User:Malik Zeshan

In chemistry, molecular orbital (MO) theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.[1] In this theory, each molecule has a set of molecular orbitals, in which it is assumed that the molecular orbital wave function ψj may be written as a simple weighted sum of the n constituent atomic orbitals χi, according to the following equation:[2]

\psi_j = \sum_{i=1}^{n} c_{ij} \chi_i.

The cij coefficients may be determined numerically by substitution of this equation into the Schrödinger equation and application of the variational principle. This method is called the linear combination of atomic orbitals (LCAO) approximation and is used in computational chemistry. An additional unitary transformation can be applied on the system to accelerate the convergence in some computational schemes. Molecular orbital theory was seen as a competitor to valence bond theory in the 1930s, before it was realized that the two methods are closely related and that when extended they become equivalent. Contents

1 History 2 Overview 3 See also 4 References 5 External links

History Main article: History of quantum mechanics

Molecular orbital theory was developed, in the years after valence bond theory had been established (1927), primarily through the efforts of Friedrich Hund, Robert Mulliken, John C. Slater, and John Lennard-Jones.[3] MO theory was originally called the Hund-Mulliken theory.[4] The word orbital was introduced by Mulliken in 1932.[4] By 1933, the molecular orbital theory had been accepted as a valid and useful theory.[5] According to German physicist and physical chemist Erich Hückel, the first quantitative use of molecular orbital theory was the 1929 paper of Lennard-Jones.[6] The first accurate calculation of a molecular orbital wavefunction was that made by Charles Coulson in 1938 on the hydrogen molecule.[7] By 1950, molecular orbitals were completely defined as eigenfunctions (wave functions) of the self-consistent field Hamiltonian and it was at this point that molecular orbital theory became fully rigorous and consistent.[8] This rigorous approach is known as the Hartree–Fock method for molecules although it had its origins in calculations on atoms. In calculations on molecules, the molecular orbitals are expanded in terms of an atomic orbital basis set, leading to the Roothaan equations.[9] This led to the development of many ab initio quantum chemistry methods. In parallel, molecular orbital theory was applied in a more approximate manner using some empirically derived parameters in methods now known as semi-empirical quantum chemistry methods.[9] Overview This section needs additional citations for verification. (July 2012)

Molecular orbital (MO) theory uses a linear combination of atomic orbitals (LCAO) to represent molecular orbitals involving the whole molecule. These are often divided into bonding orbitals, anti-bonding orbitals, and non-bonding orbitals. A molecular orbital is merely a Schrödinger orbital that includes several, but often only two, nuclei. If this orbital is of the type in which the electron(s) in the orbital have a higher probability of being between nuclei than elsewhere, the orbital will be a bonding orbital, and will tend to hold the nuclei together. If the electrons tend to be present in a molecular orbital in which they spend more time elsewhere than between the nuclei, the orbital will function as an anti-bonding orbital and will actually weaken the bond. Electrons in non-bonding orbitals tend to be in deep orbitals (nearly atomic orbitals) associated almost entirely with one nucleus or the other, and thus they spend equal time between and not between nuclei. These electrons neither contribute to nor detract from bond strength.

Molecular orbitals are further divided according to the types of atomic orbitals combining to form a bond. These orbitals are results of electron-nucleus interactions that are caused by the fundamental force of electromagnetism. Chemical substances will form a bond if their orbitals become lower in energy when they interact with each other. Different chemical bonds are distinguished that differ by electron configuration (electron cloud shape) and by energy levels.

MO theory provides a global, delocalized perspective on chemical bonding. In MO theory, any electron in a molecule may be found anywhere in the molecule, since quantum conditions allow electrons to travel under the influence of an arbitrarily large number of nuclei, as long as permitted by certain quantum rules. Although in MO theory some molecular orbitals may hold electrons that are more localized between specific pairs of molecular atoms, other orbitals may hold electrons that are spread more uniformly over the molecule. Thus, overall, bonding is far more delocalized in MO theory, than is implied in valence bond (VB) theory. This makes MO theory more useful for the description of extended systems.

An example is the MO description of benzene, C6H6, which is composed of a hexagonal ring of six carbon atoms. In this molecule, 24 of the 30 total valence bonding electrons are located in 12 σ (sigma) bonding orbitals, which are located mostly between pairs of atoms (C-C or C-H), similarly to the electrons in the valence bond description. However, in benzene the remaining six bonding electrons are located in three π (pi) molecular bonding orbitals that are delocalized around the ring. Two of these electrons are in an MO that has equal contributions from all six atoms. The other four electrons are in orbitals with vertical nodes at right angles to each other. As in the VB theory, all of these six delocalized π electrons reside in a larger space that exists above and below the ring plane. All carbon-carbon bonds in benzene are chemically equivalent. In MO theory this is a direct consequence of the fact that the three molecular π orbitals combine and evenly spread the extra six electrons over six carbon atoms.[10]

In molecules such as methane, CH4, the eight valence electrons are found in four MOs that are spread out over all five atoms. However, it is possible to approximate the MOs with four localized orbitals similar in shape to the sp3 hybrid orbitals predicted by VB theory. This is often adequate for σ bonds, but is not possible for the π orbitals. However, the delocalized MO description is more appropriate for ionization and spectroscopic predictions. When methane is ionized, a single electron is taken from the MO, which surrounds the whole molecule, weakening all four bonds equally. VB theory would predict that one electron is removed for an sp3 orbital, resulting in the need for resonance between four valence bond structures, each of which has a single one-electron bond and three two-electron bonds.

As in benzene, in substances such as beta carotene, chlorophyll, or heme, some electrons in the π orbitals are spread out in molecular orbitals over long distances in a molecule, resulting in light absorption in lower energies (the visible spectrum), which accounts for the characteristic colours of these substances. This and other spectroscopic data for molecules are better explained in MO theory, with an emphasis on electronic states associated with multicenter orbitals, including mixing of orbitals premised on principles of orbital symmetry matching. The same MO principles also more naturally explain some electrical phenomena, such as high electrical conductivity in the planar direction of the hexagonal atomic sheets that exist in graphite. In MO theory, "resonance" is a natural consequence of symmetry. For example, in graphite, as in benzene, it is not necessary to invoke the sp2 hybridization and resonance of VB theory, in order to explain electrical conduction. Instead, MO theory recognizes that some electrons in the graphite atomic sheets are completely delocalized over arbitrary distances, and reside in very large molecular orbitals that cover an entire graphite sheet, and some electrons are thus as free to move and therefore conduct electricity in the sheet plane, as if they resided in a metal. See also

Ab initio quantum chemistry methods Atomic orbital Configuration interaction Coupled cluster Hartree–Fock method

Molecular orbital Molecular orbital diagram Møller–Plesset perturbation theory Quantum chemistry computer programs Semi-empirical quantum chemistry methods cis effect Addition to pi ligands