Accurate Numerical Computation of Rovibrational G Matrices in Molecules of Arbitrary Size.
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
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ABSTRACT: A method for solving the Schrödinger equation of N-atom molecules in 3N−33N−3 Cartesian coordinates usually defined by Jacobi vectors is presented. The separation and conservation of the total angular momentum are obtained not by transforming the Hamiltonian in internal curvilinear coordinates but instead, by keeping the Cartesian formulation of the Hamiltonian operator and projecting the initial wavefunction onto the proper irreducible representation angular momentum subspace. The increased number of degrees of freedom from 3N−63N−6 to 3N−33N−3, compared to previous methods for solving the Schrödinger equation, is compensated by the simplicity of the kinetic energy operator and its finite difference representations which result in sparse Hamiltonian matrices. A parallel code in Fortran 95 has been developed and tested for model potentials of harmonic oscillators. Moreover, we compare data obtained for the three-dimensional hydrogen molecule and the six-dimensional water molecule with results from the literature. The availability of large clusters of computers with hundreds of CPUs and GBytes of memory, as well as the rapid development of distributed (Grid) computing, make the proposed method, which is unequivocally highly demanding in memory and computer time, attractive for studying Quantum Molecular Dynamics.Computer Physics Communications 11/2009; 180(11):2025-2033. DOI:10.1016/j.cpc.2009.06.004 · 2.41 Impact Factor