Mulliken analysis, wave functions

The Lowdin population analysis scheme was created to circumvent some of the unreasonable orbital populations predicted by the Mulliken scheme, which it does. It is different in that the atomic orbitals are first transformed into an orthogonal set, and the molecular orbital coefficients are transformed to give the representation of the wave function in this new basis. This is less often used since it requires more computational work to complete the orthogonalization and has been incorporated into fewer software packages. The results are still basis-set-dependent. 

Mulliken analysis is most often used with semiempirical wave functions. 

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 band-structure code, called BAND, also uses STO basis sets with STO fit functions or numerical atomic orbitals. Periodicity can be included in one, two, or three dimensions. No geometry optimization is available for band-structure calculations. The wave function can be decomposed into Mulliken, DOS, PDOS, and COOP plots. Form factors and charge analysis may also be generated. 

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 ... 

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... 

Hiickel s application of this approach to the aromatic compounds gave new confidence to those physicists and chemists following up on the Hund-Mulliken analysis. It was regarded by many people as the simplest of the quantum mechanical valence-bond methods based on the Schrodinger equation. 66 Hiickel s was part of a series of applications of the method of linear combination of atom wave functions (atomic orbitals), a method that Felix Bloch had extended from H2+ to metals in 1928 and that Fowler s student, Lennard-Jones, had further developed for diatomic molecules in 1929. Now Hiickel extended the method to polyatomic molecules.67... 

Mulliken, R. S. (1955) Electronic population analysis on LCAO-MO molecular wave functions. I. J. Chem. Phys. 23, 1833-1840. 

The degree of bonding between the atoms is a further criterion for stability and a Mulliken-type population analysis was also carried out for the optimized structure of (5) and (6) with the HFS wave function obtained for these geometries. 

The Mulliken population analysis is a simple way of gaining some useful information about the distribution of the electrons in the molecule. Let us assume again a UHF wave function ... 

Mulliken, R.S., Criteria for the construction of good self-consistent-field molecular orbital wave functions, and the significance of L.A.A.O.M.O. population analysis, J. Chem. Phys., 36, 3428-3439, 1962. 

Here we note that only a single polarizability or susceptibility exists for any system. The reconstruction from local contributions is in fact an abstraction, the result of which depends on the detail wanted macroscopic with local susceptibilities or microscopic with local polarizabilities and—more importantly—on the partitioning of such properties. However, experimental chemists are used to such procedures from well-chosen series of compounds they derive bond energies as local contributions to heats of formation and ionic radii from crystal structures. Theoretical chemists obtain atomic charges from, e.g., a Mulliken analysis of their wave functions. We are able, following similar reasoning, to construct molecular polarizabilities from atomic ones [38,60], although there is formally no connection between them. In an opposite direction we can decompose a molecular polarizability into a many-center... 

Mulliken, R.S., Electronic population analysis on ICAO—MO molecular wave functions II. Overlap populations, bond orders, and covalent bond energies. J.Chem.Phys. (1955) 23 1841-1846. 

The other major influence in the work has come from the papers of Mulliken and his co-workers, in particular the series (14) on population analysis of LCAO-MO wave functions and their relation to energies of atomization. As Mulliken suggested (14), we have attempted to relate... 

One set of quantities often evaluated from the ground-state wave function that are not quantum-mechanical observables are the various components of the Mulliken population analysis (Mulliken, 1955, 1962). For example, we could define the net Mulliken charge on an atom A as ... 

In calculating a theoretical photoelectron spectmm, the atomic ionization cross section a. is usually taken so far from the theoretical values calculated for a neutral free atom in the ground state. However, the MO calculation by DV-Xa method is carried out self consistently and provides Q. by Mulliken population analysis using the SCF MO wave function calculated. In the present calculations, the atomic orbital Xj used for the basis function flexibly expands or contracts according to reorganization of the charge density on the atom in molecule in the self-consistent field. Furthermore, excited state atomic orbitals are sometimes added to extend the basis set. In such a case, the estimation of peak intensity of the photoionization using the data of Oj previously published is not adequate. Thus a calculation of the photoionization cross section is required for the atomic orbital used in the SCF calculation in order... 

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