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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 ...
Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory. Gaussian beams are used in optical systems, microwave systems and lasers. In scale space representation, Gaussian functions are used as smoothing kernels for generating multi-scale representations in computer vision and image processing.
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 ...
In the context of the Hartree–Fock method, the best possible solution is at the Hartree–Fock limit; i.e., the limit of the Hartree–Fock energy as the basis set approaches completeness. (The other is the full-CI limit, where the last two approximations of the Hartree–Fock theory as described above are completely undone. It is only when ...
(The mixed basis sets are realised by introducing "ghost orbitals", basis set functions which have no electrons or protons. [2] It however has been shown that there is an inherent danger in using counterpoise corrected energy surfaces, due to the inconsistent effect of the correction in different areas of the energy surface. [ 3 ] )
In probability theory particularly in the Malliavin calculus, a Gaussian probability space is a probability space together with a Hilbert space of mean zero, real-valued Gaussian random variables. Important examples include the classical or abstract Wiener space with some suitable collection of Gaussian random variables. [1] [2]
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 ...
It is a special case of the configuration interaction method in which all Slater determinants (or configuration state functions, CSFs) of the proper symmetry are included in the variational procedure (i.e., all Slater determinants obtained by exciting all possible electrons to all possible virtual orbitals, orbitals which are unoccupied in the electronic ground state configuration).