Quantum chemical theory

The two selenium atoms are attached to the low-coordinated phosphorus atom, with two lengthened dative bonds (2.788 and 2.637 A). Interestingly the phosphorus atom is here strongly pyramidalized, the Z SePSe angle was 80.6°. In other words the lone pair orbital at the electrophilic phosphorus atom remains stereo chemically active, as one would expect on the basis of the quantum chemical theory of bonding within this species. 

We are referring here only to the early years of Berthier s aetivity in the field of quantum chemical theory. These were the decisive ones and from some point of view the most difficult but also exciting ones. Needless to say, everybody knows it, that he has continued since and continues still, to contribute in a most efficient way to the development and propagation of quantum chemistry and, at this time, not only in France but on the world scene. 

Much of the work presented in this chapter represents a synergistic effort from several complementary research fields quantum-chemical theory, chemical synthesis, and nonlinear optical materials characterization. This combination of expertise... 

Elementary quantum-chemical theories of atomic and molecular structure [including atomic orbitals (AO) and molecular orbitals (MO)] are part of the... 

It should be stated at the beginning that despite quite numerous partial successes the present state of the quantum-chemical theory of reactivity is far from satisfactory. First of all, it is not clear whether the present shortcomings are due to the non-adequacy of models of activated complexes or to the drastic approximations made in the calculation of the energy of the activated complex and the reactants. On the other hand, some other deficiencies of most of the reported attempts to interpret reactivity in terms of the theory are obvious the very nature of the HMO method is thought148 to make it necessary to treat as large sets of theoretical and experimental data as possible and, in addition, to respect the distinction in properties of the three classes of positions mentioned (in this connection we do not refer to the difference in the stereochemistry of these positions). 

In principle, quantum-chemical theory should be able to provide precise quantitative descriptions of molecular structures and their chemical properties however, due to mathematical and computational complexities this seems unlikely to be realized in the foreseeable future. Thus, researchers need to rely on approximate methods that have now become routine and have found wide applications. In many cases, errors due to the approximate nature of quantum-chemical calculations and the neglect of the solvation effects are largely transferable within structurally related series (Karelson and Lobanov, 1996). Thus, relative values of calculated descriptors can be meaningful even though their absolute values are not directly applicable. 

Nowadays it is very difficult to pinpoint in the classical literatures in organic chemistry the credit of attributing the relative stability of unsaturated hydrocarbon molecules to K(G) [2, 3], On the other hand, long before these quantum-chemical theories were introduced Robinson proposed using a circle inside each benzene ring of an aromatic hydrocarbon molecule to represent the six mobile electrons and also the derived aromatic stability [4], However, his symbol does not reflect any difference in the stability between I and II as,... 

Typical theoretical concepts occurring in chemical and quantum chemical theories are the various corpuscles - that is atoms , molecules , ions , and electrons - and orbital", spin , chemical bond , and electric charge . The expressions atom, molecule, electron, and ion refer to particles that are thought to... 

James R. Durig, A. J. Barnes, and W. J. Orville-Thomas, Spectroscopy and Quantum Chemical Theory Applied to Problems in Molecular Structure. A collection of invited papers in honor of Professor James E. Boggs on the occasion of his 75th birthday, in J. Mol. Struct., Vol. 376, Elsevier, Amsterdam, The Netherlands, 1996. 

Ab initio calculations of electronic wave functions are well established as useful and powerful theoretical tools to investigate physical and chemical processes at the molecular level. Many computational packages are available to perform such calculations, and a variety of mathematical methods exist to approximate the solutions of the electronic hamiltonian. Each method is based (or should be) on a well defined physical model, specified by a certain partition of the electronic hamiltonian, in such a way as to include a subset of all the interactions present in the exact one. It is expected that this subset contains the most important effects to describe consistently the situation of interest. The identification of which physical interactions to include is a major step in developing and applying quantum chemical theory to the study of real problems. 

Both examples also illustrate the state-of-the-art methodology used in molecular modeling of enzymatic reactions. Due to the size of enzymes quantum-chemical theory levels cannot be currently applied to whole systems. As the remedy for this situation the system is usually divided into at least two zones. The smaller one includes reactants and catalytically important fragments of the enzyme and is treated at the quantum level. The remaining part, which usually consists of the remaining part of the enzyme and water molecules, is treated at the molecular mechanics level. This so called QM/MM approach, suffers from many conceptual pitfalls,3-6 but still has proved to be highly successful in studying mechanisms of enzymatic reactions. 

There is something notable about this volume. In four chapters, it demonstrates the diversity of science that constitutes the field of catalysis as well as the cohesiveness of its parts. It covers technique of materials analysis, quantum chemical theory, a branch of catalytic practice, and the discussion of a major phenomenon of solids. 

Comparison with Theoretical Calculations. It appears that the polymer valence bands are (very) difficult to interpret without the aid of a theoretical basis, or a model, or of the use of a reference spectrum obtained from a model compound. Indeed, Quantum Chemical theory is nowadays able to calculate band structure and density of states for polymers, to simulate the limited resolution of the spectrometer, and to modulate these theoretical density of states to account for the photoionization cross sections that vary considerably for valence bands of polymers containing different types of atoms, and electrons with various symmetries. Consequently, one is able now to predict theoretically the energies of the various molecular orbitals, but also... 

These are descriptors for molecule bonds proposed with the aim of estimating the bond order defined in quantum-chemical theory or of generally defining bond weights so as to distinguish the bonds in a - molecular graph. 

Another approach to treating the boundary between covalently bonded QM and MM systems is the connection atom method,119 120 in which rather than a link atom, a monovalent pseudoatom is used. This connection atom is parameterized to give the correct behavior of the partitioned covalent bond. The connection atoms interact with the other QM atoms as a (specifically parameterized) QM atom, and with the other MM atoms as a standard carbon atom. This avoids the problem of a supplementary atom in the system, as the connection atom and the classical frontier atom are unified. However, the need to reparameterize for each type of covalent bond at a given level of quantum chemical theory is a laborious task.121 The connection atom method has been implemented for semiempirical molecular orbital (AMI and PM3)119 and density functional theory120 levels of theory. Tests carried out by Antes and Thiel to validate the connection atom method at the semiempirical level suggested that the connection atom approach is more accurate than the standard link atom approach.119... 

TABLE 1. Geometry of aniline determined using different levels of quantum chemical theory a and experiment... 

The major advance of the past decade is that, using quantum-chemical computations, activation energies (Eact) as well as activation entropies (AS ) can be predicted a priori for systems of catalytic interest. This implies much more reliable use of the transition-state reaction rate expression than before, since no assumption of the transition state-structure is necessary. This transition-state structure can now be predicted. However, the estimated absolute accuracy of computed transition states is approximately of the order of 20-30 kJ/mol. Here, we do not provide an extensive introduction to modern quantum-chemical theory that has led to this state of affairs excellent introductions can be found elsewhere [38,39]. Instead, we use the results of these techniques to provide structural and energetic information on catalytic intermediates and transition states. 

Mayer, 1. (1986b) On bond orders and valences in the ab initio quantum chemical theory. Int. J. Quant. Chem., 29, 73-84. 

The use of the SCRF model in a quantum-chemical theory requires that the shape and the size of the solute cavity must be defined uniquely for any set of compounds. A number of approaches to estimate these molecular characteristics have been developed [14], but no non-empirical way of their calculation is known. Therefore, it is important to study the dependence of the calculated properties of molecules in condensed media on the size and shape of the molecular cavity applied in the theory. 

The porous and amorphous structure of the resulting oxide overlayer is also interesting to discuss. The differential thermal analysis showed that at least six water molecules per C03O4 are involved in the overlayer structure. This is not surprising when one deals with a hydrous metal hydroxide layer, and the fact that such a structure behaves as amorphous in x-ray diffractometry does not preclude the existence of the crystalline domains of dimensions lower than 5x5 nm. The catalytic activity of this system is probably explained better in terms of the local interactions of the oxygen molecules with the cations of the oxide by considering a microscopic approach based on the quantum-chemical theory of the chemical bond in the small-sized solid clusters. 

During the first 25 years, 1926-1950, the Schrodinger equation was applied to many atoms and molecules, and this resulted in several quantum mechanical methods or theories, which were applicable to atoms and molecules. They are the quantum chemical theories. Here, we will mention the three major theories of the time and indicate their most conspicuous features. 

Undoubtedly, the methods most widely used to solve the Schrodinger equation are those based on the approach originally proposed by Hartree [1] and Fock [2]. Hartree-Fock (HF) theory is the simplest of the ab initio or "first principles" quantum chemical theories, which are obtained directly from the Schrodinger equation without incorporating any empirical considerations. In the HF approximation, the n-electron wavefunction is built from a set of n independent one-electron spin orbitals which contain both spatial and spin components. The HF trial wavefunction is taken as a single Slater determinant of spin orbitals. 

Transition metal oxides are the systems which make a challenge to any quantum chemical theory. Thus their theoretical investigation constitute an excellent benchmark for Density Functional Theory in both aspects methodological and practical one. Two transition metal oxide molecules are considered here in detail, VO and MoO, with emphasis put on their electronic structure, spectroscopic properties and metal - oxygen bonding features. Applicability of DFT to various electronic states is discussed and the quality of results within various computational schemes is examined. 

The first quantum chemical theory to give a convincing explanation of the shapes of molecules was the concept of hybrid orbitals. This is best illustrated by using carbon as an example, and is appropriate since the language of hybridization is still commonly used in organic chemistry. 

Quantum chemistry is the appfication of quantum mechanical principles and equations to the study of molecules. In order to nnderstand matter at its most fundamental level, we must use quantum mechanical models and methods. There are two aspects of quantum mechanics that make it different from previous models of matter. The first is the concept of wave-particle duality that is, the notion that we need to think of very small objects (such as electrons) as having characteristics of both particles and waves. Second, quantum mechanical models correctly predict that the energy of atoms and molecules is always quantized, meaning that they may have only specific amounts of energy. Quantum chemical theories allow us to explain the structure of the periodic table, and quantum chemical calculations allow us to accurately predict the structures of molecules and the spectroscopic behavior of atoms and molecules. 

MOVE molecular orbital valence bond (quantum chemical theory)... 

Most quantum chemical theories have so-called one-electron orbitals (in the future these will be referred to simply as orbitals) as their basis. To compute expectation values of physical quantities of interest it is often necessary to evaluate integrals of the type... 

It follows that, in all these cases, it is desirable and even essential to have sufficiently accurate experimental data which can be used as the basis of comparison with the theoretical values, Thus, the establishment of the experimental quantum chemistry of crystals was a great step forward in the development of a unified quantum-chemical theory of bonds in crystals. 

In this chapter, we review quantum chemical theories developed to describe chemical bonding in open-shell (transition metal) compounds. We review some important electronic structure methods that provide us with the central ingredient for an analysis of the chemical bond, the electronic wave function. We then discuss how information from the electronic wave function is extracted for a qualitative interpretation of the electronic structure. For this purpose, different approaches are described to extract local quantities from quantum states. An example is the local spin concept, which can be employed to study spin-spin interactions in terms of a Heisenberg coupling model. Finally, the difficulty of describing electronic structures of open-shell molecules accurately is highlighted as an example. 

R. F. W. Bader, Atoms in Molecules A Quantum Chemical Theory , Clarendon, Oxford,... 

Quantum chemical theory is an ever-expanding field thus constructive observations, corrections and suggestions are welcome and peer contribution is appreciated. 

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