Electronic state/configuration

The transition metal ions, Cu , Ag and Au", all have a d ( 5) electronic state-configuration, with = 3,4 and 5, respectively. The RCEP used here were generated from Dirac-Fock (DF) all electron (AE) relativistic atomic orbitals, and therefore implicitly include the indirect relativistic effects of the core electron on the valence electrons, which in these metal ion systems are the major radial scaling effect. In these RCEP the s p subshells are included in the valence orbital space together with the d, ( + l)s and ( + l)p atomic orbitals and all must be adequately represented by basis functions. The need for such semi-core or semi-valence electrons to be treated explicitly together with the traditional valence orbitals for the heavier elements has been adequately documented The gaussian function basis set on each metal atom consists of the published 4 P3 distribution which is double-zeta each in the sp and n + l)sp orbital space, and triple-zeta for the nd electrons. 

Electronic-state configurations are described by the standard quantum numbers or principal quantum number n, angular momentum quantum number L, spin quantum number S and total angular momentum quantum number J. In the so-called Russel-Saunders approximation of electron coupling, electronic states are commonly described symbolically by n For... 

Metals are fiindamentally different from insulators as they possess no gap in the excitation spectra. Under the influence of an external field, electrons can respond by readily changing from one k state to another. The ease by which the ground-state configuration is changed accounts for the high conductivity of metals. 

In this section we concentrate on the electronic and vibrational parts of the wavefimctions. It is convenient to treat the nuclear configuration in temis of nomial coordinates describing the displacements from the equilibrium position. We call these nuclear nomial coordinates Q- and use the symbol Q without a subscript to designate the whole set. Similarly, the symbol v. designates the coordinates of the th electron and v the whole set of electronic coordinates. We also use subscripts 1 and ii to designate the lower and upper electronic states of a transition, and subscripts a and b to number the vibrational states in the respective electronic states. The total wavefiinction f can be written... 

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. 

To improve upon die mean-field picture of electronic structure, one must move beyond the singleconfiguration approximation. It is essential to do so to achieve higher accuracy, but it is also important to do so to achieve a conceptually correct view of the chemical electronic structure. Although the picture of configurations in which A electrons occupy A spin orbitals may be familiar and usefiil for systematizing the electronic states of atoms and molecules, these constructs are approximations to the true states of the system. They were introduced when the mean-field approximation was made, and neither orbitals nor configurations can be claimed to describe the proper eigenstates T, . It is thus inconsistent to insist that the carbon atom... 

In most of the connnonly used ab initio quantum chemical methods [26], one fonns a set of configurations by placing N electrons into spin orbitals in a maimer that produces the spatial, spin and angular momentum syimnetry of the electronic state of interest. The correct wavefimction T is then written as a linear combination of tire mean-field configuration fimctions qj = example, to describe the... 

Aspects of the Jahn-Teller symmetry argument will be relevant in later sections. Suppose that the electronic states aie n-fold degenerate, with symmetry at some symmetiical nuclear configuration Qq. The fundamental question concerns the symmetry of the nuclear coordinates that can split the degeneracy linearly in Q — Qo, in other words those that appeal linearly in Taylor series for the matrix elements A H B). Since the bras (/1 and kets B) both transform as and H are totally symmetric, it would appear at first sight that the Jahn-Teller active modes must have symmetry Fg = F x F. There... 

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). 

Let S be any simply connected surface in nuclear configuration space, bounded by a closed-loop L. Then, if 4>(r,R) changes sign when transported adiabatically round L, there must be at least one point on S at which (r, R) is discontinuous, implying that its potential energy surface intersects that of another electronic state. 

Areen silicon and germanium are ascribed to the d electron states silicon does not have 3 d electrons, whereas germanium does. Certain transitions (e.g. carbon /3 hn) do depend upon the d character of the electronic configuration in contrast to subsequent isitions. 

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