Chemical bond, quantum mechanical description

The Car-Parrinello quantum molecular dynamics technique, introduced by Car and Parrinello in 1985 [1], has been applied to a variety of problems, mainly in physics. The apparent efficiency of the technique, and the fact that it combines a description at the quantum mechanical level with explicit molecular dynamics, suggests that this technique might be ideally suited to study chemical reactions. The bond breaking and formation phenomena characteristic of chemical reactions require a quantum mechanical description, and these phenomena inherently involve molecular dynamics. In 1994 it was shown for the first time that this technique may indeed be applied efficiently to the study of, in that particular application catalytic, chemical reactions [2]. We will discuss the results from this and related studies we have performed. 

Although there are many ways to describe a zeolite system, models are based either on classical mechanics, quantum mechanics, or a mixture of classical and quantum mechanics. Classical models employ parameterized interatomic potentials, so-called force fields, to describe the energies and forces acting in a system. Classical models have been shownto be able to describe accurately the structure and dynamics of zeolites, and they have also been employed to study aspects of adsorption in zeolites, including the interaction between adsorbates and the zeolite framework, adsorption sites, and diffusion of adsorbates. The forming and breaking of bonds, however, cannot be studied with classical models. In studies on zeolite-catalyzed chemical reactions, therefore, a quantum mechanical description is typically employed where the electronic structure of the atoms in the system is taken into account explicitly. 

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... 

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. 

A typical MD does not allow for breaking chemical bonds, and the force fields that allow this give an inadequate, classical picture, so a quantum description is sometimes a must The systems treated by MD are usually quite large, which excludes a full quantum-mechanical description. 

Putz, M. V. (2007b). Can quantum-mechanical description of chemical bond be considered complete In Kaisas, M. P. (Ed.), Quantum Chemistry Research Trends, Nova Science Publishers Inc., New York, E q)ert Commentary. 

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. 

Hybridization of Atomic Orbitals Hybridization is the quantum mechanical description of chemical bonding. Atomic orbitals are hybridized, or mixed, to form hybrid orbitals. These orbitals then interact with other atomic orbitals to form chemical bonds. Various molecular geometries can be generated by different hybridizations. The hybridization concept accounts for the exception to the octet rule and also explains the formation of double and triple bonds. 

The Lewis theory of chemical bonding provides a relatively simple way for us to visualize the arrangement of electrons in molecules. It is insufficient, however, to explain the differences beuveen the covalent bonds in compounds such as Hi, Fi, and HF. Although Lewis theory describes the bonds in these three molecules in exactly the same way, they really are quite different from one another, as evidenced by their bond lengths and bond enthalpies listed in Table 9.3. Understanding these differences and why covalent bonds form in the first place requires a bonding model that combines Lewis s notion of atoms sharing election pairs and the quantum mechanical descriptions of atomic orbitals. 

In a quantum mechanical description, the simple spring-like picture of chemical bonds, of course, breaks down and the molecule has to be described as a many-body system of interacting particles including electrons and nuclei. Nevertheless, the normal mode vibrations have their counterpart in the fundamental excitations of the nuclear vibrational degrees of freedom (DOF) of the molecule. The fundamentals can be excited by infrared radiation (IR) and characteristic absorption bands in the IR spectra immediately point to the existence of certain chemical bonds or to functional groups and hence IR (and Raman) spectroscopy are powerful tools to investigate and study the chemical structure of molecules. 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

This is in principle all we need to understand chemical bonding on surfaces and trends in reactivity. For a more accurate description of molecular orbital theory we refer to P.W. Atkins, Molecular Quantum Mechanics (1983), Oxford University Press, Oxford. The main results from molecular orbital theory are summarized in Fig. 6.8 below. 

The main handicap of MD is the knowledge of the function [/( ). There are some systems where reliable approximations to the true (7( r, ) are available. This is, for example, the case of ionic oxides. (7( rJ) is in such a case made of coulombic (pairwise) interactions and short-range terms. A second example is a closed-shell molecular system. In this case the interaction potentials are separated into intraatomic and interatomic parts. A third type of physical system for which suitable approaches to [/( r, ) exist are the transition metals and their alloys. To this class of models belong the glue model and the embedded atom method. Systems where chemical bonds of molecules are broken or created are much more difficult to describe, since the only way to get a proper description of a reaction all the way between reactant and products would be to solve the quantum-mechanical problem at each step of the reaction. 

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