Density functional theory, direct molecular

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

The ab initio methods used by most investigators include Hartree-Fock (FFF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide reliable molecular structures and are considerably faster than FFF methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. FFowever, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

Ab-initio CAChe features all of the above plus ab-initio and density functional methods. This program requires a workstation (Windows NT minimum or SGI and IBM unix-based machines) and can be used to build and visualize results from ab-initio programs (e.g., Gaussian, see description under Gaussian, Inc.). Also, CAChe directly interfaces to Dgauss , a computational chemistry package that uses density functional theory to predict molecular structures, properties, and energetics. 

One approach to the treatment of electron correlation is referred to as density functional theory. Density functional models have at their heart the electron density, p(r), as opposed to the many-electron wavefimction, F(ri, r2,...). There are both distinct similarities and distinct differences between traditional wavefunction-based approaches (see following two sections) and electron-density-based methodologies. First, the essential building blocks of a many-electron wavefunction are single-electron (molecular) orbitals, which are directly analogous to the orbitals used in density functional methodologies. Second, both the electron density and the many-electron wavefunction are constructed from an SCF approach which requires nearly identical matrix elements. 

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

Another approach closely related to the ab initio methods that has gained increasing prominence in recent years is the density functional theory (DFT). This method bypasses the determination of the wavefunction electronic probability density p directly and then calculates the energy of the system from p. 

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