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The most common minimal basis set is STO-nG, where n is an integer. The STO-nG basis sets are derived from a minimal Slater-type orbital basis set, with n representing the number of Gaussian primitive functions used to represent each Slater-type orbital. Minimal basis sets typically give rough results that are insufficient for research-quality ...
STO-nG basis sets are minimal basis sets, where primitive Gaussian orbitals are fitted to a single Slater-type orbital (STO).originally took the values 2 – 6. They were first proposed by John Pople. A minimum basis set is where only sufficient orbitals are used to contain all the electrons in the neutral atom. Thus for the hydrogen atom, only a single 1s orbital is needed, while for a carbon ...
A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator. The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry)).
The use of Gaussian orbitals in electronic structure theory (instead of the more physical Slater-type orbitals) was first proposed by Boys [2] in 1950. The principal reason for the use of Gaussian basis functions in molecular quantum chemical calculations is the 'Gaussian Product Theorem', which guarantees that the product of two GTOs centered on two different atoms is a finite sum of ...
The fact that products of two STOs on distinct atoms are more difficult to express than those of Gaussian functions (which give a displaced Gaussian) has led many to expand them in terms of Gaussians. [4] Analytical ab initio software for polyatomic molecules has been developed, e.g., STOP: a Slater Type Orbital Package in 1996. [5]
The effect of diffuse functions is assessed using an MP4 calculation with the 6-311+G(d, p) basis set. The largest basis set is 6-311+G(3df,2p) used at the MP2 level of theory. A Hartree–Fock geometry optimization with the 6-31G(d) basis set used to give a geometry for: A frequency calculation with the 6-31G(d) basis set to obtain the zero ...
Various basis sets are used in practice, most of which are composed of Gaussian functions. In some applications, an orthogonalization method such as the Gram–Schmidt process is performed in order to produce a set of orthogonal basis functions.
A Gaussian process can be used as a prior probability distribution over functions in Bayesian inference. [7] [24] Given any set of N points in the desired domain of your functions, take a multivariate Gaussian whose covariance matrix parameter is the Gram matrix of your N points with some desired kernel, and sample from that Gaussian. For ...