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Converged quantum mechanical vibrational–rotational partition functions and free energies are calculated using realistic potential energy surfaces for several chalcogen dihydrides (H2O, D2O, H2S, H2Se) over a wide range of temperatures (600–4000 K). We employ an adaptively optimized Monte Carlo integration scheme for computing vibrational–rotational partition functions by the Fourier path-integral method. The partition functions and free energies calculated in this way are compared to approximate calculations that assume the separation of vibrational motions from rotational motions. In the approximate calculations, rotations are treated as those of a classical rigid rotator, and vibrations are treated by perturbation theory methods or by the harmonic oscillator model. We find that the perturbation theory treatments yield molecular partition functions which agree closely overall (within ∼7%) with the fully coupled accurate calculations, and these treatments reduce the errors by about a factor of 2 compared to the independent-mode harmonic oscillator model (with errors of ∼16%). These calculations indicate that vibrational anharmonicity and mode–mode coupling effects are significant, but that they may be treated with useful accuracy by perturbation theory for these molecules. The quantal free energies for gaseous water agree well with previously available approximate values for this well studied molecule, and similarly accurate values are also presented for the less well studied D2O, H2S, and H2Se. [ABSTRACT FROM AUTHOR]

The Fourier coefficient path-integral representation of the quantum density matrix is used to carry out direct, accurate calculations of coupled vibrational partition functions. The present implementation of the Fourier path-integral method incorporates two noteworthy features. First, we use a Gaussian in Fourier space as a probability density function, which is sampled using the Box–Muller algorithm. Second, we introduce an adaptively optimized stratified sampling scheme in Cartesian coordinates to sample the nuclear configurations. We illustrate these strategies by applying them to a coupled stretch–bend model which resembles two of the vibrational modes of H2O. We also apply a simple, yet accurate method for estimating the statistical error of a Metropolis integration, and we compare the Box–Muller and Metropolis sampling algorithms in detail. The numerical tests of the new method are very encouraging, and the approach is promising for accurate calculations of quantum free energies for polyatomic molecules. [ABSTRACT FROM AUTHOR]

An optimized integration scheme for calculating vibrational–rotational partition functions by the Fourier path-integral method, as presented in the previous paper [R. Q. Topper and D. G. Truhlar, J. Chem. Phys. XX, ▪▪▪▪ (19▪▪)] is applied to a three-dimensional test case involving the coupled vibrational and rotational motions of a diatomic HCl molecule in Cartesian coordinates. Converged partition functions are calculated by the new Fourier path-integral Monte Carlo scheme and by standard variational methods, and the two sets of results are compared. We obtain good agreement (∼2%) between the two methods over a range of a factor of 20 in temperature. [ABSTRACT FROM AUTHOR]

A microcanonical kinetic theory of reactions based upon the structure within phase space is developed. It is shown that the dynamics of reaction across an energetic barrier is mediated by invariant manifolds embedded in phase space that have the geometry of simple cylinders. The ideas are developed by considering molecular systems modeled by two vibrational degrees of freedom, a reaction coordinate and a ‘‘bath’’ coordinate. The kinetic theory is constructed by focusing on the dynamics between n mapping planes (‘‘n-map’’) and the ‘‘reactive island’’ (RI) structure within them. We discuss how the structure of the conformer population decay in isomerization reactions can be obtained from the RI kinetic model. Formal solutions of the kinetic equations are discussed with specific attention given towards the calculation of the isomerization reaction rate. The formal theory is developed in Paper I of this series. Numerical considerations and applications to the reaction dynamics of model molecular systems with two degrees of freedom will be given in Paper II and extension of the theory and applications to multidimensional systems will be given in Paper III. [ABSTRACT FROM AUTHOR]

In Paper I we discussed the existence of cylindrical manifolds embedded in phase space which mediate the dynamics of chemical reactions. A kinetic theory of population decays and decay rate constants was developed which we called ‘‘reactive island’’ (RI) theory. In this paper we discuss the details of the numerical implementation of the theory and then apply it to several molecular models (with two coupled degrees of freedom) representing isomerization between two and three states. Numerical simulations of population decays and asymptotic decay rate constants are compared to the RI theoretical predictions as well as the predictions from the Purely Random Theory (PRT) and Transition State Theory (TST) of reactions. Of the ten systems studied we find that RI theory is generally in good to excellent agreement with the numerical simulations. Only one system exhibits significant deviation between the RI and numerical results. This deviation is seen to be a result of a strong intraconformer dynamical bottleneck. Finally, we compare the theoretical prediction and the numerical simulation for the average n-map mapping time Trxn and find that the agreement, within numerical error, is exact irrespective of the character of the dynamics (i.e., chaotic or regular). [ABSTRACT FROM AUTHOR]

Simulated annealing Monte Carlo conformer searches using the "mag-walking" algorithm are employed to locate the global minima of molecular clusters of ammonium chloride of the types (NH4Cl)n, (NH4+)(NH4Cl)n, and (Cl-)(NH4Cl)n with n = 1-13. The M06-2X density functional theory method is used to refine and predict the structures, energies, and thermodynamic properties of the neutral, cation, and anion clusters. For selected small clusters, the resulting structures are compared to those obtained from a variety of models and basis sets, including RI-MP2 and B3LYP calculations. M06-2X calculations predict enhanced stability of the (NH4+)(NH4Cl)n clusters when n = 3, 6, 8, and 13. This prediction corresponds favorably to anomalies previously observed in thermospray mass spectroscopy experiments. The (NH4Cl)n clusters show alternations in stability between even and odd values of n. Clusters of the type (Cl-)(NH4Cl)n display a magic number distribution different from that of the cation clusters, with enhanced stability predicted for n = 2, 6, and 11. None of the observed cluster structures resemble the room-temperature CsCl structure of NH4Cl(s), which is consistent with previous work. Numerous clusters have structures reminiscent of the higher-temperature, rock-salt phase of the solid ammonium halides. [ABSTRACT FROM AUTHOR]

Simulated annealing Monte Carlo conformer searches using the "mag-walking" algorithm are employed to locate the global minima of molecular clusters of ammonium chloride of the types (NH(4)Cl)(n), (NH(4)(+))(NH(4)Cl)(n), and (Cl(-))(NH(4)Cl)(n) with n = 1-13. The M06-2X density functional theory method is used to refine and predict the structures, energies, and thermodynamic properties of the neutral, cation, and anion clusters. For selected small clusters, the resulting structures are compared to those obtained from a variety of models and basis sets, including RI-MP2 and B3LYP calculations. M06-2X calculations predict enhanced stability of the (NH(4)(+))(NH(4)Cl)(n) clusters when n = 3, 6, 8, and 13. This prediction corresponds favorably to anomalies previously observed in thermospray mass spectroscopy experiments. The (NH(4)Cl)(n) clusters show alternations in stability between even and odd values of n. Clusters of the type (Cl(-))(NH(4)Cl)(n) display a magic number distribution different from that of the cation clusters, with enhanced stability predicted for n = 2, 6, and 11. None of the observed cluster structures resemble the room-temperature CsCl structure of NH(4)Cl(s), which is consistent with previous work. Numerous clusters have structures reminiscent of the higher-temperature, rock-salt phase of the solid ammonium halides.