The Principles of Molecular Mechanics

The molecular mechanics method is used to calculate molecular structures, conformational energies, and other molecular properties using concepts from classical mechanics. Electrons are not explicitly included in the molecular mechanics method, which is justified on the basis of the Born-Oppenheimer approximation stating that the movements of electrons and the nuclei can be separated. Thus, the nuclei may be viewed as moving in an average electronic potential field, and the molecular mechanics method attempts to describe this field by its force field.  

The total energy of the molecule in a given geometry is assumed to be the sum of energy contributions in Eq. [1]. 

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The discussion here is a simplified presentation of the principles of molecular mechanics calculations in MM2. The treatment in MM3 is more complex. ... 

The principles of molecular mechanics may be used in a molecular simulation calculation, which is a type of computational statistical me-chanics. The goal of molecular simulation is to analyze a theoretical model of molecular behavior in order to determine the macroscopic properties of a substance. In one approach, known as molecular dynamics (MD), Newton s laws of motion for individual particles and a set of potential energy terms describing the forces on the structures are applied to all of the atoms in the calculation. Integration of the resulting differential equations over a short time period leads to new locations and new velocities for the atoms. 

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

Quantum chemistry or molecular electronic structure theory is the application of the principles of quantum mechanics to calculate the stationary states of molecules and the transitions between these states. Today, both computational and experimental groups routinely use ab initio (meaning from first principles ) molecular orbital calculations as a means of understanding structure, bonding, reaction paths between intermediates etc. Explicit treatment of the electrons means that, in principle, one does not make assumptions concerning the bonding of a system. 

Molecular mechanics is based on the principles of classical mechanics, rather than those of quantum mechanics. Quantum mechanics is based on an explicit consideration... 

Exploiting the principles of statistical mechanics, atomistic simulations allow for the calculation of macroscopically measurable properties from microscopic interactions. Structural quantities (such as intra- and intermolecular distances) as well as thermodynamic quantities (such as heat capacities) can be obtained. If the statistical sampling is carried out using the technique of molecular dynamics, then dynamic quantities (such as transport coefficients) can be calculated. Since electronic properties are beyond the scope of the method, the atomistic simulation approach is primarily applicable to the thermodynamics half of the standard physical chemistry curriculum. 

This chapter explains the basic principles of molecular mechanics (MM), which rests on a view of molecules as balls held together by springs. MM began in the 1940s with attempts to analyze the rates of racemization of biphenyls and of SN2 reactions. 

Quantum chemistry plays vital central roles in clarifying and understanding the mechanisms of these photobiological events. Electronic structures and transitions of active centers in proteins obey the principles of quantum mechanics, and molecular properties dramatically change after the transitions. In addition, photochemical events in excited states are often transient and sometimes difficult to study in experimental approaches. If an accurate and reliable theory exists and can be applied to photobiological subjects, one can obtain not only rational explanations but also predictions on the photo-functions of the active centers and proteins. 

The nature of the chemical bond and the principles of molecular structure were formu lated along time ago to systematize an immense body of chemical knowledge. With the advent of quanmm mechanics, it became possible to actually derive the concepts of chemical bonding from more fundamental laws governing matter on the atomic scale. Remarkably, many of the empirical concepts developed by chemists have remained valid when reexpressed in terms of quantum-mechanical principles. 

Molecular orbital calculations based on the principles of quantum mechanics may be used to detennine energy minima of rotating bonds and to predict preferred conformations for the molecule. By means of molecular mechanics, theoretical contbrmational analysis has found that ACh has an energy minimum for the tz torsion angle at about 84° and that the preferred confimnation of ACh corresponds clo.sely in ttqueous solution to that found in the crystal stale. 

The general point against the suggestion that molecular chemistry can be reduced to quantum mechanics is that the decision when and where to suppress the interaction with the environment is not something that can be derived from quantum mechanics— this is where Gell-Mann s "chemical questions being asked" (mentioned earlier) enter the discussion. But it is these decisions that, as it were, abstract objects out of the quantum mechanical formalism. Quantum mechanics describes the material world, in principle, as one whole. Within quantum mechanics an object can only be defined in terms of its relations to its environment. To separate out objects from this whole requires a justification that lies outside the principles of quantum mechanics. Because "the" environment consists of the rest of the universe, it can never be given a precise description and must therefore be replaced by a model environment that mimics aspects of the real situation. 

We have four goals for this chapter 1) present an overview of the steps commonly employed to study organometallic catalysis, 2) show how the principles underlying molecular mechanics methods are applied to three specific examples (stereoselectivity in asymmetric hydrogenation, olefin polymerization, and host/guest interactions in zeolites), 3) briefly illustrate the practical applications of molecular modeling to catalysts used in industry, and 4) present a limited survey of the literature to illustrate how different workers have applied molecular mechanics to the study of properties of catalysts of importance to organometallic chemists. 

Molecular mechanics bears little resemblance to any of the previous theories. Acting under the rationale that a chemical bond can be thought of as a spring between two spheres, molecular mechanics calculations build a potential model of the system using the principles of classical mechanics and some additional empirical corrections ... 

The more recent treatment of the covalent bond, based on the application of the principles of wave mechanics, has developed in two distinct forms, usually termed the valence-bond and molecular-orbital theories, respectively. Although ultimately there is no inconsistency between these two theories, they do in fact approach the problem of chemical binding from different points of view, and we shall generally find that for our purposes the valence-bond treatment is the more suitable. This theory starts from concepts already familiar to the chemist and its conclusions can usually be expressed verbally in qualitative terms the molecular-orbital theory, on the other hand, is more mathematical in its approach and lends itself less readily to such an interpretation. We shall, therefore, first discuss the valency-bond theory, and refer only briefly to the molecular-orbital treatment later in the chapter. 

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