Split-basis calculations

Exercise 3.5. A general spreadsheet for orthonormality and split-basis calculations with Gaussian basis sets — the matching of hydrogen and lithium Is and 2s radial orbitals. 

Table 4.8 The results obtained using various optimized choices for the coefficients in the Dunning split-basis calculations to determine the hydrogen Is orbital energy.

Figure 13. Vibrational levels for the first-excited electronic state of HD2 calculated [8] using split basis (SB) technique with A(R) = tp/2 coordinate-transformation (CT) treatment with A(R) — tp/2 Eq. (A. 14) with A (R) — y(p, 9, tp). Shown by the longer line segments are the levels assuming different values in two sets of calculations.

In order to test such an application we have calculated the spin and charge structure factors from a theoretical wave function of the iron(III)hexaaquo ion by Newton and coworkers ( ). This wave function is of double zeta quality and assumes a frozen core. Since the distribution of the a and the B electrons over the components of the split basis set is different, the calculation goes beyond the RHF approximation. A crystal was simulated by placing the complex ion in a lOxIOxlOA cubic unit cell. Atomic scattering factors appropriate for the radial dependence of the Gaussian basis set were calculated and used in the analysis. 

To solve the problem put by the Hartree-Fock method with ab initio qrproximation (non-empirical calculations) was chosen. All calculations have been done with the assistance of Gaussian 98/A7 software and use the extended valence-splitting basis, which included diffusive and polarized d- and p-functions — 6-31G(d,p). The correlation amendments were performed with use of Density Functional Theory (DFT) in B3LYP approximation. 

The geometry of CF2 used in the calculations was determined with CASSCF [6e,6o]/cc-pVTZ. The active space and basis set for MRMP are CAS[12e,9o] and cc-pVTZ, respectively. The ST splitting energy calculated with MRMP(SD) is... 

In the manner of equations 1.24 and 1.25, some other of these basis sets by Dunning are listed in Table 3.2. As you see, the Dunning procedure is to renormalize over the number of primitive Gaussians in each component of the split-basis. The following spreadsheet design details are particular to the case of the (4s)/[2s] and follow straightforwardly from those used for the double-zeta Slater functions in the previous section. This alternative to the procedure applied in fig3-5.xls is important for later calculations. 

With the overlap integral of J 4 calculated, define the normalization condition on the coefficients of the split-basis, as previously using equation 3.19 and 3.20,... 

CALCULATIONS WITH SPLIT-BASIS [SPLIT-VALENCE] SETS... 

Given the third diagram in Figure 4.16, we cannot expect the (4s/2s) Dunning split-basis set for the calculation of the Is orbital energy to return a better estimate. However, as... 

The next step is to renormalize the individual primitive functions of the basis set so that the most diffuse primitive Gaussian is split from the others to form the new linear combination. There are three stages, therefore, in this analysis, the renormalization of the lsto-4g) data of Table 5.1, the calculation of the two-electron term using the split-basis set and the straightforward calculation of the one-electron kinetic and potential energy terms, as in previous spreadsheets. 

Exercise 5.4. Formation of a 4-31) split-basis set for helium using the data of Table 5.1 and the calculation of the energy of the helium ground state. 

To construct the renormalized split-basis linear combination in the manner of equations 1.24 and 1.25, we need to calculate normalization integrals for the three primitives to be taken as one group in the calculation. So, on a new spreadsheet provide for this change as shown in the first diagram of Figure 5.9. 

Figure 5.10 Determination of the best ground state energy for helium by varying the independent coefficient of the split-basis linear combination from the sto-4g) Gaussian set of Table 5.1. The energy of helium is found to be —2.85516 Hartree for the coefficients of equation 5.40 equal 0.51380 and 0.59189. The orbital energy, is, is calculated to be —0.91412 Hartree and compares well with Huzinaga s result. Table 5.2.

As you might expect there is no difference in the result of this calculation and that presented in Figure 5.8. After all, the second calculation results simply from renormalization of the original basis set. However, it is important to remember that the split-basis procedure has increased the flexibility of the calculation. It allows us to vary the two components independently by varying the Slater exponent. 

Exercise 5.5. Modify fig5-9.xls to provide for distinct Slater exponents for each component of the split-basis. Repeat the calculation of the energy of the helium atom to investigate whether a better description of the ground state can be obtained using the electronic energy as the test parameter. 

Several different basis sets, including pseudopotential LANL2DZ [100] as well as two Aldrich s valence split basis sets (triple zeta (TZVP) and quadruple zeta (QZVP) valence quality) [101] were used to calculate modeled reactions involving small FeS clusters. Employing an electron core potential (ECP) basis set such as LANL2DZ (Los Alamos National Laboratory 2 double for transition metals) has become popular in computations on a transition-metal-containing systems. Due to large size of calculated models in the case of the adsorption of nucleic acid bases on the clay mineral surfaces the 6-31G(d) basis set [102] was appUed. 

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