Molecular orbitals quantum chemistry

Simonetta, M., Gianinelti, E. In P. O. Ldwdin and B. Pullman (Editors), Molecular Orbitals in Chemistry, Physics and Biology- New York Academic Press 1964 see also Kotani, M., Ohno, K., Kayama, K. Quantum Mechanics of Electronic Structure of Simple Molecules. In 5. Flteegge (Editor), Hand-buch der I%ysik, Vol. XXXVII/2, Molek le II. Berlin-Gottingen-Heidelberg Springer 1961. 

Key words Computational chemistry - Direct selFconsistent field method - Molecular orbital -Quantum mechanics - Two-electron integrals... 

Coukon, C. A. 1964. R.S. Mulliken - his work and influence on quantum chemistry. In Molecular orbitals in chemistry, physics and biology - a tribute to R.S. Mulliken, ed. P.-O. Lowdin and B. Pullman, 1-15. New York Academic Press. 

Although a separation of electronic and nuclear motion provides an important simplification and appealing qualitative model for chemistry, the electronic Sclirodinger equation is still fomiidable. Efforts to solve it approximately and apply these solutions to the study of spectroscopy, stmcture and chemical reactions fonn the subject of what is usually called electronic structure theory or quantum chemistry. The starting point for most calculations and the foundation of molecular orbital theory is the independent-particle approximation. 

For both types of orbitals, the coordinates r, 0 and cji refer to the position of the electron relative to a set of axes attached to the centre on which the basis orbital is located. Although STOs have the proper cusp behaviour near the nuclei, they are used primarily for atomic- and linear-molecule calculations because the multi-centre integrals which arise in polyatomic-molecule calculations caimot efficiently be perfonned when STOs are employed. In contrast, such integrals can routinely be done when GTOs are used. This fiindamental advantage of GTOs has led to the dominance of these fimetions in molecular quantum chemistry. 

Molecular orbitals were one of the first molecular features that could be visualized with simple graphical hardware. The reason for this early representation is found in the complex theory of quantum chemistry. Basically, a structure is more attractive and easier to understand when orbitals are displayed, rather than numerical orbital coefficients. The molecular orbitals, calculated by semi-empirical or ab initio quantum mechanical methods, are represented by isosurfaces, corresponding to the electron density surfeces Figure 2-125a). 

Much of quantum chemistry attempts to make more quantitative these aspects of chemists view of the periodic table and of atomic valence and structure. By starting from first principles and treating atomic and molecular states as solutions of a so-called Schrodinger equation, quantum chemistry seeks to determine what underlies the empirical quantum numbers, orbitals, the aufbau principle and the concept of valence used by spectroscopists and chemists, in some cases, even prior to the advent of quantum mechanics. 

Variational methods, in particular the linear variational method, are the most widely used approximation techniques in quantum chemistry. To implement such a method one needs to know the Hamiltonian H whose energy levels are sought and one needs to construct a trial wavefunction in which some flexibility exists (e.g., as in the linear variational method where the Cj coefficients can be varied). In Section 6 this tool will be used to develop several of the most commonly used and powerful molecular orbital methods in chemistry. 

Molecular orbitals (mos) are formed by combining atomic orbitals (aos) of the constituent atoms. This is one of the most important and widely used ideas in quantum chemistry. Much of chemists understanding of chemical bonding, structure, and reactivity is founded on this point of view. 

I. N. Levine, Quantum Chemistry Fourth Edition Prentice Flail, Englewood Cliffs (1991). W. J. Flehre, L. Radom, P. v. R. Schleyer, J. A. Pople, Ah Initio Molecular Orbital Theory John Wiley Sons, New York (1986). 

Provides a survey of quantum mechanics, semi-empirical computational methods, and the application of molecular orbital theory to organic chemistry. The concepts explored in this book should be easy for most readers to understand. 

This section describes the basics of HyperChem s simple molecular orbital calculations. It interprets HyperChem s results rather than introducing quantum chemistry. For a complete discussion, you should consult textbooks in quantum chemistry, such as I. N. Levine, Quantum Chemistry, 3rd Edition, Allyn and Bacon, 1986 ... 

The supporters of this view appear to be fighting a losing battle if one considers the pervasiveness of the current orbitals paradigm in chemistry (2). Atomic and molecular orbitals are freely used at all levels of chemistry in an attempt to explain chemical structure, bonding, and reactivity. This is a very unfortunate situation since the concept of orbitals cannot be strictly maintained in the light of quantum theory from which it supposedly derives. 

However, the taxonomic effectiveness of electronic configurations is not a basis for thinking that quantum mechanics can successfully account even for the restricted field of atomic chemistry. Clearly, molecular quantum chemistry is even less secure due to the additional assumptions which must be made apart from the validity of atomic orbitals. 

PMO Theory of Organic Chemistry Plenum NY, 1975 Zimmerman, H.E. Quantum Mechanics for Organic Chemists Academic Press NY, 1975 Borden, W.T. Modem Molecular Orbital Theory for Organic Chemists Prentice-Hall Englewood Cliffs, NJ, 1975 Dewar, M.J.S. The Molecular Orbital Theory of Organic Chemistry McGraw-Hill NY, 1969 Liberies, A. Introduction to Molecular Orbital Theory Holt, Rinehart, and Winston NY, 1966. 

Dewar, M. J. S., The Molecular Orbital Theory of Organic Chemistry, McGraw-Hill, New York, 1969 R. G. Pan, The Quantum Theory of Molecular Electronic Structure, Benjamin, New York, 1963. 

Stewart HP. MOPAC A semiempirical molecular orbital program. Quantum Chemistry Program Exchange, 1983. Prog. 455. 

The SPARC (Sparc Performs Automated Reasoning in Chemistry) approach was introduced in the 1990s by Karickhoff, Carreira, Hilal and their colleagues [16-18]. This method uses LSER [19] to estimate perturbed molecular orbitals [20] to describe quantum effects such as charge distribuhon and delocalizahon, and polarizability of molecules followed by quanhtative structure-activity relationship (QSAR) studies to correlate structure with molecular properties. SPARC describes Gibbs energy of a given process (e.g. solvation in water) as a sum of ... 

It is a truism that in the past decade density functional theory has made its way from a peripheral position in quantum chemistry to center stage. Of course the often excellent accuracy of the DFT based methods has provided the primary driving force of this development. When one adds to this the computational economy of the calculations, the choice for DFT appears natural and practical. So DFT has conquered the rational minds of the quantum chemists and computational chemists, but has it also won their hearts To many, the success of DFT appeared somewhat miraculous, and maybe even unjust and unjustified. Unjust in view of the easy achievement of accuracy that was so hard to come by in the wave function based methods. And unjustified it appeared to those who doubted the soundness of the theoretical foundations. There has been misunderstanding concerning the status of the one-determinantal approach of Kohn and Sham, which superficially appeared to preclude the incorporation of correlation effects. There has been uneasiness about the molecular orbitals of the Kohn-Sham model, which chemists used qualitatively as they always have used orbitals but which in the physics literature were sometimes denoted as mathematical constructs devoid of physical (let alone chemical) meaning. 

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. 

Other approximate, more empirical methods are the extended Huckel 31> and hybrid-based Hiickel 32. 3> approaches. In these methods the electron repulsion is not taken into account explicitly. These are extensions of the early Huckel molecular orbitals 4> which have successfully been used in the n electron system of planar molecules. On account of the simplest feature of calculation, the Hiickel method has made possible the first quantum mechanical interpretation of the classical electronic theory of organic chemistry and has given a reasonable explanation for the chemical reactivity of sizable conjugated molecules. 

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