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Manuscript Title: Heuristic computation of the rovibrational G matrix in optimized molecule-fixed axes. Gmat 2.1
Authors: M.E. Castro, A. Niño, C. Muñoz-Caro
Program title: Gmat 2.1
Catalogue identifier: AECZ_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 181(2010)1471
Programming language: Standard ANSI C++.
Computer: All.
Operating system: Linux, Windows.
Keywords: Rovibrational G matrix, Rotation matrix, Optimal Euler angles, Unambiguous molecule-fixed axes.
PACS: 02.50.Ga, 02.60.Pn, 33.20.Vq, 87.55.kd.
Classification: 16.2.

Does the new version supersede the previous version?: Yes

Nature of problem:
When building molecular rovibrational Hamiltonians, the kinetic terms depend on the molecule-fixed axes orientation. Thus, an appropriate orientation can significantly simplify the treatment of pure rotation and rovibrational coupling. The kinetic terms are collected in the rovibrational G matrix. Thus, selection of an appropriate molecule-fixed reference frame is equivalent to localize the axes that minimize specific G matrix elements. From this standpoint, three different kinds of molecule-fixed axes are of interest: first, axes minimizing pure rotational elements of the G matrix; second, axes minimizing all the rovibrational G matrix elements; third, axes minimizing simultaneously pure rotational + rovibrational coupling elements.

Solution method:
In order to carry out the optimal selection of molecule-fixed axes, we add a hybrid method of minimization to the capabilities included in the first version of the program [1]. Thus, we minimize specific elements of the rovibrational G matrix. To such an end, we apply a heuristic global optimization strategy, simulated annealing [2], followed by a Powell's local minimization [3].We also include a procedure to ensure that the same minimum is used when several molecular configurations are considered. In addition, an unambiguous molecule-fixed axes ordering is implemented.

Reasons for new version:
The previous version of the program, Gmat 1.0, works in principal axes of inertia. Although this axes system is adequate for pure vibrational Hamiltonians, it is not always optimal for the construction of general rovibrational Hamiltonians. However, implementing the methods presented here, we can obtain molecule-fixed axes minimizing pure rotational or/and rovibrational interactions in the G matrix. In this form, we can derive the simplest analytical form of the rovibrational Hamiltonian.

Summary of revisions:
Some new methods have been introduced:
  1. A method to build the molecule-fixed axes rotation matrix from the Euler angles.
  2. Methods for rotating nuclear coordinates and their derivatives using the rotation matrix.
  3. A method for applying simulated annealing to the search of the global minimum of a cost function formed by rotational or rovibrational G matrix elements.
  4. A method implementing Powell

Running time:
The sample tests take a few seconds to execute.

References:
[1] M.E. Castro, A. Niño, C. Muñoz-Caro, Comput. Phys. Comm. 180 (2009) 1183
[2] S. Kirkpatrick, C.D. Gelatt Jr.; M.P. Vecchi, Science 220:4598 (1983) 671
[3] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes. The Art of Scientific Computing (Cambrige University Press, Cambridge, 2007)