Hindered rotor models with variable kinetic functions for accurate thermodynamic and kinetic predictions

Thermal behaviour of hindered rotor in static electric and laser field

We solve exactly the time independent Schrödinger equation (TISE) for hindered rotor confined in well shaped potential. Afterwards, the confined system is subjected to interact with laser and static electric field. TISE for the dressed confined rotor is solved using standard numerical method to get energy spectrum and eigenfunctions. Dependence of orientation and alignment parameters on static electric field and confining potential is studied. We also compute thermal properties like entropy and heat capacity of the system under consideration using canonical partition within statistical thermodynamic formalism. We have also studied the effect of external field parameters, confinement strength and temperature on these thermal properties.

Analysis of Partition Functions for Metallocenes: Ferrocene, Ruthenocene, and Osmocene

We present a calculation of the torsional potential of the three metallocenes of the iron group, that is, ferrocene, ruthenocene, and osmocene, calculated with the GAUSSIAN program suite. Both a variational method (through computation of the exact energy levels) and our Chebyshev imaginary time propagation method are used to calculate the hindered rotation partition function, demonstrating the efficiency of the Chebyshev scheme. The transition from a semirigid through a hindered rotor to the free rotor regime is demonstrated, and the effect of the hindered rotation (as opposed to a harmonic) treatment on the thermodynamics of metallocenes is demonstrated.

Methods for Calculating Partition Functions of Molecules Involving Large Amplitude and/or Anharmonic Motions

We present a method for calculating partition functions taking into account anharmonic contributions for systems involving both small-amplitude vibrations and hindered rotations. The Wang-Landau scheme is used in the first case, while two alternative schemes are used for hindered rotation based on imaginary time propagation and fitting of the exact energy levels as a function of quantum number. These two schemes are shown to be complementary in their ranges of applicability (in terms of the torsional rotational constant and the relevant potential). Partition functions for four different molecules are calculated and compared to simpler ones obtained using a harmonic model.

Calculated Entropies for n-Heptane, 2-Methylhexane, 2,3-Dimethylpentane, and Radicals from the Loss of H Atoms

Entropy data are reported using different calculation methods for internal rotors on n-heptane, 2-methylhexane, and 2,3-dimethylpentane and on the different radical sites of each species corresponding to the loss of a hydrogen atom for temperatures between 298 and 1500 K. Structures, moments of inertia, vibration frequencies, and internal rotor potentials are calculated at the B3LYP/6-31G(d,p) level of theory. Comparisons with experimental literature data suggest limitations inuse of the rigid-rotor harmonic-oscillator (HO) approximation and advantages to the use of internal rotation contributions for entropy relative to torsion frequencies. The comparisons suggest the need to include contributions from all internal rotors where the barriers are at or below those of the above molecules. Calculation of entropy from the use of internal rotor contributions provides acceptable approximations to available literature values. Entropy values for radicals corresponding to carbon sites on these hydrocarbons are presented.

Quantum instanton calculation of rate constant for CH4 + OH → CH3 + H2O reaction: torsional anharmonicity and kinetic isotope effect

Thermal rate constants for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The results reveal that the quantum effect is remarkable for the reaction at both low and high temperatures, and the obtained rates are in good agreement with experimental measurements at high temperatures. Compared to the harmonic approximation, the torsional anharmonic effect of the internal rotation has a little influence on the rates at low temperatures, however, it enhances the rate by about 20% at 1000 K. In addition, the free energy barriers for the isotopic reactions and the temperature dependence of kinetic isotope effects are also investigated. Generally speaking, for the title reaction, the replacement of OH with OD will reduce the free energy barrier, while substituting D for H (connected to C) will increase the free energy barrier.

An Efficient and Accurate Formalism for the Treatment of Large Amplitude Intramolecular Motion

We propose a general approach to describe large amplitude motions (LAM) with multiple degrees of freedom (DOF) in molecules or reaction intermediates, which is useful for the computation of thermochemical or kinetic data. The kinetic part of the LAM Lagrangian is derived using a Z-matrix internal coordinate representation within a new numerical procedure. This derivation is exact for a classical system, and the uncertainties on the prediction of observable quantities largely arise from uncertainties on the LAM potential energy surface (PES) itself. In order to rigorously account for these uncertainties, we present an approach based on Bayesian theory to infer a parametrized physical model of the PES using ab initio calculations. This framework allows for quantification of uncertainties associated with a PES model as well as the forward propagation of these uncertainties to the quantity of interest. A selection and generalization of some treatments accounting for the coupling of the LAM with other internal or external DOF are also presented. Finally, we discuss and validate the approach with two applications: the calculation of the partition function of 1,3-butadiene and the calculation of the high-pressure reaction rate of the CH₃ + H → CH₄ recombination.

A theoretical kinetic model of the temperature and pH dependent dimerization of orthosilicic acid in aqueous solution

The first steps in a pH- and temperature-dependent theoretical kinetic model of silicate polymerization and dissolution are examined in this work with a combined ab initio and transition state theory based study of the dimerization of H(4)SiO(4). The role of solvation has been of primary concern in this work, and its influence on theoretical activation energies and pre-exponential factors has been thoroughly benchmarked. Relatively inexpensive MP2/6-31+G(d)//HF/6-31+G(d) calculations of octahydrate clusters, with conductor-like polarizable continuum model corrections obtained in the MP2-level single-point calculations, have been shown to lead to a good description of the limited experimentally determined energetics of dimerization for most elementary reactions. Pre-exponential factors computed from this level of theory are found to be relatively insensitive to the level of theory utilized for geometry optimizations, the number of explicit waters, hindered rotor corrections, and variational effects arising from the minimization of rate constants. Within this framework, a kinetic model of the chemistry of H(4)SiO(4) and H(3)SiO(4)(-), forming H(6)Si(2)O(7) and H(5)Si(2)O(7)(-), has been compiled. Numerical simulations over pH = 3-12 show that a number of pH- and temperature dependent trends in reaction rates and positions of equilibrium are well described with this simple dimerization model. More specifically to the dimerization process, we obtain dimerization constants, log K(dim), of 1.85 and -7.15 for the formation of H(6)Si(2)O(7) and H(5)Si(2)O(7)(-) respectively, which compare well with experimentally determined values of 1.2 and -8.5, respectively.