Computational Chemistry - Electrons to Airplanes

Computational chemistry has long been at the forefront of simulation technology and scientific computing in general. From studying the energetics of a hydrogen molecule to developing new materials for aircraft design, computational chemistry has established itself as an indispensible piece of the world's research efforts. In this installment, we'll examine the basic methods of computational chemistry and briefly discuss the kinds of problems for which each is best suited. Quantum Mechanics

Quantum mechanics as applied to chemistry problems is a complex field of study with a very rich history. In general terms, quantum chemistry involves using the rules of quantum mechanics to divine information about the wave functions and interaction potentials of sytems of atoms and molecules. The formalism of quantum chemistry is based on the solutions of the hydrogen atom problem. This is one of those very special cases for which there exists an analytical solution : in most instances, we're not so lucky, and some sort of sophisticated approximations must be made.

Quantum chemistry problems are approached from one of two standpoints: ab initio or semiempirical. In an ab initio calculation, the mathematical formalism needed to describe a problem is retained in full, and no experimental data is figured into the calculation. In other words, there are no funny shortcuts introduced in the formulation of the problem, although some "tricks" may be used to arrive at an answer. A semiempirical approach, however, employs a less-stringent mathematical model and may make use of experimental data to offset some of the computational intricacies.

Whether ab initio or semiempirical, quantum methods are used to explore interactions among particles, learn more about the properties of an atom or molecule, help define reaction pathways, and for many other important issues pertaining to the small-scale chemical problem (small-scale being one to maybe 100 atoms total).

Classical Mechanics

Classical mechanics, as the name implies, uses the so-called classical, usually Newtonian, equations of motion to study systems of particles. In this case, because we are not starting from first-principles, it is necessary to supply some information about how the particles in a system interact. This is most typically done with a semi-empirical force field. A semi-empirical force field is a mathematical construct which desribes how one chemical species interacts with any other chemical species it might encounter. These pairwise interactions are parameterized based on experimental data and quantum mechanical calculations. The great advantage to employing classical over quantum methods is that the calculations involved in the former are much less complicated than those necessary for the latter. As a consequence, much larger computational problems, in terms of the number of atoms involved, can be "solved" much more

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