CALCULATION OF OSCILLATOR STRENGTHS

We recall that the definition of the generalized oscillator strength may be written [see (II.4)] 

We have used the Born Oppenheimer approximation to factor 4 0/3, I,ma into electronic and nuclear parts and have further assumed that the former are orthogonal to enable us to reduce V. Both wave functions may be approximated by products of electronic, nuclear rotation and vibrational wave functions. The last of these may be factored out at once, and 

For continuum transitions an analogous expression must be used. In both discrete and continuum transitions several problems may arise  

A fundamental requirement of the derivation of (III. 1) and (III.2) is that j ma must be orthogonal to ( 0/8. If they are not initially orthogonal, they must be Schmidt orthogonalized in the normal way. However, such orthoganalization may lead to serious errors even in simple systems, as Bell and Kingston found for the helium l S- 3 5 transition.41 

A related but somewhat different approach has been suggested by the recently introduced MS Xa method. Calculation of the continuum functions within this method is relatively straightforward,51 52 and the method has been applied to the AT-shell X-ray absorption spectrum53 of N2 and very recently to photoionization of N2 and CO near threshold.54 This last 

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Very few ab initio calculations of oscillator strengths have been done due to the difficulties of the calculations. Oscillator strengths for atomic transitions calculated with RHF wave functions are fouhd to differ from experimental / values by factors of 2 or 3 when Cl is included, good agreement with experiment is obtained. Ab initio RHF oscillator strengths have been calculated for a number of diatomic molecules, and found to differ from experimental values by factors of 3 or 4. For details, see Schaefer, pp. 102-109, 168-176. 

In some of our calculations of oscillator strengths on different isoelectronic sequences we have sought the possible regularities complied with by different transitions. We next summarise the theoretical methodologies we have mostly employed to yield the results we show as examples. 

In order to explicitly account for core-polarization effects in the calculation of oscillator strengths, a corrected transition operator is frequently employed in our calculations,... 

Expressions for , which are necessary for calculations of oscillator strengths, are summarized in Table 2. For the sake of completeness, let us mention the Cl treatment of quartet states. The... 

P. G. Ellis and O. Goscinski Transition State Calculations of Oscillator Strengths in the Local Exchange Approximation Physica Scripta 9, 104 (1974). 

A problem with this procedure is that the solvent perturbs each electronic state of the solute molecule in a different way, i.e., each state is an eigenfunction of a different Hamiltonian consequendy, the different states are not mutually orthogonal. This fact complicates the calculation of oscillator strength and other transition properties of the system. 

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