Showing papers on "Potential energy surface published in 1983"

CO binding to heme proteins: A model for barrier height distributions and slow conformational changes

Abstract: A model for the dependence of the potential energy barrier on a ‘‘protein coordinate’’ is constructed. It is based on a two dimensional potential energy surface having as variables the CO–iron distance and a conceptual protein coordinate. The distribution of barrier heights observed in kinetics follows from an initial Boltzmann distribution for the protein coordinate. The experimental nonexponential rebinding kinetics at low temperatures or large viscosities (when the protein coordinates can be assumed ‘‘frozen’’) can be fit with a simply parametrized energy surface. Using the same energy surfaces and the theory of bounded diffusion perpendicular to the reaction coordinate, we generate (in qualitative agreement with experiment) the survival probability curves for larger diffusivity, when the constraint on the protein coordinate is relaxed. On the basis of our results, the outcomes of new experiments which examine the concepts underlying the theory can be predicted.

Variational transition state theory and tunneling for a heavy–light–heavy reaction using an ab initio potential energy surface. 37Cl+H(D) 35Cl→H(D) 37Cl+35Cl

Abstract: Ab initio POL–CI calculations, augmented by a dispersion term, are used to predict the potential energy surface for the reaction Cl+HCl. The saddle point is found to be nonlinear. The surface is represented by a rotated‐Morse‐oscillator spline fit for collinear geometries plus an analytic bend potential. Variational transition state theory calculations, based on a linear reference path, are carried out, and they yield much smaller rate constants than conventional transition state theory, confirming that earlier similar results for this heavy–light–heavy mass combination were consequences of the small skew angle and were not artifacts of the more approximate potential energy surfaces used in those studies. Transmission coefficients are calculated using approximations valid for large‐reaction‐path curvature and the potential along the reference path is scaled so that the calculated rate constant agrees with experiment. The resulting surface is used to compute the H/D kinetic isotope effect which is in qualitative agreement with experiment.

Exact quantum and vibrationally adiabatic quantum, semiclassical and quasiclassical study of the collinear reactions Cl + MuCl, Cl + HCl, Cl + DCl

Abstract: Accurate quantum calculations of reaction probabilities have been carried out using Delves' polar coordinates for the collinear reactions Cl + XCl(ν) →ClX(ν′) + Cl (X = Mu, H, D) An extended London-Eyring-Polanyi-Sato potential energy surface with a linear symmetric barrier height of 35·77 kJ mol-1 has been used in the calculations The diagonal ν →ν reaction probabilities dominate over the off-diagonal ν →ν′ ≠ ν reaction probabilities and show sinusoidal oscillations as a function of energy Superimposed on these oscillations for X = H, D is a spectrum of narrow resonances The positions of the resonances can be predicted very accurately from the solution of a vibrationally adiabatic (VA) single channel Schrodinger equation provided the diagonal corrections to the VA potential are also included The sinusoidal oscillations are analysed using VA semiclassical and quasiclassical theories There is good agreement between the quantum, semiclassical and quasiclassical results at low energies, but differences

Variational transition state theory calculations for an atom--radical reaction with no saddle point: O+OH

Abstract: We have extended the general polyatomic canonical variational theory formalism of Isaacson and one of the authors to improved canonical and microcanonical variational theory. We have calculated the rate constants for the reaction in the title over the temperature range 200–2500 K using all three variational theories and the Melius–Blint ab initio potential energy surface. The results are compared to canonical variational calculations based on the reaction‐path interpolation scheme of Quack and Troe, to the trajectory calculations of Miller, and to experiment. We find that the microcanonical variational transition states have a strong energy dependence and the generalized free energy of activation curves have two maxima. Quantization effects appear to be important at the lower temperatures, and recrossing effects may be important at higher temperatures.

Vibrational and rotational excitation in molecular collisions

Abstract: Publisher Summary This chapter focuses on the vibrational and rotational excitation in molecular collisions. The dynamics of a molecular collision is governed by the interaction forces between and within the colliding molecules. For given molecular electronic states, these can be summarized in potential energy functions of the respective internuclear distances and, when excluding electronic transitions, only one potential energy surface is relevant for the molecular collision. Differential vibrationally and rotationally inelastic scattering experiments measure the angular dependence of fully resolved state-to-state cross sections or, when internal state resolution cannot be completely achieved, inelastic excitation cross sections for energetically close groups of states. The joint experimental and theoretical studies of microscopic vibration–rotation inelastic cross sections are also well suited for the understanding and quantitative prediction of macroscopic phenomena such as gas-phase transport properties and internal-state relaxation processes of non-spherical molecules onto firmer microscopic grounds.

Formaldehyde: Abinitio MCSCF+CI transition state for H2CO → CO+H2 on the S0 surface

Abstract: Ab initio multiconfiguration self‐consistent field (MCSCF) and configuration interaction (CI) calculations have yielded an activation energy of 80.9±3.0 kcal/mol for the dissociation of formaldehyde to H2 and CO on the ground state potential energy surface. The error limits are estimates based on an analysis of the effects of one‐particle basis set, electron correlation, and transition state structure on the activation energy. Accurate structures and harmonic frequencies are presented for H2CO (X 1A1) and the transition state.

Dynamical study of nonadiabatic unimolecular reactions: The conical intersection between the B̃ 2B2 and à 2A1 states of H2O+

Abstract: The conical intersection connecting the B 2A′ and A 2A′ states of the H2O+ ion is studied. The two potential energy surfaces are calculated ab initio by the SCF/CI method within the CS point group. The nonadiabatic coupling matrix elements 〈A‖∂/∂q‖B〉 are computed for several cross sections throughout the potential energy surfaces. A transformation to the diabatic representation is performed. The linear model is found to be a good approximation in the region close to the apex of the cone. The global functions t(s) and T(S) governing the nonadiabatic transition probability are calculated; their shapes are those predicted by the Landau–Zener model (in the Nikitin bidimensional version). A dynamical study is undertaken by means of classical trajectory calculations on the upper adiabatic potential energy surface. An averaged transition probability Ptr is derived. Excitation of rotation or of the bending mode of H2O before photon impact has no influence on Ptr. Excitation of the symmetrical or antisymmetr...

Spectroscopic properties of the methyl radical calculated from UHF SCEP wavefunctions

Abstract: The potential energy surface of symmetric stretching and out-of-plane bending motions for the methyl radical has been calculated from UHF SCEP wavefunctions. Anharmonic vibrational frequencies are computed by a variational method and transition dipole moments and Einstein coefficients of spontaneous emission are reported. Isotropic hyperfine coupling constants are obtained in agreement with experiment to within 4% when calculated by differentiation of the perturbed CEPA-1 energy and taking vibrational averaging into account. Also, the temperature dependence of the proton hyperfine coupling constant compares well with experimental results. The vibrational fine structure of the first band of the photoelectron spectra of CH 3 and CD 3 is calculated in good agreement with experiment.

Semiclassical determination of adiabatic barriers on a three‐dimensional potential energy surface

Abstract: A recently proposed method, based on periodic orbits, for finding vibrationally adiabatic barriers and wells in collinear collisions is generalized to the full three‐dimensional case. The main idea is a consistent use of the adiabatic approximation—one first solves for the fast vibrational motion to obtain an effective Hamiltonian for the slower bend motion which in turn is solved to obtain an effective Hamiltonian for the overall rotation. The method is applied to the hydrogen exchange reaction. We find the bend‐vibration adiabatic barrier levels for the H2(v=1) state. The zero point motion in the bend degree of freedom is found to be substantial (0.1 eV) and is a source for nonnegligible discrepancies between approximate theories such as the infinite order sudden and quasiclassical trajectory approach and exact quantal scattering computations. Having found the barrier levels we are able to evaluate the collision cross section. Our analysis points out that differences between experimental cross sections and theoretical predictions may be due to inaccuracy in the potential energy surfaces. The available surfaces probably overestimate the adiabatic barrier height.

Three‐dimensional vibrational predissociation of the van der Waals complex He⋅⋅⋅I2(B). A quasiclassical study

Abstract: We apply a quasiclassical trajectory method to treat vibrational predissociation of the van der Waals molecule He⋅⋅⋅I2(B 3Π). In order to compare with quantum mechanical calculations and the experimental data, we have introduced the rotational degree of freedom by using an approximate treatment. The potential energy surface used was a sum of pairwise atom–atom potentials. The initial conditions were selected at random taking into account previous quantal results. The final rotational distribution for the I2 fragment and the total rate for vibrational predissociation, as functions of vibrational excitation, are in good agreement with the quantum mechanical values and with the experimental measurements.

Theoretical three-dimensional potential-energy surface for the reaction of Be with HF

Abstract: The three-dimensional potential-energy surface for reaction of Be and HF has been computed and fit with an analytic form. Several hundred points on the surface were obtained from a two-configuration MC SCF function using a DZ GTO basis set. Comparisons with much larger calculations at a smalle rnumber of points suggest that this level of approximation gives a good qualitative and probably a reasonable quantitative description. The present surface is in good accord with a previous collinear surface (although the barrier is significantly higher in the present work) and also with a recently published valence-bond calculation. The surface is found to be quite insensitive to orientation for angles of approach between collinear and perpendicular: the minimum-energy path is not collinear. An analytic fit to the surface has been obtained. The general features are reproduced by a three-structure effective hamiltonian which is motivated by valence-bond-like ideas and which accurately reproduces the asymptotic diatomic limits. In the region of strong interaction this model is augmented by a damped fourth-order polynomial in the internuclear separations. Despite the complexity of this fitting function, it provides only a fair quantitative representation.

Vibrational frequencies of the cyanocarbene (HCCN) molecule. A near degeneracy between bent cyanocarbene and linear allene-related geometries

Abstract: The geometrical structure and vibrational frequencies of the ground triplet electronic state of HCCN have been examined at a wide range of levels of ab initio electronic structure theory. The potential energy surface of HCC bending is very flat for HCCN owing to a competition between linear allene OHC=C=N and bent carbene HCC=N valence structures. Evidence is presented that both the restricted Hartree-Fock (RHF) and unrestricted Hartree-Fock (UHF) methods treat this potential surface in a somewhat uneven manner. When the effects of electron correlation are included, however, RHF- and UHF-based methods converge to a similar set of structural and energetic predictions. The most reliable levels of theory suggest the HCCN is a quasi-linear molecule, with THETA/sub e/(HCC) approx. = 138/sup 0/ and a barrier to linearity of only about 2 kcal/mol.

Rotational rainbow scattering in collisions of Ar with Cl2

Abstract: The pulsed molecular beam technique has been used to measure speed and angle‐resolved differential cross sections for scattering of Ar by Cl2, over the range of initial relative kinetic energies from 0.09 to 0.16 eV. Angular rainbows are observed at small scattering angles. At large scattering angles, the product speed distributions at constant center‐of‐mass scattering angles display rotational rainbow structure which corresponds to a large fraction of the initial relative kinetic energy appearing as rotational energy in the Cl2 product. The large‐angle data may be interpreted in terms of the classical rigid‐ellipsoid model, which expresses the anisotropy of the potential energy surface with a single parameter.

Reaction-path interpolation models for variational transition state theory

Abstract: We present interpolation formulas for estimating parameters in the reaction‐path Hamiltonian from known data in three vicinities—reactants, saddle point, and products. Whereas conventional transition state theory calculations are usually based on a quadratic expansion of the potential energy surface at the saddle point, the present approach attempts to estimate the variational transition state theory rate constant by also using selected cubic and quartic force constants of the saddle point or by using quadratic force constants determined over a small range of the reaction path, not necessarily including the variational transition state. The method is illustrated and the formulas are tested for four collinear classical reactions.

Vibrational predissociation of hydrogen, deuterium, and hydrogen deuteride-argon van der Waals molecules

Abstract: Accurate close-coupling calculations are performed for vibrationally predissociating states of H/sub 2/-Ar, D/sub 2/-Ar, and HD-Ar, using the best potential energy surface available. All the states examined have very small widths (GAMMA 20 ..mu..s). There is a pronounced tendency for predissociation to yield rotationally hot diatomic molecules, even for the H/sub 2/-Ar and D/sub 2/-Ar complexes where the present potential has no anisotropic terms of higher order than P/sub 2/(cos theta). This near-resonant effect is particularly strong for HD-Ar, where all Legendre terms are present in the potential; in this case, about 50% of the HD products are formed in the highest two accessible rotational levels. There is some evidence for a rotational rainbow effect in the product rotational state distributions. Perturbation theory calculations which attempt to reproduce the accurate calculations are also reported. They successfully model the qualitative features of the close-coupling results, but are not quantitatively accurate even for these weakly coupled systems. It appears that this inadequacy is due to the need for a very accurate representation of the bound state wave function and to the neglect of important couplings between the different open channels. This conclusion ismore » supported by the observation that very large basis sets are required to obtain convergence of the close-coupling calculations. 4 figures, 7 tables.« less

Comparison of variational transition state theory and quantum sudden calculations of three‐dimensional rate coefficients for the reactions D(H)+BrH → DBr(HBr)+H

Abstract: We calculate rate coefficients for the three‐dimensional reactions H+BrH → HBr+H and D+BrH → DBr+H using two different dynamical methods but with the same potential energy surface. One method is a three‐dimensional quantum mechanical technique in which the energy sudden approximation is used for the entrance reaction channel and the centrifugal sudden approximation is applied to the exit reaction channel. The second method is improved canonical variational transition state theory with small‐curvature‐tunneling semiclassical adiabatic ground‐state transmission coefficients. The potential energy surface is an empirically adjusted diatomics‐in‐molecules surface which has a very narrow barrier to reaction. The rate coefficients predicted by the two very different dynamical theories are in excellent agreement—they differ by less than 20% over the temperature range from 150 to 500 K.

Improved parametrization of diatomics‐in‐molecules potential energy surface for Na(3p 2P)+H2 → Na(3s 2S)+H2

Abstract: We report a new set of diatomics‐in‐molecules potential energy surfaces and electronically adiabatic couplings for the process Na(3p 2P) +H2 → Na(3s 2S)+H2. The surfaces of our previous paper [D. G. Truhlar, J. W. Duff, N. C. Blais, J. C. Tully, and B. C. Garrett, J. Chem. Phys. 77, 764 (1982)] are improved by employing a new parametrization for the 3Σ+ diabatic potential energy curves of NaH. The 3Σ+ diabatic Hamiltonian matrix Hn is based on small‐basis‐set valence‐bond calculations for Hn12, and the diagonal elements are adjusted to yield accurate 3Σ+ adiabatic potential curves. The new surfaces are compared to the recent ab initio results obtained by the coupled‐electron‐pairs approximation [P. Botschwina, W. Meyer, I. V. Hertel, and W. Reiland, J. Chem. Phys. 75, 5438 (1981)], and the comparison indicates good agreement between the semiempirical and ab initio surfaces.

Dynamics of a prototype alkali-hydrogen-halide exchange reaction on an ab initio potential-energy surface

Abstract: We report the results of a quasiclassical trajectory (QCT) study of a prototype alkali-hydrogen-halide exchange reaction Li + FH → LiF + H on an ab initio potential-energy surface for collinear as well as non-collinear geometries. A vibrational threshold equal to that of the barrier (21 kcal mol −1 ) noted for the collinear collisions is not found for the 3D collisions. Nevertheless, we do find that vibrational energy ( V ) is much more efficient than translational energy ( T ) in causing this reaction. There is a unique effect of reagent rotation on the reaction cross section ( S r ) in that with increase in the rotational quantum number ( J ) from 0 through 15 for the vibrational state ν = 2 at T = 8.7 kcal mol −l , S r decreases initially and then increases steeply . This is followed by a decline and a possible levelling off in S t . We attribute the initial decline in S r ( J ) to the disruption of the preferred alignment due to rotation. Further increase in rotation brings the molecule back into alignment and with much more rotational velocity, the molecule appears as a blur explaining the levelling off of S r . Interestingly, for ν = 0, there is a moderate rotational enhancement partly due to the increase in the number of product states becoming available with increase in the total energy. The effect of various forms of energy on other reaction attributes like product vibrational- and rotational-energy distribution and angular distribution has also been studied. Our calculated value of S r as well as the product angular distribution and the coplanarity of the reaction are in good agreement with the exerimental results for ν = 0, but they differ significantly from the QCT results of Shapiro and co-workers on their semi-empirical PES.

Rotational and vibrational‐rotational relaxation in collisions of CO2(0110) with He atoms

Abstract: Rotational and vibrational‐rotational relaxation of CO2(0110) in collisions with He atoms is studied theoretically. Cross sections and rate coefficients have been calculated using a vibrational close‐coupling, rotational infinite‐order sudden method, together with an ab initio potential energy surface. Comparisons with previous calculations and experiments on rotational relaxation in He+CO2(0001) are made. The rotational relaxation cross sections are found to be insensitive to the vibrational dependence of the He–CO2 potential. Transitions between even and odd rotational states of the (0110) level have relatively small cross sections. Interesting oscillating structures are predicted for the rotational dependence of the cross section distributions for transitions involving the (0110) level.

Degenerate Carbocation Rearrangements

Abstract: Publisher Summary This chapter discusses the structures, reactions, and mechanisms of carbocations undergoing degenerate rearrangements. The study of such reactions is of fundamental importance in carbocation chemistry because the symmetry of their potential energy surfaces allows a special insight into their structures as well as their reactions and mechanisms. The class of rearrangements in which the products are chemically identical with the reactants is known as degenerate rearrangements. Molecules show varying degrees of degeneracy. In a totally degenerate rearrangement, all atoms of the same kind exchange with each other. If the exchange of atoms in the molecule is less extensive, then the rearrangement is considered partially degenerate. For a degenerate reaction, the potential energy of the reactant equals that of the product, that is, the potential energy surface shows symmetry. There are three types of degeneracy of carbocations observed: carbon atom degeneracy, hydrogen atom degeneracy, and combined carbon and hydrogen atom degeneracy. The method that has been dominating the study of degenerate carbocations in solution for more than a decade is nuclear magnetic resonance (NMR) spectroscopy. This method yields direct information, through chemical shifts, coupling constants and the temperature dependence of band shapes, about the structure and dynamics of the cations. Degenerate rearrangements, if fast enough, result in temperature dependent NMR spectra. At slow exchange, the signals of the exchanging nuclei show up as separate absorptions.

Theoretical studies of van der Waals molecules: the H2-CO dimer

Abstract: The M80 potential energy surface of Meyer, Schaefer and Liu (1983) is used to obtain the bound-state energies of dimers of deuterium in both its ortho and para modifications. The quantum mechanical close-coupling equations have been solved by direct numerical integration. Scattering calculations have yielded the energies and widths of rotationally predissociating states of ortho-D2-ortho-D2. That some of these resonances have dual Feshbach/shape character is noted. The dimer structure accompanying the observed near-infrared S1(0) and Q1(0)+S0(0) spectra in ortho-deuterium, is modelled by treating the two D2 molecules as distinguishable rigid rotors. The conclusions, that the 1974 measurements of McKellar and Welsh provide evidence both for rotational splitting and internal rotational predissociation, are examined in the light of new spectroscopic results.