# Solving Inverse Problems of Molecular Spectroscopy and Analysis of Molecular Force Fields

## Document Type

Presentation Abstract

## Presentation Date

10-20-2005

## Abstract

A force constant matrix F (consisted from second derivatives of the molecular potential with respect to nucleus coordinates in the equilibrium configuration) is one of the most important information about the intramolecular dynamics and defines vibrational properties (including infrared and Raman spectra, vibration-rotational spectra, etc.).

There are two main sources for the molecular force field determination. The first way is solving the inverse problem using an experimental data on molecular spectra and electron diffraction measurement. Both (vibrational or generalized structural) problems belong to the class of nonlinear ill-posed problems [1]. Other way is to estimate the molecular force field by carrying out quantum mechanical calculations with a goal to obtain the theoretical equilibrium configuration and force constants.

We have proposed to join these two approaches in the unique statement based on joint treatment of experimental and quantum mechanical data. On this base the concept of regularized quantum mechanical force field (RQMFF) was proposed, and new formulations of inverse problems were given. Stable numerical methods for the solving corresponding inverse problems have been developed. New regularizing algorithms allow us to carry out a special modeling of matrix F based on the different constraints which take into account the relative order of intramolecular forces. Force fields of extended molecular systems (clusters, polymers etc.) are constructed on a base of synthesis of separate blocks of force constants. For the estimation of intermolecular force constants we use the regularizing algorithm based on the joint use of empirical data on the second virial coefficients and results of quantum mechanical calculations.

The next scheme for the calculations of vibrational spectra of the large size molecules such as polymers, nanostructures, biological systems, etc. can be proposed:

- quantum mechanical analysis of moderate size molecules chosen as key or model molecules which are the fragments of large molecular systems;
- joint treatment of ab initio and experimental data on vibrational spectra, ED and MW data for model molecules with stable numerical methods with a goal to estimate the accurate molecular force field;
- organizing a database on structural data and force field parameters transferable in a series of related compounds;
- synthesis (construction) of a large molecular system from separate fragments included in the database and calculation of its vibrational spectra and thermodynamical functions.

## Recommended Citation

Kuramshina, Gulnara, "Solving Inverse Problems of Molecular Spectroscopy and Analysis of Molecular Force Fields" (2005). *Colloquia of the Department of Mathematical Sciences*. 203.

https://scholarworks.umt.edu/mathcolloquia/203

## Additional Details

Thursday, 20 October 2005

4:10 p.m. in Math 109