International Journal of Quantum ChemistryVolume 9, Issue S9 p. 403-414 Article Three-dimensional quantum mechanical studies of the H + H2 and F + H2 reactions Michael J. Redmon, Michael J. Redmon Department of Chemistry, University of Texas, Austin, Texas 78712Search for more papers by this authorRobert E. Wyatt, Robert E. Wyatt Department of Chemistry, University of Texas, Austin, Texas 78712 Alfred P. Sloan Foundation Fellow.Search for more papers by this author Michael J. Redmon, Michael J. Redmon Department of Chemistry, University of Texas, Austin, Texas 78712Search for more papers by this authorRobert E. Wyatt, Robert E. Wyatt Department of Chemistry, University of Texas, Austin, Texas 78712 Alfred P. Sloan Foundation Fellow.Search for more papers by this author First published: 19/25 January 1975 https://doi.org/10.1002/qua.560090850Citations: 28 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract New results are presented for quantum mechanical reactive scattering in H + H2, including a comparison of close-coupling cross sections for para to ortho conversion with results obtained through momentum decoupling approximations. Information-theoretic analysis of product rotational distributions is given for one total energy. Results are also presented of the first three-dimensional coupled-channel study of the F + H2 reaction, showing the energy dependence of the probability distribution for vibrational excitation and population inversion. Citing Literature Volume9, IssueS9Supplement: Proceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory and Quantum Statistics19/25 January 1975Pages 403-414 RelatedInformation

Two methods of obtaining unimodular sector transformation matrices required in quantum scattering calculations employing locally adiabatic basis sets are discussed, one being particularly useful for three-dimensional reactive scattering. These are shown to lead to improved unitarity and detailed balance in a computed S-matrix. New results arc presented for the H + D2, and F + H2 reactions, including total cross sections obtained within a J2-conserving approximation. In particular, evidence is presented which indicates that the strong n = 2 vibrational resonance appearing in collinear studies of the F + H2 reaction is drastically affected by rotational broadening, indicating that collinear studies of exoergic reactions may be of limited practical utility in predicting resonance widths.

: Novel state-of-the-art computational techniques were developed and validated for studying collisional processes responsible for producing infrared and ultraviolet signatures in rocket plumes. The promising new methods involve computation of cross sections and rates within a semiclassical methodology. Two of the key beneficiary programs are the SPURC and the CHARM programs which require detailed microscopic dynamical information (kinetic rates and cross sections) about such collisional processes for successful modeling of the chemistry within appropriate flowfield simulation codes. Successful prediction and interpretation of ultraviolet signatures require treating collision induced transitions between different electronic states caused by the coupling between electronic and nuclear motions in molecules during collisions. Electronic transitions bring in inherently quantum mechanical effects that have no analog in classical mechanics. The task of numerically solving the quantum mechanical equations of motion is still an unsolvable computational problem for many realistic molecular systems. The semiclassical theory is accurate enough to reproduce specific quantum mechanical features necessary, because it leads to ordinary differential equations instead of the partial differential equations of quantum mechanics. Electronic structure information required in modelling the production of candidate excited species, nitrogen, nitric oxide, and hydroxyl radical molecules in some elementary reactions was analyzed. It was determined that modern quantum chemistry can provide all the required information involving excited hydroxyl production and less extensive data for other systems.

: In order to assess the potential of energetic molecules to be advanced rocket propellants, the Air Force High Energy Density Materials Program requires theoretical methods to predict the lifetimes of energetic molecules in condensed phase. This research met this need by developing novel dynamical methods which can be used to elucidate the microscopic dynamics controlling lifetimes relevant to energy storage in isolated and matrix-embedded molecules. This has resulted in the capability to identify important quenching pathways in gas and condensed phases using computational methods. This research consisted of (1) developing novel semiclassical methods and computer simulation technology and (2) applications to the dynamics of electronically inelastic chemistry of light metastables, including helium and hydrogen in the gas and condensed phase. The key accomplishments in this research program include (1) development and validation of general and powerful semiclassical methods for energetic polyatomic species, (2) development of reduced heatbath models of condensed phase helium, (3) development of models of condensed phase hydrogen and (4) development of simulation procedures for solution-phase reaction and cluster formation of high energy density materials (HEDMs) with solvents.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTAlgorithms and accuracy requirements for computing reaction paths by the method of steepest descentBruce C. Garrett, Michael J. Redmon, Rozeanne Steckler, Donald G. Truhlar, Kim K. Baldridge, David Bartol, Michael W. Schmidt, and Mark S. GordonCite this: J. Phys. Chem. 1988, 92, 6, 1476–1488Publication Date (Print):March 1, 1988Publication History Published online1 May 2002Published inissue 1 March 1988https://pubs.acs.org/doi/10.1021/j100317a022https://doi.org/10.1021/j100317a022research-articleACS PublicationsRequest reuse permissionsArticle Views275Altmetric-Citations188LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

The interaction energy of two HF molecules at 1332 individual points has been calculated with Moeller–Plesset (many–body) perturbation theory at the MP4-SDTQ level using a 6-311G** basis set. 293 of the points correspond to stretching of one HF molecule from its equilibrium geometry. No attempt was made to use a sufficiently fine grid to accurately describe the well region corresponding to hydrogen bonding. However, the location and minimum energy are consistent with experiment and other accurate theoretical results. An extensive global fit (rms error of 1 kcal/mol) is reported of 1319 points (below 10 eV of potential energy) using a modified London potential with corrections obtained using polynomials through four-body interactions. A model electrostatic potential represents the long-range interaction. In addition, the use of an expansion in products of three Legendre functions is discussed. It is shown that the latter approach, although accurately fitting the ab initio data, has difficulties interpolating in regions of the surface exhibiting diverse magnitudes of potential energy, and therefore must be used with caution. This surface should be useful for studies of T–V–R processes in this system.

We present a computer program for calculating rate constants of gas-phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction pathe and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.

A variable time step algorithm has been implemented for solving the stochastic equations of motion for gas–surface collisions. It has been tested for a simple model of electronically inelastic collisions with an insulator surface in which the phonon manifold acts as a heat bath and electronic states are localized. In addition to reproducing the accurate nuclear dynamics of the surface atoms, numerical calculations have shown the algorithm to yield accurate ensemble averages of physical observables such as electronic transition probabilities and total energy loss of the gas atom to the surface. This new algorithm offers a gain in efficiency of up to an order of magnitude compared to fixed time step integration.

A recently developed impact-parameter method is applied to electron-impact dissociation processes involving the A${\mathrm{}}^{1}$\ensuremath{\Pi} state of HCl. Calculations were performed for initial vibrational levels of the X${\mathrm{}}^{1}$${\ensuremath{\Sigma}}^{+}$ state up to ${v}_{i}$=2 and for rotational temperatures to 1000 K. The cross sections increase by approximately 50% from ${v}_{i}$=0 to ${v}_{i}$=2. The dependence on rotational temperature is small except for an anomalous enhancement at 0 K that the theory predicts for \ensuremath{\Pi} states. Since the predicted cross sections are an order of magnitude larger than those for photodissociation, electron-impact dissociation processes will play an important role in lasers involving HCl.

The quasiclassical trajectory method is used to calculate cross sections for vibrational excitation in O(3P)+H2O(000) collisions. The potential surface is a Sorbie–Murrell fit to the ab initio MBPT calculation of Bartlett and Purvis. State-to-state transition probabilities are evaluated using the histogram method to discretize the H2O good action variables obtained from a classical perturbative treatment of the molecular Hamilton–Jacobi equation. Integral cross sections are presented for all one-quantum excitations [(010), (100), and (001)] plus some multiquantum excitations. Rotational distributions for each final vibrational state indicate that significant rotational excitation accompanies vibrational excitation. The angular distributions for vibrationally excited final states indicate sidewards peaking. The resulting (001) cross section is in reasonable agreement with experimental shock tube results. The analogous (010) excitation cross section is larger than the corresponding experimental value. Although the experimental error is large, at least part of the difference between theory and experiment is associated with a small time dependence in the computed actions for this very floppy mode.

The impact-parameter method is used to calculate integral cross sections for electronic excitation and dissociation of ${\mathrm{O}}_{2}$ and ${\mathrm{S}}_{2}$ by electron impact. For both molecules, excitations to bound and dissociative states are considered for transitions from the ground electronic state (X ${\mathrm{}}^{3}$${\ensuremath{\Sigma}}_{g}^{\mathrm{\ensuremath{-}}}$) to the two lowest states of $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\mathrm{\ensuremath{-}}}$ symmetry (labeled B and E for ${\mathrm{O}}_{2}$ and B and 2 for ${\mathrm{S}}_{2}$) and the lowest state of $^{3}\mathrm{\ensuremath{\Pi}}_{\mathrm{u}}$ symmetry. The dependence of the cross sections upon initial vibrational and rotational states is studied for low collision energies (threshold to 25 eV). For some transitions a change in initial vibrational state can have a significant effect upon the cross sections, but, in general, the effect of changing the initial rotational state is small.

The impact-parameter method for electron-impact excitation of diatomic molecules is reformulated to explicitly treat molecular vibration and rotation and to permit the study of molecular dissociation. Applications are made to optically allowed transitions involving the X ${}^{1}$${\ensuremath{\Sigma}}_{g}^{+}$, B ${}^{1}$${\ensuremath{\Sigma}}_{u}^{+}$, and B' ${}^{1}$${\ensuremath{\Sigma}}_{u}^{+}$ states of ${\mathrm{H}}_{2}$. The resulting cross sections are compared to other theoretical calculations and to experimental data. This method is applicable to heavy diatomic molecules and is expected to be useful in studying trends in electronic excitation and dissociation cross sections associated with variations in internal energy.