Molecular electronic state theory,

Quantum chemistry or molecular electronic structure theory is the application of the principles of quantum mechanics to calculate the stationary states of molecules and the transitions between these states. Today, both computational and experimental groups routinely use ab initio (meaning from first principles ) molecular orbital calculations as a means of understanding structure, bonding, reaction paths between intermediates etc. Explicit treatment of the electrons means that, in principle, one does not make assumptions concerning the bonding of a system. 

We will see in due course that there are important correlation rules between atomic term symbols and molecular electronic states, rules that are important in understanding both the formation and dissociation of diatomic molecules. Elementary accounts of the theory of atomic structure are to be found in books by Softley [3] and Richards and Scott [4], Among the more comprehensive descriptions of the quantum mechanical aspects, that by Pauling and Wilson [5] remains as good as any whilst group theoretical aspects are described by Judd [6],... 

There are a number of different approaches to the description of molecular electronic states. In this section we describe molecular orbital theory, which has been by far the most significant and popular approach to both the qualitative and quantitative description of molecular electronic structure. In subsequent sections we will describe the theory of the correlation of molecular states to the Russell Saunders states of the separated atoms we will also discuss what is known as the united atom approach to the description of molecular electronic states, an approach which is confined to diatomic molecules. 

In chapter 6 we described the theory of molecular electronic states, particularly as it applies to diatomic molecules. We introduced the united atom nomenclature for describing the orbitals, and pointed out that this was particularly useful for tightly bound molecules with small intemuclear distances, like H2. We also discussed the more conventional nomenclature for describing electronic states, which is based upon the assumption that the component of electronic orbital angular momentum along the direction of the intemuclear axis is conserved, i.e. is a good quantum number. The latter description is therefore appropriate for molecules in electronic states which conform to Hund s case (a) or case (b) coupling. 

A direct consequence of the observation that Eqs. (12.55) provide also golden-rule expressions for transition rates between molecular electronic states in the shifted parallel harmonic potential surfaces model, is that the same theory can be applied to the calculation of optical absorption spectra. The electronic absorption lineshape expresses the photon-frequency dependent transition rate from the molecular ground state dressed by a photon, g) = g, hco ), to an electronically excited state without a photon, x). This absorption is broadened by electronic-vibrational coupling, and the resulting spectrum is sometimes referred to as the Franck-Condon envelope of the absorption lineshape. To see how this spectrum is obtained from the present formalism we start from the Hamiltonian (12.7) in which states L and R are replaced by g) and x) and Vlr becomes Pgx—the coupling between molecule and radiation field. The modes a represent intramolecular as well as intermolecular vibrational motions that couple to the electronic transition... 

Sudden polarization phenomenon was investigated in ethylene using nonempiri-cal molecular electronic structural theory [38]. The studies predicted that D2d symmetry of the ground state ethylene undergoes twisting in the excited state to attain a pyramidalized shape. 

Dola Pahari received her M.Sc. degree in chemistry in 2000 from the Indian Institute of Technology, Kanpur, India. She is doing Ph.D. on the development and apphcations of molecular electronic structure theory under the supervision of Debashis Mukher-jee. She is interested in developing spin-adapted state-specihc many-body theories. 

As well as reviewing progress and prospects of the state-specific Brillouin-Wigner approach, we describe the new methods of communication that were deployed to facilitate effective collaboration between researchers located as geographically distributed sites. A web-based collaborative virtual environment (cvE) was designed for research on molecular electronic structure theory which... 

The Hartree-Fock approximation [13, 14] plays a central role in the molecular electronic structure theory. In most cases, it provides a qualitatively correct description of the electronic structure of many electron atoms and molecules in their ground electronic state. In addition, it constitutes a basis upon which more accurate methods can be developed. A detailed derivation and discussion of the method can be found in textbooks such as [10, 11]. The Hartree-Fock approximation assumes the simplest possible form for the electronic wavefunction, i.e a single Slater determinant given by Eq. (2.41). Starting from the electronic TISE Eq. (2.5), the Hartree-Fock energy is simply... 

Hiickel s theory gives two molecular electronic states for the electron system of the ethylene molecule, a bonding one and an antibonding one. Both states in first approximation are described by linear combinations of the atomic 2p eigenfunctions of the two carbon atoms. We call the energies of the two states E b) and... 

For RX, there is an alternative method for calculating this correction. Kaledin et al. (1996a) described the molecular electronic states of RX (R = Ce-Yb and X = F, Cl, Br, I) in a wide range of energies in terms of the ligand field theory (LFT), which takes into account the perturbation of the energy levels of the R ion by the ligand X . These results were supported by DFT calculations of low-l)dng electronic states for RF (Dai et al., 1998 Ren et al., 1998). 

Chapters 1-3 introduce second quantization, emphasizing those aspects of the theory that are useful for molecular electronic-structure theory. In Chapter 1, second quantization is introduced in the spin-orbital basis, and we show how first-quantization operators and states are represented in the language of second quantization. Next, in Chapter 2, we make spin adaptations of such operators and states, introducing spin tensor operators and configuration state functions. Finally, in Chapter 3, we discuss unitary transformations and, in particular, their nonredundant formulation in terms of exponentials of matrices and operators. Of particular importance is the exponential parametrization of unitary orbital transformations, used in the subsequent chapters of the book. 

We now turn to electronic selection rules for syimnetrical nonlinear molecules. The procedure here is to examme the structure of a molecule to detennine what synnnetry operations exist which will leave the molecular framework in an equivalent configuration. Then one looks at the various possible point groups to see what group would consist of those particular operations. The character table for that group will then pennit one to classify electronic states by symmetry and to work out the selection rules. Character tables for all relevant groups can be found in many books on spectroscopy or group theory. Ftere we will only pick one very sunple point group called 2 and look at some simple examples to illustrate the method. 

In quantum theory, physical systems move in vector spaces that are, unlike those in classical physics, essentially complex. This difference has had considerable impact on the status, interpretation, and mathematics of the theory. These aspects will be discussed in this chapter within the general context of simple molecular systems, while concentrating at the same time on instances in which the electronic states of the molecule are exactly or neatly degenerate. It is hoped... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

The starting point for the theory of molecular dynamics, and indeed the basis for most of theoretical chemistry, is the separation of the nuclear and electionic motion. In the standard, adiabatic, picture this leads to the concept of nuclei moving over PES corresponding to the electronic states of a system. 

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