Is Li2 diatomic or paramagnetic

Molecular orbital theory

Molecular orbital theory, MO method (Abbreviation of engl. molecular Orbital method), a quantum mechanical approximation method for calculating the electronic structure and the energy of molecules, which was mainly developed by Hund, Mulliken, Lennard-Jones and Hückel (1927-29). Analogous to the central field model of atoms, one considers an electron that moves in an effective potential of the nuclei and the other electrons. The resulting one-electron states of the molecule are referred to as Molecular orbitals (Abbr. MO) φ. They extend over the entire molecule and are characterized by an orbital energy. The occupation of the energetically lowest molecular orbitals while observing the Pauli principle leads to the electron configuration of the molecules in the ground state. The mathematical representation of the molecular orbitals φ as a linear combination of atomic orbitals χi represents a suitable approximation (MO-LCAO approach, Abbr. Of molecular Orbitals - linear ccombination of atomic Orbitals):



.

In the variation method, the coefficients ci chosen so that the energy of the overall system assumes a minimum value. The principle of M. can be most easily applied to homonuclear diatomic molecules, e.g. B. for the H2Molecule, demonstrate. The combination of the 1s orbitals of the two hydrogen atoms leads to two molecular orbitals φ ± = N±a ± χb), in which N± denotes the normalization factor of the plus or minus combination. The corresponding orbital energies ε+ and ε- have a lower or higher energy than the energy of the atomic orbitals. Therefore one denotes φ+ as binding and φ- as loosening (antibonding) Molecular orbital. In the ground state of the hydrogen molecule, both electrons occupy the binding molecular orbital (Fig. 1). This can be used to explain the chemical bond in the hydrogen molecule. The binding energy corresponds to twice the value of Δε. The extent of the splitting of the orbital energies is the size of the overlap proportional to the atomic orbitals involved. Mathematically, the overlap between the atomic orbitals becomes χa, χb

by the Overlap integral S.from = ∫ χaχb dv expressed. The overlap is large when the atomic orbitals in the same area of ​​space have significant contributions. Analogous to the 1s orbitals, other atomic orbitals can also combine to form molecular orbitals.



Molecular orbital theory. Fig. 1: Energy of the molecular orbitals for H2.

Due to the symmetry and directional dependence of the atomic orbitals determined by the angular parts (atomic model), a distinction is made between various possibilities of overlap. The combination of orbitals arranged rotationally symmetrical to the bond axis yields σ-Molecular orbitals. They are characterized by an area of ​​overlap in the bond axis. The interaction of atomic orbitals, which have an anti-symmetry plane in the bond axis, leads to π-Molecular orbitals. They form two overlapping areas outside the bond axis, which are separated by a nodal plane. If there are four overlapping areas outside the bond axis, which are separated by two vertically aligned nodal planes, then there is a δ-Molecular orbital in front. The bonds formed in this way are called σ-, π- or δ-binding designated. The loosening molecular orbitals are also marked with an asterisk, e.g. B. σ *, π *, δ *. In addition to the nodal areas of the atomic orbitals involved, they also have an additional nodal area between the atoms perpendicular to the core connection axis. Some combinations of atomic orbitals to molecular orbitals are given in Fig. 2. When combining two atomic orbitals with different symmetry with respect to the bond axis, the overlap integral is zero and they cannot jointly participate in a molecular orbital (Fig. 3). Based on the overlap possibilities of the atomic orbitals, the molecular orbital treatment can be applied to homonuclear two atomic molecules of elements of the 2nd period (Li2, B2, C2, N2, O2, F2) can be expanded.