Evaluation of vibrational partition functions for polyatomic systems: quantum versus classical methods for H2O and Ar···CN

Calculation of the Rovibrational Partition Function Using Classical Methods with Quantum Corrections

“…For comparison, we also report the results obtained by using the Fourier path integral formalism 64 (q vr FPI ) based on the same potential curve. As expected, 13 Table 6 shows that similar considerations apply for ArO but for much lower temperatures than in the cases of q Vr LCP/QFH (T) ) 1 h 3 ∫ ∫ dr dθ dφ dp r dp θ dp φ 13 where T is in K, and 0 in cm -1 . Table 7 reports the values of the ratios q vr CM /q vr QM and q vr LCP/QFH /q vr QM as a function of τ; for reference, the corresponding T values are also tabulated.…”

“…This employs an hybrid effective potential which is built from effective potentials reported by previous authors. Our purpose follows a claim made in previous work 13,46 (hereafter referred to as papers I and II) to seek a general economical procedure for calculating accurate values of internal partition functions based on realistic potential energy surfaces.…”

“…A major advantage of the classical approach is the appreciably smaller computational cost in comparison to the quantum one, which allows a treatment of molecular systems with a large number of degrees of freedom. Yet, it is well-known that q vr CM overestimates q vr QM at low temperatures, while converging to the latter at the high-temperature limit; 1 for a recent discussion on the range of applicability of classical statistical mechanics to calculate the vibrational partition function for triatomic systems, see ref 13.…”

“…Some conclusions are in section 5. where B is a scalar and F a k -dimensional function. An example is the classical partition function, for which we have employed 13,46 an efficient Monte Carlo scheme to evaluate it for polyatomic systems. This method is an adaptation of Barker's algorithm, 47 which is based on stratified (guided) sampling procedures.…”

On the Rovibrational Partition Function of Molecular Hydrogen at High Temperatures

“…Thus, the classical rovibrational partition function assumes the form where H(q,p) is the classical Hamiltonian, q is the vector of generalized coordinates, and p is the vector of conjugate momenta; we will assume as reference throughout this work the energy of the minimum of the potential energy surface (curve). Note that in some situations [13][14][15][16] the classical picture gives results accurate enough to make quantum calculations * To whom correspondence should be addressed. E-mail: varandas@ qtvs1.qui.uc.pt.…”