P-type Gaussian

Table 1.4 Erpotients and contiaction coefficients for the three s-type and the two p-type Gaussian functions in the t >is s t of Dunning far nitrogen Dunning 1970],...

IG, 6-3IG. The 6-3IG Basis Set in which non-hydrogen atoms are supplemented by d-type Gaussians and (for 6-3IG ) hydrogen atoms are supplemented by p-type Gaussians (Polarization Functions). 6-3IG and 6-3IG are Polarization Basis Sets. 

G, 6-31+G. Basis Sets that are identical to 6-31G and 6-3IG except that all non-hydrogen atoms are supplemented by diffuse s and p-type Gaussians (Diffuse Functions). 6-31+G and 6-31+G are supplemented Polarization Basis Sets. 

The 6-3IG basis differs from the 6-31G basis by the addition of one set of uncontracted p-type Gaussian primitives for each H. A standard Gaussian exponent of a = 1.1 has been suggested for these functions. The... 

The set made by the three p-type functions in a Gaussian type orbital (GTO) framework is sufQciently simple to be used as an example but at the same time provides a yet unexplored context, which can show how QS techniques can handle quantum system states, even degenerate ones. The set of p-type Gaussian functions can be collected into a vector, which can be associated in turn to three degenerate model wavefunctions Ip) = qr exp(-alrP) where q is a normalization factor, r = (x,y,z), and a is an arbitrary positive-definite parameter. The set of attached DF can be also written as a vector Id) = q (r r) exp (-2alrP), where the position vector product symbol is defined employing the inward product (r r) = Thus, the components... 

The sputter sectioning technique was applied to specimens which were essentially dislocation-free, and p-type. Gaussian penetration profiles were observed, and diffusion coefficients for 1320 to 1660K were obtained. The results could be described by ... 

Species with significant electron density far removed from the nuclear centers such as anions, lone pairs, and excited states require diffuse functions to account for the outermost weakly bound electrons. The addition of diffuse s- and p-type Gaussian functions to nonhydrogen atoms is denoted by a plus sign, as in 3-21 -i- G. 

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