Quasiclassical trajectory study of reactive and dissociative processes in H2+H2: comparison with quantum-mechanical calculations

Quasiclassical trajectory calculations have been carried out for H(2)(v(1)=high)+H(2)(v(2)=low) collisions within a three degrees of freedom model where five different geometries of the colliding complex were considered. Within this approach, probabilities for different competitive processes are studied: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. The purpose is to compare in detail with equivalent quantum-mechanical wave packet calculations [Bartolomei et al., J. Chem. Phys 122, 064305 (2005)], especially the behavior of the probabilities near reaction thresholds. Quasiclassical calculations compare quite well with the quantum-mechanical ones for collision induced dissociation as well as for the four center reaction, although quantum effects become very important near thresholds, particularly for lower v(1)'s and for the four center process. Less quantitative agreement is found for reactive dissociation and three-body complex formation. It is found that most quantum effects are due to differences between quantum and classical vibrational distributions of H(2)(v(1)=high). Zero point energy violation has been found in the classical reactive-dissociative probabilities. Extension of these findings to full-dimensional treatments is examined.     

The double Renner effect in the X(2)A" and A(2)A' electronic states of HO(2)

A theoretical investigation of the X(2)A" and A(2)A' electronic states of the HO(2) radical is reported. Both electronic states have nonlinear equilibrium geometries and they correlate with a (2)Pi state at linear geometries so that they exhibit the Renner effect. In highly excited bending states, there is tunneling between two equivalent minima (with geometries where the H nucleus is bound to one, or the other, of the two O nuclei), and the two linear geometries H-O-O and O-O-H become accessible to the molecule. Thus, HO(2) affords an example of the so-called double Renner effect. Three-dimensional potential energy surfaces for the X(2)A" and A(2)A' electronic states of HO(2) have been calculated ab initio and the global potential energy surfaces for the states have been constructed. These surfaces have been used, in conjunction with the computer program DR [Odaka et al., J. Mol. Structure 795, 14 (2006); Odaka et al., J. Chem. Phys. 126, 094301 (2007)], for calculating HO(2) rovibronic energies in the "double-Renner"-degenerate electronic states X(2)A" and A(2)A'. The results of the ab initio calculations, the rovibronic energies obtained, and analyses of the wavefunctions for selected states are presented.     

Six-dimensional quantum dynamics of (v=0,j=0)D2 and of (v=1,j=0)H2 scattering from Cu111

We report six-dimensional quantum dynamics calculations of the dissociative scattering of molecular hydrogen from the copper111 surface. Two potential energy surfaces are investigated and the results are compared with experiment. Our study completes the preliminary work of Somers et al. [Chem. Phys. Lett. 360, 390 (2002)] and focuses on the role of initial vibrational excitation and on isotopic effects. None of the two investigated potential energy surfaces is found satisfactory: the use of neither potential yields reaction and vibrational excitation probabilities and vibrational efficacies that are in close agreement with experiment. In addition to showing the shortcomings of existing potential energy surfaces we point out an inconsistency in the experimental fits for D2.     

Infrared spectra of the Li+-(H2)n (n=1-3) cation complexes

The Li+-(H2)n n=1-3 complexes are investigated through infrared spectra recorded in the H-H stretch region (3980-4120 cm-1) and through ab initio calculations at the MP2/aug-cc-pVQZ level. The rotationally resolved H-H stretch band of Li+-H2 is centered at 4053.4 cm-1 [a -108 cm-1 shift from the Q1(0) transition of H2]. The spectrum exhibits rotational substructure consistent with the complex possessing a T-shaped equilibrium geometry, with the Li+ ion attached to a slightly perturbed H2 molecule. Around 100 rovibrational transitions belonging to parallel Ka=0-0, 1-1, 2-2, and 3-3 subbands are observed. The Ka=0-0 and 1-1 transitions are fitted by a Watson A-reduced Hamiltonian yielding effective molecular parameters. The vibrationally averaged intermolecular separation in the ground vibrational state is estimated as 2.056 A increasing by 0.004 A when the H2 subunit is vibrationally excited. The spectroscopic data are compared to results from rovibrational calculations using recent three dimensional Li+-H2 potential energy surfaces [Martinazzo et al., J. Chem. Phys. 119, 11241 (2003); Kraemer and Spirko, Chem. Phys. 330, 190 (2006)]. The H-H stretch band of Li+-(H2)2, which is centered at 4055.5 cm-1 also exhibits resolved rovibrational structure. The spectroscopic data along with ab initio calculations support a H2-Li+-H2 geometry, in which the two H2 molecules are disposed on opposite sides of the central Li+ ion. The two equivalent Li+...H2 bonds have approximately the same length as the intermolecular bond in Li+-H2. The Li+-(H2)3 cluster is predicted to possess a trigonal structure in which a central Li+ ion is surrounded by three equivalent H2 molecules. Its infrared spectrum features a broad unresolved band centered at 4060 cm-1.     

Full-dimensional time-dependent wave packet dynamics of H2 + D2 reaction

Collision induced dissociation (CID), four center reaction (4C), and single exchange reaction (SE) in H(2) (v(1) = high) + D(2) (v(2) = low) were studied by means of time-dependent wave packet approach within a full-dimensional model. Initial state-selected total reaction probabilities for the three competitive processes have been computed on two realistic global potential energy surfaces of Aguado-Suárez-Paniagua and Boothroyd-Martin-Keogh-Peterson (BMKP) with the total angular momentum J = 0. The role of both vibrationally excited and rotationally excited reagents was examined by varying the initial vibrational and rotational states. The vibrational excitation of the hot diatom gives an enhancement effect on the CID process, while the vibrational excitation of the cold diatom gives an inhibition effect. The rotational excitation of both reagents has a significant effect on the reaction process. The 4C and SE probabilities are at least one order of magnitude smaller than the CID probabilities over the energy range considered. Isotope substitution effects were also studied by substituting the collider D(2) by H(2) and HD on the BMKP potential energy surfaces. The CID process is most efficient for the H(2) + D(2) combination and least efficient for the H(2) + H(2) combination and is different for the 4C and SE processes.     

State-to-state reaction probabilities for the H+O2(v,j)-->O+OH(v',j') reaction on three potential energy surfaces

We report state-to-state and total reaction probabilities for J=0 and total reaction probabilities for J=2 and 4 for the title reaction, both for ground-state and initially rovibrationally excited reactants. The results for three different potential energy surfaces are compared and contrasted. The potential energy surfaces employed are the DMBE IV surface by Pastrana et al. [J. Phys. Chem. 94, 8073 (1990)], the surface by Troe and Ushakov (TU) [J. Chem. Phys. 115, 3621 (2001)], and the new XXZLG ab initio surface by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. Our results show that the total reaction probabilities from both the TU and XXZLG surfaces are much smaller in magnitude for collision energies above 1.2 eV compared to the DMBE IV surface. The three surfaces also show different behavior with regards to the effect of initial state excitation. The reactivity is increased on the XXZLG and the TU surfaces and decreased on the DMBE IV surface. Vibrational and rotational product state distributions for the XXZLG and the DMBE IV surface show different behaviors for both types of distributions. Our results show that for energies above 1.25 eV the dynamics on the DMBE IV surface are not statistical. However, there is also evidence that the dynamics on the XXZLG surface are not purely statistical for energies above the onset of the first excited product vibrational state v'=1. The magnitude of the total reaction probability is decreased for J>0 for the DMBE IV and the XXZLG surfaces for ground-state reactants. However, for initially rovibrationally excited reactants, the total reaction probability does not decrease as expected for both surfaces. As a result the total cross section averaged over all Boltzmann accessible rotational states may well be larger than the cross section reported in the literature for j=1.     

State-to-state rotational transitions in H2+H2 collisions at low temperatures

We present quantum mechanical close-coupling calculations of collisions between two hydrogen molecules over a wide range of energies, extending from the ultracold limit to the superthermal region. The two most recently published potential energy surfaces for the H(2)-H(2) complex, the so-called Diep-Johnson (DJ) [J. Chem. Phys. 112, 4465 (2000); 113, 3480 (2000)] and Boothroyd-Martin-Keogh-Peterson (BMKP) [J. Chem. Phys. 116, 666 (2002)] surfaces, are quantitatively evaluated and compared through the investigation of rotational transitions in H(2)+H(2) collisions within rigid rotor approximation. The BMKP surface is expected to be an improvement, approaching chemical accuracy, over all conformations of the potential energy surface compared to previous calculations of H(2)-H(2) interaction. We found significant differences in rotational excitation/deexcitation cross sections computed on the two surfaces in collisions between two para-H(2) molecules. The discrepancy persists over a large range of energies from the ultracold regime to thermal energies and occurs for several low-lying initial rotational levels. Good agreement is found with experiment B. Mate et al., [J. Chem. Phys. 122, 064313 (2005)] for the lowest rotational excitation process, but only with the use of the DJ potential. Rate coefficients computed with the BMKP potential are an order of magnitude smaller.     

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.     

Discrete variable approaches to tetratomic molecules: part II: application to H2O2 and H2CO

We have carried out large-scale calculations for accurate vibrational energy levels of formaldehyde and hydrogen peroxide. The discrete variable representations of the radial and angular coordinates are employed together with the contraction scheme resulting from several diagonalization/truncation steps. The global potential energy surface due to Carter et al. [J. Mol. Spectrosc. 90 (1997) 729] is used for H2CO and due to Koput et al. [J. Phys. Chem. A 102 (1998) 6325] for H2O2. For both molecules, the calculated vibrational energy levels are characterized by combining vibrationally averaged geometries and expectation values of rotational constants with several adiabatic projection schemes for automatic quantum number assignments. The energy levels of H2CO involving the excited v2 and v3 vibrations appear as resonances beyond the zero-order picture consisting of uncoupled 3D stretching and 2D bending modes. The torsional energy levels of H2O2 are studied in great detail and different energy patterns occurring below and above the cis barrier are discussed. Our full dimensional calculations for H2O2 have shown that the OH triad levels, 2vOH, are symmetry adapted local mode states.     

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.     

Dynamically biased statistical model for the ortho/para conversion in the H(2)+H(3) (+) → H(3) (+)+ H(2) reaction

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007)]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H(5) (+) complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H(5) (+) complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011)] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.     

A quasiclassical trajectory study of collisional energy transfer and dissociation in He + H2(v,j) using a new potential energy surface

Quasiclassical trajectories for He + H2 were carried out using the recent ab initio potential of Boothroyd, Martin, and Peterson (J. Chem. Phys. 2003, 119, 3187) and results for the 348 (v, j) states of H2 are compared to those of earlier calculations that used the potential of Wilson, Kapral, and Burns (Chem. Phys. Lett. 1974, 24, 4884). Examined are the cross sections for energy transfer and dissociation, the extent of threshold elevation, and the interconversion of vibrational and rotational energy. Implications for modeling the interstellar medium are discussed.     

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.     

Rovibrational states of the H2O-H2 complex: an ab initio calculation

All bound rovibrational levels of the H(2)O-H(2) dimer are calculated for total angular momentum J = 0-5 on two recent intermolecular potential surfaces reported by Valiron et al. [J. Chem. Phys. 129, 134306 (2008)] and Hodges et al. [J. Chem. Phys. 120, 710 (2004)] obtained through ab initio calculations. The method used handles correctly the large amplitude internal motions in this complex; it involves a discrete variable representation of the intermolecular distance coordinate R and a basis of coupled free rotor wave functions for the hindered internal rotations and the overall rotation of the dimer. The basis is adapted to the permutation symmetry associated with the para/ortho (p/o) nature of both H(2)O and H(2) as well as to inversion symmetry. Dimers containing oH(2) are more strongly bound than dimers with pH(2), as expected, with dissociation energies D(0) of 33.57, 36.63, 53.60, and 59.04 cm(-1)for pH(2)O-pH(2), oH(2)O-pH(2), pH(2)O-oH(2), and oH(2)O-oH(2), respectively, on the potential of Valiron et al. that corresponds to a binding energy D(e) of 235.14 cm(-1). Rovibrational wave functions are computed as well and the nature of the bound states in the four different dimer species is discussed. Converged rovibrational levels on both potentials agree well with the high-resolution spectrum reported by Weida and Nesbitt [J. Chem. Phys. 110, 156 (1999)]; the hindered internal rotor model that was used to interpret this spectrum is qualitatively correct.     

Resonant States of H3+ and D2H+

Vibrational resonances for H(3) (+) and D(2)H(+), as well as H(3) (+) at J=3, are calculated using a complex absorbing potential (CAP) method with an automated procedure to find stability points in the complex plane. Two different CAP functional forms and different CAP extents are used to analyze the consistency of the results. Calculations are performed using discrete variable representation continuum basis elements calculated to high levels of accuracy by diagonalizing large, dense, Hamiltonian matrices. For D(2)H(+), two energy regions are analyzed: the one where D(2)+H(+) is the only dissociation product and the one where HD+D(+) can also be formed. Branching ratios are obtained in the latter case by using different CAPs. It is shown that H(3) (+) and D(2)H(+) support some narrow Feshbach-type resonances but that higher angular momentum states must be studied to model the pre-dissociation spectrum recorded by Carrington and co-workers [J. Chem. Phys. 98, 1073 (1993)].     

Communication: rigorous calculation of dissociation energies (D0) of the water trimer, (H2O)3 and (D2O)3

Using a recent, full-dimensional, ab initio potential energy surface [Y. Wang, X. Huang, B. C. Shepler, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 134, 094509 (2011)] together with rigorous diffusion Monte Carlo calculations of the zero-point energy of the water trimer, we report dissociation energies, D(0), to form one monomer plus the water dimer and three monomers. The calculations make use of essentially exact zero-point energies for the water trimer, dimer, and monomer, and benchmark values of the electronic dissociation energies, D(e), of the water trimer [J. A. Anderson, K. Crager, L. Fedoroff, and G. S. Tschumper, J. Chem. Phys. 121, 11023 (2004)]. The D(0) results are 3855 and 2726 cm(-1) for the 3H(2)O and H(2)O + (H(2)O)(2) dissociation channels, respectively, and 4206 and 2947 cm(-1) for 3D(2)O and D(2)O + (D(2)O)(2) dissociation channels, respectively. The results have estimated uncertainties of 20 and 30 cm(-1) for the monomer plus dimer and three monomer of dissociation channels, respectively.     

Inelastic scattering matrix elements for the nonadiabatic collision B(2P1/2)+H2(1Sigmag+,j)<-->B(2P3/2)+H2(1Sigmag+,j')

Inelastic scattering matrix elements for the nonadiabatic collision B(2P1/2)+H2(1Sigmag+,j)<-->B(2P3/2)+H2(1Sigmag+,j') are calculated using the time dependent channel packet method (CPM). The calculation employs 1 2A', 2 2A', and 1 2A" adiabatic electronic potential energy surfaces determined by numerical computation at the multireference configuration-interaction level [M. H. Alexander, J. Chem. Phys. 99, 6041 (1993)]. The 1 2A' and 2 2A', adiabatic electronic potential energy surfaces are transformed to yield diabatic electronic potential energy surfaces that, when combined with the total B+H2 rotational kinetic energy, yield a set of effective potential energy surfaces [M. H. Alexander et al., J. Chem. Phys. 103, 7956 (1995)]. Within the framework of the CPM, the number of effective potential energy surfaces used for the scattering matrix calculation is then determined by the size of the angular momentum basis used as a representation. Twenty basis vectors are employed for these calculations, and the corresponding effective potential energy surfaces are identified in the asymptotic limit by the H2 rotor quantum numbers j=0, 2, 4, 6 and B electronic states 2Pja, ja=1/2, 3/2. Scattering matrix elements are obtained from the Fourier transform of the correlation function between channel packets evolving in time on these effective potential energy surfaces. For these calculations the H2 bond length is constrained to a constant value of req=1.402 a.u. and state to state scattering matrix elements corresponding to a total angular momentum of J=1/2 are discussed for j=0<-->j'=0,2,4 and 2P1/2<-->2P1/2, 2P3/2 over a range of total energy between 0.0 and 0.01 a.u.     

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.     

Vibrationally inelastic collisions in H+ +CO system: comparing quantum calculations with experiments

State-resolved cross beam experiments [H. Udseth et al., J. Chem. Phys. 60, 3051 (1974); J. Krutein and F. Linder, J. Chem. Phys. 71, 599 (1979); G. Niedner-Schatteburg and J. P. Toennies, Adv. Chem. Phys. LXXXII, 553 (1992)], coupled with proton energy loss spectroscopy for the inelastic scattering of H(+) from CO in the collision range of 10-30 eV show very low vibrational excitation of the target molecule. Stimulated by the experimentally observed low vibrational inelasticity in the system the ground and the first two low-lying excited electronic potential-energy surfaces have been computed using the ab initio multireference configuration interaction method. Quantum dynamics has been performed on the ground potential energy surface in the framework of vibrational close-coupling rotational infinite-order sudden approximation. The various computed dynamical attributes such as differential and integral cross sections, and average vibrational energy transfer are analyzed in detail, and compared successfully with the available experimental results.