Showing papers on "Potential energy surface published in 1987"
TL;DR: In this paper, a variant of the Truncated Newton nonlinear optimization procedure is proposed for potential energy minimization of large molecular systems, which shows particular promise for large molecular system.
Abstract: Techniques from numerical analysis and crystallographic refinement have been combined to produce a variant of the Truncated Newton nonlinear optimization procedure. The new algorithm shows particular promise for potential energy minimization of large molecular systems. Usual implementations of Newton's method require storage space proportional to the number of atoms squared (i.e., O(N2)) and computer time of O(N3). Our suggested implementation of the Truncated Newton technique requires storage of less than O(N1.5) and CPU time of less than O(N2) for structures containing several hundred to a few thousand atoms. The algorithm exhibits quadratic convergence near the minimum and is also very tolerant of poor initial structures. A comparison with existing optimization procedures is detailed for cyclohexane, arachidonic acid, and the small protein crambin. In particular, a structure for crambin (662 atoms) has been refined to an RMS gradient of 3.6 × 10−6 kcal/mol/A per atom on the MM2 potential energy surface. Several suggestions are made which may lead to further improvement of the new method.
858 citations
Book•
01 Jan 1987
TL;DR: In this article, the Hartree-Fock-Roothaan-Hall method for the calculation of molecular wavefunctions was used to calculate the molecular energy expectation value, which is the fundamental quantum mechanical observable.
Abstract: 1. The Molecular Energy Expectation Value. Energy, the fundamental quantum mechanical observable. The Born-Oppenheimer approximation and the concept of nuclear geometry. Generalizations of nuclear coordinates. Global and local coordinate systems and the concept of nuclear configuration space. Intersections of Energy Hypersurfaces: adiabatic and diabatic representations. 2. Geometrical Properties of Energy Hypersurfaces. Energy derivatives: forces and force constants. Minima, saddle points and general critical points. Minimum energy path and the intrinsic reaction coordinate. Differential geometry of energy hypersurfaces. 3. Calculation and Representation of Energy Hypersurfaces. The Hartree-Fock-Roothaan-Hall method for the calculation of molecular wavefunctions. The electron correlation problem and the correlation energy. Calculation of semiempirical and empirical potential functions. The force method and calculation of higher derivatives. Minimum search methods for the determination of stable chemical species. Saddle point search methods for the determination of transition structures. Fitting of potential energy hypersurfaces, polynomials, splines and trigonometric functions. 4. The Quantum Chemical Concept of Molecules Revisited. Quantization and continuity. Wave packet topology. The topology of nuclear configurations. 5. Molecular Topology. The reduced nuclear configuration space: metric space M. Catchment regions of potential energy hypersurfaces: the representation of chemical species. Manifold theory of potential energy surfaces and catchment regions. Potential defying chemical species. The role of nuclear charges and relations between potential surfaces: convexity theorems in space w Z. Catchment regions and symmetry. 6. Reaction Topology. Topological reaction paths and quantum chemical reaction mechanisms. The algebraic structure of the complete set of reaction paths. The fundamental group of reaction mechanisms. The reaction globe, the reaction polyhedron, and homology group theory of reaction mechanisms. Quantum chemical reaction networks. The future of computer based quantum chemical synthesis design and molecular engineering. Appendix 1: Review of topological concepts. Appendix 2: Physical units and conversion factors. References. Subject Index.
307 citations
TL;DR: In this paper, a sequence of three successively improved semi-empirical potential energy surfaces for the reaction CH3+H2→CH4+H was presented based on ab initio electronic structure calculations and experimental thermochemical data.
Abstract: We present a sequence of three successively improved new semiempirical potential energy surfaces for the reaction CH3+H2→CH4+H. The semiempirical calibration is based on ab initio electronic structure calculations and experimental thermochemical data, vibrational frequencies, reaction rate constants, Arrhenius parameters, and kinetic isotope effects (KIE’s). To compare to the experimental kinetic data we apply variational transition state theory and semiclassical estimates of tunneling probabilities. We also provide detailed factorization analyses of the KIE’s to illustrate the way in which various surface features contribute to the overall KIE’s, and we discuss the substantial difficulties in attributing specific kinetic results to isolated potential energy surface features. Each of the three new surfaces, called J1, J2, and J3, has a thinner barrier than the one before. In addition, we provide one example, called surface J2A, showing the effect of making the barrier even thinner than on the best surface...
118 citations
TL;DR: Canonical variational transition state theory is used to calculate bimolecular rate constants for H+CH3 and D + CH3 recombination in this paper, which is performed on an analytic potential energy surface derived from recent ab initio calculations.
Abstract: Canonical variational transition state theory is used to calculate bimolecular rate constants for H + CH3 and D + CH3 recombination. The calculations are performed on an analytic potential energy surface derived from recent ab initio calculations. Rate constants calculated for this surface are in very good agreement with the experimental values. The H(D)---CH3 transitional rocking modes are treated as quantum harmonic oscillators or classical hindered rotors in the calculations. These two treatments give rate constants which agree to within 15%. The variational transition states become tighter as the temperature is increased.
107 citations
TL;DR: In this article, a successful analytic fit of the ab initio potential energy surface of McLaughlin and Thompson for the ground state HeH+2 system and also the results of a three-dimensional quasiclassical trajectory study of the exchange reaction over a wide range of vibrational states and relative translational energies of the reactants were reported.
Abstract: We report herein a successful analytic fit of the ab initio potential‐energy surface of McLaughlin and Thompson for the ground state HeH+2 system and also the results of a three‐dimensional quasiclassical trajectory study of the exchange reaction over a wide range of vibrational states and relative translational energies of the reactants. While there is good agreement between theory and experiment in many respects, there are some quantitative discrepancies remaining with respect to some of the experimental results.
103 citations
TL;DR: In this paper, a multidimensional potential energy surface for the interaction of a diatomic molecule with a metal surface is presented, which includes the effects of an activation barrier to the adsorption process which has a value changing with position within the surface unit cell.
84 citations
TL;DR: In this paper, the dominant features of the molecule surface potential energy surface which governs the dynamics of molecular and dissociative chemisorption are probed by molecular beam techniques coupled to electron spectroscopy.
Abstract: The dominant features of the molecule–surface potential energy surface which governs the dynamics of molecular and dissociative chemisorption are probed by molecular beam techniques coupled to electron spectroscopy. The collision energy and the vibrational energy of the incident adsorbate are the convenient probes of the interaction potential and high‐resolution electron energy‐loss spectroscopy is the sensitive and chemically specific detector of the result of the dissociative chemisorption event. The dissociative and molecular chemisorption of CH4 and CO on Ni (111) have been studied with these techniques. The results of these studies are summarized to illustrate the power of these techniques to provide information on the mechanism and dynamics of chemisorption.
82 citations
TL;DR: The present calculations confirm the mechanism of the field induced changes in the bond lengths and vibrational frequencies for both chemisorbed CO and CN as a Stark effect, and chemical changes are shown to be small.
Abstract: : We have studied the coupling of the metal-ligand and the intra-molecular ligand stretching vibrations for CO and CN chemisorbed on Cu(100) using potential energy surfaces obtained with ab initio cluster model wave functions. When there is no applied electric field, approximate internal coordinate modes for these vibrations and the fully coupled normal modes give essentially the same results, showing that their coupling is small. In the presence of an applied field, the coupling is important for CN. The origin of the coupling is shown to arise from the large field induced changes in the metal-ligand distance for the ionic bond between metal and CN. The present calculations also confirm the mechanism of the field induced changes in the bond lengths and vibrational frequencies for both chemisorbed CO and CN as a Stark effect. Chemical changes are shown to be small. Keywords: Chemisorption, Vibrational modes, Potential energy surface, Electrochemistry.
72 citations
TL;DR: In this paper, the coupling of CH stretching and CH bending vibrations in trisubstituted methanes is analyzed and the part of the coupling which arises from the kinetic energy as expressed in curvilinear coordinates is calculated and compared to the coupling calculated using the more conventional rectilinear treatment.
Abstract: The coupling of CH stretching and CH bending vibrations in trisubstituted methanes is analyzed. Improved spectroscopic constants, especially the cubic anharmonic stretch–bend coupling constants, are extracted from Fermi resonances in the overtone spectra of HCF3 and HCCl3. Both harmonic oscillator and Morse oscillator basis functions are used in the analysis and the results compared. That part of the coupling which arises from the kinetic energy as expressed in curvilinear coordinates is calculated and compared to the coupling calculated using the more conventional rectilinear treatment. Use of curvilinear coordinates is found to provide significant advantages. The formalism for curvilinear normal coordinates is clarified and generalized. From these calculations and the spectral analysis, one of the cubic anharmonic constants of the potential energy surface is extracted for comparison with ab initio calculations. The curvilinear model of the CH stretch–bend interaction tested for these isolated CH chromop...
70 citations
TL;DR: In this paper, the second-order configuration interaction (SOCI) calculations of low-lying electronic states [2B2,2A1] of Au3 as well as the 1Σ+g state of Au2 are carried out.
Abstract: Complete active space MCSCF (CASSCF) and second‐order configuration interaction (SOCI) calculations of low‐lying electronic states [2B2,2A1] of Au3 as well as the 1Σ+g state of Au2 are carried out. The bending potential energy surfaces of 2A1 and 2B2 states are also presented. A barrier is found in the potential energy surface of the 2A1 state in moving from the linear to bent structure. Two nearly‐degenerate structures are found for the ground state. The 2Σ+u state arising from the linear structure with an Au–Au bond length of 2.66 A is only 3.2 kcal/mol below the 2A1 bent state. The equilibrium geometry of the 2A1 state is an isosceles triangle with an apex angle of 54°. The Au3 cluster is found to be more stable than the gold dimer. The effect of d correlation is studied on Au2 by carrying out MRSDCI (multireference singles and doubles CI) calculations on the 1Σ+g state of Au2 which include excitations from the d orbitals.
67 citations
TL;DR: In this paper, the photodissociation of H2O and D2O in the second band (λ≳120 nm) is investigated using two-dimensional (translation and rotation) classical trajectories.
Abstract: The photodissociation of H2O and D2O in the second band (λ≳120 nm) is investigated using two‐dimensional (translation and rotation) classical trajectories. The calculations include all electronic states which are involved in the dissociation dynamics, i.e., B 1A1, X 1A1, and A 1B1. The nonadiabatic transitions B→X and B→A near linearity are modeled in a very simple way, which does not yield the OH(2Σ)/OH(2Π) branching ratio. The rotational distributions for OH(2Σ) and OD(2Σ) agree qualitatively very well with the measurements. They are highly inverted and peak close to the highest accessible state. Comparing the OH(2Π) rotational distributions with recent experimental results we conclude that B→X is probably the main dissociation pathway, although contributions from a B→A transition cannot be excluded. The OH(2Π) distribution is also highly inverted with a peak near j∼43 in excellent agreement with experiment. The majority of trajectories on all three potential energy surfaces is direct. The shape of the various rotational distributions is determined by the first step of the dissociation from the FC region up to linearity where the crossing to the X or the A state might occur. As envisioned a long time ago the strong angular force near the FC region on the B potential energy surface is responsible for the extremely high degree of rotational excitation for OH(2Σ) as well as for OH(2Π).
TL;DR: In this article, the authors analyzed potential energy surfaces that have been proposed by one of the authors, Bunker, and Chapman and by Raff for the reaction CH3+H2↔CH4+H. The surfaces are modified to remove discontinuities and zero frequencies, where present, and the modified surfaces are compared to each other in terms of reactionpath properties and to ab initio calculations for stationary point properties.
Abstract: We analyze potential energy surfaces that have been proposed by one of the authors, Bunker, and Chapman and by Raff for the reaction CH3+H2↔CH4+H. The surfaces are modified to remove discontinuities and zero frequencies, where present, and the modified surfaces are compared to each other in terms of reaction‐path properties and to ab initio calculations for stationary point properties. They are also used for rate constant calculations which are compared to experiment. The rate constants were calculated by improved canonical variational transition state theory with small‐curvature semiclassical adiabatic ground‐state transmission coefficients (ICVT/SCSAG) over a wide temperature range, 298–1340 K. Both surfaces yield rate constants in poor agreement with experimental values. The reaction‐path analysis leads to a list of potential energy surface features that are important for the rate constants but inaccurate in the existing surfaces and that should be improved in subsequent work.
TL;DR: In this article, the reaction I2M + hn -> I2(B,v',j') + M (M = rare gas atom) was studied exptl. for excitation above the dissocn.
Abstract: The reaction I2M + hn -> I2(B,v',j') + M (M = rare gas atom) was studied exptl. for excitation above the dissocn. limit of the I2M B state. A surprisingly large amt. of the available energy is found as relative translational energy of the I2 and M products. These results were interpreted in terms of a one atom cage effect, where the I atoms are prevented from dissocg. by the presence of M. A purely kinematic cage effect could occur on a single electronically excited potential energy surface, namely the one correlating to the I2(B) state plus M in its electronic ground state. Another possible mechanism for a pathway leading to bound I2, which involves an electronic nonadiabatic transition is discussed. Above the I2M(B) threshold the 1P1u electronic state can also be excited. Since the 1P1u and the B states can be coupled by the presence of the rare gas atom, there is a finite probability for an electronic transition from 1P1u to B, with the energy difference being transformed into relative kinetic energy of the rare gas atom with respect to I2 after a fraction of the available energy was used to break the van der Waals bond. The relation between this mechanism and the electronic predissocn. of I2M(B) van der Waals mols. at much lower energies, as well as the collision induced electronic predissocn. of I2(B), are also mentioned. The possibility of observing similar transitions in other halogen-rare gas clusters is considered.
TL;DR: In this article, the authors 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, which can be used in conjunction with variational transition state theory (VTST) calculations based on ab initio gradients and Hessian calculations.
TL;DR: In this article, the rotational levels with J ≤ 4 were fitted to standard vibration-rotation Hamiltonians due to W. Meyer et al. The results were in excellent agreement with the experimental results where available.
TL;DR: In this article, cross-beam reactive scattering experiments employing electrostatic hexapole fields to control the initial collision geometry of chemical reactions are described and the effects of rotational coupling and nonzero impact parameters in changing the molecular precollisions orientation selected by the hexapoles fields to a different in-collision orientation at the moment of impact with the reaction partner are discussed.
Abstract: Crossed-beam reactive scattering experiments employing electrostatic hexapole fields to control the initial collision geometry of chemical reactions are described New results are presented on the reactions of oriented NO with ozone and oriented N/sub 2/O with Ba Preliminary results are also given for the oriented CH/sub 3/F + Ca* --> CaF* + CH/sub 3/ reaction Recent technical advances in state selection and product detection are detailed They discuss the effects of rotational coupling and nonzero impact parameters in changing the molecular precollisions orientation selected by the hexapole fields to a different in-collision orientation at the moment of impact with the reaction partner Uncoupling of l doubling in N/sub 2/O at strong orientation fields is demonstrated via the observed reactive anisotropy Steric effects are found to govern many aspects of the reactions investigated thus far Strong correlations are observed of the reactivity, product recoil, and rotational angular momentum distributions with the collisional orientation These correlations ultimately provide information on the anisotropic part of the reaction potential energy surface They conclude with a brief outline of possible future directions in oriented molecule scattering
TL;DR: In this paper, a semiclassical impulsive model was proposed to describe photoproduct rotation as developing during fragmentation successfully describes the rotational state distributions of NH(a 1Δ) produced by HNCO photodissociation over a wide range of wavelengths.
Abstract: We have examined the photofragmentation HNCO→NH(a 1Δ)+CO using radiation at wavelengths shorter than 230 nm. Nascent NH(a 1Δ) shows relatively little rotational excitation, accounting for less than 12% of the energy in excess of the dissociation energy. The rotational state distributions evidence less population in high rotational states than predicted by statistical theories but more than expected on the basis of a simple impulsive dissociation. A semiclassical impulsive model that describes photoproduct rotation as developing during fragmentation successfully describes the rotational state distributions of NH(a 1Δ) produced by HNCO photodissociation over a wide range of wavelengths. The success of this model in describing the NH rotational state distributions and previously measured CO rotational state distributions suggests that the excited state potential energy surface may be repulsive with minima in HNC and NCO bond angles each near 120°.
TL;DR: In this paper, a two-dimensional, quantal study of the photodissociation of CH3O-NO within the first continuum (S0→S1, 300-400 nm) taking into account only the O−N and the N=O separations is presented.
Abstract: We report the results of a two‐dimensional, quantal study of the photodissociation of CH3O–NO within the first continuum (S0→S1, 300–400 nm) taking into account only the O–N and the N=O separations. The S1 potential energy surface is taken from recent ab initio calculations. The calculated absorption spectrum consists of two band progressions of narrow resonance lines with widths of ∼0.3 and ∼5 meV, respectively. These resonances can be associated with excitation of the O–N bond (m=0,1) and excitation of the N=O chromophore (n*=0,1,2,...). The intensities of the m=1 band are negligibly small compared to those of the m=0 band. The decay mechanism in the two cases is different: The m=0 resonances decay primarily via vibrational predissociation, i.e., a nonadiabatic transition from n* to n*−1, and yield NO products with a preferential population of the (n*−1) level. The m=1 resonances decay mainly via tunneling through a potential barrier yielding preferentially NO products in state n*. Several of the theore...
Journal Article•
TL;DR: In this article, the kinetics of the reaction of formyl radicals with atomic hydrogen were studied as a function of temperature, and the reaction was isolated for direct investigation in a tubular reactor coupled to a photoionization mass spectrometer.
Abstract: The kinetics of the reaction of formyl radicals with atomic hydrogen was studied as a function of temperature. The reaction was isolated for direct investigation in a tubular reactor coupled to a photoionization mass spectrometer. Rate constants were obtained for the overall reaction H + HCO ..-->.. products. They are 1.4 x 10/sup -10/ (296 K), 1.3 x 10/sup -10/ (350 K), and 0.96 x 10/sup -10/ (418 K) cm/sup 3/ molecule/sup -1/ s/sup -1/. Estimated error limits are +/- 30%. These measured rate constants are in close agreement with recently calculated values obtained by Harding and Wagner using an ab initio potential energy surface for H/sub 2/CO characterized along the reactive pathways of this reaction.
TL;DR: In this paper, the C→A emission spectra for H2O and D2O were measured and calculated based on an exact treatment of the dissociation dynamics of the A state using a calculated potential energy surface.
Abstract: The C→A emission spectra for H2O and D2O are measured and calculated The theoretical model is based on an exact treatment of the dissociation dynamics of the A state using a calculated potential energy surface Agreement with the measurements is excellent The spectra extend from λ∼380 nm up to λ∼600 nm with maxima around 425 (H2O) and 440 nm (D2O)
TL;DR: In this paper, a comprehensive first-principles theoretical investigation of the gas phase reaction Ca + HF - CaF + H is reported, along with the fitting of the computed potential energy points to a suitable analytical functional form.
Abstract: A comprehensive first-principles theoretical investigation of the gas phase reaction Ca + HF - CaF + H is reported. Ab initio potential energy calculations are first discussed, along with characteristics of the computed potential energy surface. Next, the fitting of the computed potential energy points to a suitable analytical functional form is described, and maps of the fitted potential surface are displayed. The methodology and results of a classical trajectory calculation utilizing the fitted potential surface are presented. Finally, the significance of the trajectory study results is discussed, and generalizations concerning dynamical aspects of Ca + HF scattering are drawn.
TL;DR: In this article, a model for the hydrogen atom transfer reaction Cl + HCl was used to investigate the occurrence of oscillations in the reactivity as a function of collision energy for reactions in which a light atom L is transferred between two heavy atoms H and H + LH'..-->.. HL + H'.
Abstract: The hydrogen atom transfer reaction Cl + HCl ..-->.. ClH + Cl was used as a model for investigating the occurrence of oscillations in the reactivity as a function of collision energy for reactions in which a light atom L is transferred between two heavy atoms H and H', H + LH' ..-->.. HL + H'. Very extensive three-dimensional quasi-classical trajectory calculations, under a variety of conditions and employing three LEPS potential energy surfaces, were carried out for this purpose. The three surfaces have very similar properties for the collinear Cl-H-Cl configuration but considerably different widths of the reactive cone of acceptance. Significant oscillations were obtained for two of the surfaces. The surface for which the strongest oscillations were observed is characterized by strong anisotropic attractive forces which lead to reorientation of the reagents to a nearly collinear configuration even when the initial orientation angle (the angle between the relative velocity vector and the axis of the HCl molecule) is large. The results of this study indicate that the most promising experiments for detecting oscillations should be scattering experiments with oriented molecular beams.
TL;DR: In this article, the authors discuss in as pedagogic a fashion as possible and from the point of view of theory some aspects of collision phenomena at surfaces, such as dissociation of molecules.
Abstract: The aim of this lecture is to discuss in as pedagogic a fashion as possible and from the point of view of theory some aspects of collision phenomena at surfaces. These phenomena can be very complicated. In particular collisions that result in chemical reaction – e.g., dissociation of molecules – are complex in the sense that the adiabatic approximation, where the electrons are assumed to adapt instantaneously to the motion of the nuclei, is invariably suspect and often manifestly irrelevant. The theoretical problem posed by such collisions is therefore rather intractable and only very simple model systems can be treated [1]. I restrict myself of mechanical collisions characterized by a single potential energy surface V(rp, {ri}), where rp, {ri} are the coordinates of the particle, P, and the lattice nuclei, respectively. V is the electronic ground-state energy with the nuclear coordinates held fixed. This restriction simplifies the problem, which, however, remains far from trivial. We are still left with a many-body-problem involving a potentially infinite number of particles that has been solved only numerically and in the classical limit. If we want more than this, we have to pick away at the problem as best we can using intuition and taking guidance from experiment.
TL;DR: In this paper, the canonical variational transition state theory was used to study the kinetics of Li++(CH3)2O association and the rate constants were calculated for a complete analytic potential energy surface which includes all inter-and intramolecular coordinates, and for an ion-dipole/ion-induced Δ-body potential.
Abstract: Canonical variational transition state theory is used to study the kinetics of Li++(CH3)2O association. Transition states and rate constants are calculated for a complete analytic potential energy surface which includes all inter‐ and intramolecular coordinates, and for an ion–dipole/ion–induced‐dipole two‐body potential. These surfaces have a single transition state at each temperature. Anisotropy in the polarizability is found to have a negligible effect on the association transition states and rate constants. The canonical variational transition state theory rate constants are in good agreement with those calculated by other formalisms.
TL;DR: In this article, a switching function formalism is used to derive an analytic potential energy surface for the O + OH in equilibrium HO/sub 2/ in equilibrium H + O/ sub 2/ reactive system.
Abstract: A switching function formalism is used to derive an analytic potential energy surface for the O + OH in equilibrium HO/sub 2/ in equilibrium H + O/sub 2/ reactive system. Both experimental and ab initio data are used to derive parameters for the potential energy surface. Trajectory calculations for highly excited HO/sub 2/ are performed on this surface. From these trajectories quasi-periodic eigentrajectories are found for vibrational levels near the HO/sub 2/ dissociation threshold with small amounts of quanta in the OH stretch mode and large amounts of quanta in the OO stretch mode.
TL;DR: In this paper, the problem of translational to vibrational energy redistribution occurring in collisions between diatomic molecules and solid surfaces is considered, focusing solely on a mechanism which is a consequence of a molecule-surface interaction giving rise to an intramolecular potential whose equilibrium separation is a function of distance from the surface.
Abstract: The problem of translational to vibrational energy redistribution occurring in collisions between diatomic molecules and solid surfaces is considered. Attention is focused solely on a mechanism which is a consequence of a molecule–surface interaction giving rise to an intramolecular potential whose equilibrium separation is a function of distance from the surface. This ‘‘three‐body’’ chemical effect is totally unrelated to mechanical excitation due to spring compression. While past work has emphasized the specific process of charge transfer/harpooning as a means for obtaining such an interaction, the mechanism is more general in the sense that it depends only upon the topology of the potential energy surface (PES) and not on what electronic properties gave rise to the topology. The T to V energy redistribution is treated both within the context of analytical models over necessarily simplified PES as well as numerically evaluated classical trajectories over more complex and realistic ones. Systematic studies are presented in which the relationship between energy conversion and PES characteristics are established. Conditions under which the analytic models provide reasonable representations of the collision are noted. I2 is the molecule of choice in this work.
TL;DR: In this article, a simple kinematic model based on the concept of an orientation-dependent critical configuration for reaction is introduced and applied to the Li + HF and O + HCl reactions where the HX molecules are pumped by a polarized laser.
Abstract: A simple kinematic model based on the concept of an orientation-dependent critical configuration for reaction is introduced and applied. The model serves two complementary purposes. In the predictive mode the model provides an easily implemented procedure for computing the reactivity of oriented reagents (including those actually amenable to measure) from a given potential energy surface. The predictions of the model are compared against classical trajectory results for the H + D/sub 2/ reaction. By use of realistic potential energy surfaces the model is applied to the Li + HF and O + HCl reactions where the HX molecules are pumped by a polarized laser. A given classical trajectory is deemed reactive or not according to whether it can surmount the barrier at that particular orientation. The essential difference with the model of Levine and Bernstein is that the averaging over initial conditions is performed by using a Monte Carlo integration. One can therefore use the correct orientation-dependent shape (and not only height) of the barrier to reaction and, furthermore, use oriented or aligned reagents. Since the only numerical step is a Monte Carlo sampling of initial conditions, very many trajectories can be run. This suffices to determine the reaction crossmore » section for different initial conditions. To probe the products, they have employed the kinematic approach of Elsum and Gordon. The result is a model where, under varying initial conditions, examining final-state distributions or screening different potential energy surfaces can be efficiently carried out.« less
TL;DR: In this paper, complete active space MC SCF (CAS SCF) followed by second-order configuration interaction (SOCI) calculations are carried out for the three lowest-lying states of ScH 2.