Ab initio electronic structure theory

The relative compute times required for different ab initio methods are compared in Table 1 for the Cl 4- CH3CI Sn2 reaction. This comparison illustrates the utility of the MP2 method. Though it gives more accurate structures and energies than does HF, the MP2 calculations do not require appreciably more compute time that is, only approximately a factor of 3 more is needed for Cl + CH3CI. At the present time, a very high-level electronic structure theory such as CCSD(T) is not feasible for direct dynamics. Multiconfiguration ab initio methods are practical for direct dynamics simulations, as illustrated by the use of CASSCF in a recent study of the unimolecular dynamics of the cyclopropyl radical.  

In contrast to the wavefunction approach for electronic structure calculations, described above, the density functional theory (DFT) is based on the Hohenberg-Kohn theorem that the complete ground-state properties of the 

Energies are in kcal/mol, distances in angstroms, and angles in degrees. The relative direct dynamics CPU time is for calculations using one processor on a SGI/MIPS RIOOOO workstation. 

When using a point mass model for the nuclei and electrons, and ignoring spin-orbit coupling, the full Hamiltonian operator with nuclei and electronic degrees of freedom can be written as 

For convenience the last term in Eq. [13], which is the nuclear repulsion Vnn is also included in the electronic Hamiltonian operator. This is because, for each nuclear configuration, this term is a constant and does not affect the electronic wavefunction. 

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We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

Only a very concise description of quantum chemistry is presented in this section the reader is referred to standard texts for a more complete treatment. " The aim of quantum chemistry or ab initio electronic structure theory is the solution of the time-independent Schrodinger equation ... 

Examples. There are by now several reactions for which the best available levels of ab initio electronic structure theory find a plateau on the PE hypersurface, in the vicinity of a singlet-state biradical. Several of these have been studied by MD simulation and/or experiment, and in each case the conclusion is that application of statistical kinetic models will give a misleading description of how the reaction really occurs. There is not room to describe each of these studies, and so just one is chosen as a representative, and described in Section 3.2.3.1. 

Although all his research applications are in the realm of ab initio electronic structure theory and computations, Rauk has taught the theory of structure and bonding from a frontier orbital point of view. He is the author of a graduate-level textbook on the orbital interaction theory of organic chemistry.208... 

The last years have witnessed tremendous progress in the theoretical description of surfaces and processes on surfaces. A variety of surface properties can now be described from first principles, i.e. without invoking any empirical parameters [1], In particular, whole potential energy surfaces (PES) can nowadays be mapped out by total energy calculations based on ab initio electronic structure theory. This development has also motivated new efforts in the dynamical treatment of adsorption/desorption processes in the last decade such as the development of efficient schemes for high-dimensional quantum dynamical simulations [2, 3]. 

The Hartree-Fock model is the simplest, most basic model in ab initio electronic structure theory [28], In this model, the wave function is approximated by a single Slater determinant constructed from a set of orthonormal spin orbitals ... 

At present, reaction path methods represent the best approach for utilizing ab initio electronic structure theory directly in chemical reaction dynamics. To study reaction dynamics we need to evaluate accurately the Born-Oppenheimer molecular potential energy surface. Our experience suggests that chemical reaction may take place within in a restricted range of molecular configurations (i.e., there is a defined mechanism for the reaction). Hence we may not need to know the PES everywhere. Reaction path methods provide a means of evaluating the PES for the most relevant molecular geometries and in a form that we can use directly in dynamical calculations. 

As indicated before, the ab initio electronic-structure theory of solid-state materials has largely profited from density-functional theory (DFT), and the performance of DFT has turned out well even when the one of its molecular quantum-chemical competitors - Hartree-Fock theory - has been weakest, namely for metallic materials. For these, and also for covalent materials, DFT is a very reasonable choice. On the other hand, ionic compounds (with both metals and nonmetals present) are often discussed using only the ionic model, on which most of Section 1.2 was based, and the quantum-mechanical approach is not considered at all, at least in introductory textbooks. Nonetheless, let us see, as a first instructive example, how a t5q)ical ionic material can be described and understood by the ionic and the quantum-chemical (DFT and HF) approaches, and let us also analyze the strengths and weaknesses. 

We can expect the new millennium to spawn a new age of routine quantitative absolute rate predictions based on the confluence of chemically accurate ab initio electronic structure theory with continued refinement of Eyring s TST. 

The approach taken in the research described here is characterized by a very simple model construction phase, followed by an extensive series of tests involving information from ab initio electronic structure theory, mineralogy, aqueous chemistry, and high vacuum surface science. As of the time of this review, classical models are the only models simple enough to perform the necessary benchmarking calculations in all these areas and also are the only models that can be extended to 10,000 atom/nanosecond timescale simulations of interfacial phenomena. 

Rustad JR, Dixon DA, Kubicki JD, Felmy AR (2000a). The gas phase acidities of tetrahedral oxyacids from ab initio electronic structure theory. J Phys Chem A 104 4051-4057 Rustad JR, Dixon DA, Rosso KM, Felmy AR (1999a) Trivalent ion hydrolysis reactions A linear free energy relationship based on density functional electronic structure calculations. J Am Chem Soc... 

It should be apparent that ab initio electronic structure theory is capable of genuine contributions to the understanding of simple fluorine atom reactions. This research is by no means a closed book, and an example from our current research should make... 

Dixon, D. A. Gutowski, M., Thermodynamic properties of molecular borane amines and the [BHj KNHJ ] salt for chemical hydrogen storage systems from ab initio electronic structure theory, J. Phys. Chem. A 2005,109,5129 5135. 

Compared with other areas such as ab initio electronic structure theory and molecular dynamics and Monte Carlo calculations, path integral simulation is a relative latecomer to the field of computational chemistry. While the analytical advantages of formulating quantum mechanics in terms of path integrals have influenced modem physics profoundly for the past 40 years, its computational advantages in areas of chemistry were not appreciated until rather late. 

Another recent application of relativistic ab initio electronic structure theory is the determination of relativistic... 

The earliest origins of ab initio electronic structure theory are found in the work leading to the seminal 1956 article in Nature by Boys et al., which both reported on their computational methodology and presented results for BH, HaO, and H3. Extensions and continuation of this work led eventually to POLYATOM, the first ab initio electronic structure program. " ... 

Because the electronic energy Ee(q) in Eq. [8] and its derivatives must be calculated at each integration step of a classical trajectory, a direct dynamics simulation is usually very computationally intense. A standard numerical integration time step is /St = 10 " s. Thus, if a trajectory is integrated for 10 s, 10" evaluations of Eq. (8) are required for each trajectory. An ensemble for a trajectory simulation may be as small as 100 events, but even with such a small ensemble 10 " electronic structure calculations are required. Because of such computational demands, it is of interest to determine the lowest level of electronic structure theory and smallest basis set that gives an adequate representation for the system under study. In the following parts of this section, semiempirical and ab initio electronic structure theories and mixed electronic structure theory (quantum mechanical) and molecular mechanical (i.e. QM/MM) approaches for performing direct dynamics are surveyed. 

We begin our survey of the standard models of quantum chemistry with a discussion of the Hartiee-Fock model - the simplest wave-function model in ab initio electronic-structure theory. It serves not only as a useful approximation in its own right, but also constitutes a convenient starting point for other, more accurate models of molecular electronic structure. 

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