Electron Configuration. Electronic States

Krauss, M. Compendium of ab Initio Calculations of Molecular Energies and Properties NBS-TN-438 [1967] 1/139. 

Richards, W. G. Walker, T. E. H. Hinkley, R. K. A Bibliography of ab initio Molecular Wave Functions, Clarendon Press, Oxford 1971. 

Richards, W. G. Walker, T. E. H. Farnell, L. Scott, P. R. Bibliography of ab initio Molecular Wave Functions. Supplement for 1970-1974, Clarendon Press, Oxford 1974. Richards, W. G. Scott, P. R. Colburn, E. A. Marchington, A. F. Bibliography of ab initio Molecular Wave Functions. Supplement for 1974-1977, Clarendon Press, Oxford 1978. 

In the following sections on molecular properties and spectra of NH, only a few relevant calculations will be occasionally quoted in order to supplement the experimental results or in cases where experimental results either are not available or are disagreeing or uncertain. Otherwise, the reader is referred to the bibliographies. 

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Electron Configuration. Electronic States. The NH ion is isoelectronic with the CH radical. Its ground state X 11 results from the ionization of the Iti MO in the NH(X 2 ) radical (cf. p. 31), and the lowest excited valence states arise from l7i-<-3a, and... 

Geometric Structure. Electron Configuration. Electronic States. 

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. 

Some excited configurations of the lithium atom, involving promotion of only the valence electron, are given in Table 7.4, which also lists the states arising from these configurations. Similar states can easily be derived for other alkali metals. 

The coefficients indicate the composition of the electronic state in terms of a linear combination of the various electronic configurations defined earlier in the output. Here is an example from a 4,4 CAS showing the first two excited state configurations ... 

The only electronic states that can be treated are those that correspond to the highest spin multiplet of a given orbital configuration. 

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