Molecular orbital theory
In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century.
See also: Molecular orbital
In molecular orbital theory, electrons in a molecule are not assigned to individual chemical bonds between atoms, but are treated as moving under the influence of the atomic nuclei in the whole molecule.[1] Quantum mechanics describes the spatial and energetic properties of electrons as molecular orbitals that surround two or more atoms in a molecule and contain valence electrons between atoms.
Molecular orbital theory revolutionized the study of chemical bonding by approximating the states of bonded electrons—the molecular orbitals—as linear combinations of atomic orbitals (LCAO). These approximations are made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the Schrödinger equation.
Molecular orbital theory and valence bond theory are the foundational theories of quantum chemistry.
History[edit]
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.[4] MO theory was originally called the Hund-Mulliken theory.[5] According to physicist and physical chemist Erich Hückel, the first quantitative use of molecular orbital theory was the 1929 paper of Lennard-Jones.[6][7] This paper predicted a triplet ground state for the dioxygen molecule which explained its paramagnetism[8] (see Molecular orbital diagram § Dioxygen) before valence bond theory, which came up with its own explanation in 1931.[9] The word orbital was introduced by Mulliken in 1932.[5] By 1933, the molecular orbital theory had been accepted as a valid and useful theory.[10]
Erich Hückel applied molecular orbital theory to unsaturated hydrocarbon molecules starting in 1931 with his Hückel molecular orbital (HMO) method for the determination of MO energies for pi electrons, which he applied to conjugated and aromatic hydrocarbons.[11][12] This method provided an explanation of the stability of molecules with six pi-electrons such as benzene.
The first accurate calculation of a molecular orbital wavefunction was that made by Charles Coulson in 1938 on the hydrogen molecule.[13] 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.[14] 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.[15] 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.[15]
The success of Molecular Orbital Theory also spawned ligand field theory, which was developed during the 1930s and 1940s as an alternative to crystal field theory.