Computational methods that can be employed to investigate fundamental questions concerning the complex chemical and structural behavior of biological molecules such as proteins, carbohydrates, and nucleic acids have been traditionally limited by the large number of atoms that comprise even the simplest system of biochemical interest. As a consequence, highly parameterized, empirical force field methods have been developed that describe the energy of macromolecular structures as a function of the spatial locations of the atomic nuclei. In combination with algorithms for simulating molecular dynamics, these classical models allow relatively accurate calculations of the structural and thermodynamic properties associated with proteins and nucleic acids. On the other hand, empirical approaches cannot be used to model molecular behavior that is directly dependent on electrons and their energies. For example, no information can be obtained concerning the electronic spectra of macromolecule/ligand complexes, electron transfer reactions such as those that occur within the photosynthetic reaction center, nitrogenase, an enzyme involved in nitrogen fixation, or cytochrome c oxidase which catalyzes the reduction of oxygen in the last step of aerobic respiration. Accurate modeling of transition states, excited states, and intermediates in biological catalysis requires application of quantummechanical (QM) representations since all of these phenomena depend on the distribution and/or excitation of electrons. At present, the most accurate ab initio algorithms for calculating electronic structure cannot be applied to systems comprised of hundreds of atoms, as such calculations scale as N4–N7 on most workstations, where N is the number of functions used in constructing the many-electron, molecular wavefunction. Even with the implementation of ab initio codes optimized for use on parallel computing engines, and density functional approaches, it is likely that high-accuracy QM calculations in the near future will remain limited to systems that comprise tens, rather than hundreds, of nonhydrogen atoms. Semi-empirical quantum-mechanical methods combine fundamental theoretical treatments of electronic behavior with parameters obtained from experiment to obtain approximate wavefunctions for molecules composed of hundreds of atoms.
