Showing papers on "Potential energy surface published in 1976"

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H+H2

Abstract: Accurate three‐dimensional reactive and nonreactive quantum mechanical cross sections for the H+H_2 exchange reaction on the Porter–Karplus potential energy surface are presented. Tests of convergence in the calculations indicate an accuracy of better than 5% for most of the results in the energy range considered (0.3 to 0.7 eV total energy). The reactive differential cross sections are exclusively backward peaked, with peak widths increasing monotonically from about 32° at 0.4 eV to 51° at 0.7 eV. Nonreactive inelastic differential cross sections show backwards to sidewards peaking, while elastic ones are strongly forward peaked with a nearly monotonic decrease with increasing scattering angle. Some oscillations due to interferences between the direct and exchange amplitudes are obtained in the para‐to‐para and ortho‐to‐ortho antisymmetrized cross sections above the effective threshold for reaction. Nonreactive collisions do not show a tendency to satisfy a "j_z‐conserving" selection rule. The reactive cross sections show significant rotational angular momentum polarization with the m_j=m′_j=0 transition dominating for low reagent rotational quantum number j. In constrast, the degeneracy averaged rotational distributions can be fitted to statistical temperaturelike expressions to a high degree of accuracy. The integral cross sections have an effective threshold total energy of about 0.55 eV, and differences between this quantity and the corresponding 1D and 2D results can largely be interpreted as resulting from bending motions in the transition state. In comparing these results with those of previous approximate dynamical calculations, we find best overall agreement between our reactive integral and differential cross sections and the quasiclassical ones of Karplus, Porter, and Sharma [J. Chem. Phys. 43, 3259 (1965)], at energies above the quasiclassical effective thresholds. This results in the near equality of the quantum and quasiclassical thermal rate constants at 600 K. At lower temperatures, however, the effects of tunneling become very important with the quantum rate constant achieving a value larger than the quasiclassical one by a factor of 3.2 at 300 K and 18 at 200 K.

Unified statistical model for ’’complex’’ and ’’direct’’ reaction mechanisms

Abstract: A unified statistical theory for bimolecular chemical reactions is developed. In the limit of a ’’direct’’ mechanism it becomes the usual transition state theory, which is correct for this situation, and if the reaction proceeds via a long‐lived collision complex it reduces to the statistical model of Light and Nikitin. A general criterion for locating the ’’dividing surfaces’’ that are central to statistical theory is also discussed. This prescription (Keck’s variational principle) is shown not only to locate the usual dividing surfaces that pass through saddle points and minima of the potential energy surface, but it also selects the critical surfaces relevant to the ’’orbiting’’ and ’’nonadiabatic trapping’’ models of complex formation.

An ab initio potential‐energy surface study of several electronic states of NO2

Abstract: The results of ab initio potential‐energy surface calculations are presented for 12 doublet and four quartet states of NO2. In several cases Cs as well as C2v conformations have been studied. The predicted equilibrium conformations and the character of the wavefunctions are discussed. Vertical excitation energies are given for 40 doublet and 12 quartet states. The electronic spectrum of NO2 is discussed, and barriers to photodissociation are estimated for several electronic states. Whether states will be strongly Jahn–Teller coupled by a symmetry‐reducing vibrational interaction depends on their potential surfaces and the character of their wavefunctions. This vibronic interaction in some cases is expected to produce non‐C2v equilibrium conformations.

Classical trajectory methods in molecular collisions

Abstract: The dynamics of a molecular scattering process is described in exact terms by the solutions to the Schrodinger equation in which the kinetic energy and the electrodynamical interactions of all the nuclei and electrons of the colliding partners are used. If the process to be studied can be assumed to be adiabatic, the Born-Oppenheimer separation can be invoked, and the Schrodinger equation for the scattering is reduced to the problem of nuclear motion on a potential energy surface known as a function of all the internuclear distances. The accuracy of quantum mechanical calculations of the measurable attributes of molecular collisions is limited only by the accuracy of the potential energy surface and by the number of basis functions that can be afforded in terms of computer core storage size and processing time. The technical and economic questions are therefore 1 How accurate must a calculation be in order to test predictions of a given theory against a given experimental result, and how is this accuracy most efficiently achieved? 2 What calculational expense is commensurate with the scientific value of the result?

Monte Carlo trajectory study of Ar+H2 collisions. I. Potential energy surface and cross sections for dissociation, recombination, and inelastic scattering

Abstract: Modified statistical electron–gas calculations using the methods of Gordon, Kim, Rae, Cohen, and Pack are carried out to obtain the interaction energy of Ar with H2 as a function of geometry. The results are combined with the accurate pairwise interactions, the long‐range nonpairwise interaction, and the potential LeRoy and van Kranendonk fit to spectral data on the van der Waals’ complex to obtain a potential energy surface which is as accurate as possible at all geometries. This surface and the pairwise additive surface are then used in a Monte Carlo quasiclassical trajectory study of the cross sections (under shock‐tube high‐energy collision conditions) for complete dissociation, for production of quasibound states of H2, and for V–T, R–T, and V–R–T energy transfer. Except for R–T energy transfer, the accurate surface yields smaller cross sections than the pairwise additive surface does. The cross sections for dissociation are much smaller than predicted by the available‐energy hard‐sphere model but ar...

Nonadiabatic Processes in Molecular Collisions

Abstract: Substantial effort has been directed toward developing methods for describing molecular collision processes that are electronically adiabatic, i.e., for which it can be assumed that nuclear motion evolves on a single potential energy hypersurface. A number of recent reviews are devoted to this subject.(1–8) Considerably less attention has been paid to processes that are nonadiabatic,i.e., that involve electronic transitions between potential energy surfaces. This is in spite of the fact that nonadiabatic behavior is both common and important, even in thermal energy collisions.

Theoretical and experimental studies of the N2O− and N2O ground state potential energy surfaces. Implications for the O−+N2→N2O+e and other processes

Abstract: The ground state potential energy surface of the nitrous oxide negative ion is characterized and related to that of the neutral molecule by a synergetic theoretical–experimental approach. Ab initio multiconfiguration self‐consistent‐field/configuration interaction (MCSCF/CI) and other calculations for N2O−(X 2A′) yield the minimum energy geometry (ReNN, ReNO, AeNNO) = (1.222±0.05 A, 1.375±0.10 A, 132.7±2°), the vibrational frequencies (ν1,ν2,ν3) = (912±100 cm−1, 555±100 cm−1, 1666±100 cm−1), the dipole moment μ =2.42±0.3 D, and other properties. The N2O− molecular ion in the X 2A′ state is found to have a compact electronic wavefunction—one with very little diffuse character. The MCSCF/CI bending potential energy curve from 70° to 180° for the X 1Σ+(1 1A′) state of N2O as well as the bending curve for the X 2A′ state of N2O− are also reported. The dissociation energy D (N2–O−) =0.43±0.1 eV and, thus, the adiabatic electron affinity E.A.(N2O) =0.22±0.1 eV and the dissociation energy D (N–NO−) =5.1±0.1 eV a...

Energy partitioning and isotope effects in the fragmentation of triatomic negative ions: Monte Carlo scheme for a classical trajectory study

Abstract: A simple molecular model is associated with an analytical semiempirical potential energy surface and a Wigner representation of the initial conditions of dissociation. This model is used to interpret some experimental data dealing with the dissociation of triatomic negative ions, i.e., the isotope effects and the partitioning of available energy between translational and internal energies of the recoiling fragments.

Quantum mechanical streamlines. III. Idealized reactive atom–diatomic molecule collision

Abstract: An atom–diatomic molecule collision is simulated by considering an idealized potential energy surface which is a two‐dimensional duct with an adjustable potential in the corner region. This potential is symmetric with respect to an interchange of the x and y Cartesian coordinates. Explicit expressions for the wavefunctions are obtained which make use of this symmetry. Also analytical relations are obtained between the transmission and reflection coefficients and their phases. Quantum mechanical streamlines are computer graphed for a large number of energies and positive, negative, and zero values of the potential energy in the corner region. Special attention is given to the quantized vortices (surrounding wavefunction nodes) which appear in the streamlines. When only one energy channel is open, the streamlines are symmetric and the flux is antisymmetric. This occurs because the wavefunction is a linear combination (with complex coefficients) of two real solutions, one symmetric, the other antisymmetric. ...

Cross sections for rotational energy transfer: An information‐theoretic synthesis

Abstract: State‐to‐state cross sections are readily computed by combining the capabilities of the classical trajectories method with an information‐theoretic (’’surprisal’’) synthesis. The method is illustrated by an application to rotational energy transfer in several systems, (Ar+N2, Li++H2, Li++D2, H+CO). It is shown that by using classical trajectories to compute a single moment of the distribution of final rotational energy (for a given initial rotational energy) and then maximizing the entropy of the distribution subject to the given value of the moment one can obtain a good prediction of the distribution. Invoking microscopic reversibility, the entire matrix of state‐to‐state, σ (j→j′), rotational energy transfer cross sections (at the given total energy) is then determined. More averaged quantities, such as the cross sections for inelastic collisions σ (j), are thereby easily obtained. When a realistic potential energy surface is not available or when one requires a simple but reliable prediction, the synthesis can be based on invoking a sum rule. Here the moment of the distribution is not computed via classical trajectories but is expressed as a simple function of the initial conditions. It is shown that available cross sections often satisfy the simplest possible sum rule and hence a synthesis can be readily carried out where the only inputs are the total energy and the rotational constant of the diatomic molecule. The distribution of final rotational states predicted in this way is independent of the nature of the collision partner. The method is illustrated by applications to H+CO, Ar+N2, Li++H2, He+HD, H+H2, and H+D2. Results for the distribution of final rotational state and the dependence of the cross section on the initial rotational state and on the collision energy are in very good accord with classical trajectory and with quantal close‐coupling computations.

Validity of the coupled states approximation for molecular collisions

Abstract: The process of rotational excitation in the body-fixed frame is examined in detail. Physical arguments are presented to justify the coupled states approximation which involves a diagonalization of the body-fixed centrifugal potential. Cross sections for rotational transitions in HeHCN and in ArN2 collisions are reported and are compared to exact close coupling cross sections. The coupled states method is found to maintain its high accuracy for the extremely strong-coupling HeHCN system and also for the large Δj transitions in the ArN2 system even when many partial waves are required. General rules are given for the applicability of this approach in terms of the strength and the position of the anisotropy in the potential energy surface.

Coupled‐channel study of rotational excitation of a rigid asymmetric top by atom impact: (H2CO,He) at interstellar temperatures

Abstract: A quantum mechanical scattering study is carried out to test a collisional pumping model for cooling the 6 and 2 cm doublets of interstellar formaldehyde. The Arthurs and Dalgarno formalism is extended to the collision of an s‐state atom with a rigid asymmetric top molecule and applied to rotational excitation of ortho formaldehyde by helium impact. Using a previously determined configuration interaction potential energy surface, the coupled‐channel (CC) equations are integrated at 12 scattering energies between 20 and 95°K. Up to 16 ortho formaldehyde states, yielding a maximum of 62 CC equations, are retained to test convergence of computed cross sections. Resonance structure is obtained at ∼20.2, 32.7, and 47.7°K. The computed inelastic cross sections are averaged over a Maxwell–Boltzmann distribution and the resultant rates used to solve the equations of statistical equilibrium for the relative populations. The 6 and 2 cm doublets are found to be cooled only upon inclusion of the j=3 doublet.

Chemical reaction theory for asymmetric atom–molecule collisions

Abstract: A theoretical framework for describing the quantum dynamics of an atom–diatom system (A+BC) in three physical dimensions is presented. This theory explicitly treats the case where A, B, and C are each distinct, and hence no simplifications arise from the symmetry of a homonuclear diatomic. A natural collision coordinate system, depending primarily on the masses A, B, and C and the asymptotic potential energy surface is engineered appropriate to the system yielding a tractable expression for the kinetic energy operator. Close coupled equations for both free and hindered rotor expansions of the wavefunction are derived and the matching procedure and boundary conditions required to obtain the full scattering matrix (S matrix) are given.

Dynamics of Unimolecular Reactions

Abstract: The subject of unimolecular dynamics deals with the intermolecular and intramolecular microscopic details of unimolecular reactions. Theories of unimolecular dynamics are concerned with molecular motion over potential energy surfaces and the behavior of molecular coordinates as a function of time. Most studies of unimolecular reactions have involved measurements and predictions of the rate at which an energized molecule will undergo a uni-molecular reaction. The basic postulate of all unimolecular theories is the rapidity of intramolecular vibrational energy relaxation. Experimentalists were awarded a rare opportunity to test two conflicting assumptions regarding this postulate by the simultaneous advent of the Slater(1) and Rice-Ramsperger-Kassel-Marcus (RRKM)(2) theories in the 1950s. Slater’s theory, which is dynamical, pictures a molecule as an assembly of harmonic oscillators. Within this framework vibrational energy relaxation between the normal modes is forbidden, and reaction occurs only when some coordinate, the reaction coordinate, reaches a critical extension by superposition of the various normal modes. In contrast, the RRKM theory, which is an extension by R. A. Marcus of the statistical theory developed by O. K. Rice, H. C. Ramsperger, and L. S. Kassel, assumes rapid relaxation of vibrational energy. The experimental tests overwhelmingly endorsed the RRKM theory, and the controversy involving intramolecular vibrational energy relaxation was seemingly laid to rest. It also appeared as though dynamical treatments of unimolecular reactions were unnecessary.

Surprisal analysis of classical trajectory calculations of rotationally inelastic cross sections for the Ar–N2 system; influence of the potential energy surface

Abstract: Rotationally inelastic Ar–N2scattering on two different empirical potential energy surfaces has been investigated by the classical trajectory method. For each potential surface, state‐to‐state rotational transition cross sections σ j′j (E) have been calculated at five total energiesE and several initial rotational quantum states j of the N2. Results obtained from the two potentials differ significantly with respect to final rotational state distributions, but the total inelastic cross sections are very similar. Consideration of the moments of the rotational energy transfer leads to the conclusion that the potential surface of Kistemaker and de Vries is the preferred one to represent the Ar–N2 interaction. A surprisal analysis of the computed cross sections has been carried out. At energies below ?3000 K, near‐linear surprisal plots are obtained, as found earlier by Levine, Bernstein, Procaccia e t a l., thus confirming the exponential gap law of Polanyi, Ding, and Woodall for rotational relaxation. Complete cross section matrices (at a given E) can thereby be generated from a two‐parameter surprisal fit of a single column of a σ j′j matrix (or even from a classically derived first moment from the state j=0). As expected, the rotational surprisal parameter ϑ R is essentially independent of j, but it shows a significant, positive E dependence and differs in magnitude for the two potentials.

MCSCF potential energy surface for photodissociation of formaldehyde

Abstract: The ground state potential energy surface for the dissociation of formaldehyde (H2CO to H2 and CO) is calculated with the ab initio MCSCF method with an extended (4-31G) basis set. The location, barrier height, and force constants of the transition state are determined, and the normal coordinate analysis is carried out. The calculated barrier height is 4.5 eV. Based on the calculated quantities, the detailed mechanism of the photochemical dissociation is discussed.

Quantum mechanical reactive scattering for planar atom plus H2 * diatom systems. II. Accurate cross sections for H+H2 *

Abstract: The results of an accurate quantum mechanical treatment of the planar H+H_2 exchange reaction on a realistic potential energy surface are presented. Full vibration–rotation convergence was achieved in the calculations, and this, together with a large number of auxiliary convergence and invariance tests, indicates that the cross sections are accurate to 5% or better. The reactive differential cross sections are always backward peaked over the range of total energies from 0.3 to 0.65 eV. Nonreactive j=0 to j′=2 cross sections are backward peaked at low energy (0.4 eV) shifting to sidewards peaking for E≳0.5 eV. Quantum symmetry interference oscillations are very significant in the j=0 to j′=2 para‐to‐para cross sections for E≥0.6 eV. Reactive integral cross sections show two distinct kinds of energy dependence. At low energy (<0.5 eV), barrier tunneling gives them a largely exponential energy dependence while above 0.5 eV (the effective threshold energy) the cross sections vary nearly linearly. Comparison of collinear and coplanar transition probabilities indicates similar 1D and 2D energy dependence but with a shift in energy from 1D to 2D due to bending motions in the transition state. An analysis of rotational distributions indicates surprisingly good correspondence with temperaturelike distributions. The results of a one‐vibration‐approximation calculation are examined, and errors of as much as three orders of magnitude are found at some energies. Shapes of angular distributions are, however, accurately predicted by this approximate method. Additional analyses include comparisons with previous distorted wave and coupled‐channel results, and calculations of thermal rate constants.

Potential surface for the collinear collision of Ne and H2

Abstract: A potential energy surface for the Ne–H2+ reaction has been obtained in the LCAO–MO–SCF approximation. Analysis of the surface indicates that the reaction Ne+H2+→NeH++H should proceed with an endoergicity of 12 kcal/mole, in agreement with the experimental results of Chupka and Russell. Several procedures for parameterizing a diatomics‐in‐molecules (DIM) representation of the NeH2+ surface are considered. The results show that an accurate representation of the SCF surface can be obtained from the DIM model using a minimum of diatomic and triatomic data.

Potential Energy Surfaces for the Fission of the Actinide Nuclei

Abstract: Collective potential energy surfaces have been systematically calculated for the symmet­ ric fission of the five isotopes of the elements Th, Pu, Cm, Cf, Fm and No and the eight isotopes of the element U. The calculation is performed on the basis of Strutinsky's pre­ scription in which the liquid drop model of v. Groote and Hilf and the modified two-center harmonic oscillator shell model are used for macroscopic and microscopic parts, respectively. Effects of mass asymmetry at the second saddle point are investigated. The properties of the ground state, the second minim urn and the first and second saddle points along the static fission path are discussed in comparison with the results of Moller and Nix. The structure of the potential energy surface is found to come mainly from the shell structure which is strongly related to the distance between the mass centers of the nascent fragments. Special attentions are given to the fragment mass distributions and the constancy of the heavy fragment masses is partially explained on the basis of the properties of the second barrier. § I. Introduction Since the late 1960's, a renewed interest has been aroused 111 the structure of the potential energy surface for the fission process. It was motivated mainly by the discoveries of the fission isomer!) and the related resonant structure of the fission cross section. 2J The calculation based on the liquid drop model was proved not to be able to reproduce these featuers and in 1967 a new method for the calculation of the potential energy-- the macroscopic-microscopic model'J __ was proposed. Since then, calculations based on this model have been widely made and the fission isomer has been theoretically explained as a shape isomer. It is caused by the shell structure of a largely deformed nucleus and the fact that the shell structure appears at such a large deformation has made a drastic change m our knowledge of the nuclear structure. 4J The structure of the potential energy surfaces of the heavy nuclei is at present fairly well known. 5 J~sJ For the actinide nuclei, a typical feature is that there exists a second minimum and as a result the fission barrier is split into two, the inner barrier and the outer barrier. The calculated heights of these barriers and the second minimum were compared with the experimental data and overall agreement

The least-motion insertion reaction methylene(1A1) + molecular hydrogen .fwdarw. methane. Theoretical study of a process forbidden by orbital symmetry

Abstract: Ab initio electronic structure theory has been applied to the insertion reaction of singlet methylene with molecular hydrogen. Since the molecular orbital descriptions of CH/sub 2/(/sup 1/A/sub 1/) + H/sub 2/ and CH/sub 4/ differ by two electrons, the least-motion approach considered here is forbidden in the sense of Woodward and Hoffmann. Electron correlation was explicitly taken into account via configuration interaction (Cl). The Cl included all singly and doubly excited configureations (a total of 1192) with respect to three reference configurations. A primary goal was the location of the saddle point or transition state (within the constraints of the least motion approach adopted) geometry with R = 2.20 A, r = 0.76 A, and theta = 172/sup 0/. This stationary point on the potential energy surface lies 26.7 kcal/mol above separated CH/sub 2/(/sup 1/A/sub 1/) + H/sub 2/. The portion of the minimum energy path near the saddle point has been obtained by following the gradient of the potential energy in the direction of most negative curvature. The electronic structure at the transition state is compared with that of the reactants and product in terms of the natural orbitals resulting from the wave functions.

Rotational excitation of HCl by ArIMPACT

Abstract: Making use of an empirical potential energy surface, the coupled states approximation has been employed to study elastic and rotationally inelastic ArHCl collisions. Converged integral and differential cross sections are presented for transitions j → j ′ out of the j = 0 and 1 initial rotational states of HCl. The behaviour of the experimental total differential cross section of Farrar and Lee cannot be explained with the assumed potential surface. Modifications of the anisotropy in the surface are considered and a correlation is found between the deepest potential well and the rainbow angle in the total differential cross section.

Features of Potential Energy Surfaces and Their Effect on Collisions

Abstract: In this chapter we shall discuss molecular rearrangement collisions that take place on a single potential energy surface. Nonreactive collisions, particularly those involving vibrational energy transfer, are treated in Chapter 4 of Part A; multipotential processes are treated in Chapter 5 of Part B. Because most of the work devoted to the correlation of collision phenomena with features of potential energy functions has been done within the framework of classical mechanics, the major part of the discussion will utilize the language appropriate to such a description of the motion. For most chemical systems, such a treatment is entirely adequate.

Quantum mechanical scattering studies using 2D cubic spline interpolation of a potential‐energy surface

Abstract: The quantum mechanical scattering results for a collinear A+BC exchange reaction using an analytic surface are compared with those obtained by the use of the corresponding spline fitted surface (AIP)

A modified model for quenching and electronic—vibrational energy transfer

Abstract: A new computational procedure and a new transition probability expression have been incorporated into the Bauer, Fisher, and Gilmore (BFG) model for quenching and E—V energy transfer. The new transition probability expression takes into account trajectories that are classically allowed on the lower adiabatic potential energy surface, but are classically forbidden on the diabatic surfaces. The calculated quenching cross section reported are in substantially better agreement with experiment than those calculated according to the original BFG model. Further modifications to the BFG model are proposed that could have major effects on the calculated cross sections.

The Ne3 nonadditive potential energy surface

Abstract: The Ne3 potential energy surface is calculated in the SCF–MO–LCAO approximation in order to estimate the nonadditive contributions at short range separations. Several geometrical configurations are presented comprising diverse isosceles triangles and linear symmetrical and asymmetrical Ne3 geometries.