Atomic electronic structure methods

Ab initio molecular orbital theory is concerned with predicting the properties of atomic and molecular systems. It is based upon the fundamental laws of quantum mechanics and uses a variety of mathematical transformation and approximation techniques to solve the fundamental equations. This appendix provides an introductory overview of the theory underlying ab initio electronic structure methods. The final section provides a similar overview of the theory underlying Density Functional Theory methods. 

Pitzer, R.M. and Winter, N.W (1991) Electronic-Structure Methods for Heavy-Atom Molecules. International Journal of Quantum Chemistry, 40, 773-780. 

Vibrational spectroscopy is of utmost importance in many areas of chemical research and the application of electronic structure methods for the calculation of harmonic frequencies has been of great value for the interpretation of complex experimental spectra. Numerous unusual molecules have been identified by comparison of computed and observed frequencies. Another standard use of harmonic frequencies in first principles computations is the derivation of thermochemical and kinetic data by statistical thermodynamics for which the frequencies are an important ingredient (see, e. g., Hehre et al. 1986). The theoretical evaluation of harmonic vibrational frequencies is efficiently done in modem programs by evaluation of analytic second derivatives of the total energy with respect to cartesian coordinates (see, e. g., Johnson and Frisch, 1994, for the corresponding DFT implementation and Stratman etal., 1997, for further developments). Alternatively, if the second derivatives are not available analytically, they are obtained by numerical differentiation of analytic first derivatives (i. e., by evaluating gradient differences obtained after finite displacements of atomic coordinates). In the past two decades, most of these calculations have been carried... 

In combined QM/MM potentials, the system is divided into a QM region and an MM region. The QM region typically includes atoms that are directly involved in the chemical step and they are treated explicitly by a quantum mechanical electronic structure method. The MM region consists of the rest of the system and is approximated by an MM force field. The QM/MM potential is given by ... 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

For the first time in the history of chemical sciences, theoretical predictions have achieved the level of reliability that allows them to rival experimental measurements in accuracy on a routine basis. Only a decade ago, such a statement would be valid only with severe qualifications as high-level quantum-chemical calculations were feasible only for molecules composed of a few atoms. Improvements in both hardware performance and the level of sophistication of electronic structure methods have contributed equally to this impressive progress that has taken place only recently. 

The major drawback for employing the Car-Parrinello approach in dynamics simulations is that since a variational wavefunction is required, the electronic energy should in principle be minimized before the forces on the atoms are calculated. This greatly increases the amount of computer time required at each step of the simulation. Furthermore, the energies calculated with the electronic structure methods currently used in this approach are not exceptionally accurate. For example, it is well established that potential energy barriers, which are of importance to chemical reactivity, often require sophisticated methods to be accurately determined. Nonetheless, the Tirst-principles calculation of the forces during the dynamics is an appealing idea, and will continue to be developed as computer resources expand. 

In the last few years, the improvements in computer hardware and software have allowed the simulation of molecules and materials with an increasing number of atoms. However, the most accurate electronic structure methods based on N-particle wavefunctions, for example, the configuration interaction (Cl) method or the coupled-cluster (CC) method, are computationally too expensive to be applied to large systems. There is a great need for treatments of electron correlation that scale favorably with the number of electrons. 

Methods of density functional theory (DFT) originate from the Xa method originally proposed by Slater [78] on the base of statistical description of atomic electron structure within the Thomas-Fermi theory [79]. From the point of view of Eq. (3), fundamental idea of the DFT based methods consist first of all in approximate treatment of the electron-electron interaction energy which is represented as ... 

The main purpose of this chapter is to present the basics of ab initio molecular dynamics, focusing on the practical aspects of the simulations, and in particular, on modeling chemical reactions. Although CP-MD is a general molecular dynamics scheme which potentially can be applied in combination with any electronic structure method, the Car-Parinello MD is usually implemented within the framework of density functional theory with plane-waves as the basis set. Such an approach is conceptually quite distant from the commonly applied static approaches of quantum-chemistry with atom-centered basis sets. Therefore, a main... 

The Car-Parinello MD approach is usually applied in combination with plane wave based electronic structure methods. Use of plane waves in Car-Parinello MD is in many ways easier than the atom-centered basis sets (Gaussian-type or Slater-type... 

Quantum dynamics effects for hydride transfer in enzyme catalysis have been analyzed by Alhambra et. al., 2000. This process is simulated using canonically variational transition-states for overbarrier dynamics and optimized multidimensional paths for tunneling. A system is divided into a primary zone (substrate-enzyme-coenzyme), which is embedded in a secondary zone (substrate-enzyme-coenzyme-solvent). The potential energy surface of the first zone is treated by quantum mechanical electronic structure methods, and protein, coenzyme, and solvent atoms by molecular mechanical force fields. The theory allows the calculation of Schaad-Swain exponents for primary (aprim) and secondary (asec) KIE... 

It was, therefore, clear in 1974 that electronic-structure methods were not sufficiently advanced to reproduce experimental data accurately for even a simple ionic oxide such as MgO. The emphasis at the time was on the determination of the effects of different approximations upon the calculated results. Comparison was usually made between one calculation and another rather than between calculation and experiment. The theoretical papers reported the quantities arising directly from the calculations, such as orbital eigenvalues and atomic-orbital charge decompositions, and spectral properties were interpreted primarily in terms of orbital energies. No attempt was made to evaluate equilibrium structural or energetic properties. 

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