Semiempirical Potential Energy Surface Research Articles

Simple semiempirical potential energy surfaces for the reaction of alkali metal atoms with the bromine molecule

Potential energy surfaces for the reactions of the alkali metals M (Li, Na, K, Rb, and Cs) with Br2 are computed using a simple semiempirical procedure. The calculations show that there is a vibrational barrier between M+Br2 and M++Br2− along the Br–Br coordinate which plays an important role in the reaction. A potential well exists for all angles of approach of the metal to the molecule; this M+Br2− species is lower in energy than any product channel. The calculated ionic/covalent coupling matrix elements between M+Br2 and M++Br2− agree well with the experimental values.

Bond-length alternation and vibrational spectra of polyacetylene

The effect of bond-length alternation on the main features of the Raman vibrational spectra of polyacetylene is examined. It is shown that the semiempirical potential energy surfaces for cyclic polyene models, which display the bond-length alternating equilibrium geometry, yield vibrational frequencies that are in reasonable agreement with observed principal Raman bands. However, these frequencies are rather insensitive to the details of the potential energy surface employed, thus explaining the controversy between earlier computations (Ovchinnikov et al.) and the experimental evidence of bond-length alternation in all-trans polyacetylene (Fincher, Jr., et al.). Nevertheless, the normal mode character of these vibrations qualitatively changes with the introduction of the bond-length alternation.

Quasiclassical trajectory studies of the chlorine–hydrogen system. IV. The effect of reagent vibrational excitation and of the location of the potential energy barrier on the dynamics

Three dimensional quasiclassical trajectory calculations were performed for the reaction of chlorine atoms with hydrogen molecules (H2, D2, and HD). Three LEPS semiempirical potential energy surfaces, all having the same barrier heights but with slightly different saddle point locations, were used for the calculations. Surface I, the surface used in our earlier studies of this reaction for the reactants in their ground vibrational state v=0, was employed here to investigate the effect of vibrational excitation of the reactants on the dynamics of this reaction. This was done by carrying out calculations for H2(v=1–4 and v=7), HD(v=1), and for D2(v=1) and comparing the results to those obtained earlier for v=0. The two other surfaces EN and EX were used to investigate the effect of the position of the barrier on the dynamics of the reaction. These two surfaces are very similar to surface I, but in surface EN the barrier is slightly shifted in the direction of the entry valley, while in surface EX it is slightly shifted in the direction of the exit valley. The interatomic distances at the saddle points of surfaces EN and EX differ by only 0.03 to 0.05 Å from those of surface I. For surfaces EN and EX, calculations were carried out for H2(v=0 and 1), D2(v=0), and HD(v=0) and the results were compared to those obtained for surface I. The results of the calculations on surface I show that the rate of reaction is significantly enhanced by the vibrational excitation of the reagents [kr(v=1)/kr(v=0)=400 for Cl+H2 Cl+H2(v) at 300 K)] that vibrational energy of the reactants (Ev) is very efficiently transferred into vibrational energy of the products (Ev′), and that the average scattering angle of the products decreases with the increase of either translational or vibrational energy of the reactants. The results of the calculations on surfaces EN and EX show that the rate constants are very sensitive to the location of the energy barrier, being significantly higher for surface EX than for surfaces I and EN. The energy partitioning among reaction products, as well as the scattering angle at low collision energies, also depend on the position of the potential energy barrier.

The reaction Hg+I2→HgI+I revisited

The crossed molecular beam study of Mayer et al. (1977) on the subject reaction is revisited. The present work employs a different beam configuration and thus kinematic framework, and a larger range of relative translational energies is covered (i.e., from the threshold of 1.15 to 3.75 eV). Measurements include in-plane angular distributions and relative values of integral reaction cross sections as a function of energy. At low energies, the results of the present experiments are in good agreement with the previous work. Starting at the threshold, the reaction proceeds through the formation of a long-lived complex, presumed to be IHgI. At higher energies, the c.m. angular distributions show a gradual increase of the so-called ‘‘backscattered component.’’ This is interpreted as the opening of a new reaction path: the direct-mode abstraction of I via collinear approach of the Hg atom to the I2 molecule. The overall dynamics of this reaction are interpreted in the context of the semiempirical potential energy surfaces and electronic state correlation diagrams of Muckerman et al. (1977). From the present experimental results, the height of the barrier in the exit channel for the collinear configuration can be estimated to be in the range 2.0–2.3 eV. The excitation function rises from threshold and reaches a maximum at collision energy of 2.6 eV, falling off monotonically thereafter.

A quasiclassical trajectory test for a potential energy surface of the Li+HF reaction

A three-dimensional quasiclassical trajectory study of the Li→HF→LiF+H reaction has been performed on a recently proposed analytical potential energy surface (PES) fitted to ab initio points. The results of the calculations are compared with the experiment. Previous related work on a semiempirical PES is noted.

Semi-empirical potential energy surfaces for the linear HXY (X, Y = F, Cl, Br, I) systems

The modified diatomics-in-molecules method including the three-center term was applied to calculate the linear potential energy surfaces of fourteen H + XY and X + HY reactions where X and Y are halogen atoms. All calculations were performed using a common set of three adjustable parameters. The adjustable parameters were determined by fitting the potential barrier heights of the HFF, HClCl and FHF systems.

Semiempirical valence bond potential energy surfaces for simple chemical reactions:1A′ states of H2O and H2F+

A semiemprical valence bond method is employed to study the potential energy surfaces (PESs) of the lowest 1 A′ states of H2O and isoelectronic H2F+. The calculation is based on the search for the electronic configurations which play the most important rôle in the formation of the stable electronic states of the molecules and the relevant diatomic fragments. Several approximations are used to reduce the number of permutations in the calculation of the energy matrix. The Moffit atoms-in-molecule approximation is used to correct for the atomic errors arising from the poor basis set. The computed data for the lowest electronic states of OH, HF, HF+, H2O and H2F+, as well as the general behaviour of the PESs for different molecular geometries, are in good agreement with the available ab initio and experimental data.

A classical mechanical study of the LiFH system

A three dimensional and collinear quasiclassical study of the Li + HF → LiF + H reaction is performed on the Zeiri—Shapiro semi-empirical potential energy surface. The results are compared to a recent experimental study. In agreement with experiment ≈43% of available energy is channeled to the internal (vibrational and rotational) mode of the LiF product, most of which, we show, ends up as rotation (≈33%) and only the remaining 10% as vibration. The differential cross section is shown to peak in the forward—backward directions as also observed experimentally. The calculated cross section is more backward peaked than the experimental one. The accuracy of the quasiclassical method for this system is assessed by comparison of collinear results with available quantal calculations. It is shown that the average product vibrational distributions are adequately given by the quasiclassical method. The results are analyzed using periodic-orbit-dividing surfaces which predict correctly the onset of the various dynamic barriers.

Semiempirical three-dimensional potential energy surfaces suitable for both reaction channels of the XH2 system (X = F, Cl)

Three-dimensional potential energy surfaces for Reactions (1) F+H2→HF+H, (2) H′+HF→H′F+H, (3) H+HCl→H2+Cl and (4) H′+HCl→H′Cl+H were calculated by a modified version of the diatomics-in-molecules (DIM) method. In this version a term which incorporates contributions of three-center molecular integrals neglected by the DIM method is added to the DIM energy. This is the first time that both reaction channels of all of these systems were considered simultaneously. The potential barriers of Reactions (1) and (2) and the difference between the potential barriers (3) and (4) were fitted by adjusting three parameters. The potential barrier of Reaction (3) was then predicted to be 4.9 kcal/mole. The dependence of the barrier heights, saddle points, and other features of the potential energy surfaces on the geometry were investigated. The transition state geometry was proved to be linear for Reactions (1), (3), and (4) and nonlinear for Reaction (2).

Quasiclassical trajectory study of colinear Cl − + HBr → HCl + Br −

Energy distributions in the products of the ion-molecule reaction Cl − + HBr → HC1 + Br − have been studied using quasiclassical trajectories on a semi-empirical collinear potential energy surface. Vibrational energy is favored in the products. While some trajectories are long-lived, the kinematic factor of the light central atom prevents effective energy redistribution.

A quantum mechanical study of the collinear Li+FH reaction

A quantum mechanical collinear model of the LiFH reaction is studied using the semiempirical potential energy surface of Zeiri and Shapiro. Accurate reaction probabilities are presented over the total scattering energy range from 0.5 to 1.6 eV. At 1.6 eV, three HF reactant vibrational states are energetically accessible, and 15 LiF product vibrational states are accessible. The reaction probabilities show extensive resonance features over the energy range considered, and there is considerable evidence for the formation of a long-lived collision complex from the initial v=1 state of HF.

Variational transition state theory and vibrationally adiabatic transmission coefficients for kinetic isotope effects in the Cl–H–H reaction system

Variational transition state theory and semiclassical adiabatic ground-state transmission coefficients are applied to calculate the kinetic isotope effects for D and T substitution in the reaction Cl+H2 at 245–445 K. The calculated isotope effects differ significantly from those calculated previously using conventional transition state theory and semiempirical potential energy surfaces. We use variational transition state theory and conventional transition state theory with the Wigner tunneling correction to adjust three new semiempirical surfaces to the experimental data. No one set of calculations is completely successful. The potential energy surfaces that are most successful at predicting the HD/DH intramolecular kinetic isotope effect have the earliest saddle points (the saddle points are collinear with R‡Cl–H=2.64–2.78a0, R‡H–H=1.88–1.72a0). For each surface studied except one, the canonical variational transition states are located past the saddle point for some of the isotopic reactions and earlier than the saddle point for others. The exceptional surface is the one of Valencich and co-workers; that surface has an early saddle point, but the variational transition states are always earlier than the saddle point.

Semi-empirical potential energy surfaces for the reactions H + HCl → H 2 + Cl and H' + HCl → H' Cl + H

The H + HC1 potential surfaces for both reaction channels are calculated by a modified diatomics-in-molecules method including three-center molecular integrals Using the same adjustable parameters as for the FH 2 system, we obtain barrier heights of 5.2 kcal mole (abstraction) and 14.2 kcal mole (exchange). Changing one adjustable parameter only and fitting the experimental difference between the activation energies of the two reaction channels, we obtain 4.9 and 3.9 kcal mole respectively for the abstraction and exchange barrier heights.

Comparison of reactive and inelastic scattering of H2+D2 using four semiempirical potential energy surfaces

Collisions between hydrogen and deuterium molecules are examined using quasiclassical dynamical trajectory calculations with the intermolecular field specified by four semiempirical potential energy surfaces. Three of the surfaces are calculated within the valence bond model with semiempirical evaluation of the integrals, and the fourth is the London type. Various degrees of agreement are observed between these four surfaces and ab initio results. The trajectory calculations are performed at high system energies to permit the possibility of reactions. In addition to nonreactive collisions, four reaction paths are found on each surface with the product species 2H+D2, H2+2D, HD+H+D, and 2HD. The results are analyzed to determine the effect of surface properties on reaction probabilities, average final state properties of the molecules and average final state energy distributions. Dynamical results are found to be strongly dependent on surface characteristics.

ChemInform Abstract: PRACTICAL APPLICATION OF EXTENDED VALENCE BOND DIATOMIC CALCULATIONS TO THE METHOD OF DIATOMICS‐IN‐MOLECULES FOR NEHE+2

Potential energy curves for the lowest two 2Σ states and the lowest 2Π state of NeHe+ were calculated using the valence bond method with minimal and extended basis sets. It is shown how this ab initio information, together with information on the He2, He+2, and NeHe molecules obtained from other sources, can be incorporated into a minimal basis diatomics‐in‐molecules (DIM) description of NeHe+2. Particular emphasis is given to the incorporation of the extended ab initio wave functions into the DIM procedure. Two sets of semiempirical DIM potential energy surfaces for NeHe+2 were computed using the minimal and extended valence bond diatomic wave functions and energies as input. These surfaces are compared and discussed with regard to other electronic structure calculations on NeHe+2. The lower potential surfaces for NeHe+2 are particularly relevant to the collision‐induced dissociation of He+2 by Ne to form Ne+ ions.

Practical application of extended valence bond diatomic calculations to the method of diatomics-in-molecules for NeHe+2

Potential energy curves for the lowest two 2Σ states and the lowest 2Π state of NeHe+ were calculated using the valence bond method with minimal and extended basis sets. It is shown how this ab initio information, together with information on the He2, He+2, and NeHe molecules obtained from other sources, can be incorporated into a minimal basis diatomics-in-molecules (DIM) description of NeHe+2. Particular emphasis is given to the incorporation of the extended ab initio wave functions into the DIM procedure. Two sets of semiempirical DIM potential energy surfaces for NeHe+2 were computed using the minimal and extended valence bond diatomic wave functions and energies as input. These surfaces are compared and discussed with regard to other electronic structure calculations on NeHe+2. The lower potential surfaces for NeHe+2 are particularly relevant to the collision-induced dissociation of He+2 by Ne to form Ne+ ions.

A survey of reactions involving H',H'', and chlorine atoms

Experimental and theoretical rate constants for the reactions H/sub 2/ + Cl in equilibrium H + HCl, H' + ClH'' ..-->.. H'Cl + H'', and H' + H''Cl(upsilon = 1) ..-->.. H' + H''Cl(upsilon = 0) are discussed in detail (H' and H'' are H, D, or T). For the reaction H/sub 2/ + Cl in equilibrium H + HCl, experimental rate constant data for the forward and reverse reactions are in good shape. Semiempirical potential energy surfaces have been found which, combined with trajectory calculations or activated complex theory, give rate constants in reasonable agreement with experiment. However, these potential energy surfaces cannot be extended to include the exchange reaction, H' + H''Cl ..-->.. H'Cl + H'', and neither the experimental determinations or theoretical predictions of the abstraction/exchange branching ratios are well established. Relaxation of HCl(upsilon = 1) by H or D atoms may result from either reactive or nonreactive collisions; theory and experiment disagree as to the relative importance of these two channels. 8 figures, 8 tables.

Leps potential energy surfaces for symmetrical alkali trimers

Semi-empirical potential energy surfaces for M 3 (where M = Li through Cs) complexes are derived from the simplest form of the London approximation, by evaluating the Coulomb and exchange integrals as half of the sum and difference of two new interaction potential curves for the 1Σ + g and 3Σ + u states of M 2. For comparison the Morse and a modified an tiMorse potential have been included in the calculations. At small internuclear distances the potential surfaces show a shallow well which extends into the entrance and exit valleys without an energy barrier. The M 3 complexes attain maximum stability in the linear symmetric configuration; they remain almost equally stable, however, in the isosceles triangular configuration. The force constants corresponding to stretching and bending deformations of the trimers have been calculated for the linear configuration. It has been observed that unlike the stretching, the bending deformation does not sensitively affect the energy variation of the ground state of the trimers.

On the rate and activation energy of the Br + Br 2 ataom-exchange reaction

The Br + Br 2 atom-exchange reaction has been studied using quasiclassical trajectories and a semi-empirical potential-energy surface with shallow, long-range wells. The computed reaction rate coefficient is in good agreement with experiment. The computed reaction activation energy is ≲ 1 kcal/mole.

Potential Energy Surfaces for Alkali-Trimers

Semi-empirical potential energy surfaces for alkali-trimers are derived from the simplest form of London's approximation, by evaluating the Coulomb and exchange integrals as half of the sum and difference of two new interaction potential curves for the 1Σg + and 3Σu + states of the corresponding alkali dimers. The trimers attain maximum stability in their linear symmetric configuration. The force constants corresponding to stretching and bending deformations of the homonuclear trimers have been calculated for the linear symmetric configuration. Unlike the stretching, the bending deformation is seen to be very much insensitive to the ground state energy variation of the trimers.