Computational methods
- Introduction
All chemists use models[2]. Undergraduates chemistry students use plastic "ball-and-stick" models to help them understand and visualize the structure of molecules. During the last decade, researchers have begun to use computer programs for the same purpose.
Not all models are physical or pictorial objects. For example, the SN2 mechanism is a simple model for a particular class of reactions that successfully explains a lot of chemistry. What all of these things have in common is that they use a set of pre-defined objects and rules to approximate real chemical entities and process.
In a similar way, computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws of physics. It allows chemists to study chemical phenomena by running calculations on computers rather than by examining reactions and compounds experimentally. Some methods can be used to model not only stable molecules, but also short -lived, unstable intermediates and transition states. In this way, they can provide information about molecules and reactions which is impossible to obtain through observation.
There are two broad areas within computational chemistry devoted to the structure of molecules and their reactivity : molecular mechanics and electronic structure theory. They perform the same basic types of calculations :
- Computing the energy of a particular molecular structure. Properties related to the energy may also be predicted by some methods
- Performing geometry optimizations, which are an attempt to locate the lowest energy molecular conformation
- Computing the vibrational frequencies of molecules resulting from interatomic motion within the molecule.
- Molecular mechanicsMolecular mechanics simulations use the laws of classical physics to predict the structures and properties of molecules. They are many different molecular mechanics methods. Each one is characterized by a force field. A force field has the following components :
- A set of equations defining how the potential energy of a molecule varies with the locations of its component atoms.
- A series of atom types, defining the characteristics of an element within a specific chemical context. The atom type prescribes different characteristics and behavior for an element depending upon its environment. The atom type depends on hybridization, charge and the types of the other atoms to which an atom is bonded.
- One or more parameter sets that fit the equations and atom types to experimental data. Parameter sets define force constants, which are values used in the equations to relate atomic characteristics to energy components, and structural data such as bond lengths.
Molecular mechanics calculations do not explicitly treat the electrons in a molecular system. Instead, they perform computations based upon the interactions among nuclei. Electronic effects are implicitly included in force fields via its parametrization.
This approximation makes molecular mechanics computations quite inexpensive in computation time, and allows them to be used for very large systems containing thousands of atoms. However, it also carries several limitations :- Particular force fields achieve good results only for a limited class of molecules, related to those for which it was parametrised. No force field can be generally used for all molecular systems.
- Neglect of electrons means that molecular mechanics methods cannot treat chemical problems where electronic effects predominate.
- Electronic structure methods Electronic structure methods use the laws of quantum mechanics rather than classical physics as the basis for their computations. Quantum mechanics states that the energy and other related properties of a molecule may be obtained by solving the Schrödinger equation :
H
= E
| (1) |
-
For any but the smallest, totally symmetric systems, however, exact solutions to the Schrödinger equation are not practical. Electronic structure methods are characterized by their various mathematical approximations to its solution. There are two major classes of electronic structure methods :
- Semi-empirical methods.
- These methods use parameter derived from experimental data to simplify the computation. They solve an approximate form of the Schrödinger equation that depends on having appropriate parameters available for the type of chemical system in question.
- Ab Initio methods.
- Unlike either molecular mechanics or semi-empirical methods, these methods use no experimental parameters in their computations. Instead, their computations are based solely on the laws of quantum mechanics —the first principles referred to in the name ab initio— and on the values of a small number of physical constants:
- The speed of light
- The masses and charges of electrons and nuclei
- Plank's constant.