Double-zeta model

Comparison of correlation energies (all signs reversed) for a double zeta model of the ground state of the H2O molecule (in mhartree). The differences from FCI are enclosed in parentheses. The AL-RMR-CCSD-f methods are simply designated as AL-RMR-L... 

In order to overcome the shortcommings of standard post-Hartree-Fock approaches in their handling of the dynamic and nondynamic correlations, we investigate the possibility of mutual enhancement between variational and perturbative approaches, as represented by various Cl and CC methods, respectively. This is achieved either via the amplitude-corrections to the one- and two-body CCSD cluster amplitudes based on some external source, in particular a modest size MR CISD wave function, in the so-called reduced multireference (RMR) CCSD method, or via the energy-corrections to the standard CCSD based on the same MR CISD wave function. The latter corrections are based on the asymmetric energy formula and may be interpreted either as the MR CISD corrections to CCSD or RMR CCSD, or as the CCSD corrections to MR CISD. This reciprocity is pointed out and a new perturbative correction within the MR CISD is also formulated. The earlier results are briefly summarized and compared with those introduced here for the first time using the exactly solvable double-zeta model of the HF and N2 molecules. 

There is no experimental way to measure y. (As we mentioned before, the zeta potential - as obtained, for example, from electrophoretic measurments - is in a not readily definable way - smaller than y.) But as discussed in section 3.3 we can obtain the surface charge (Eq. 3.2) and then compute the surface potential y on the basis of the diffuse double layer model with Eq. (3.8a) Eq. (3.8a) in simplified form for 25° C is... 

The choice of the exchange correlation functional in the density functional theory (DFT) calculations is not very important, so long as a reasonable double-zeta basis set is used. In general, the parameterized model will not fit the quantum mechanical calculations well enough for improved DFT calculations to actually produce better-fitted parameters. In other words, the differences between the different DFT functionals will usually be small relative to the errors inherent in the potential model. A robust way to fit parameters is to use the downhill simplex method in the parameter space. Having available an initial set of parameters, taken from an analogous ion, facilities the fitting processes. 

Practically all of the calculation studies we discuss here were performed within the HF or DFT formalism, and most employed acid site cluster models that may contain anywhere between one and five Si and A1 atoms. Basis sets used to represent the electrons of the system were usually of double-zeta quality or higher i.e., each filled orbital of an atom has been represented by two separate exponential functions. In addition, extra functions have been added—so-called polarization functions—to represent orbitals that are empty. These allow the orbital more flexibility and result in better theoretical predictions. 

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 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... 

To model the copper (100) surface a two-layer cluster of C4V symmetry, with 5 copper atoms in one layer and 4 copper atoms in the other layer, has been used. In this cluster, all the 9 metal atoms were described by the LANL2DZ basis set. The LANL2DZ basis set treats the 3s 3p 3d 4s Cu valence shell with a double zeta basis set and treats all the remainder inner shell electrons with the effective core potential of Hay and Wadt [33]. The non-metallic atoms (C and H) were described by the 6-3IG basis set of double zeta quality with p polarization functions in... 

In the present work, the interaction of the ethylene molecule with the (100) surfaces of platinum, palladium and nickel is studied using the cluster model approach. All these metals have a face centered cubic crystal structure. The three metal surfaces are modelled by a two-layer M9(5,4) cluster of C4V symmetry, as shown in Fig. 6, where the numbers inside brackets indicate the number of metal atoms in the first and second layer respectively. In the three metal clusters, all the metal atoms are described by the large LANL2DZ basis set. This basis set treats the outer 18 electrons of platinum, palladium and nickel atoms with a double zeta basis set and treats all the remainder electrons with the effective core potential of Hay and Wadt... 

The matrix isolation experiments using epr, ir, uv-visible and other spectroscopic techniques on transition metal-olefin complexes [8,49] have naturally attracted the attention of theoretical chemists and calculations on the Ni-C2H4 system were reported in one of the first theoretical-experimental papers mentioned in the introduction [16]. These results were later supplemented with a larger (double-zeta) basis set [3Q] and also [31] extended for a Ni(C2H4)2 system. The main conclusions are that a net charge transfer of almost 1/5 of an electron from the metal to the ethylene is evident and that a donation and back donation mechanism consistent with a classical Dewar-Chatt-Duncanson model exists. The Ni-ethylene binding energy is 12.8 kcal/mol. 

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... 

---