RKR inversion

RKR inversion of spectra. b A, alkali atom R, rare gas atom M, molecule. 

For diatomic reagents, the potential energy curves can often be obtained through inversion of experimental data. If sufficient spectroscopic data are available, an RKR inversion - o can be performed with very high accuracy. More recently, Bernstein, Zewail, and co-workers inverted femtosecond temporal spectra to obtain diatomic potentials of high accuracy. 

This ratio is in good agreement with the spectrum shown in Figure 2. The term values for v = 0-12 (N 14,16) of the a ZQ" " state are then used to determine the rotationless potential curve through an RKR Inversion procedure. 

However it is now becoming possible to calculate the infra-red spectra of van der Waals complexes in considerable detail , and this will provide a much more detailed source of information about the validity of the intermolecular potential surface than has been available in the past. Some progress has also been made with the RKR inversion of spectroscopic data to provide potential-energy surfaces for polyatomic molecules. With the help of this information it should be possible to improve the calculation of intermolecular potential energy surfaces over the next few years. 

Direct RKR inversion of vibrationally and rotationally resolved spectroscopic data for diatomics is now a fairly routine procedure. In normal RKR applications, however, the spectral data are exploited in a relatively limited fashion. One simply uses B(v) and E(v), the rotational constant and term value dependence on vibrational quantum v, respectively, to infer the inner and outer classical turning points at each v from a semiclassical analysis. In high resolution spectroscopy of van der Waals complexes, however, there is often far more rotational than vibrational data available. Consequently extensive information exists on very high order centrifugal effects on the radial coordinate, sometimes up to, and by virtue of centrifugal barriers, beyond the dissociation limit The hope is that a simple extension of RKR ideas might be able to extract a 1-D potential directly from rotational data alone. 

The potential curves derived from such calculations can often be empirically improved by comparison with so-called experimental curves derived from observed spectroscopic data, using Rydberg-Klein-Rees (RKR) or other inversion procedures. It is often found, particularly for the atmospheric systems, that the remaining correlation errors in a configuration interaction (Cl) calculation are similar for many excited electronic states of the same symmetry or principal molecular-orbital description. Thus it is often possible to calibrate an entire family of calculated excited-state potential curves to near-spectroscopic accuracy. Such a procedure has been applied to the systems described here. 

Inversion of experimental data to calculate the potential function (RKR)... 

The unavailability of an RKR-like inversion (hence the impossiblity of obtaining the potential energy surface, V(Q), and exact vibrational eigenfunctions directly from experimental data) makes it convenient to use products of simple harmonic or Morse-oscillator basis functions as vibrational basis states... 

C. Schwartz and R. J. LeRoy, J. Chem. Phys., 81,3996 (1984). A Two-Isotope Higher-Order RKR-Type Inversion Procedure. 

Diatomic molecules are a special case. Firstly, the dynamics of atomic collisions can usually be calculated accurately, and there are some inversion techniques that allow one to predict the potential from the experimental data the RKR method of analysing spectroscopic data is the most well known of these [1]. Secondly, the potential energy functions are one dimensional and even "complicated functions are simple compared with those of polyatomic molecules. 

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