Effect of the Basis Set

We chose the basis set 6-3IG as standard for HF calculations of the electronic couplings because it offers a reasonable compromise between accuracy and computational effort see Table 1 for relative computer times. 

Moreover, as will be shown below, electronic coupHngs are very sensitive to conformational changes of DNA fragments their magnitude can change 

Adiabatic splitting estimated as energy difference of HOMO and HOMO-1 of the neutral system 

Also for other systems, V a values for hole transfer depend only weakly on the basis set [14, 41, 46]. This is at variance with results for the coupling of excess electron transfer where energies of more diffuse states are involved in the ground strategy this would correspond to employing energies of unoccupied molecular orbitals. 

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With the LDBS study on / ran.y-l,2-difluoropropene. Fig. 3, we wanted to investigate primarily the effect of the basis sets for the carbon atom in the methyl group. Therefore, we used the minimal basis set for the methyl hydrogens in all... 

That study at the MP2 correlated level for the dimers investigated are summarized in Table 7. In Table 7, we use the following notations SM denotes the values obtained in the super-molecule, while CP denotes those obtained in the counter-poise corrected calculations. The results clearly show, that the E(intra/net) values are close to each other (using any basis sets) for the monomers in both of SM and CP systems. This suggests that the SMO-LMBPT scheme takes into account the benefit effect of the basis set superposition. The deviations found in the intra terms between the SM and CP systems are explained recently (Kapuy etal, 1998) in detail. 

TABLE 10. B3LYP activation barriers (AE, kcal mol ) for the epox-idation of a series of atkenes with peroxyformic acid (PFA) showing the effect of the basis set (the first barriers are at the B3LYP/6-31G(d) level of theory, the barriers in parentheses are at the B3LYP/6-31+G(d,p) level)... 

Table 1 Effect of the basis set on the hole coupling matrix element Vd between the two guanine units of the WCP dimer [(GC),(GC)], calculated at the HF level with the GMH and FCD...

We explored the effect of the basis set on the binding energy of the system Na -H20. Optimized structures and the ground state energy corresponding to the end points of the reaction Na + H2O —> Na (H20) were obtained. The binding enthalpies were compared to experimental values and the results shown in Table 1 clearly illustrate the effect of increase of basis set on the calculation of binding enthalpies. 

Table 1. Effect of the basis set on DFT (B3PW91) Na -HjO binding enthalpies H at 298 K (in kcal/mol), compared to a high-level ab initio (G2) method and to the experimental value. ...

Kirtman and Luis review some of the theoretical/computational methods which have been proposed over the past fifteen years for the calculation of vibrational contributions to the linear and NLO properties. They discuss (i) the time-dependent sum-over-states perturbation theory and the alternative nuclear relaxation/curvature approach, (ii) the static field-induced vibrational coordinates which reduce the number of n -order derivatives to be evaluated, (hi) tire convergence behavior of the perturbation series, (iv) an approach to treat large amplitude (low frequency) vibrations, (v) the effect of the basis set and electron correlation on the vibrational properties, and (vi) techniques to compute the linear and NLO properties of infinite polymers. 

A classic illustration of the quality of a calculation is provided considering the effect of the basis set of say, a Hartree-Fock (HF) calculation. (See Sect. 3 for further discussion of the HF method). For MO schemes like HF theory, the variational principle states that the lower the computed total energy, the better the result [1]. The energy can be lowered by increasing the basis set size and so large basis set calculations are often described as good quality. However, this need not imply that experiment is also well reproduced. If the basic assumptions of the HF approximation are inappropriate, then it may not be possible to predict experimental data reliably, irrespective of the basis set size. As will be seen later, this is often the case for HF calculations on TM systems. 

Alkorta I, Villar HO, Perez JJ. Effect of the basis set on the computation of molecular polarization. J Phys Chem 1993 97 9113-9119. 

The second-order correlation energies were determined to show whether electron correlation effects might favour one conformation of the 2-hydroxy-acetamide molecule over the other. The effects of the basis set on the calculated correlation energy is also of interest. 

The effect of the basis set on the bulk properties of MgO is documented in Table 17. Basis set (c), as containing three valence sp shells at oxygen, two... 

Several studies employ the so-called G2 and G3 procedures. 106.117.127.137.143.144,148 effects of the basis set continued to demand... 

Cox and Williams [154] pay attention to the effect of the basis set and to the comparison of PD-AC values with Mulliken charges. In fact the PD/LSF procedure is still time-consuming, and the possibility of coming back to Mulliken charges computed on smaller basis sets, with an appropriate scaling with respect to more precise results must not be ruled out as irrelevant for numerical applications. In their paper, Cox and Williams examine the performances of three basis sets, STO-3G,... 

The geometry of HSO (1) shown here is that reported from the analysis of its emission spectrum in the gas phase [29]. The geometry of the methylsulfinyl radical (2) optimized at the 6-3 G d) level is also shown [46]. Further expansion of the basis set to 6 - 31 G(2d, p) has little effect on the geometry except for a decrease in the S-O bond length to 1.499 A. There is also a pronounced effect of the basis set on the atomic charges that increases the polarity of the SO bond. 

To give an idea of the performance of some popular GGA and HGGA functionals, and also to show the effect of the basis set, the dependence of the H-O-H angle in water is reported in O Table 4-4 as an exemplary case. Accurate bond angles (within 1.0° from the experimental value) can be achieved with aU functionals and moderate basis sets. 

Morokuma and co-workers have also used an extrapolation scheme called IMOMO(G2MS) that connects the G2-type and IMOMO (integrated molecular orbital molecular orbital) approaches. In the G2 approach, the energy of the system is determined at a highly correlated ab initio method using a moderate basis set. The effect of the basis set is obtained at a lower ab initio level. In the IMOMO scheme, a high level of calculation is used in the study of a model system, while the effect of substituents is taken into account at a lower level. 

N-electron error is the difference between the result obtained with a given A -electron model and the result that would be obtained using the FCI wave function in the same basis set. As illustrated in Figure 15.1, we may think of the apparent error as the combined effect of the basis-set error and the iV-electron error. It should be noted that the A -electron error depends on the basis set employed in the calculation. Of interest is also the A-electron error in the limit of a complete basis, which we shall refer to as the intrinsic N-electron error or simply the intrinsic error. 

It can be observed that both the dimension of the space of the valence functions and the use of pseudopotentials affect the relative stabilities of the two conform-ers. With triple and quadruple basis sets, the zwitterionic form is more stable than the charge-solvated one, whereas with the SNSD (double-Q basis, the stability order is inverted. Furthermore, use of a pseudopotential for describing core electrons seems to increase the stability of the CSl structure, as shown by corn-parson between the AVTZ and AVTZ-PP and between the AVQZ and AVQZ-PP calculations. The effect of the method seems to be smaller than the effect of the basis set on the overall energetics. 

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