Polish Academy of Sciences

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Data Analysis

Inverted Perturbation Approach (IPA)

Inverted Perturbation Approach (IPA) is a fully quantum technique, developed in our group, and used for describing shapes of real molecular potentials. The main goal in this technique is to find a correction δU(R) to the initial, approximate potential U0(R). A set of eigenenergies obtained by numerical solving of Schrödinger equation with the potential U0(R)+δU(R) should reproduce experimental values of molecular energies. It is an iterative procedure, treating the improved potential U0(R)+δU(R) as a next, better approximation, which serves as an initial potential in the subsequent step of calculation. Such procedure should be repeated untill the discrepancies between calculated and experimental values of eigenenergies will be small enough, where “small enough” is an arbitrary condition.
Finding an “ideal” correction δU(R) would make possible a calculation of its influence on the energies of molecular levels, using the well known perturbation approach. Usually in such an approach the correction to the potential is known and corrections to eigenenergies values are sought. This case is opposite – the goal of the method is to find an “ideal” correction δU(R) to the potential, basing on known differences (corrections) to the energies of molecular levels, what explains the name of the method.
The potential U0(R) as well as the corrections to the potential δU(R) may be defined as a set of points, connected with spline functions. This form is versatile and allows for an accurate and smooth approximation of potential energy curves in case of many different, even exotic shapes of potentials, for example functions with more than one minimum or with shelves. In case of more complicated functions only a larger number of points describing the potential is needed. Additionally in our version of the IPA method the values of potential corrections δU(R) for each point are at the same time fitting parameters. Defining of uncertainties of the fit is much easier in this case.


Asen Pashov, Włodzimierz Jastrzębski, Paweł Kowalczyk Computer Physics Communications, 128(3), 622-634 (2000)

DOI: 10.1016/S0010-4655(00)00010-2


The IPA method allows for describing molecular potential energy curves of very exotic shapes.

An exemplary potential energy curve of the double-minimum 21Σu+ state (solid line) generated with IPA method compared with theoretical calculation (pluses).