Choice of Basis Set

A prerequisite for the application of all-electron approaches is the availability of a reliable basis set for the particular f element and the chosen Hamiltonian. Ideally one would like to be able to assess the size of basis set errors by being able to benchmark the results with a basis set large enough to exclude significant errors due to truncation effects. In atomic calculations one may do so by choosing a very large universal basis set. In this approach a set of exponents is generated via the recurrence relation 

In all cases one should be aware of the fact that exponents and contraction coefficients are obtained for a particular choice for electronic configuration of the atom. Due to the importance of the 6d in actinides, and the 5d in early lanthanides, the configuration of choice is either (Faegri, Noro [40,45]) the configuration or an average of different configu- 

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To solve the Kohn-Sham equations a number of different approaches and strategies have been proposed. One important way in which these can differ is in the choice of basis set for expanding the Kohn-Sham orbitals. In most (but not all) DPT programs for calculating the properties of molecular systems (rather than for solid-state materials) the Kohn-Sham orbitals are expressed as a linear combination of atomic-centred basis functions ... 

In any case, the argument ignores the fact that molecular HF calculations are invariably done at the HF-LCAO level and the choice of basis set often turns out to be the dominant source of error. 

The choice of basis set in ab initio calculations has been the subject of numerous theoretical studies. Early SCF calculations utilized mainly spht-va-lence basis sets such as 3-21G and 4-31G. The importance of inclusion of d polarization functions on sulfur atoms has been stressed by several authors. For instance, Suleimenov and Ha found that the omission of d polarization functions leads to a substantially lower barrier for the internal rotation ( 16 kj mol for the central bond of H2S4) and produces an unreahstically large S-S bond length for the most stable rotamer [4]. In general, the use of... 

For practical implementations it is necessary to represent the molecular electronic wave functions as a linear combination of some convenient set of basis functions. In principle any choice of basis set is permissible although the basis set must span any electronic configuration of the molecule. This implies that the basis must form a complete set. 

However, the values in Tables 26-30 are directly calculated BDEs, according to equation 1. Taking only those molecules for which there are reliable experimental information (Table 26), and excluding the problematic (S 2) cases (CCH-, COOH-, NCO-, CN-, NC-, CHCH2- and N3 ) and the decomposed radical (CH3CO2 ), the average MP2 error for CH3—Y is 2.0 kcalmol-1 (21 cases) and for MP4 is 3.8 kcal mol-1 (19 cases). It thus seems that the particular choice of basis set and level of calculation used here gives the best cancellation of errors for the MP2 method. 

A determined by X-ray crystallography [56], whereas the distance to the amine groups deviates less, 2.09 A in this work and 2.01 A experimentally. Previous theoretical studies by Carloni et al. [63] and Zhang et al. [64] yielded Pt-Cl distances of 2.34 and 2.37 A, respectively. The difference from the more recently obtained value is related to the choice of basis set and exchange-correlation functional. 

At this point we should mention that we encountered instability problems in the linear response calculations for some of the MCSCF wavefunctions at intemuclear distances larger than R—S a.u. We believe those instabilities to be artifacts of the calculations because their existence or position depends on the choice of basis set, active space or number of electrons allowed in the RAS3 space. This implies that even though it might not be possible to generate... 

In this form, it becomes possible to analyze the merits of Mulliken charge distributions in comparisons with physical observables. Namely, we want to learn the true value of n and the appropriate value of A for given choices of basis sets. Three approaches were followed to this end ... 

Calculated CX stretching frequencies for these compounds (repeating the data in Appendix A7) are provided in Table 7-3 and compared to measured values. As expected, limiting (6-311+G basis set) Hartree-Fock frequencies are all larger than experimental values. In fact, with the sole exception of methyl chloride at the 3-2IG level, Hartree-Fock frequencies are always larger than experimental frequencies, irrespective of choice of basis set. 

These systems provide a useful example because the calculations often work, but occasionally fail, either by distortion from planarity or by failure to locate a stable minimum for one of the tautomers. Thus, the students learn to consider their results critically with a healthy dose of skepticism, to analyze the success or failure of the calculation, to consider the influence of the choice of method (semi-empirical or ab initio), to consider the influence of the choice of basis set, and to determine the answer to the research question posed. 

Since the second term is constant for a given geometry, the total energy depends on the choice of basis set through the HF energy. This dependence is illustrated in Table 2.1. 

The dimension of the secular determinant for a given molecule depends on the choice of basis set. EHT adopts two critical conventions. First, all core electrons are ignored. It is assumed that core electrons are sufficiently invariant to differing chemical environments that changes in their orbitals as a function of environment are of no chemical consequence, energetic or otherwise. All modern semiempirical methodologies make this approximation. In EHT calculations, if an atom has occupied d orbitals, typically the highest occupied level of d orbitals is considered to contribute to the set of valence orbitals. 

Having discussed ways to reduce the scope of the MCSCF problem, it is appropriate to consider the other limiting case. What if we carry out a CASSCF calculation for all electrons including all orbitals in the complete active space Such a calculation is called full configuration interaction or full CF. Witliin the choice of basis set, it is the best possible calculation that can be done, because it considers the contribution of every possible CSF. Thus, a full CI with an infinite basis set is an exact solution of the (non-relativistic, Bom-Oppenheimer, time-independent) Schrodinger equation. 

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