Basis set valence double zeta

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)... 

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 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. 

The insertion of acetylene into the Pd-CH3 bond of the complex PdCl(NH3)(CH3) has been studied by de Vaal and Dedieu [63] by using the valence double-zeta basis sets. The geometries of the prereaction complex [PdCl(NH3)(CH3)(C2H2)], the transition state, and product have been optimized at the SCF level, and their energetics has been improved at the CASSCF and Cl level. It has been shown that acetylene is quite weakly bound (5.8 kcal/mol) in the square-planar Pd(II) complexes because of weak 7T back-donation from Pd to the tt orbital of C2H2. The insertion barrier calculated relative to the acetylene complex is 20.5, 22.6, and 17.1 kcal/ mol at the SCF, CASSCF, and Cl levels of theory, respectively, and the transition state corresponding to this barrier displays monohapto coordination of acetylene. The entire insertion reaction is calculated to be exothermic by 26.0, 19.3, and 22.4 kcal/mol at the SCF, CASSCF, and Cl levels, respectively, relative to the acetylene complex. 

An alternative to the double zeta basis approach is to double the number of functions used to describe the valence electrons but to keep a single fxmction for the iimer shells. The rationale for this approach is that the core orbitals, unlike the valence orbitals, do not affect chemical properties very much and vary only slightly from one molecule to another. The notation used for such split valence double zeta basis sets is exemplified by 3-21G. In this basis set three Gaussian functions are used to describe the core orbitals. The valence electrons are also represented by three Gaussians the contracted part by two Gaussians and the diffuse part by one Gaussian. The most commonly used split valence basis sets are 3-21G, 4-31G and 6-31G. 

In addition, simple and efficient CCSD(T)-F12 approximations x = a, b) [57] were proposed and benchmarked [58] by Werner s group. They obtained improvements in basis set convergence for calculations of equilibrium geometries, harmonic vibrational frequencies, atomization energies, electron affinities, ionization potentials, and reaction energies of open- and closed-shell reaction systems, where chemical accuracy of total reaction energies was obtained for the first time using valence double-zeta basis sets. 

Test calculations were performed for three molecules, cyclopropane, benzene, and adamantane. First, we performed geometry optimization of the three molecules by Hartree-Fock calculations with a valence double-zeta basis set with a single set of polarization functions [28]. This was done with the purpose to save expansion coefficients of occupied molecular orbitals for a subsequent evaluation of A terms [Eq. (15)] and for calculation of differential cross sections. Details of our scattering calculations have been... 

Calculations were carried out with the GAUSSIAN 98 program [10]. Geometries of the structures were optimized with the B3LYP functional. Harmonic vibration frequencies were calculated for each structure. LANL2DZ basis set (the Hay-Wadt effective core potential [11] plus double-zeta basis for molybdenum and aluminium atoms, Dunning-Huzinaga valence double-zeta basis set for other elements) was employed. 

---