Quantum Mechanical Description of the Chemical Bond

The first ah initio simulation of a room temperature molten salt, dimethylimi-dazolium chloride (]MMIM]Q), appeared at the beginning of 2005 [21]. The work aimed at providing information on the liquid structure, in order to compare with results from classical force-field simulations and neutron diffraction experiments. Urdike non-associating fluids, in ionic liquids the distribution of ions around certain chemical bonds may depend strongly on the instantaneous electronic structure. Therefore, site-site distribution functions and three-dimensional densities may change when passing from a classical to a quantum mechanical description of the interactions. 

The modern theory of chemical bonding begins with the article The Atom and the Molecule published by the American chemist G. N. Lewis in 1916 [1], In this article, which is still well worth reading, Lewis for the first time associates a single chemical bond with one pair of electrons held in common by the two atoms "After a brief review of Lewis model we turn to a quantum-mechanical description of the simplest of all molecules, viz. the hydrogen molecule ion H J. Since this molecule contains only one electron, the Schrodinger equation can be solved exactly once the distance between the nuclei has been fixed. We shall not write down these solutions since they require the use of a rather exotic coordinate system. Instead we shall show how approximate wavefunctions can be written as linear combinations of atomic orbitals of the two atoms. Finally we shall discuss so-called molecular orbital calculations on the simplest two-electron atom, viz. the hydrogen molecule. 

If one has the programs to solve the Schrodinger equation in atoms, one can think about a quantum mechanical description of simple chemical systems. In NaCl e.g., one already has to deal with 28 electrons, and only 8 out of them determine the chemical bond. In more complex systems, the total number of electrons becomes fairly large, and the number of valence electrons is substantially lower. This is a rather frustrating situation, if one realizes that the core electrons are essentially chemically inactif, and remain intimately bound to their nucleus. 

It will be clear from the above discussion that the delocalization of the electron plays an important part in the theory of the chemical bond. In place of the fixed orbits of Bohr, quantum mechanics leads to a statistically probable description of the state of the electron when it exists both in the field of a single or of several nuclei. 

The characterization of the interrelations between chemical bonding and molecular shape requires a detailed analysis of the electronic density of molecules. Chemical bonding is a quantum mechanical phenomenon, and the shorthand notations of formal single, double, triple, and aromatic bonds used by chemists are a useful but rather severe oversimplification of reality. Similarly, the classical concepts of body and surface , the usual tools for the shape characterization of macroscopic objects, can be applied to molecules only indirectly. The quantum mechanical uncertainty of both electronic and nuclear positions within a molecule implies that valid descriptions of both chemical bonding and molecular shape must be based on the fuzzy, delocalize properties of electronic density distributions. These electron distributions are dominated by the nuclear arrangements and hence quantum mechanical uncertainly affects electrons on two levels by the lesser positional uncertainty of the more massive nuclei, and by the more prominent positional uncertainty of the electrons themselves. These two factors play important roles in chemistry and affect both chemical bonding and molecular shape. 

The exact foundation of modem quantum mechanics was laid in 1925-1926, by Wemer Heisenberg, Max Bom and Pascual Jordan, and by the Austrian physicist Erwin Schrodinger. The latter s formulation in terms of wave functions has, in particular, proved well suited for the description of atoms, molecules and solids, and their interaction with light. Thus, the Schrodinger equation supplies the basis for our understanding of the chemical bond and for the description of, say, atomic and molecular spectra. 

In Spite of Dirac s pessimistic viewpoint on the applicability of laws of quantum mechanics to chemistry, the quantum-mechanical description of chemical bonds and reactions has been one of the most prominent and active areas of theoretical chemistry since the early days of quantum mechanics. As anticipated by Dirac, applying the laws of quantum mechanics to systems of chemical interest was frustrated by great computational difficulties for many years, with the exception perhaps of the simplest molecules. However, with recent developments both in conceptual quantum chemistry, i.e. the application of density... 

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