Accurate Numerical Computation of Rovibrational G Matrices in Molecules of Arbitrary Size

Abstract

Abstract. In this work we present a methodology for the accurate numerical computation of the rovibrational G matrix in any molecule. A C++ program is developed to apply this methodology. Using polymorphism, the program can handle the output of any of the available electronic structure codes. The objective is to compute the kinetic contribution to the rovibrational Hamiltonian from the results of molecular structure scans, performed in heterogeneous and distributed systems such as Internet-based Grids of computers. The numerical derivatives needed to compute the G matrix in curvilinear, internal coordinates are obtained from an adapted Richardson extrapolation. The procedure is optimized to maximize the number of significant digits in the derivatives. Using the program, we compute the vibrational kinetic terms for several simultaneous torsional motions in Glycolaldehyde, Methyl formate and Ethyl methyl ether. The results show the existence of an important coupling among the torsional vibration modes.

Gmat. A software tool for the computation of the rovibrational G matrix

“…[8] applies the previous procedure to the case of internal coordinates (bond distances, valence and dihedral angles) on [8] show that a nine levels Richardson extrapolations procedure with initial step values of 10 −2 Angstroms, for bond lengths and 10 −4 degrees, for valence and dihedral angles, provides the more accurate results.…”

“…The GmatrixZ class extends Gmatrix by inheritance, and it handles the G matrix in arbitrary internal coordinates. This class implements the methodology developed in Section 3 for computing accurate numerical derivatives [8]. GmatrixQ extends Gmatrix by inheritance, allowing the use of normal modes as vibrational coordinates.…”

“…(5) represents the optimal step size for the computation of the whole set of derivatives. Finally, to enhance the accuracy of the computed derivatives we apply a Richardson extrapolation [8].…”

“…To obtain accurate numerical derivatives the general approach described in Ref. [8] is used. Thus, we start by determining the optimal increment of the vibrational coordinate, q i , which minimizes the truncation plus roundoff errors in the central differences expression.…”

“…Therefore, except the potential function, it provides all the information needed to build any non-rigid, anharmonic, rovibrational Hamiltonian. Thus, for instance, in pure vibrational studies, reliable Hamiltonians including anharmonicity and coupling among several vibrational motions [5][6][7][8] can be constructed.…”