Molecular orbitals Mulliken

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. 

Energy, geometry, dipole moment, and the electrostatic potential all have a clear relation to experimental values. Calculated atomic charges are a different matter. There are various ways to define atomic charges. HyperChem uses Mulliken atomic charges, which are commonly used in Molecular Orbital theory. These quantities have only an approximate relation to experiment their values are sensitive to the basis set and to the method of calculation. 

R. S. Mulliken (Chicago) fundamental work concerning chemical bonds and the electronic structure of molecules by the molecular orbital method. 

Coulson, C. A., and Jacobs, J., Proc. Roy. Soc. London) A206, 287, Electronic levels in simple conjugated systems. II. Butadiene." Best possible molecular orbital is obtained. The idea is the same as that developed by Roothaan (1951). The work has been done quite independently with the similar work by Parr and Mulliken (1950). 

Mulliken, R.S. Electronic Structures of Molecules. XI. Electroaffinity, Molecular Orbitals and Dipole Moments J. Chem. Phys. 1935, 3, 573-585. 

In more detail, the interaction energy between donor and acceptor is determined by the ionisation potential of the donor and the electron affinity of the acceptor. The interaction energy increases with lowering of the former and raising of the latter. In the Mulliken picture (Scheme 2) it refers to a raising of the HOMO (highest occupied molecular orbital) and lowering of the LUMO (lowest unoccupied molecular orbital). Alternatively to this picture donor-acceptor formation can be viewed in a Born-Haber cycle, within two different steps (Scheme 3). 

The analytical determination of the derivative dEtotldrir of the total energy Etot with respect to population n, of the r-th molecular orbital is a very complicated task in the case of methods like the BMV one for three reasons (a), those methods assume that the atomic orbital (AO) basis is non-orthogonal (b), they involve nonlinear expressions in the AO populations (c) the latter may have to be determined as Mulliken or Lbwdin population, if they must have a physical significance [6]. The rest of this paper is devoted to the presentation of that derivation on a scheme having the essential features of the BMV scheme, but simplified to keep control of the relation between the symbols introduced and their physical significance. Before devoting ourselves to that derivation, however, we with to mention the reason why the MO occupation should be treated in certain problems as a continuous variable. 

The name molecular orbital was coined by Robert S. Mulliken. 

Quotation from Robert Mulliken, "Spectroscopy, Molecular Orbitals, and Chemical Bonding," Nobel Lectures. Chemistry. 19631970 (Amsterdam Elsevier, 1972) 131160, on 137. See Friedrich Hund, "Zur Deutung der Molekulspektren. IV." ZP 40 (1927) 742764, 42 (1927) 93120, 43 (1927) 805826 and Oyvind Burrau, "Berechnung des Energiewertes des Wasserstoff-Molekel-Ions (H2+) im Normalzustand," Danske Videnskabernes Selskab. Mat.-fys. Meddelser 7 (1927) 14. 

Robert Mulliken, "Spectroscopy, Molecular Orbitals, and Chemical Bonding," 133138, 141142. 

Mulliken introduced the term "orbital" distinct from "orbital wave function" in 1932 in the second of fourteen papers carrying the general title, "Electronic Structures of Polyatomic Molecules and Valence." Mulliken defined atomic orbitals (AOs) and molecular orbitals (MOs) as something like the... 

Mulliken, Life, 90. On the "orbital," Mulliken wrote in 1932 "From here on, one-electron orbital wave functions will be referred to for brevity as orbitals. The method followed here will be to describe unshared electrons always in terms of atomic orbitals but to use molecular orbitals for shared electrons." In Robert Mulliken, "Electronic Structures of Polyatomic Molecules and Valence," Physical Review 41 (1932) 4971, on 50. 

Using the molecular orbital method, Coulson showed how certain electrons in benzene, namely, the p electrons, can move over the whole molecule instead of being restricted to the region between two particular atoms. 93 Coulson, collaborating later with Longuet-Higgins and the French theoreticians Pascaline and Raymond Daudel and Alberte and Bernard Pullman, was to become a major presence in quantum chemistry. But on the whole, Coulson said, he was inclined to characterize the period from 1933 until the end of the Second World War as the "Mulliken Era. "94... 

Practitioners of quantum chemistry employed both the visual imagery of nineteenth-century theoretical chemists like Kekule and Crum Brown and the abstract symbolism of twentieth-century mathematical physicists like Dirac and Schrodinger. Pauling s Nature of the Chemical Bond abounded in pictures of hexagons, tetrahedrons, spheres, and dumbbells. Mulliken s 1948 memoir on the theory of molecular orbitals included a list of 120 entries for symbols and words having exact definitions and usages in the new mathematical language of quantum chemistry. 

Based on Mulliken population analysis of ab initio molecular orbital wavefunctions for inner-sphere complexes (28). 

The first calculations on a two-electron bond was undertaken by Heitler and London for the H2 molecule and led to what is known as the valence bond approach. While the valence bond approach gained general acceptance in the chemical community, Robert S. Mulliken and others developed the molecular orbital approach for solving the electronic structure problem for molecules. The molecular orbital approach for molecules is the analogue of the atomic orbital approach for atoms. Each electron is subject to the electric field created by the nuclei plus that of the other electrons. Thus, one was led to a Hartree-Fock approach for molecules just as one had been for atoms. The molecular orbitals were written as linear combinations of atomic orbitals (i.e. hydrogen atom type atomic orbitals). The integrals that needed to be calculated presented great difficulty and the computations needed were... 

Mulliken R. S. (1934). A new electroaffinity scale together with data on valence states and on valence ionization potentials and electron affinities. J. Chem. Phys., 2 782-793. Mulliken R. S. (1935). Electronic structure of molecules, XI Electroaffinity, molecular orbitals, and dipole moments. J. Chem. Phys., 3 573-591. 

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