Chemical bonding model

Chemical bonding models are theoretical models used to explain atomic bonding structure, molecular geometry, properties, and reactivity of physical matter.^{[1][2][3][4][5]}

Overview

There are a variety of known chemical bonding interactions including covalent, ionic, and metallic bonding among others. The theories associated with bonding are often developed around the covalent bonds and extended to ionic and metallic bonding. There are a variety of active theories or models associated with covalent bonding, the building block of molecules. These theories make various approximations rendering each them useful for describing different nuances of common molecular bonding.

VSEPR

The simplest and most primitive of the theories currently taught. Describes molecular geometry through the repulsion of electron fields which include bonds and lone pairs. It does not require any application of orbital shape.

Wave function models

Valence bond theory

In 1927, valence bond theory was formulated and it argues that a covalent bond forms when two valence electrons, in their respective atomic orbitals, work or function to hold two nuclei together, by virtue of effects of lowering system energies. Building on this theory, the chemist Linus Pauling published in 1931 what some consider one of the most important papers in the history of chemistry: "On the Nature of the Chemical Bond". In this paper, elaborating on the works of Lewis, and the valence bond theory (VB) of Heitler and London, and his own earlier works, Pauling presented six rules for the shared electron bond, the first three of which were already generally known:

1. The electron-pair bond forms through the interaction of an unpaired electron on each of two atoms.
2. The spins of the electrons have to be opposed.
3. Once paired, the two electrons cannot take part in additional bonds.

His last three rules were new:

Building on this article, Pauling's 1939 textbook: On the Nature of the Chemical Bond would become what some have called the bible of modern chemistry. This book helped experimental chemists to understand the impact of quantum theory on chemistry. However, the later edition in 1959 failed to adequately address the problems that appeared to be better understood by molecular orbital theory. The impact of valence theory declined during the 1960s and 1970s as molecular orbital theory grew in usefulness as it was implemented in large digital computer programs. Since the 1980s, the more difficult problems, of implementing valence bond theory into computer programs, have been solved largely, and valence bond theory has seen a resurgence.

Molecular orbital theory

Molecular orbitals were first introduced by Friedrich Hund^[6][7] and Robert S. Mulliken^[8][9] in 1927 and 1928.^[10][11] The linear combination of atomic orbitals or "LCAO" approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones.^[12] Linear combinations of atomic orbitals (LCAO) can be used to estimate the molecular orbitals that are formed upon bonding between the molecule's constituent atoms. Similar to an atomic orbital, a Schrödinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond to the independent-particle approximation of the molecular Schrödinger equation.

When atomic orbitals interact, the resulting molecular orbital can be of three types: bonding, antibonding, or nonbonding.

Bonding MOs:

• Bonding interactions between atomic orbitals are constructive (in-phase) interactions.
• Bonding MOs are lower in energy than the atomic orbitals that combine to produce them.

Antibonding MOs:

• Antibonding interactions between atomic orbitals are destructive (out-of-phase) interactions, with a nodal plane where the wavefunction of the antibonding orbital is zero between the two interacting atoms
• Antibonding MOs are higher in energy than the atomic orbitals that combine to produce them.

Nonbonding MOs:

• Nonbonding MOs are the result of no interaction between atomic orbitals because of lack of compatible symmetries.
• Nonbonding MOs will have the same energy as the atomic orbitals of one of the atoms in the molecule.

Comparison

The two theories differ in the order that the electron configuration of the molecule is built up.^[13] For valence bond theory, the atomic hybrid orbitals are filled first to produce a full valence configuration of bonding pairs and lone pairs. If several such configurations exist, a weighted superposition of these configurations is then applied. In contrast, for molecular orbital theory a weighted superposition of atomic orbitals is performed first, followed by the filling of the resulting molecular orbitals by the aufbau principle.

Either theory has its advantages and uses. As valence bond theory builds the molecular wavefunction out of localized bonds, it is more suited for the calculation of bond energies and the understanding of reaction mechanisms. In particular, valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple molecular orbital theory predicts dissociation into a mixture of atoms and ions. Molecular orbital theory, with delocalized orbitals that obey its symmetry, is more suited for the calculation of ionization energies and the understanding of spectral absorption bands. Molecular orbitals are orthogonal, which significantly increases feasibility and speed of computer calculations compared to nonorthogonal valence bond orbitals.

Although the wavefunctions generated by both theories do not agree and do not match the stabilization energy by experiment, they can be corrected by configuration interaction.^[13] This is done by combining the valence bond covalent function with the functions describing all possible ionic configurations or by combining the molecular orbital ground state function with the functions describing all possible excited states using unoccupied orbitals. It can then be seen that the simple molecular orbital approach gives too much weight to the ionic structures while the simple valence bond approach gives too little. This can also be described as saying that the molecular orbital approach neglects electron correlation while the valence bond approach overestimates it.^[13]

The two approaches are now regarded as complementary, each providing its own insights into the problem of chemical bonding. Modern calculations in quantum chemistry usually start from (but ultimately go far beyond) a molecular orbital rather than a valence bond approach, not because of any intrinsic superiority in the former but rather because the MO approach is more readily adapted to numerical computations. However, better valence bond programs are now available.

Models for transition metals

Crystal field theory

This approximation begins with the geometries of the d orbitals derived from quantum mechanics. Ligands with their electron density are assumed to destabilize the metal d orbitals they interact with raising their energy while the remain d-orbitals drop in energy to balance the overall change in energy.

Ligand field theory

Considered a hybrid of CFT and MO Theory or simply an approximate application of MO Theory to transition metal complexes.

Computational Chemistry

Modern computational chemistry applies components of bonding models to simulate various chemical phenomenon associated with bonding. Computational chemistry also extends beyond covalent bonding to investigate the interactions of groups of molecules and higher order structure. In these systems the chemical bond is often simplified and approximated to reduce computing time.

References