Mulliken-population analysis

In spite of its deficiencies, the Mulliken population scheme is very popular. One reason is that it is very easy to implement so it is available in many software packages. Probably the most important reason for its popularity is the fact 

There is some ambiguity about Mulliken population analysis in the literature. This is because various software packages print different portions of the analysis and may name them slightly differently. The description here follows some of the more common conventions. 

A molecular orbital is a linear combination of basis functions. Normalization requires that the integral of a molecular orbital squared is equal to 1. The square of a molecular orbital gives many terms, some of which are the square of a basis function and others are products of basis functions, which yield the overlap when integrated. Thus, the orbital integral is actually a sum of integrals over one or two center basis functions. 

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Mulliken population analysis is a trivial calculation to perform once a self-consistent field has been established and the elements of the density matrix have been determined. 

Recent progress in this field has been made in predicting individual atoms contribution to optical activity. This is done using a wave-functioning, partitioning technique roughly analogous to Mulliken population analysis. 

The consistent total energy makes it possible to compute singlet-triplet gaps using RHF for the singlet and the half-electron calculation for the triplet. Koopman s theorem is not followed for half-electron calculations. Also, no spin densities can be obtained. The Mulliken population analysis is usually fairly reasonable. 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

By default, Gaussian jobs perform a Mulliken population analysis, which partitions the total charge among the atoms in the molecule. Here is the key part of output for formaldehyde ... 

Let s compare the Mulliken population analysis for ethylene and fluoroethylene ... 

This exercise will examine other ways of computing charges other than Mulliken population analysis. Since atomic charge is not a quantum mechanical observable, all methods for computing it are necessarily arbitrary. We ll explore the relative merits of various schemes for partitioning the electron density among the atoms in a molecular system. 

The Mulliken scheme places the negative charge more or less evenly on the three carbons, and splits the positive charge among the hydrogens. Mulliken population analysis computes charges by dividing orbital overlap evenly between the two atoms involved. 

The KS-LCAO orbitals may be visualized by all the popular methods, or one may just focus on the Mulliken population analysis indices (Figure 13.5). 

Population analysis with semi-empirical methods requires a special comment. These methods normally employ the ZDO approximation, i.e. the overlap S is a unit matrix. The population analysis can therefore be performed directly on the density matrix. In some cases, however, a Mulliken population analysis is performed with DS, which requires an explicit calculation of the S matrix. 

The quality of the ) states has been tested through their energy and also their transition moment. Moreover from the natural orbitals and Mulliken populations analysis, we have determined the predominant electronic configuration of each ) state and its Rydberg character. Such an analysis is particularly interesting since it explains the contribution of each ) to the calculation of the static or dynamic polarizability it allows a better understanding in the case of the CO molecule the difficulty of the calculation and the wide range of published values for the parallel component while the computation of the perpendicular component is easier. In effect in the case of CO ... 

An example of quantum mechanical schemes is the oldest and most widely used Mulliken population analysis [1], which simply divides the part of the electron density localized between two atoms, the overlap population that identifies a bond, equally between the two atoms of a bond. Alternatively, empirical methods to allocate atomic charges to directly bonded atoms in a reasonable way use appropriate rules which combine the atomic electronegativities with experimental structural information on the bonds linking the atoms of interest. A widely used approach included in many programs is the Gasteiger-Hiickel scheme [1]. 

The information obtainable upon solution of the eigenvalue problem includes the orbital energies eK and the corresponding wave function as a linear combination of the atomic basis set xi- The wave functions can then be subjected to a Mulliken population analysis<88) to provide the overlap populations Ptj ... 

Stuchebrukhov AA (1997) Tunneling currents in proteins nonorthogonal atomic basis sets and Mulliken population analysis. J Chem Phys 107(16) 6495-6498... 

Two general techniques are used to extract charges from wave functions - the Mulliken population analysis, based on partitioning the electron distribution, and the ESP method, based on fitting properties which depend on the electron distribution to a model which replaces this distribution by a set of atomic... 

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