Hund-Mulliken theory

Explain the primary difference between the Heitler-London and Hund-Mulliken theories of covalent bonding. 

Hund-Mulliken theory. Mulliken said he would have been glad to share the prize with Hund. 

For lattices with more than one atom per lattice point, combinations of Bloch sums have to be considered. In general, the LCAO approach requires that the result be the same number of MOs (COs in sohds) as the number of atomic orbitals (Bloch sums in sohds) with which was started. Thus, expressing the electron-wave functions in acrystaUine sohd as linear combinations of atomic orbitals (Bloch sums) is really the same approach used in the 1930s by Hund, Mulliken, Htickel, and others to construct MOs for discrete molecules (the LCAO-MO theory). 

VSEPR theory indicates nothing about the nature of the chemical bond (localized Heitler-London versus delocalized Hund-Mulliken). It simply predicts the geometrical shape, specifically, the X-X, M-X and/or X-M-X bond angles in the molecule. 

The problems for quantum chemists in the mid-forties were how to improve the methods of describing the electronic structure of molecules, valence theory, properties of the low excited states of small molecules, particularly aromatic hydrocarbons, and the theory of reactions. It seemed that the physics needed was by then all to hand. Quantum mechanics had been applied by Heitler, London, Slater and Pauling, and by Hund, Mulliken and Hiickei and others to the electronic structure of molecules, and there was a good basis in statistical mechanics. Although quantum electrodynamics had not yet been developed in a form convenient for treating the interaction of radiation with slow moving electrons in molecules, there were semi-classical methods that were adequate in many cases. 

Even if no integral parametrizations are introduced and the HF equations are all correctly solved, the method eventually turns out to be theoretically incomplete. Despite the correct treatment of electronic exchange (X) within Hartree-Fock theory, electronic correlation (C) is totally missing. This is easily shown for the case of the H2 molecule in which we use the bonding solution of the H2 molecular ion ( + = cr from Equation (2.15)) to build up an antisymmetrized molecular wave function. This means that we put both electrons (ri and rz) of the H2 molecule into the same ip+ orbital, and Pauli s principle is obeyed by means of the ct/ spinors. Neglecting orbital overlap and any pre-factors, for simplicity, the so-called Hund-Mulliken [124] (another name... 

German chemist Eriedrich Hund and American chemist Robert S. Mulliken propose the Hund-Mulliken interpretation of molecular spectra, which gives a description of the molecular orbital theory of bonding. 

Mulliken (1927) went on to publish a summary of Hund s theory and to provide an extensive discussion of the empirical evidence for it, which relied heavily on his own work. Hund s quantum mechanical approach to molecules found corroboration in the evidence largely gathered by Mulliken in his work in the systematization of band spectra, and Mulliken s phenomenological theory gained a legitimizing framework it did not possess before. He thought that Hund s first papers explained with... 

The fourth part deals with spectroscopy. Since this part also contains some of the papers of Hund which are relevant to the theory of the chemical bond, there is an overlap with the third part here. I have chosen to place Hund s work in the spectroscopy section, mainly because spectroscopy is what Hund set out to do. The Hund-Mulliken or molecular orbital (MO) approach to the chemical bond, some of which is piloted here, became prominent after the emergence of quantum chemistry in the United States, mainly through the series of papers by Pauling. Much of the material discussed in this section can also be found in the books by Herzberg (Herzberg 1950 Herzberg 1966). 

The molecular orbital theory of Hund, Mulliken, Herzberg, and Lennard-Jones " starts from the motion of the electron in the field of two separated H nuclei a and b), i.e., the ion The eigen-... 

R. S. Mulliken, Life of a Scientist. An Autobiographical Account of the Development of Molecular Orbital Theory, with an Introductory Memoir by Friedrich Hund, ed. B. J. Ransil, Springer-Verlag, Berlin, 1989. 

All quantum chemical calculations are based on the self-consistent field (SCF) method of Hatree and Fock (1928-1930) and the MO theory of Hund, Lennard-Jones, and Mulliken (1927-1929). A method of obtaining SCF orbitals for closed shell systems was developed independently by Roothaan and Hall in 1951. In solving the so-called Roothan equations, ab initio calculations, in contrast to semiempirical treatments, do not use experimental data other than the values of the fundamental physical constants. 

Figure 3.4. (a) The overlap of two one-electron atomic wave functions, each centered on a different atom, constitutes the Heitler-London (valence-bond) theory, (b) A one-electron molecular wave function, or molecular orbital, in the molecular orbital theory of Hund and Mulliken. 

Molecular orbital theory originated from the theoretical work of German physicist Friederich Hund (1896-1997) and its apphcation to the interpretation of the spectra of diatomic molecules by American physical chemist Robert S. MuUiken (1896-1986) (Hund, 1926, 1927a, b Mulliken, 1926, 1928a, b, 1932). Inspired by the success of Heitler and London s approach, Finklestein and Horowitz introduced the linear combination of atomic orbitals (LCAO) method for approximating the MOs (Finkelstein and Horowitz, 1928). The British physicist John Edward Lennard-Jones (1894-1954) later suggested that only valence electrons need be treated as delocalized inner electrons could be considered as remaining in atomic orbitals (Lennard-Jones, 1929). 

The success of the preceding scheme for diatomic molecules I7,i8,i , 20,21) ied Hund 22> and Mulliken 23> to apply the same theory to polyatomic molecules. In the beginning, there seemed to be no direct relation between molecular orbitals (MO s) and the bonds in a chemical formula, because MO s normally extend over the whole molecule and are not restricted to the region between two atoms. The difficulty was overcome by using equivalent localized MO s instead of the delocalized ones 24>25>. The mathematical definition of equivalent MO s was given only in 1949 by Lennard-Jones and his coworkers 26.27), but the concept of localization... 

Molecular-orbital theory, especially Hiickel theory (1931) and its extensions, is by now widely appreciated by chemists in all areas of research and teaching. This was not always so. Actually, the method of linear combinations of atomic orbitals was used by Bloch in 1928 for wave functions in crystals. Molecular wave-functions were introduced by Mulliken (1928), Hund (1928), Herzberg (1929) and Lennard-Jones (1929) for diatomic molecules, and the extensions to polyatomic molecules followed quickly thereafter. 

Ransil, B.J. 1989, Life of a scientist an autobiographical account of the development of molecular orbital theory with an introductory memoir by Friedrich Hund /Robert S. Mulliken, Springer, Berlin. 

The quantum mechanical procedure for calculating the electronic structure and physical properties of polyatomic molecules has been developed by the use of a powerful tool, the molecular orbital theory proposed by Hund and Mulliken. The theory has been applied to large molecules with considerable vigor. However, because of the difficulty of carrying out all the molecular integral calculations involved, various approximations have been used. 

In 1927, Burrau calculated the energy of Hj and Heitler and London treated the hydrogen molecule. In 1928, the Heitler-London or valence bond method was applied to many electron systems, and simultaneously Hund and Mulliken started the development of the molecular orbital theory. In 1931, Slater expressed the v/avefunctions of complex molecules in terms of Slater determinants made up of linear combinations of atomic orbitals. Thus, the Golden Age was born. 

Knowledge of the physical forces that influence the total energy of a system thus reveals the theoretical underpinnings of nearly all of experimental chemistry. In fact, much of the early activity in chemical bonding theory was the result of attempts to understand the results of molecular spectroscopy experiments. The developers of what came to be called molecular orbital theory, Robert Mulliken (US) and Friedrich Hund (Germany), established a professional and personal relationship based on their common interest in the spectra of diatomic molecules especially in the influence of isotope effects. When compared to other theories of the time, a major advantage of their theoretical approach was the ability to directly apply the results to the elucidation of molecular spectra. ... 

In subsequent independent papers, Pauling [4] and Slater [6] generalized the valence-bond treatment made for the H2 molecule to polyatomic systems as H2O, NH3, CH4 etc. .. where an atom of the first period (the second row) is linked to hydrogens by several two-electron bonds they described the valence orbitals coming from the central atom by appropriate s and p combinations known later as hybrid orbitals. At the same time Hund [7] and Mulliken [8] presented another quantum theory of valence, the molecular orbital method in LCAO form, using the spectroscopic concept of molecular configuration built from s, p, d. ..pure atomic orbitals. The actual status of the hybridization process was clarified by Van Vleck [9], who showed that the various approximations... 

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