Lobe functions, Gaussian

A minimal basis set of STO (expanded in Gaussian lobe functions) was used, and the least-energy pathway determined, assuming fixed values for some of the parameters. The complete optimization is not practicable for systems of this size and most surface studies make physically reasonable approximations to reduce the number of variables. The computed pathway is a non-least-motion rearrangement. The implications of the results with respect to the stability of F2NOF relative to F3NO were also discussed. 

The Gaussian lobe function method was introduced by Preuss and developed for routine calculations by Whitten. The contraction of Gaussian lobe function (GLF) basis sets is made along the same lines as with Cartesian GTF s. As regards the primitives, the s-type functions are expressed in the usual way. But the primitives of p, d, f,. .. types are expressed as linear combinations of s-Gaussians (lobe functions) placed at different points so as to retain the proper symmetry (see Fig. 2,4 ). Thus, a p-type function on nucleus A may be... 

Gaussian lobe functions representation Other than LCAO Methods. ... 

Our first computer implementation of Eq. 31 was used to evaluate the difference between the energy of the total system and that of the environment (Es pa, Pu Ehk[pb ) at the LDA level50, ft was developed as an interface for hybrid quantum mechanics/classical molecular dynamics simulations52,50,51. The atomic basis sets used in this implementations were restricted to have the form of gaussian lobe functions introduced by Whitten115. 

In other cases, as for example in the study of cis-trans isomerization of glyoxal i68), the basis was constructed upon gaussian lobe functions, as prescribed by Whitten 16 ). 

Li+ + H2 (H2 distance close to equilibrium) SCF + estimate of correlation energy (extended sp basis of Gaussian lobe functions) 2 60... 

Peyerimhoff and Buenker [24] calculated the ground and certain closed-shell excited states. Their SCF-MO calculation used Whitten s Gaussian-lobe functions [25], with the N-N separation fixed at 1.15 A (2.18 a.u.). Their results for N3... 

Calculations using Gaussian lobe functions (47, 48, 85) are not used in modem program packages. However, since it is not possible to carry out a spreadsheet calculation with higher order Gaussian functions, because the function library of the EXCEL software does not include the derivatives of the Error Function, a simple Gaussian lobe calculation illustrates well the effect of polarization functions. 

The above inequality, which was first derived by Ahlrichs, provides an upper bound for the magnitudes of the [ssjss] integrals in terms of a product of two quantities that can be readily evaluated. Unfortunately, the inequality [22] does not hold for other types of ERIs, and therefore it can be rigorously used only for the Gaussian lobe functions. Despite this limitation, the estimate [22] was successfully applied in prescreening of all ERIs by Cremer and Gauss. Another nonrigorous estimate was derived and used by Almlof et al. ... 

J. L. Whitten, Gaussian lobe function expansions of Hartree-Fock solutions for the first-row atoms and ethylene, J, Chem. Phys. 44 359 (1966). 

A few ab initio SCF-MO calculations showed that i is very sensitive to changes in basis set. Minimal basis sets of Slater and of Gaussian lobe functions gave i = +0.656 [2, 3] and +0.506... 

The rnethod used constructs the one-electron Bloch orbitals as a linear combination of a double-C (split-shell) type atomic basis set, i.e., 10 and 18 contracted atomic orbitals are applied on atoms N and S, respectively. These atomic orbitals themselves are taken as contractions of Gaussian lobe functions using 25 and 46 primitive functions for atoms N and S, respectively. The exponents of the Gaussians as well as the contraction coefficients were taken from the paper of Roos et Based... 

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