Molecular quantum theory, semi-empirical

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. 

Molecular geometries may be calculated by means of quantum-chemical semi-empirical valence electron theories, such as Dewar s MINDO/3 , MNDO " or AMl procedures, or by classical molecular force-field methods, such as Allinger s MM2 procedure. Alternatively, inirio Hartree-Fock SCF MO methods allow, by virtue of analytical gradient evaluations , the determination of molecular geometries independent of experimentally adjusted integral values. 

On the Bridge between Semi-Empirical and Ab-Initio Methods in Atomic and Molecular Quantum Theory. 

Thiel W 1996 Perspectives on semiempirical molecular orbital theory New Methods in Computationai Quantum Meohanios (Adv. Chem. Phys. XCiti) ed I Prigogine I and S A Rice (New York Wiley) pp 703-57 Earlier texts dealing with semi-empirical methods include ... 

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). 

Presents the basic theory of quantum mechanics, particularly, semi-empirical molecular orbital theory. The authors detail and justify the approximations inherent in the semi-empirical Hamiltonians. Includes useful discussions of the applications of these methods to specific research problems. 

Semi-empirical quantum mechanics methods have evolved over the last three decades. Using today s microcomputers, they can produce meaningful, often quantitative, results for large molecular systems. The roots of the methods lie in the theory of % electrons, now largely superseded by all-valence electron theories. 

J. N. Murrell and A. J. Harget, Semi-empirical Self-consistent Molecular Orbital Theory of Molecules, Wiley-Interscience, London, 1972 G. H. Wagniere, Introduction to Elementary Molecular Orbital Theory and to Semiempirical Methods, Springer-Verlag, Berlin, 1976 J. Sadleij, Semi-empirical Methods of Quantum Chemistry, Wiley, New York, 1985. 

HyperChem Release 7 , available in 2002, is a full 32-bit application, developed for the Windows 95, 98, NT, ME, 2000 and XP operating systems. Density Functional Theory (DFT) has been added to complement Molecular Mechanics, Semi-Empirical Quantum Mechanics and Ab Initio Quantum Mechanics already available. The HyperNMR package has been integrated into the core of HyperChem, allowing for the simulation of NMR spectra. A full database capability is integrated into HyperChem 7. Many other features are updated and improved. 

The advent of semi-empirical molecular orbital calculations and density functional theory, which employ mathematical assumptions to simplify the application of quantum mechanics to drug molecules of intermediate to large size. 

J.-F. Labarre Conformational Analysis in Inorganic Chemistry Semi-Empiric Quantum Calculations vs. Experiment D. B. Cook Hie Approximate Calculation of Molecular Electronic Structures as a Theory ofValence... 

In the final exploration of the quantum chemistry unit students use a computational chemistry package (eg. Spartan, Gaussian, CaChe, etc.) to calculate the ground state energies, molecular orbitals, and in some cases the excited state energies, of two proton transfer tautomers. Calculations are performed at several different levels of theory, and use both semi-empirical and ab initio methods. Several different basis sets are compared in the ab initio calculations. The students use the results of these calculations to estimate the likelihood of excited state proton transfer. The calculations require CPU time ranging from a couple of minutes to a couple of hours on the PCs available to the students in the laboratory. 

A semi-empirical ir-electron theory that takes electron repulsion into account is the Pariser-Parr-Pople (PPP) method (R.G. Parr. Quantum Theory of Molecular Electronic Structure, Benjamin, N.Y., 1963). 

Semi-empirical molecular orbital, MO, theory uses a combination of experimental data and quantum mechanical MO methods to model the valence electronic structure of molecules. In the MNDO (8) method each atom is parameterized using experimental data. This calculation provides molecular orbital descriptions of the valence electrons, as well as effective charges of each atom in the molecule. 

The construction of exchange correlation potentials and energies becomes a task for which not much guidance can be obtained from fundamental theory. The form of dependence on the electron density is generally not known and can only to a limited extent be obtained from theoretical considerations. The best one can do is to assume some functional dependence on the density with parameters to satisfy some consistency criteria and to fit calculated results to some model systems for which applications of proper quantum mechanical theory can be used as comparisons. At best this results in some form of ad-hoc semi-empirical method, which may be used with success for simulations of molecular ground state properties, but is certainly not universal. 

In terms of graph theory, it is convenient to represent several non-empiri-cal and semi-empirical methods of quantum chemistry. Energy and charge characteristics of molecules are treated as various structural characteristics of molecular graphs. 

The contributions of Erich Hiickel to the development of molecular orbital theory have already been mentioned in the subsection on Germany (Section 5.4.1) the development of semi-empirical quantum mechanical treatments in organic chemistry by M. J. S. Dewar has been discussed in Section 5.5. In the early development of the application of quantum mechanics to chemistry, Linus Pauling (1901-1994)359 was pre-eminent. He was associated with CalTech for most of his career. His work before World War II generated two influential books the Introduction to Quantum Mechanics (with E. Bright Wilson, 1935)360 and The Nature of the Chemical Bond (1939).361 He favoured the valence-bond treatment and the theory of resonance. 

The theoretical tools of quantum chemistry briefly described in the previous chapter are numerously implemented, sometimes explicitly and sometimes implicitly, in ab initio, density functional (DFT), and semi-empirical theories of quantum chemistry and in the computer program suits based upon them. It is usually believed that the difference between the methods stems from different approximations used for the one- and two-electron matrix elements of the molecular Hamiltonian eq. (1.177) employed throughout the calculation. However, this type of classification is not particularly suitable in the context of hybrid methods where attention must be drawn to the way of separating the entire molecular system (eventually - the universe itself) into parts, of which some are treated explicitly on a quantum mechanical/chemical level, while others are considered classically and the rest is not addressed at all. That general formulation allows us to cover both the traditional quantum chemistry methods based on the wave functions and the DFT-based methods, which generally claim... 

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