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calculation of () Radial distribution function for the Lennard-Jones model fluid at =, =.. In statistical mechanics, the radial distribution function, (or pair correlation function) () in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle.
There are typically three mathematical forms for the radial functions R(r) which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons: The hydrogen-like orbitals are derived from the exact solutions of the Schrödinger equation for one electron and a nucleus, for a hydrogen-like atom.
The radial distribution function (RDF), also termed the pair distribution function or the pair correlation function, is a measure of local structuring in a mixture. The RDF between components and positioned at and , respectively, is defined as:
Hydrogen atomic orbitals of different energy levels. The more opaque areas are where one is most likely to find an electron at any given time. In quantum mechanics, a spherically symmetric potential is a system of which the potential only depends on the radial distance from the spherical center and a location in space.
Using cc-pVDZ, orbitals are [1s, 2s, 2p, 3s, 3s, 3p, 3p, 3d'] (where ' represents the added in polarisation orbitals), with 4 s orbitals (4 basis functions), 3 sets of p orbitals (3 × 3 = 9 basis functions), and 1 set of d orbitals (5 basis functions). Adding up the basis functions gives a total of 18 functions for Ar with the cc-pVDZ basis-set.
If the molecule has some symmetry, the degenerate atomic orbitals (with the same atomic energy) are grouped in linear combinations (called symmetry-adapted atomic orbitals (SO)), which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations (SALC).
Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. They are named after the physicist John C. Slater , who introduced them in 1930.
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 ...