Quantum chemistry perturbation molecular orbital theory

By ab initio we refer to quantum chemical methods in which all the integrals of the theory, be it variational or perturbative, are exactly evaluated. The level of theory then refers to the type of theory employed. Common levels of theory would include Hartree-Fock, or molecular orbital theory, configuration interaction (Cl) theory, perturbation theory (PT), coupled-cluster theory (CC, or coupled-perturbed many-electron theory, CPMET), etc. - We will use the word model to designate approximations to the Hamiltonian. For example, the zero differential overlap models can be applied at any level of theory. The distinction between semiempirical and ab initio quantum chemistry is often not clean. Basis sets, for example, are empirical in nature, as are effective core potentials. The search for basis set parameters is not usually considered to render a model empirical, whereas the search for parameters in effective core potentials is so considered. 

The first target of quantum chemistry was how to solve the SchrOdinger equation for electronic motions in molecules. To address this challenge, the Hartree-Fock method (Hartree 1928) and its variational method (Slater 1928), molecular orbital theory (Hund 1926 Mulliken 1927), and the Slater determinant (Slater 1929) were developed, resulting in the Hartree-Fock method (Fock 1930 Slater 1930), which is accepted as the precursor of quantum chemistry. Soon afterward, the configuration interaction (Cl) method (Condon 1930), M0ller-Plesset perturbation method (Mpller and Plesset 1934), and multiconflgurational SCF method (Frenkel... 

The computationally viable description of electron correlation for stationary state molecular systems has been the subject of considerable research in the past two decades. A recent review1 gives a historical perspective on the developments in the field of quantum chemistry. The predominant methods for the description of electron correlation have been configuration interactions (Cl) and perturbation theory (PT) more recently, the variant of Cl involving reoptimization of the molecular orbitals [i.e., multiconfiguration self-consistent field (MCSCF)] has received much attention.1 As is reasonable to expect, neither Cl nor PT is wholly satisfactory a possible alternative is the use of cluster operators, in the electron excitations, to describe the correlation.2-3... 

The question for a more systematic inclusion of electronic correlation brings us back to the realm of molecular quantum chemistry [51,182]. Recall that (see Section 2.11.3) the exact solution (configuration interaction. Cl) is found on the basis of the self-consistent Hartree-Fock wave function, namely by the excitation of the electrons into the virtual, unoccupied molecular orbitals. Unfortunately, the ultimate goal oi full Cl is obtainable for very small systems only, and restricted Cl is size-inconsistent the amount of electron correlation depends on the size of the system (Section 2.11.3). Thus, size-consistent but perturbative approaches (Moller-Plesset theory) are often used, and the simplest practical procedure (of second order, thus dubbed MP2 [129]) already scales with the fifth order of the system s size N, in contrast to Hartree-Fock theory ( N ). The accuracy of these methods may be systematically improved by going up to higher orders but this makes the calculations even more expensive and slow (MP3 N, MP4 N ). Fortunately, restricted Cl can be mathematically rephrased in the form of the so-called coupled clus-... 

Today we know that the HF method gives a very precise description of the electronic structure for most closed-shell molecules in their ground electronic state. The molecular structure and physical properties can be computed with only small errors. The electron density is well described. The HF wave function is also used as a reference in treatments of electron correlation, such as perturbation theory (MP2), configuration interaction (Cl), coupled-cluster (CC) theory, etc. Many semi-empirical procedures, such as CNDO, INDO, the Pariser-Parr-Pople method for rr-eleetron systems, ete. are based on the HF method. Density functional theory (DFT) can be considered as HF theory that includes a semiempirical estimate of the correlation error. The HF theory is the basie building block in modern quantum chemistry, and the basic entity in HF theory is the moleeular orbital. 

The initial attempts to relate this language to quantum mechanics were understandably done through the orbital model that underlies the valence bond and molecular orbital methods employed to obtain the approximate solutions to Schrodinger s equation. The one-electron model, as embodied in the molecular orbital method or its extension to solids, is the method for classifying and predicting the electronic structure of any system (save a superconductor whose properties are a result of collective behavior). The orbital classification of electronic states, in conjunction with perturbation theory, is a powerful tool in relating a system s chemical reactivity and its response to external fields to its electronic structure and to the symmetry of this abstract structure. The conceptual basis of chemistry is, however, a consequence of structure that is evident in real space. 

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