STO-3G set

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. 

Some of the basis sets discussed here are used more often than others. The STO—3G set is the most widely used minimal basis set. The Pople sets, particularly, 3—21G, 6—31G, and 6—311G, with the extra functions described previously are widely used for quantitative results, particularly for organic molecules. The correlation consistent sets have been most widely used in recent years for high-accuracy calculations. The CBS and G2 methods are becoming popular for very-high-accuracy results. The Wachters and Hay sets are popular for transition metals. The core potential sets, particularly Hay-Wadt, LANL2DZ, Dolg, and SBKJC, are used for heavy elements, Rb and heavier. 

The second possible improvement that we might seek is to vary the Slater exponent so that a better match to the boron function is obtained. This is a matter best investigated after Chapter 3, when we have considered the role of orthogonality as a fundamental requirement in solution procedures for calculation of orbital energies and orbital functions. But, it is a good exercise, to demonstrate the versatility of the spreadsheet approach. A better result is shown in Figure 1.25. It follows, simply, from setting the Slater exponents for the Slater function and the sto-3g) set equal to 1.00 in cells G 3 and G47. 

Construction of the 2s-A1s) numerical radial function for the lithium atom, using the miniinal Pople el al sto-3g> sets. 

Layout the usual input data and scaling adjustments for the sto-3g) sets of Table 1.6 in cells D 2 to I 7. 

Divide the overlap integral cell 1 5 of fig4-10.xls into components to check the normalization of the two sto-3g) sets and their overlap, with... 

Chapter 1 ended with a short survey of modem methodology in the application of Gaussian basis set theory to molecular orbital theory calculations. In real calculations it is standard to use a variety of larger basis sets tailored to particular applications (49) with the minimum basis sto-3g) sets widely used for general use and then these more complicated basis sets being applied to obtain better agreement with particular experimental results. 

Split valence basis sets generally give much better results than minimal ones, but at a cost. Remember that the number of two-electron integrals is proportional to kf , where W is the number of basis functions. Whereas STO-3G has only live ba.sis functions for carbon, 6-31G has nine, resulting in more than a tenfold increase in the size of the calculation,... 

Because th e calculation of m n Iti-ceiiter in tegrals that are in evitable for ah iniiio method is very difficult and time-con sum in g. Ilyper-Chem uses Gaussian Type Orbital (GTO) for ah initio methods. In truly reflecting a atomic orbital. STO may he better than GTO. so HyperC hem uses several GTOs to construct a STO. The number of GTOs depends on the basis sets. For example, in the minimum STO-3G basis set IlyperGhem uses three GTOs to construct a STO. 

Once the least-squares fits to Slater functions with orbital exponents e = 1.0 are available, fits to Slater function s with oth er orbital expon cn ts can be obtained by siin ply m ii Itiplyin g th e cc s in th e above three equations by It remains to be determined what Slater orbital exponents to use in electronic structure calculation s. The two possibilities may be to use the "best atom" exponents (e = 1. f) for II. for exam pie) or to opiim i/e exponents in each calculation. The "best atom expon en ts m igh t be a rather poor ch oicc for mo lecular en viron men ts, and optirn i/.at ion of non linear exponents is not practical for large molecules, where the dimension of the space to be searched is very large.. 4 com prom isc is to use a set of standard exponents where the average values of expon en ts are optirn i/ed for a set of sin all rn olecules, fh e recom -mended STO-3G exponents are... 

In eonPast to the low-Ievel ealeulations using the STO-3G basis set, very high level ealeulations ean be earried out on atoms by using the Complete Basis Set-4 (CBS-4) proeedure of Petersson et al. (1991,1994). For atoms more eomplieated than H or He, the first ionization potential (IP[) ealeulation is a many-eleePon ealeulation in which we ealeulate the total energy of an atom and its monopositive ion and determine the IP of the first ionization reaetion... 

We now have two ways of inserting the correct parameters into the STO-2G calculation. We can write them out in a gen file like Input File 8-1 or we can use the stored parameters as in Input File 8-2. You may be wondering where all the parameters come from that are stored for use in the STO-xG types of calculation. They were determined a long time ago (Hehre et al, 1969) by curve fitting Gaussian sums to the STO. See Szabo and Ostlund (1989) for more detail. There are parameters for many basis sets in the literature, and many can be simply called up from the GAUSSIAN data base by keywords such as STO-3G, 3-21G, 6-31G, etc. 

Calculate the H—H bond length in ground-state H2 using the STO-3G basis set in the GAUSSIAN for Windows implementation. 

Plot the curve of the bond energy of H2 vs. intemuclear distance for the H2 molecule using the STO-3G, double zeta valence (DZV), and triple zeta valence (TZV) basis sets in the GAMESS implementation. 

The second approximation in HF calculations is due to the fact that the wave function must be described by some mathematical function, which is known exactly for only a few one-electron systems. The functions used most often are linear combinations of Gaussian-type orbitals exp(—nr ), abbreviated GTO. The wave function is formed from linear combinations of atomic orbitals or, stated more correctly, from linear combinations of basis functions. Because of this approximation, most HF calculations give a computed energy greater than the Hartree-Fock limit. The exact set of basis functions used is often specified by an abbreviation, such as STO—3G or 6—311++g. Basis sets are discussed further in Chapters 10 and 28. 

STO—nG n = 2—6) n primitives per shell per occupied angular momentum s,p,d). STO—3G is heavily used for large systems and qualitative results. The STO—3G functions have been made for H with three primitives (3.v) through Xe(15.vl2/i6r/). STO—2G is seldom used due to the poor quality of its results. The larger STO—nG sets are seldom used because they have too little flexibility. 

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