Path integral calculation of thermal rate constants within the quantum instanton approximation: application to the H + CH4 --> H2 + CH3 hydrogen abstraction reaction in full Cartesian space

The quantum instanton approximation for thermal rate constants of chemical reactions [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)], which is modeled after the earlier semiclassical instanton approach, is applied to the hydrogen abstraction reaction from methane by a hydrogen atom, H + CH4 --> H2 + CH3, using a modified and recalibrated version of the Jordan-Gilbert potential surface. The quantum instanton rate is evaluated using path integral Monte Carlo approaches based on the recently proposed implementation schemes [Yamamoto and Miller, J. Chem. Phys. 120, 3086 (2004)]. The calculations were carried out using the Cartesian coordinates of all the atoms (thus involving 18 degrees of freedom), thereby taking explicit account of rotational effects of the whole system and also allowing the equivalent treatment of the four methane hydrogens. To achieve such a treatment, we present extended forms of the path integral estimators for relevant quantities that may be used for general N-atom systems with any generalized reaction coordinates. The quantum instanton rates thus obtained for the temperature range T = 200-2000 K show good agreement with available experimental data, which gives support to the accuracy of the underlying potential surface used.     

State-to-state reactive differential cross sections for the H+H2-->H2+H reaction on five different potential energy surfaces employing a new quantum wavepacket computer code: DIFFREALWAVE

State-to-state differential cross sections have been calculated for the hydrogen exchange reaction, H+H2-->H2+H, using five different high quality potential energy surfaces with the objective of examining the sensitivity of these detailed cross sections to the underlying potential energy surfaces. The calculations were performed using a new parallel computer code, DIFFREALWAVE. The code is based on the real wavepacket approach of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. The calculations are parallelized over the helicity quantum number Omega' (i.e., the quantum number for the body-fixed z component of the total angular momentum) and wavepackets for each J,Omega' set are assigned to different processors, similar in spirit to the Coriolis-coupled processors approach of Goldfield and Gray [Comput. Phys. Commun. 84, 1 (1996)]. Calculations for J=0-24 have been performed to obtain converged state-to-state differential cross sections in the energy range from 0.4 to 1.2 eV. The calculations employ five different potential energy surfaces, the BKMP2 surface and a hierarchical family of four new ab initio surfaces [S. L. Mielke, et al., J. Chem. Phys. 116, 4142 (2002)]. This family of four surfaces has been calculated using three different hierarchical sets of basis functions and also an extrapolation to the complete basis set limit, the so called CCI surface. The CCI surface is the most accurate surface for the H3 system reported to date. Our calculations of differential cross sections are the first to be reported for the A2, A3, A4, and CCI surfaces. They show that there are some small differences in the cross sections obtained from the five different surfaces, particularly at higher energies. The calculations also show that the BKMP2 performs well and gives cross sections in very good agreement with the results from the CCI surface, displaying only small divergences at higher energies.     

Full-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surface

We report quantum diffusion Monte Carlo (DMC) and variational calculations in full dimensionality for selected vibrational states of H(5)O(2) (+) using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calculations. OH-stretch fundamentals are also calculated using "fixed-node" DMC calculations and variationally using two versions of the code MULTIMODE. These results are compared with infrared multiphoton dissociation measurements of Yeh et al. [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)]. Some preliminary results for the energies of several modes of the shared hydrogen are also reported.     

Complexes of type C6H7(+)·L (L = N2 and CO2) studied by explicitly correlated coupled cluster theory

Complexes of the benzenium ion (C(6)H(7)(+)) with N(2) or CO(2) have been studied by explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x = a, b) level [T. B. Adler et al., J. Chem. Phys. 127, 221106 (2007)] and the double-hybrid density functional B2PLYP-D [T. Schwabe and S. Grimme, Phys. Chem. Chem. Phys. 9, 3397 (2007)]. Improved harmonic vibrational wavenumbers for C(6)H(7)(+) have been obtained by CCSD(T?)-F12a calculations with the VTZ-F12 basis set. Combining them with previous B2PLYP-D anharmonic contributions we arrive at anharmonic wavenumbers which are in excellent agreement with recent experimental data from p-H(2) matrix isolation IR spectroscopy [M. Bahou et al., J. Chem. Phys. 136, 154304 (2012)]. The energetically most favourable conformer of C(6)H(7)(+)·N(2) shows a π-bonded structure similar to C(6)H(7)(+)·Rg (Rg = Ne, Ar) [P. Botschwina and R. Oswald, J. Phys. Chem. A 115, 13664 (2011)] with D(e) ≈ 870 cm(-1). For C(6)H(7)(+)·CO(2), a slightly lower energy is calculated for a conformer with the CO(2) ligand lying in the ring-plane of the C(6)H(7)(+) moiety (D(e) ≈ 1508 cm(-1)). It may be discriminated from other conformers through a strong band predicted at 1218 cm(-1), red-shifted by 21 cm(-1) from the corresponding band of free C(6)H(7)(+).     

Quantum dynamics study of H+NH3-->H2+NH2 reaction

We report in this paper a quantum dynamics study for the reaction H+NH3-->NH2+H2 on the potential energy surface of Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The quantum dynamics calculation employs the semirigid vibrating rotor target model [J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999)] and time-dependent wave packet method to propagate the wave function. Initial state-specific reaction probabilities are obtained, and an energy correction scheme is employed to account for zero point energy changes for the neglected degrees of freedom in the dynamics treatment. Tunneling effect is observed in the energy dependency of reaction probability, similar to those found in H+CH4 reaction. The influence of rovibrational excitation on reaction probability and stereodynamical effect are investigated. Reaction rate constants from the initial ground state are calculated and are compared to those from the transition state theory and experimental measurement.     

Pair-correlated speed distributions for the OH+CH4/CD4 reactions: Further remarks on their classical trajectory calculations in a quantum spirit

Ten years ago, Liu and co-workers measured pair-correlated speed distributions for OH+CH₄/CD₄ reactions by means of velocity map imaging (VMI) techniques at a collision energy of ∼10 kcal/mol [B. Zhang, W. Shiu, J. J. Lin and K. Liu, J. Chem. Phys 122, 131102 (2005); B. Zhang, W. Shiu and K. Liu, J. Phys. Chem. A 109, 8989 (2005)]. Recently, two of us could semi-quantitatively reproduce these measurements by performing full-dimensional quasi-classical trajectory calculations in a quantum spirit on an ab-initio potential energy surface of their own [J. Espinosa-Garcia and J. C. Corchado, Theor. Chem. Acc. (2015) 134: 6; J. Phys. Chem. B 120, 1446 (2016)]. The goal of the present work is to show that these results can be significantly improved by adding a few more constraints in order to better comply with the restrictions imposed by VMI. Overall, the level of agreement between theory and experiment is remarkable owing to the large dimensionality of the reactions under scrutiny. This is an encouraging result considering the computational challenges of quantum scattering calculations for such large processes.     

Quantum optimal control strategies for photoisomerization via electronically excited states

Optimal control of the photoisomerization of Li₂Na from the stable acute to the near-degenerate obtuse triangular configuration is simulated by means of representative wave packet dynamics on two ab initio potential energy surfaces for the electronic ground (X²A′) and excited (4²A′) states. Product state specifity is achieved by means of new iteration methods [W. Zhu, J. Botina and H. Rabitz, J. Chem. Phys. 108 (1998) 1953] which incorporate feedback from the control field. An additional restriction yields a smooth switch on and off behaviour of the optimized pulses. A windowed Fourier transform decomposes the optimized laser field into efficient pump–dump pulses     

Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.     

On the role of dynamical barriers in barrierless reactions at low energies: S(1D) + H2

Reaction probabilities as a function of total angular momentum (opacity functions) and the resulting reaction cross sections for the collision of open shell S((1)D) atoms with para-hydrogen have been calculated in the kinetic energy range 0.09-10 meV (1-120 K). The quantum mechanical hyperspherical reactive scattering method and quasi-classical trajectory and statistical quasi-classical trajectory approaches were used. Two different ab initio potential energy surfaces (PESs) have been considered. The widely used reproducing kernel Hilbert space (RKHS) PES by Ho et al. [T.-S. Ho, T. Hollebeek, H. Rabitz, S. D. Chao, R. T. Skodje, A. S. Zyubin, and A. M. Mebel, J. Chem. Phys 116, 4124 (2002)] and the recently published accurate double many-body expansion (DMBE)/complete basis set (CBS) PES by Song and Varandas [Y. Z. Song and A. J. C. Varandas, J. Chem. Phys. 130, 134317 (2009)]. The calculations at low collision energies reveal very different dynamical behaviors on the two PESs. The reactivity on the RKHS PES is found to be considerably larger than that on the DMBE/CBS PES as a result of larger reaction probabilities at low total (here also orbital) angular momentum values and to opacity functions which extend to significantly larger total angular momentum values. The observed differences have their origin in two major distinct topographic features. Although both PESs are essentially barrierless for equilibrium H-H distances, when the H-H bond is compressed the DMBE/CBS PES gives rise to a dynamical barrier which limits the reactivity of the system. This barrier is completely absent in the RHKS PES. In addition, the latter PES exhibits a van der Walls well in the entrance channel which reduces the height of the centrifugal barrier and is able to support resonances. As a result, a significant larger cross section is found on this PES, with marked oscillations attributable to shape resonances and/or to the opening of partial wave contributions. The comparison of the results on both PESs is illustrative of the wealth of the dynamics at low collision energy. It is also illuminating about the difficulties encountered in modeling an all-purpose global potential energy surface.     

Ab initio design of picosecond infrared laser pulses for controlling vibrational-rotational excitation of CO molecules

Optimal control of rovibrational excitations of the CO molecule using picosecond infrared laser pulses is described in the framework of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)]. The potential energy surface of the CO molecule in the presence of an electric field is calculated using coupled cluster theory with a large orbital basis set. The quantum dynamics of the process is treated using a full three dimensional treatment of the molecule in the laser field. The detailed mechanisms leading to efficient control of the selected excitation processes are discussed.     

Study of the H+O2 reaction by means of quantum mechanical and statistical approaches: the dynamics on two different potential energy surfaces

The possible existence of a complex-forming pathway for the H+O(2) reaction has been investigated by means of both quantum mechanical and statistical techniques. Reaction probabilities, integral cross sections, and differential cross sections have been obtained with a statistical quantum method and the mean potential phase space theory. The statistical predictions are compared to exact results calculated by means of time dependent wave packet methods and a previously reported time independent exact quantum mechanical approach using the double many-body expansion (DMBE IV) potential energy surface (PES) [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)] and the recently developed surface (denoted XXZLG) by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. The statistical approaches are found to reproduce only some of the exact total reaction probabilities for low total angular momenta obtained with the DMBE IV PES and some of the cross sections calculated at energy values close to the reaction threshold for the XXZLG surface. Serious discrepancies with the exact integral cross sections at higher energy put into question the possible statistical nature of the title reaction. However, at a collision energy of 1.6 eV, statistical rotationally resolved cross sections managed to reproduce the experimental cross sections for the H+O(2)(v=0,j=1)-->OH(v(')=1,j('))+O process reasonably well.     

Simulation of vibrational dephasing of I(2) in solid Kr using the semiclassical Liouville method

In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.     

Electronic structure and spectrum of UO2 2+ and UO2Cl4 2-

A theoretical study is presented of the electronic spectra of the UO(2) (2+) and UO(2)Cl(4) (2-) ions, based on multiconfigurational perturbation theory (CASSCF/CASPT2), combined with a recently developed method to treat spin-orbit coupling [P.-A. Malmqvist et al., Chem. Phys. Lett. 357, 230 (2002); B. O. Roos and P.-A. Malmqvist, Phys. Chem. Chem. Phys. 6, 2919 (2004)]. The results are compared to the experimental spectroscopic data obtained for uranyl ions in Cs(2)UO(2)Cl(4) crystals from Denning [Struct. Bonding (Berlin) 79, 215 (1992)] and to previous theoretical calculations performed using a combined configuration-interaction spin-orbit treatment [Z. Zhang and R. M. Pitzer, J. Phys. Chem. A 103, 6880 (1999); S. Matsika and R. M. Pitzer, J. Phys. Chem. A. 105, 637 (2001)]. As opposed to the latter results, the calculations performed in this work point to a significant effect of the weakly bound equatorial chlorine ligands on the excitation energies.     

Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: applications to condensed phase systems

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquidlike) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo results at 25 K [A. Nakayama and N. Makri, J. Chem. Phys. 125, 024503 (2006)]. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.     

Bound state potential energy surface construction: ab initio zero-point energies and vibrationally averaged rotational constants

Collins' method of interpolating a potential energy surface (PES) from quantum chemical calculations for reactive systems (Jordan, M. J. T.; Thompson, K. C.; Collins, M. A. J. Chem. Phys. 1995, 102, 5647. Thompson, K. C.; Jordan, M. J. T.; Collins, M. A. J. Chem. Phys. 1998, 108, 8302. Bettens, R. P. A.; Collins, M. A. J. Chem. Phys. 1999, 111, 816) has been applied to a bound state problem. The interpolation method has been combined for the first time with quantum diffusion Monte Carlo calculations to obtain an accurate ground state zero-point energy, the vibrationally average rotational constants, and the vibrationally averaged internal coordinates. In particular, the system studied was fluoromethane using a composite method approximating the QCISD(T)/6-311++G(2df,2p) level of theory. The approach adopted in this work (a) is fully automated, (b) is fully ab initio, (c) includes all nine nuclear degrees of freedom, (d) requires no assumption of the functional form of the PES, (e) possesses the full symmetry of the system, (f) does not involve fitting any parameters of any kind, and (g) is generally applicable to any system amenable to quantum chemical calculations and Collins' interpolation method. The calculated zero-point energy agrees to within 0.2% of its current best estimate. A0 and B0 are within 0.9 and 0.3%, respectively, of experiment.     

Approach to nonadiabatic transitions by density matrix evolution and molecular dynamics simulations

Many biological processes are characterized by an essentially quantum dynamical event, such as electron or proton transfer, in a complex classical environment. To treat such processes properly by computer simulation, allowing nonadiabatic transitions involving excited states, we recently developed a density matrix evolution (DME ) method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem, 97 , 13464 (1993)] which simulates the dynamics of quantum systems embedded in a classical environment. The formalism of the method is presented and an overview of the applications ranging from collisions of a quantum harmonic oscillator with noble gas atoms to proton tunneling in a double-well hydrogen bond is given. The methodology for treatment of proton-transfer processes with inclusion of excited states is presented. Future application of the method on biologically interesting processes, such as proton transfer in enzymatic reactions, is discussed. © 1996 John Wiley & Sons, Inc.     

Inelastic collisions of molecular hydrogen: a comparison of results from quantum and classical mechanics

Full-dimensional quantum and classical calculations have been carried out for inelastic (nonreactive) energy transfer in H2+H2 on the ab initio potential energy surface of Boothroyd et al. [J. Chem. Phys. 116, 666 (2002)]. State-to-state cross sections are determined and compared for transitions from H2(0,j(ab))+H2(1,j(cd)). While there is excellent agreement for transitions involving small Deltaj, for larger Deltaj and for vibrational relaxation, significant differences are observed which exhibit no systematic trends. Reasons for this disagreement are discussed.     

Higher excitations for an exponential multireference wavefunction Ansatz and single-reference based multireference coupled cluster Ansatz: application to model systems H(4), P(4), and BeH(2)

This article reports on the convergence of the exponential multireference wavefunction Ansatz (MRexpT) [J. Chem. Phys. 123, 84102 (2005)] and the single-reference based multireference coupled cluster Ansatz [J. Chem. Phys. 94, 1229 (1991)] with respect to higher cluster excitations. The approaches are applied to the H(4), P(4), and BeH(2) model systems according to the recently published analysis by Evangelista et al. [J. Chem. Phys. 125, 154113 (2006)]. The results show both MRexpT and SRMRCC to be highly accurate although SRMRCC shows problems due to its lack of Fermi vacuum invariance (symmetry breaking).     

Quasiclassical trajectory study of the reaction H+CH4(nu3 = 0,1)-->CH3+H2 using a new ab initio potential energy surface

Detailed quasiclassical trajectory calculations of the reaction H+CH4(nu3 = 0,1)-->CH3 + H2 using a slightly updated version of a recent ab initio-based CH5 potential energy surface [X. Zhang et al., J. Chem. Phys. 124, 021104 (2006)] are reported. The reaction cross sections are calculated at initial relative translational energies of 1.52, 1.85, and 2.20 eV in order to make direct comparison with experiment. The relative reaction cross section enhancement ratio due to the excitation of the C-H antisymmetric stretch varies from 2.2 to 3.0 over this energy range, in good agreement with the experimental result of 3.0 +/- 1.5 [J. P. Camden et al., J. Chem. Phys. 123, 134301 (2005)]. The laboratory-frame speed and center-of-mass angular distributions of CH3 are calculated as are the vibrational and rotational distributions of H2 and CH3. We confirm that this reaction occurs with a combination of stripping and rebound mechanisms by presenting the impact parameter dependence of these distributions and also by direct examination of trajectories.