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Gaussian-type primitives

Sometimes it turns out that we need to include a number of polarization functions, not just one of each type. The notation 4-31G(3d, 2p) indicates a standard 4-31G basis set augmented with three d-type primitive Cartesian Gaussians per centre and two p-type primitives on every hydrogen atom. Again, details of the... [Pg.170]

On the convergence of the many-body perturbation theory second-order energy component for negative ions using systematically constructed basis sets of primitive Gaussian-type functions... [Pg.283]

Using the F ion as a prototype, the convergence of the many-body perturbation theory second-order energy component for negative ions is studied when a systematic procedure for the construction of even-tempered btisis sets of primitive Gaussian type functions is employed. Calculations are reported for sequences of even-tempered basis sets originally developed for neutral atoms and for basis sets containing supplementary diffuse functions. [Pg.283]

Figure 2.2. Radial dependence of basis functions a) correct exponential decay (STO) (b) primitive Gaussian-type function (solid line) vs. an STO (dotted line) (c) least-squares expansion of the STO in terms of three Gaussian-type orbitals (STO-3G). Figure 2.2. Radial dependence of basis functions a) correct exponential decay (STO) (b) primitive Gaussian-type function (solid line) vs. an STO (dotted line) (c) least-squares expansion of the STO in terms of three Gaussian-type orbitals (STO-3G).
The molecular electron density function needed for EP calculation can be obtained through ab initio as well as various semi-empirical methods. Since ab initio calculations are not economical for large molecules (several hundred atoms), the use of well-parameterized semi-empirical methods are still justified. When semi-empirical methods are used the three-center potential integrals usually disappear, and therefore the electronic contribution can be easily calculated by Slater-type orbitals. In ab initio methods (primitive or contracted) Gaussian-type orbitals are used for calculating the three-center integrals because their calculations are clumsy with Slater-type orbitals. [Pg.48]

For computational reasons only (particularly for ab initio calculations), the atomic orbitals are usually expressed as a linear combination of primitive functions centered on the atom (Eq. [3]). These primitives are typically Gaussian-type functions, but Slater-type functions have also been used. [Pg.172]

For a given molecular structure characterised by initial nuclear coordinates the basis set functions are attributed to each atom. These simulate the behaviour of atomic orbitals and are given in terms of a (fixed) linear combination of the primitive (usually Gaussian type) functions p as follows... [Pg.21]

Appendix 1 Fitting of 5-type Primitive Gaussian Orbitals that Best Reproduce Two-Electron Coulomb Integrals over 5-Type Slater Orbitals... [Pg.411]

In this appendix, we describe how we found the exponents given in Table 1, which are of x-type primitive Gaussian orbitals such that the two-electron Coulomb integrals over them best reproduce those over s-type Slater orbitals. We construct... [Pg.411]

II2 = s/if f)i is the L -norm, is the two-electron Coulomb integral over, r-type primitive Gaussian orbitals... [Pg.412]

In this equation, the original Gaussian-type functions are called primitive functions to distinguish them from the contracted ones. The primitive functions are specified only by the orbital exponent, a p, contracted coefficient, c p, and coordinate vector of the center of the function, Ra. By using these contracted Gaussian-type functions as basis functions, it was expected that highly accurate results could be obtained with far fewer basis functions. [Pg.50]


See other pages where Gaussian-type primitives is mentioned: [Pg.144]    [Pg.256]    [Pg.517]    [Pg.144]    [Pg.256]    [Pg.517]    [Pg.310]    [Pg.116]    [Pg.712]    [Pg.380]    [Pg.284]    [Pg.307]    [Pg.244]    [Pg.181]    [Pg.100]    [Pg.461]    [Pg.267]    [Pg.164]    [Pg.102]    [Pg.22]    [Pg.24]    [Pg.221]    [Pg.719]    [Pg.184]    [Pg.410]    [Pg.145]    [Pg.285]    [Pg.194]    [Pg.399]    [Pg.489]    [Pg.489]   
See also in sourсe #XX -- [ Pg.144 ]




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Gaussian type

Gaussian, primitive

Primitive Gaussians

Primitives

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