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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 ...
Given an eigenvalue λ, every corresponding Jordan block gives rise to a Jordan chain of linearly independent vectors p i, i = 1, ..., b, where b is the size of the Jordan block. The generator , or lead vector , p b of the chain is a generalized eigenvector such that ( A − λ I ) b p b = 0 {\displaystyle (A-\lambda I)^{b}p_{b}=0} .
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 ...
Some authors use the term Gaussian elimination to refer only to the procedure until the matrix is in echelon form, and use the term Gauss–Jordan elimination to refer to the procedure which ends in reduced echelon form. The name is used because it is a variation of Gaussian elimination as described by Wilhelm Jordan in 1888. However, the ...
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 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 ...
The Vienna Ab initio Simulation Package, better known as VASP, is a package written primarily in Fortran for performing ab initio quantum mechanical calculations using either Vanderbilt pseudopotentials, or the projector augmented wave method, and a plane wave basis set. [2]
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 ...