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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]

The thermodynamic and structural properties of (NH4Cl)n clusters, n=3–10 are studied. Using the method of simulated annealing, the geometries of several isomers for each cluster size are examined. Jump-walking Monte Carlo simulations are then used to compute the constant-volume heat capacity for each cluster size over a wide temperature range. To carry out these simulations a new parallel algorithm is developed using the parallel virtual machine (PVM) software package. Features of the cluster potential energy surfaces, such as energy differences among isomers and rotational barriers of the ammonium ions, are found to play important roles in determining the shape of the heat capacity curves. © 1996 American Institute of Physics. [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]

Presents corrections to the article, entitled `Quantum free-energy calculations: A Three-dimensional test case' published in the volume 97 issue of the `Journal of Chemical Physics'.

Abstract: After hepatic activation, the carcinogen N-acetyl-2-aminofluorene (AAF) may form a major or a minor adduct with DNA, both in vivo and in vitro. The structure of the minor adduct has not been experimentally determined but is believed to be of importance due to its persistence in vivo. In the present study, four varieties of modified AAF have been studied computationally; AAF bonded to C8 of guanine or deoxyguanosine (major adduct), and AAF bonded to N2 of guanine or deoxyguanosine (minor adduct). A computational cascade was employed to search for low-energy conformers of each molecule. Each adduct was subjected to a series of systematic searches of thousands of structures using molecular mechanics. After convergence with respect to the search parameters was obtained, the resulting conformers were then geometry optimized via the semi-empirical AM1 method. Subsets were then submitted to non-local Becke–Perdew density functional theory geometry optimization. The structures thus predicted of the guanine major adduct compare favorably with NMR and X-ray crystallographic data. The major adducts reveal an energetic preference for adoption of one of two orientations, with guanine or deoxyguanosine oriented either perpendicular to the fluorenyl ring moiety or approximately 45° with respect to the fluorenyl structure. Repulsion between the ribose sugar and acetyl group in deoxyguanosine disrupts the ‘ideal’ dihedral angles observed in the guanine adduct. Results for the N2 structures similarly point toward two general conformer classes, one of which is characterized by hydrogen bonding between the acetyl O and the H bonded to N2 of guanine, and the other by minimization of repulsion between the guanine structure and the acetyl group. In the case of deoxyguanosine, results differ somewhat from guanine due to an attractive interaction between the acetyl group and the ribose O5′. These results provide substantial motivation for further experimental work on AAF adduct complexes. [Copyright &y& Elsevier]

The generation of free energy landscapes corresponding to conformational equilibria in complex molecular systems remains a significant computational challenge. Adding to this challenge is the need to represent, store, and manipulate the often high-dimensional surfaces that result from rare-event sampling approaches employed to compute them. In this Letter, we propose the use of artificial neural networks as a solution to these issues. Using specific examples, we discuss network training using enhanced-sampling methods and the use of the networks in the calculation of ensemble averages. [ABSTRACT FROM AUTHOR]

Structural studies of ammonium halide nanoparticles can help to reveal fundamental information about the detailed nature of intermolecular forces. This study focuses on small ammonium fluoride clusters, which exhibit complex behavior in comparison to other ammonium halide clusters due to the weak acidity and strong hydrogen-bonding ability of HF. Calculations of optimized structures and binding energies are presented for cation, anion, and neutral clusters using MP2, CCSD(T), FNO-CCSD(T), ωB97M-V, and MN15 methods. The extent to which proton transfer occurs between two given cluster components was quantified using a dimensionless proton-transfer parameter (ξ PT ), leading to a classification of different types of hydrogen bonds within the clusters. Whereas the neutral clusters exhibit a complex transition from ordinary hydrogen bonding to a combination of shared-proton hydrogen bonds and complete proton transfers, the anion and cation systems exhibit a rapid transition toward complete proton transfer from HF to NH 3 , with incomplete proton transfer observed only in the smallest anion and cation clusters. Ionic interaction energies of these clusters were also computed and found to exhibit trends which can be interpreted by the size-dependent behavior of ξ PT . This work extends our understanding of the size-dependent trends in intermolecular forces which govern the formation of anhydrous ammonium halide clusters as well as the relationship between strong hydrogen bonding and proton transfer.

Free energy surfaces of chemical and physical systems are often generated using a popular class of enhanced sampling methods that target a set of collective variables (CVs) chosen to distinguish the characteristic features of these surfaces. While some of these approaches are typically limited to low (∼1-3)-dimensional CV subspaces, methods such as driven adiabatic free-energy dynamics/temperature-accelerated molecular dynamics have been shown to be capable of generating free energy surfaces of quite high dimension by sampling the associated marginal probability distribution via full sweeps over the CV landscape. These approaches repeatedly visit conformational basins, producing a scattering of points within the basins on each visit. Consequently, they are particularly amenable to synergistic combination with regression machine learning methods for filling in the surfaces between the sampled points and for providing a compact and continuous (or semicontinuous) representation of the surfaces that can be easily stored and used for further computation of observable properties. Given the central role of machine learning techniques in this combined approach, it is timely to provide a detailed comparison of the performance of different machine learning strategies and models, including neural networks, kernel ridge regression, support vector machines, and weighted neighbor schemes, for their ability to learn these high-dimensional surfaces as a function of the amount of sampled training data and, once trained, to subsequently generate accurate ensemble averages corresponding to observable properties of the systems. In this article, we perform such a comparison on a set of oligopeptides, in both gas and aqueous phases, corresponding to CV spaces of 2-10 dimensions and assess their ability to provide a global representation of the free energy surfaces and to generate accurate ensemble averages.

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.