# Theoretical Chemistry

# Theoretical Chemistry

Theoretical chemistry is the discipline that uses quantum mechanics, classical mechanics, and statistical mechanics to explain the structures and dynamics of chemical systems and to correlate, understand, and predict their thermodynamic and kinetic properties. Modern theoretical chemistry may be roughly divided into the study of chemical structure and the study of chemical dynamics. The former includes studies of: (1) electronic structure, potential energy surfaces, and force fields; (2) vibrational-rotational motion; and (3) **equilibrium** properties of condensed-phase systems and macro-molecules. Chemical dynamics includes: (1) bimolecular kinetics and the collision theory of reactions and energy transfer; (2) unimolecular rate theory and metastable states; and (3) condensed-phase and macromolecular aspects of dynamics.

A critical issue crossing all boundaries is the interaction of matter and radiation. Spectroscope experiments are used as both structural and dynamic probes and to initiate chemical processes (as in photochemistry and laserinduced chemistry), and such experiments must be understood theoretically. There are also many subfields of theoretical chemistry—for example, biomedical structure-activity relationships, the molecular theory of nuclear magnetic resonance spectra, and electron-molecule scattering—that fit into two or more of the areas listed.

Another source of overlap among the categories is that some of the techniques of theoretical chemistry are used in more than one area. For example, statistical mechanics includes the theory and the set of techniques used to relate **macroscopic phenomena** to properties at the atomic level, and it is used in all six subfields listed. Furthermore, the techniques of **quantum mechanics** and classical-mechanical approximations to quantum mechanics are used profitably in all six subfields as well. Condensed-phase phenomena are often treated with gas-phase theories in instances in which the effects of liquid-phase solvent or solid-state **lattice** are not expected to dominate. There are many specialized theories, models, and approximations as well.

Because quantum and statistical mechanics are also parts of physics, theoretical chemistry is sometimes considered a part of chemical physics. There is no clear border between theoretical physical chemistry and theoretical chemical physics.

## Three Modes of Science

Modern science is sometimes said to proceed by three modes—experiment, theory, and computation. This same division may be applied to chemistry. From this point of view, theoretical chemistry is based on analytical theory, whereas computational chemistry is concerned with predicting the properties of a complex system in terms of the laws of quantum mechanics (or classical approximations to quantum mechanics, in the domains in which such classical approximations are valid that govern the system's constituent atoms or its constituent nuclei and electrons, without using intermediate levels of analytical chemical theory. Thus, in principle, computational chemistry assumes only such basic laws as the Schrödinger equation, Newton's laws of motion, and the Boltzmann distribution of energy states. In practice, though, computational chemistry is a subfield of theoretical chemistry, and predictions based on approximate theories, such as the dielectric continuum model of solvents, often require considerable computer programming and number crunching. The number of subfields of chemistry in which significant progress can be made without large-scale computer calculations is dwindling to zero. In fact, computational advances and theoretical understanding are becoming more and more closely linked as the field progresses. Computational chemistry is sometimes called molecular modeling or molecular simulation.

## Electronic Structure

Perhaps the single most important concept in theoretical chemistry is the separation of electronic and nuclear motions, often called the Born-Oppenheimer approximation, after the seminal work of Max Born and Robert Oppenheimer(1927), although the basic idea must also be credited to Walter Heitler, Fritz London, Friedrich Hund, and John Slater. The critical facts that form a basis for this approximation are that electrons are coupled to nuclei by Coulomb forces, but electrons are much lighter—by a factor of 1,800 to 500,000—and thus, under most circumstances, they may be considered to adjust instantaneously to nuclear motion. Technically we would describe the consequence of this large mass ratio by saying that a chemical system is usually electronically adiabatic. When electronic adiabaticity does hold, the treatment of a chemical system is greatly simplified. For example, the H2 molecule is reduced from a four-body problem to a pair of two-body problems: one, called the electronic structure problem, considers the motion of two electrons moving in the field of fixed nuclei; and another, called the vibration-rotation problem or the dynamics problem, treats the two nuclei as moving under the influence of a force field set up by the electronic structure. In general, because the energy of the electronic subsystem depends on the nuclear coordinates, the electronic structure problem provides an effective potential energy function for nuclear motion. This is also called the potential energy hypersurface. The atomic force field (i.e., the set of all the forces between the atoms) is the gradient of this potential energy function.

Thus, when the Born-Oppenheimer approximation is valid and electronic motion is adiabatic, the end result of electronic structure theory is a potential energy function or atomic force field that provides a starting point for treating vibrations, equilibrium properties of materials, and dynamics. Robert Mulliken, Road Hoffman, Kenichi Fukui, John Pople, and Walter Kohn won Nobel Prizes in chemistry for their studies of electronic structure, including molecular orbital theory. Some important problem areas in which the Born-Oppenheimer separation breaks down are photochemical reactions involving visible and **ultraviolet radiation** and electrical conductivity. Even for such cases, though, it provides a starting point for more complete treatments of electronic-nuclear coupling.

## Dynamics

In the subfield of theoretical dynamics, the most important unifying concept is transition state theory, which was developed by Henry Eyring, Eugene Wigner, M. G. Evans, and Michael Polanyi. A transition state is a fleeting intermediate state (having a lifetime on the order of 10 femtoseconds) that represents the hardest-to-achieve configuration of a molecular system in the process of transforming itself from reactants to products. A transition state is sometimes called an activated complex or a dynamical bottleneck. In the language of quantum mechanics, it is a set of resonances or metastable states, and in the language of classical mechanics, it is a hypersurface in phase space. Transition states are often studied by semiclassical methods as well; these methods represent a hybrid of quantum mechanical and classical equations. Transition state theory assumes that a good first approximation to the rate of reaction is the rate of accessing the transition state. Transition state theory is not useful for all dynamical processes, and in a more general context a variety of simulation techniques (often called molecular dynamics) are used to explain observable dynamics in terms of atomic motions.

## Predictive Power

In the early days of theoretical chemistry, the field served mainly as a tool for understanding and correlating data. Now, however, owing to advances in computational science, theory and computation can often provide reliable predictions of unmeasured properties and rates. In other cases, where measurements do exist, theoretical results are sometimes more accurate than measured ones. Examples are the properties of simple molecules and reactions such as D + H_{2}→HD + H, or the heats of formation of reactive species. Computational chemistry often provides other advantages over experimentation. For example, it provides a more detailed view of phenomena such as the structure of transition states or a faster way to screen possibilities. An example of the latter is provided in the field of drug design, in which thousands of candidate molecules may be screened for their likely efficiency or bioavailability by approximate calculations—for example, of the electronic structure or free energy of desolvation—and, relying on the results of these calculations, candidates may be prioritized for **synthesis** and testing in laboratory studies. In conclusion, theoretical chemistry, by combining tools of quantum mechanics, classical mechanics, and statistical mechanics, allows chemists to predict materials' properties and rates of chemical processes, even in many cases in which they have not yet been measured or even observed in the laboratory; whereas for processes that have been observed, it provides a deeper level of understanding and explanations of trends in the data.

see also Computational Chemistry; Molecular Modeling; Quantum Chemistry.

*Donald G. Truhlar*

## Bibliography

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Baer, Michael, ed. (1985). *Theory of Chemical Reaction Dynamics*, Vol. 1. Boca Raton, FL: CRC Press.

Cramer, Christopher J. (2002). *Essentials of Computational Chemistry: Theories and Models.* New York: Wiley.

Eyring, Henry; Walter, John; and Kimball, George E., eds. (1944). *Quantum Chemistry.* New York: Wiley.

Irikura, Karl K., and Frurip, David J., eds. (1998). *Computational Thermochemistry: Prediction and Estimation of Molecular Thermodynamics.* Washington, DC: American Chemical Society.

Jensen, Frank (1999). *Introduction to Computational Chemistry.* New York: Wiley.

Leach, Andrew R. (2001). *Molecular Modeling: Principles and Applications*, 2nd edition. Upper Saddle River, NJ: Prentice Hall.

Levine, Raphael D., and Bernstein, Richard B. (1987). *Molecular Reaction Dynamics and Chemical Reactivity.* New York: Oxford University Press.

Lipkowitz, Kenny B., and Boyd, Donald B., eds. (1990–2001). *Reviews in Computational Chemistry*, Vols. 1–17. New York: VCH.

McQuarrie, Donald A. (1976). *Statistical Mechanics.* New York: Harper & Row.

Ratner, Mark A., and Schatz, George C. (2000). *Introduction to Quantum Mechanics in Chemistry.* Upper Saddle River, NJ: Prentice Hall.

Simons, Jack, and Nichols, Jeff (1997). *Quantum Mechanics in Chemistry.* New York: Oxford University Press.

Thompson, Donald L., ed. (1998). *Modern Methods for Multidimensional Dynamics Computations in Chemistry.* River Edge, NJ: World Scientific.

Truhlar, Donald G.; Howe, W. Jeffrey; Hopfinger, Anthony J.; et al., eds. (1999). *Rational Drug Design.* New York: Springer.

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