracy usually lies mid-way between that of M P2 and that of the CCSD(T) or G2 conventional wave-function methods. 

The A -representability conditions on the 2-RDM can be systematically strengthened by adding some of the 3-positivity constraints to the 2-positivity conditions. For three molecules in valence double-zeta basis sets Table II shows... 

Figure 2. Comparison of the 2-RDM, coupled-cluster, MRPT2, and FCI potential energy surfaces of CO in a valence double-zeta basis set, where all valence electrons are correlated (a) without an electric field and (b) with an electric field of strength 0.10 an apphed in the direction of the permanent dipole moment. The 2-RDM and MRPT2 methods accurately describe the features of the FCI potential energy surface.

For Three Molecules in Valence Double-Zeta Basis Sets, a Comparison of Energies in Hartrees (H) from the 2-RDM Method with the T2 Condition (DQGT2) with the Energies from Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Method with Single-Double Excitations and a Perturbative Triples Correction (CCSD(T)), and Full Configuration Interaction (FCI)... 

At the SCF or MCSCF level, the basis set requirements are fairly simple. We can imagine that the occupied molecular orbitals are given as a simple linear combination of atomic orbitals this corresponds to a minimal basis set. The results so obtained are fairly crude, but by admitting extra functions to represent the atomic orbitals more flexibly (split-valence, double zeta, etc) we can obtain a much better description. However, some effects require going beyond the occupied atomic orbitals ... 

The calculations were performed in three steps. For each structure considered, a geometry optimization was performed using the hybrid density functional B3LYP method (21). For open shell systems unrestricted DFT was used. In this first step, a standard valence double zeta basis set (the lacvp basis set) was used. Since models including also second shell amino acid residues were used, a full geometry optimization is not possible. The second shell residues would then move in unrealistic ways. For this reason, one atom of each amino acid residue was frozen from the X-ray structure. This procedure has been found to work very well in previous studies (22,23). It might be thought that this... 

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. 

In this article, we will compare the energetics of the conventional Halpern mechanism with that of the Brown mechanism. The basis functions used are the 3-21G for ethylene and hydrides, the ST0-2G for spectator ligands, PH and Cl, and valence double zeta basis functions for Rh with effective core potential replacing the core electrons (up to 4p) (5a.b.6). In addition, we carried out the MP2 calculations at selected, RHF-optimized structures with a larger basis set, which consists of uncontracted (3s,3p,4d) functions from the above valence DZ set for Rh, 4-31G for the ethyl group,... 

The column (AE(MP2/G3)) contains the differences between the MP2(full) energies with a basis set of augmented-triple-zeta quality and the 6-31G(d) basis set. The size of these numbers clearly demonstrates the fact that the split-valence double-zeta basis sets are far from being complete. 

By analogy with the earlier studies (Reference 729), the PES search of the phenol-(water) complexes was initially performed by using a spht-valence double-zeta 6-31G(d) basis set via a GAUSSIAN 98 suit of packages. 

Owing to computational limitations, the model used to represent the first shell of CA was the (NH3)3M (H20) system. This complex has been widely used in ab initio calculations of different mechanistic aspects of the CA enzyme [31]. Furthermore, the validity of this model, where the three imidazole ligands are substituted by three ammonia groups, has been previously assessed [31e, 32]. In the present study, full geometry optimizations of all eight minima with no symmetry constraints were performed. Pseudopotential wave functions have been preferred to full-electron calculations, because valence Similarity can be more easily related to reactivity than all-electron Similarity [33]. Dunning s valence double zeta quality basis set [34] together with the Hay and Wadt ECPs... 

The Hartree-Fock calculations were performed at the experimental (32) octahedral geometry with a S-F bond length of 1.564A. A standard double zeta basis was used for the fluorine atoms (33), while the sulfur was described by an effective potential (34) with a valence double zeta s-p basis. In a separate calculation a single d polarization function with exponent. 532 was added to the sulfur basis to assess the importance of d functions. 

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