Gaussian exponent

Diffuse functions are those functions with small Gaussian exponents, thus describing the wave function far from the nucleus. It is common to add additional diffuse functions to a basis. The most frequent reason for doing this is to describe orbitals with a large spatial extent, such as the HOMO of an anion or Rydberg orbitals. Adding diffuse functions can also result in a greater tendency to develop basis set superposition error (BSSE), as described later in this chapter. 

The breakthrough for molecular applications came with Boys s classic paper (1950) on the use of Gaussian-type orbitals (GTOs). These basis functions have an exponential dependence of exp (— (ar /al)) rather than exp(—( r/ao))-The quantity a is called the Gaussian exponent. Normalized Is and 2p GTOs are... 

Gaussian exponents are usually stored internally it isn t necessary to know the details. 

TABLE 2. Polarization and diffuse Gaussian exponents 3 Polarization... 

Because the N2 molecule in the complex is still expected to have partial multiple bond character, the d-type functions could be needed. Therefore, d-type function have been added to nitrogen atoms (using a Gaussian exponent of 0.8) of the dinitrogen molecule. Our preliminary test of the effect of phosphorus atom d-type functions on the calculated Zr-PH3 bond lengths of model complexes A1 and A7 showed that the influence of d-type functions on the P atom is insignificant. Therefore, here we will not include d-type of functions for P-atoms. 

Expansion coefficients and Gaussian exponents for 3-2IG and 6-31G representations have been determined by Hartree-Fock energy minimization on atomic ground states. In the case of 6-3IIG representations, minimizations have been carried out at the MP2 level rather than at the Hartree-Fock level. 

Attempts to achieve perfection may give poor results. Normal AOs are optimized for neutral molecules, so they are too small to give good descriptions of anions, particularly in the gas phase. A better model is obtained by a slight contraction of the Gaussian exponents. However, if these exponents had been completely optimized, the anions would become so stable that they would lose all reactivity for example, a hydride ion H will arrive at a carbonyl group, bounce on it and go away without reacting ... 

Note that the same number of Gaussians, N, is used for each STO and that common Gaussian exponents are shared between ns and np or-... 

As regards the hydrogen 2p Gaussian exponent, a reasonable choice 99 121... 

Gaussian exponents as noted with polarization functions in Section 2,F,... 

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