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Manuscript Title: Polyatomic surface fitting, vibrational-rotational analysis, expectation value and intensity program.
Authors: W.C. Ermler, H.C. Hsieh, L.B. Harding
Program title: SURVIBTM
Catalogue identifier: ABDZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 51(1988)257
Programming language: Fortran.
Computer: VAX.
Operating system: VAX/VMS.
RAM: 4000K words
Peripherals: disc.
Keywords: Molecular, Vibration, Rotation, Potential energy surface, Surface fit, Perturbation approach, Transition dipole moment, Intensity, Normal mode analysis, Constants spectroscopic, Vibrational average, Normal coordinates, Valence force field, Force constant.
Classification: 16.3.

Nature of problem:
The Assignment of specific bands and other spectral information for polyatomic molecules is a continuing problem. Theoretical vibrational- rotational analysis is needed to aid in the identification and explanation of many measured spectra. In addition, many molecules not currently amenable to spectroscopic analysis may be studied using ab initio potential energy surfaces. There have been significant advances in the studies of molecular potential energy and property surfaces in recent years. A simple, precise analytic form that includes anharmonicity and provides good reproducibility over a specified range of geometries is necessary. Also, a standard error propagation associated with the fitting is essential in order to gauge the accuracy of the subsequent vibrational-rotational analysis.

Solution method:
The program SURVIBTM has been developed for the calculation of vibrational-rotational spectra of polyatomic molecules. Starting from pointwise representations of potential energy and property surfaces, SURVIBTM calculates the frequencies and intensities of vibrational transitions and vibrational expectation values of any property represented as an analytical expression. A least squares fitting procedure is implemented for Taylor series, Fourier series, Simons-Parr- Finlan (SPF) and Ogilvie expansions, and associated Lengendre polynomials as a function of both x and cos(x). Harmonic and anharmonic force constants in terms of internal and normal coordinates are calculated. Coriolis and centrifugal distortion effects are analyzed and included in the spectroscopic constants, which are derived from second-order perturbation theory. Vibrational energies and expectation values of properties for low-lying vibrational states are calculated. Using normal coordinate expansion constants from potential energy and dipole moment surfaces, transition dipole moments and band absorption intensities are calculated by means of an analytical formalism derived from perturbation theory.

Calculations correspond to the following cases:
1. Nonlinear molecules with 3-24 internal coordinates -> normal mode analysis. (NVAR = 24)
2. Symmetric and asymmetric top molecules with 3-12 internal coordinates -> anaharmonic spectroscopic constants and property expectation values. (NVAR = 12)
3. Asymmetric top molecules with 3-12 internal coordinates -> intensity analysis. (NVAR = 12)
4. Maximum number of atoms: NATOMS = 10
5. Maximum number of surface points: NPTS = 600
6. Maximum number of terms in polynomial: NINTERM = 534

Running time:
Approximately two minutes for the energy, property and intensity analysis for a three-atom molecule represented by surface of 36 geometries. Approximately ten minutes for the energy analysis (quartic anharmonicity) of a four atom molecule represented by 200-300 geometries.