Electronic structure molecular

The approximation to the electron-electron repulsion has a mathematical effect of converting an N-electron problem of some original electronic Schrodinger equation to N one-electron problems by means of an effective one-electron potential operator, g. This is combined with the operator corresponding to an electron s kinetic energy and its attraction for the nuclei, fi  

In general, separability of a Schrodinger equation comes about if there are independent, additive pieces of the Hamiltonian. The separability of an N-electron Schrodinger equation into the N one-electron equations represented by Equation 10.51 means the approximation corresponds to a many-electron Hamiltonian that is simply the sum of Fock operators for each electron, and we designate this Hamiltonian Hq. 

The Fock operators in Equation 10.52 are subscripted to indicate that each acts on independent position coordinates for the N electrons. Separability also means that the energy is a sum, and in this case, we have 

Eq is the eigenenergy of Hq. The orbital energies provide a framework for chemical energetics. For instance, since the net energy needed to form a molecule from separated nuclei and electrons is (approximately) Eq, a reaction energy can be approximately obtained as a difference in orbital energies of reactants and products. 

Comparison of Calculated and Measured Values of Certain Molecular Properties 

---

Ortiz J V 1997 The electron propagator picture of molecular electronic structure Computational Chemistry Reviews of Current Trends vo 2, ed J Leszczynski (Singapore World Scientific) pp 1-61... 

The trends in chemical and physical properties of the elements described beautifully in the periodic table and the ability of early spectroscopists to fit atomic line spectra by simple mathematical formulas and to interpret atomic electronic states in terms of empirical quantum numbers provide compelling evidence that some relatively simple framework must exist for understanding the electronic structures of all atoms. The great predictive power of the concept of atomic valence further suggests that molecular electronic structure should be understandable in terms of those of the constituent atoms. 

E. Kracka, T. H. Dunning, Jr., Advances in Molecular Electronic Structure Theory Calculation and Characterization of Molecular Potential Energy Surfaces T. H. Dunning, Jr. Ed., 129, JAI, Greenwich (1990). 

W. C. Ennler, H. C. Hsieh, Advances in Molecular Electronic Structure Theory T. H. 

GAMESS stands for general atomic and molecular electronic structure system (we reviewed a version dated Dec. 2, 1998). It is an ah initio and semiempirical program, and has seen the most widespread use for ah initio calculations. The ASCII input hie format is usable but somewhat more lengthy than some other programs. The fact that GAMESS is a free, high-quality software makes it a favorite of many academic researchers. 

For the purposes of a purely theoretical analysis of molecular electronic structure, we need more detailed information. The term population analysis was introduced in a series of papers by Mulliken in 1955, but the basic ideas had already been anticipated by Mulliken himself, and by other authors. The technique has been widely applied since Mulliken s 1955 papers, because it is very simple and has the apparent virtue of being quantitative . The word quantitative seems to mean two different things to different authors ... 

Hiickel models of molecular electronic structure enjoyed many years of popularity, particularly the r-electron variants. Authors sought to extract the last possible amount of information from these models, perhaps because nothing more refined was technically feasible at the time. Thus, for example, the inductive effect was studied. The inductive effect is a key concept in organic chemistry a group R should show a - -1 or a —I effect (according to the nature of the group R) when it is substituted into a benzene ring. 

Over the last thirty years, international collaboration and cooperation on a scale rarely witnessed in science has led to the development of several very sophisticated software packages for ab initio molecular electronic structure calculations. In the early days, such packages were freely distributed amongst workers in the field. Today, you buy executable code, a licence and professional documentation just as with any software package. 

Schaefer, H.F., III. Quantum Chemistry. The Development of ab initio Methods in Molecular Electronic Structure Theory . Clarendon Press Oxford, 1984. 

C.J. Ballhausen, Molecular Electronic Structures of Transition Metal Complexes, McGraw-Hill, New York, 1979. 

GAMESS general atomic and molecular electronic structure system... 

In some cases, chemical substituents can bring about unusual monotropic liquid crystalline phases which only exist upon heating or cooling. The diphenyl-diacetylenes are examples in this category [22]. Early theoretical connections between molecular electronic structure and orientational order... 

A simple example of how molecular electronic structure can influence condensed phase liquid crystalline properties exists for molecules containing strongly dipolar units. These tend to exhibit dipolar associations in condensed phases which influence many thermodynamic properties [29]. Local structural correlations are usually measured using the Kirkwood factor g defined as... 

The factors Kn are elastic constants for the nematic phase and Icb is the Boltzmann constant. Therefore a combination of molecular electronic structure, orientational order and continuum elasticity are all involved in determining the flexoelectric polarisation. Polarisation can also be produced in the presence of an average gradient in the density of quadrupoles. This is... 

It is clear from the forgoing discussions that the important material properties of liquid crystals are closely related to the details of the structure and bonding of the individual molecules. However, emphasis in computer simulations has focused on refining and implementing intermolecular interactions for condensed phase simulations. It is clear that further work aimed at better understanding of molecular electronic structure of liquid crystal molecules will be a major step forward in the design and application of new materials. In the following section we outline a number of techniques for predictive calculation of molecular properties. 

In this section we aim to introduce some of the main theoretical ideas which underlie the strategies for modelling liquid crystal molecules. It is clear that there are a very wide range of methods available and we will not attempt to be comprehensive. Instead, we will begin with a brief overview of traditional semi-empirical approaches and then progress to concentrate on treating fully predictive parameter-free calculations of molecular electronic structure and properties in some depth. 

Since plane waves are delocalised and of infinite spatial extent, it is natural to perform these calculations in a periodic environment and periodic boundary conditions can be used to enforce this periodicity. Periodic boundary conditions for an isolated molecule are shown schematically in Fig. 8. The molecular problem then becomes formally equivalent to an electronic structure calculation for a periodic solid consisting of one molecule per unit cell. In the limit of large separation between molecules, the molecular electronic structure of the isolated gas phase molecule is obtained accurately. 

Fig. 8. Illustration of the use of periodic boundary conditions in the determination of molecular electronic structure. The unit cell is shown by the dashed line. As the unit cell size is increased the calculated properties converge toward those of the isolated molecule...

Cook DB (1978) The Approximate Calculation of Molecular Electronic Structures as Theory of Valence. 35 37-86... 

Carved wooden bears in all shapes and sizes overwhelmed Yngve and me at our visit to Noboribetsu in 1976. There was an afternoon to spare before the opening of the "Oji International Seminar on Theories and Ab Initio Computations of Molecular Electronic Structure" at Tomakomai, Hokkaido in the fall of 1976 so we wished to experience the hot springs. The train left us with a choice of buses, the desdnations of which were clearly indicated in Japanese writing. We found the right one and came to a city in a canyon where the sulfur fumes and hot water let themselves out. The kind reception by Kimio Ohno and Fukashi Sasaki at Hokkaido University remains a vivid memory. 

One-electron pictures of molecular electronic structure continue to inform interpretations of structure and spectra. These models are the successors of qualitative valence theories that attempt to impose patterns on chemical data and to stimulate experimental tests of predictions. Therefore, in formulating a one-electron theory of chemical bonding, it is desirable to retain the following conceptual advantages. 

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. 

Parr RG. Quantum theory of molecular electronic structure. New York Benjamin, 1963. 

Many of the initial theoretical models used to vahdate the concept of coherent control and optimal control have been based on the interaction of the electric field of the laser light with a molecular dipole moment [43, 60, 105]. This represents just the first, or lowest, term in the expression for the interaction of an electric field with a molecule. Many of the successful optimal control experiments have used electric fields that are capable of ionizing the molecules and involve the use of electric field strengths that lead to major distortions of the molecular electronic structure. With this in mind, there has been discussion in the... 

M. W. Schmidt et al., Gamess General atomic and molecular electronic structure system (2006), see http //www.msg.ameslab.gov/GAMESS/GAMESS.html and / Comput. Chem. 14, 1347 (1993). 

R.G. Parr, The Quantum Theory of Molecular Electronic Structure. A. Benjamin Inc., New York, 1963. 

---