STO-nG basis sets

The smallest basis sets are called minimal basis sets. The most popular minimal basis set is the STO—3G set. This notation indicates that the basis set approximates the shape of a STO orbital by using a single contraction of three GTO orbitals. One such contraction would then be used for each orbital, which is the dehnition of a minimal basis. Minimal basis sets are used for very large molecules, qualitative results, and in certain cases quantitative results. There are STO—nG basis sets for n — 2—6. Another popular minimal basis set is the MINI set described below. 

The contraction exponents and coefficients of the d-type functions were optimized using five d-primitives (the first set of d-type functions) for the STO-NG basis sets and six d-primitives (the second set of d-type functions) for the split-valence basis sets. Thus, five d orbitals are recommended for the STO-NG basis sets and six d orbitals for the split-valence basis sets. 

The Slater exponents partially listed in the table above are used for all the STO-NG basis sets. The exponents for all the atoms with atomic numbers less than and equal to 54 are available from HyperChem basis function. BAS files. 

The STO-nG basis sets are made up this way. Table A.l gives the STO-3G expansions of STOs of lx, 2s, and 2p type, with exponents of unity. To obtain other STOs with other exponents one needs only to multiply the exponents of the primitive Gaussians given in Table A.l by the square of /. 

It became apparent that these STO-nG minimal basis sets were not particularly adequate for the accurate prediction of molecular geometries, and this failing was attributed to their lack of flexibility in the valence region. The next step was to give a little more flexibility to the STO-nG basis sets, whilst retaining their computational attractiveness. The classic paper is that by Ditchfield, Hehre and Pople. 

It should be noted that calculations may of course be made also with Gaussian expansions of STO s which are free of the restrictions imposed on the STO-NG basis sets. Nevertheless almost all our experience with Gaussian expansion originates from the results of calculations with STO-NG and related basis sets. So it seems to us tolerable to restrict the discussion just to the functions of these types. 

As N is increased, the convergence of STO-NG basis sets towards the STO results is rather satisfactory. A typical example is shown in Table 2,9, It is seen that the energy of atomization converges much... 

Convergence of STO-NG basis sets towards full STO results for CO... 

For different reasons, STO-NG basis sets give total energies inferior to those given by other Gaussian basis sets with approximately the same number of primitive Gaussians, though some other molecular properties are reproduced well (see for example the first two rows in... 

STO-nG basis sets Slater Type Orbital consisting of n PGTOs. This is a minimum hydrogen 6-31G basis is (10s4p/4s) [3s2p/2s]. In terms of contracted basis... 

The results, displayed in Figures 1.20 and 1.21, emphasize the great distinction between the approximations for the Is and 2s orbitals. Since there is no attempt to reproduce the nodal behaviour of the numerical functions, both the Slater and sto-ng) basis sets are deficient, although as you can see, they agree with each other. The matches can be improved by relaxing the manner in which the Slater exponents are determined, but more importantly, as you will see in later chapters, by re-imposing the fundamental requirement that the atomic functions should be orthonormal. 

Nowadays, sto-ng) basis sets have been proposed for most atoms of the elements of the Periodic Table. The William Wiley Environmental Molecular Sciences Laboratory maintains a basis set service at http //www.emsl.pnl.gov 2080/forms/basisform.htmU which database includes performance information for each basis set in comparisons with HFS atomic structure calculations. 

Figure 3.15 Application of the canonical procedure to render the Is and 2s sto-ng> basis sets of Table 1.6 mutually orthogonal as is seen in the value of the overlap integral in cell G 16 compared to the value 0.4846, cell D 16 of the unmixed originals. Note that the new functions are not normalized, cells G 15 and G 17 and that multiplication by the appropriate normalization constants cells I 12 and I 13 is required.

Look at the expression for the energy in equation 4.10. The numerator requires various differentiations and terms involving 1/r" to be integrated over the atomic space. The denominator requires the calculation of the norm. Both of these terms can be evaluated numerically for the choice of Slater orbitals or the sto-ng> basis sets, although for real calculations the normal procedure is to evaluate the various integrals analytically. For the present purposes, the advantage of the numerical procedure is that we begin to understand clearly what the implications are of the use of the different approximate representations. 

Exercise 4.9. Calculation of the Is orbital energy in hydrogen using the sto-ng) basis sets, Table 1.6, proposed by Hehre, Pople and Stewart. 

Modify the links in this worksheet to collect the overlap and Fock matrix data for the direct diagonalization of the Fock matrix over the sto-ng) basis sets. 

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