Minimal basis set calculations

The main obstacles to the solution of this problem lie in the formidable number of multicentered integrals which arise even with the use of a minimal basis set, and the difficulty involved in their evaluation. This is illustrated in Table 1, where the number of electron interaction integrals is computed for a minimal basis set calculation of various compounds. The total number of such bielectronic integrals can be computed by the following equation. 

The simple model predicts that the highly electronegative CF3- radical should add preferentially to CH2 in vinyl fluoride and CHF in trifluoroethylene. For the weakly electropositive methyl radical, either weak thermodynamic control or even contrathermodynamic control is predicted. The ab initio minimal basis set calculations fall in line with these qualitative predictions, except that for the attack of CH3 on trifluoroethylene no preferential site of attack is found. The activation energy differences calculated by Salem are compared with the experimental results in Table 21. Although the absolute values of the activation energies are too large, the differences reproduce qualitatively the experimental trend. 

The (primarily) minimal basis set calculations of Linnett and co-workers [19] demonstrate clearly that the npso structures with one-electron bonds... 

The results of these calculations are essentially consistent with the conclusions drawn from EPR measurements (Chapter III). There is complete agreement about the ground state of five-fold coordinated complexes, which is invariably 1 z, Ai >. For the four-fold coordinated complexes, all semi-empirical calculations predict 1 yz, A2 > ground state, whereas an ab initio minimal basis set calculation (23) favours the lz, Ai > ground state in the case of Co(acacen). 

The fact that doping does indeed largely perturb the geometry of ID chains has been confirmed by several computer experiments on isolated chains of equidistant hydrogen atoms [49] and on a more realistic model of polyacetylene [50]. In both cases, the doping is shown to have the same effect, i.e. the amount of bond alternation is calculated to be drastically reduced bond lengths of 1.41 and 1.43 A versus 1.33 and 1.48 A for the double and single bonds, respectively (already in minimal basis sets calculations). 

The calculations of Lehn and Wipff (1975) included d-functions to a very limited extent. Similarly, Gorenstein and coworkers have almost exclusively employed a minimal STO-3G basis set in ab initio calculations on P(K) species (Gorenstein et al., 1979). This appears to be a major omission. However, two observations suggest that, despite the use of a minimal basis set, calculations on the stereoelectronic effect may remain valid. Firstly, the inclusion of d-functions in Lehn and Wipflf s (1975) study shows similar effects with and without these functions. Secondly, recent studies at the STO-3G and 3-21G( ) level on H2SO4 and dimethyl sulphate indicate the presence of similar stereoelectronic effects, independent of the inclusion of d-functions on sulphur (Lowe et al., 1988). 

Non-empirical, minimal-basis-set calculations of the geometric and electronic structures of cyclotriborazane, (BH2NH2)3, indicate the preferred conformation to be the eclipsed boat form. It has also been predicted to be thermodynamically unstable with respect to disproportionation. ... 

For formaldehyde (a) Work out the symmetry orbitals for a minimal-basis-set calculation give the symmetry species of each symmetry orbital. (Choose the x axis perpendicular to the molecular plane.) (b) How many <7 and how many v canonical MOs will result from a minimal-basis-set calculation (See the Section 15.10 discussion of ethylene for the definition of <7 and TT MOs.) How many occupied <7 and occupied ir MOs are there for the ground state (c) For each of the eight energy-localized MOs, state which AOs will make significant contributions, (d) What is the maximum-size secular determinant that occurs in finding the minimal-basis-set canonical MOs ... 

Write symmetry orbitals for a minimal-basis-set calculation of H2. 

The next assumption in the HMO method is to approximate the tt MOs as LCAOs. In a minimal-basis-set calculation of a planar conjugated hydrocarbon, the only AOs of tt symmetry are the carbon Ipir orbitals, where by Ipir we mean the real 2p AOs that are perpendicular to the molecular plane. We thus write... 

By Restricted we mean that two electrons with different spins a and P do occupy the same spatial orbital. The horizontal mirror symmetry (D h) of H2 requires that the two active orbitals belong to two different irreducible representations Og and Ou. Hence, for a minimal basis set calculation, the composition of the MOs is given by symmetry and the wave function does thus have no degree of freedom at all. The situation is quite different in case of unrestricted MO calculation vide infra). As expected, the dissociation behavior is not correctly reproduced because of the restricted approximation. But it is worth to note, that the singlet-triplet separation, for which the correct behavior is to vanish when the inter-atomic distance increases. 

One question we can ask is this Is a minimal basis set equally appropriate for calculating an MO wavefunction for, say, B2 as F2 In each case we use 10 AOs and 2 spin functions producing a total of 20 spin MOs. With B2, however, we have 10 electrons to go into these spin MOs, and in F2 we have 18 electrons. In all but the crudest MO calculations, the total energy is minimized in a maimer that depends on the natures of only the occupied MOs. In effect, then, the calculation for B2 produces the 10 best spin MOs from a basis set of 20 spin-AOs, whereas that for F2 produces the 18 best MOs from a different basis set of 20 spin-AOs. In a sense, then, the basis for F2 is less flexible than that for B2. Of course, the use of separated atom orbitals is a conscious effort to choose that basis that best spans the same function space as the best MOs. To the extent that this strategy is successful, the above problem is obviated (i.e., if both sets are perfect, additional flexibility is useless). The strategy is not completely successful, however, and conparison of results of minimal basis set calculations down a series of molecules such as B2, C2, N2,02, and F2 may be partially hampered by this... 

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