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The radial distribution function is of fundamental importance since it can be used, using the Kirkwood–Buff solution theory, to link the microscopic details to macroscopic properties. Moreover, by the reversion of the Kirkwood–Buff theory, it is possible to attain the microscopic details of the radial distribution function from the ...
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:
One common correlation function is the radial distribution function which is seen often in statistical mechanics and fluid mechanics. The correlation function can be calculated in exactly solvable models (one-dimensional Bose gas, spin chains, Hubbard model) by means of Quantum inverse scattering method and Bethe ansatz. In an isotropic XY ...
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.
In statistical mechanics the hypernetted-chain equation is a closure relation to solve the Ornstein–Zernike equation which relates the direct correlation function to the total correlation function. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. It is given by:
When examining a system computationally one may be interested in knowing how the free energy changes as a function of some inter- or intramolecular coordinate (such as the distance between two atoms or a torsional angle). The free energy surface along the chosen coordinate is referred to as the potential of mean force (PMF). If the system of ...
Approximate solutions for the pair distribution function in the extensional and compressional sectors of shear flow and hence the angular-averaged radial distribution function can be obtained, as shown in Ref., [6] which are in good parameter-free agreement with numerical data up to packing fractions .