Showing papers on "Potential energy surface published in 1981"

On finding transition states

Abstract: An algorithm for locating transition states on a potential energy surface is described. The most important feature of the algorithm, which makes explicit use of the second derivative matrix of the potential surface, is that it is able to ’’walk uphill’’ from the minimum on a potential surface to the transition state essentially automatically. The method is illustrated by application to a two dimensional model problem, to the vinylidene–acetylene rearrangement (H2C = C:↔HC≡CH), and to the dissociation and rearrangement of formaldehyde (H2CO↔H2+CO, HCOH). The algorithm is also seen to provide an improved way of following a reaction path from a transition state down to reactants or products.

Collisions of excited Na atoms with H2 molecules. I. Ab initio potential energy surfaces and qualitative discussion of the quenching process

Abstract: Potential energy surfaces have been calculated for the four lowest electronic states of Na (3 2S, 3 2P)+H2(1Σ+g) by means of the RHF–SCF and PNO–CEPA methods. For the so‐called quenching process of Na (3 2P) by H2 at low initial translational energies (E–VRT energy transfer) the energetically most favorable path occurs in C2v symmetry, since—at intermediate Na–H2 separation—the ? 2B2 potential energy surface is attractive. From the CEPA calculations, the crossing point of minimal energy between the ? 2A1 and ? 2B2 surfaces is obtained at Rc = 3.57 a.u. and rc = 2.17 a.u. with an energy difference to the asymptotic limit (R = ∞, r = re) of −0.06 eV. It is thus classically accessible without any initial translational energy, but at low initial translational energies (∼0.1 eV) quenching will be efficient only for arrangements of collision partners close to C2v symmetry. There is little indication of an avoiding crossing with an ionic intermediate correlating asymptotically with Na+ and H2− as was assumed in ...

Vinylidene: a very shallow minimum on the C2H2 potential energy surface

Abstract: The potential energy surface for the singlet vinylidene → acetylene rearrangement has been investigated in this study by using nonempirical molecular electronic structure theory. A double-ζ plus polarization basis set was used in conjunction with configuration interaction (CI) including single and double excitations, a total of 13,861 configurations. Newly developed analytic CI gradient techniques were used to locate precisely the vinylidene and acetylene minima and the transition state connecting them. Single point calculations were carried out with a larger triple-ζ plus polarization basis. The classical barrier height is calculated to be 6.4 kcal, or 5.4 kcal after correction for the effects of higher excitations, and our best estimate of the true classical barrier is 4 kcal. Harmonic vibrational analyses were carried out about each of the three stationary points, and zero-point energy effects lower the effective barrier by 1.8 kcal. Even for energies below this, however, tunneling through the barrier is found to be extremely rapid; for instance, with no vibrational excitation energy (above its zero point energy) the lifetime of vinylidene with respect to rearrangement to acetylene is calculated to be only ~ 10-9 s, and with 2 kcal of excitation energy this decreases to ~ 10-12 s. Inmore » addition, these predictions appear to be consistent with the experimental findings of Skell (1972) and Steinfeld (1980).« less

Quasiclassical trajectory studies of the H+H2 reaction on an accurate potential‐energy surface. III. Comparison of rate constants and cross sections with experiment

Abstract: Quasiclassical trajectories computed for the H+H2 reaction on the accurate Siegbahn–Liu–Truhlar–Horowitz potential‐energy surface are presented. Reaction rate constants as a function of temperature for H2 in the ground and first excited vibrational state are compared with experimental rate data. For v = 0, agreement is found to be excellent for all isotopic combinations. For v = 1, however, all theoretical results predict much smaller rate constants than are observed experimentally. This discrepancy cannot be ascribed to the absence of tunneling inherent in classical mechanics and is unlikely to be due to errors in the surface. Angular distributions in the laboratory frame have been computed from theoretical results for D+H2 and H+T2 and compared with recent experiments. Agreement is fairly good.

Quantum study of vibrational excitation in the three‐dimensional collisions of CO2 with rare gas atoms

Abstract: A combined vibrational close‐coupling and rotational infinite order sudden technique is described for calculating vibrational excitation cross sections σvv′ for the three‐dimensional collisions of atoms with linear triatomic molecules. The method treats anharmonic, Coriolis, and vibrational angular momentum terms in the molecular Hamiltonian accurately, and is applicable to any realistic potential energy surface expressed in numerical or functional form. Application of the method to X–CO2(v1v2λv3) collisions, where X = He, Ne, or Ar, is described. An accurate anharmonic CO2 potential, expressed in terms of bond and angle displacements, is employed. The X–CO2 interaction potentials are more approximate and are expanded in terms of atom–atom pair potentials. Calculations of σvv′, over a grid of energies sufficient to give rate coefficients kvv′ for transitions between the low‐lying states of CO2 for temperatures up to 300 K, have been performed. Propensities for particular collisional excitations involving ...

Mode specificity in unimolecular reaction dynamics: The Henon-Heiles potential energy surface

Abstract: Energies and lifetimes (with respect to tunneling) for metastable states of the Henon–Heiles potential energy surface [V(x,y) = 1/2x2−1/3x3+1/2y2+xy2] have been computed quantum mechanically (via the method of complex scaling). This is a potential surface for which the classical dynamics is known to change from quasiperiodic at low energies to ergodic‐like at higher energies. The rate constants (i.e., inverse lifetimes) for unimolecular decay as a function of energy, however, are seen to be well described by standard statistical theory (microcanonical transition state theory, RRKM plus tunneling) over the entire energy region. This is thus another example indicating that mode specificity in unimolecular reaction dynamics is not determined solely by the quasiperiodic/ergodic character of the intramolecular mechanics.

The effect of vibration and translational energy on the reaction dynamics of the H+2 +H2 system

Abstract: A new experimental technique combining molecular beams, photoionization, and guided beam ion optics has been used to study several isotopic H2+ +H2 reactions. The technique is described. By using this method we are able to observe the effects of both reagent translational and vibrational energy. Cross sections are reported for charge transfer, H3+ formation, and collision induced dissociation. Evidence is seen for competition betwen the channels, charge hopping in the reaction entrance channel, potential energy surface hopping, reaction on excited potential surfaces, and isotopic scrambling. A model for the reaction which takes into account the multisurface nature of the systems seems to explain the results satisfactorily.

Ab initio SCF calculations on the potential energy surface of potassium cyanide (KCN)

Abstract: The potential energy surface of KCN has been generated by ab initio SCF calculations in the region of equilibrium bond distances. An analytic representation of the surface is presented. The calculations show that the bonding between K and CN is ionic, and that the structure of KCN is triangular, which confirms recent experimental findings. The computed geometry is &KCN = 62.4°, rCK = 5.492a0, and rCN = 2.186a0.

Quasiclassical trajectory studies of the H+H2 reaction on an accurate potential energy surface. II. Effect of initial vibration and rotation on reactivity

Abstract: Classical trajectory calculations have been carried out on the semiempirical Porter–Karplus and the accurate Siegbahn–Liu–Truhlar–Horowitz potential energy surfaces for the H+H2 (v, j) reaction. The results reveal that initial vibration in the diatom increases reactivity at a given translational energy, and broadens the final rotational and angular distributions. Initial rotation reduces reactivity near threshold, but the effect decreases far from theshold. Initial rotation broadens the final rotational but not the angular distribution. The results on both surfaces are similar, with total cross sections larger for the Porter–Karplus surface. The trends are in qualitative agreement with most available quantum mechanical calculations.

A classical determination of vibrationally adiabatic barriers and wells of a collinear potential energy surface

Abstract: A necessary and sufficient condition for the existence of a classical vibrationally adiabatic barrier or well in collinear systems is the existence of periodic orbit dividing surfaces. Knowledge of all pods immediately provides all adiabatic barriers and wells. Furthermore, the classical equation connecting the barriers and wells to the masses and potential energy surface of the system is shown, under mild conditions, to be identical in form to the corresponding quantal equation. The only difference is in the determination of the vibrational state which is obtained by WKB quantization classically. The classical barriers and wells can therefore be used to analyze quantal computations. Such analysis is provided for the hydrogen exchange reaction and the F+HH system. A novel result is the existence of vibrationally adiabatic barriers even where no saddle point exists on the static potential energy surface. These barriers are an outcome of competition between the increase of potential energy and decrease of vibrational force constant along the reaction coordinate. Their existence is therefore of general nature — not limited to the specific structure of a given potential energy surface. The experimental significance of these barriers is discussed. The implications on the use of forward or reverse quasiclassical computations is analyzed. A definite conclusion is that one should not average over initial vibrational action in such calculations.

The helium-hydrogen fluoride potential surface

Abstract: Hartree-Fock calculations have been used to determine the He-HF interaction potential for the HF molecule in its equilibrium separation. The data has been fitted to a series of Legendre polynomials at twelve separations in the range 3 a 0-10 a 0. Rayleigh-Schrodinger perturbation theory is used to determine long range electron correlation terms, expressed as Legendre coefficients of inverse powers of the He-HF separations. An empirical damping function is used to combine the Hartree-Fock and dispersion terms. The resulting potential energy surface is compared with previous results. Further calculations have been used to determine the potential energy surface for H-F bond lengths as large as those found in the first excited vibrational state.

Trajectory studies of model H–C–C→H+C = C dissociation. II. Angular momenta and energy partitioning and their relation to non‐RRKM dynamics

Abstract: The model alkyl dissociation reaction H–C–C→H+C = C has been studied on a potential energy surface derived from an analytic potential energy function for ethyl radical dissociation. Nonrandom excitation of H–C–C is simulated by the chemical activation reaction H+C = C→H–C–C, and different initial relative translational, rotational, and vibrational energies are investigated. Comparisons are made between the unimolecular dynamics of nonrandomly excited H–C–C radicals and those excited randomly. These two types of excitation yield strikingly different unimolecular lifetime distributions, each non‐RRKM. However, if angular momentum constraints are propertly included, the partitioning of product energies is independent of the excitation process. For total energies slightly in excess of the dissociation energy the energy distributions at the dissociation barrier are in excellent agreement with the RRKM predictions, and the nonstatistical product energies arise from the preferential release of potential energy i...

A diatomics‐in‐molecules case study on the system Be+HF→BeF+H. I. Bonding models and the use of valence bond information

Abstract: DIM calculations on the ground state potential energy surface for Be+HF→BeF+H are approached on the basis of a variety of bonding models, involving from three up to 18 structures. A considerable input of diatomic fragment information is required. To this end two sets of ab initio valence bond calculations have been carried out on the fragments, the first restricted to just those structures contributing to the largest DIM model and the second containing many additional fragment structures. VB calculations at the first level were extended to compute the full triatomic potential surface and this is found to agree qualitatively fairly closely with that from a DIM model based on the same structures and fragment curves. A preliminary survey highlights two practical difficulties in using data from large VB calculations to support smaller DIM models (a) in numerical interpolation of coupling constants and (b) in identification of the appropriate fragment curves to use. It is also shown that inclusion of additiona...

Theoretical investigation of rotational rainbow structures in X–Na2 collisions using CI potential surfaces. I. Rigid‐rotor X = He scattering and comparison with state‐to‐state experiments

Abstract: An accurate CI potential energy surface for He–Na2 is determined, which is suitable for rigid‐rotor scattering calculations for collision energies below 1 eV. In the calculation of the interaction potential electron correlation effects have been considered for the bond orbital of Na2 and the 1s orbital of He together with the dispersion attraction between these orbitals using the method of self‐consistent electron pairs (SCEP). A very shallow van der Waals minimum of about 0.1 meV is obtained at large internuclear distances. Rigid‐rotor infinite‐order‐sudden (IOS) calculations have been performed for collision energies of 0.05⩽E⩽0.15 eV using an analytical representation for the potential surface constructed with the 52 original ab initio points. The differential cross sections for rotationally elastic and inelastic transitions exhibit the recently predicted rotational rainbow structures. The comparison with the state‐to‐state experimental data of Bergmann et al. [J. Chem. Phys. 72, 4777 (1980)] is perfor...

The evaluation of fitting functions for the representation of an O( 3P)+H2 potential energy surface. I

Abstract: The DIM surface of Whitlock, Muckerman, and Fisher for the O(3P)+H2 system is used as a test case to evaluate the usefulness of a variety of fitting functions for the representation of potential energy surfaces. Fitting functions based on LEPS, BEBO, and rotated Morse oscillator (RMO) forms are examined. Fitting procedures are developed for combining information about a small portion of the surface and the fitting function to predict where on the surface more information must be obtained to improve the accuracy of the fit. Both unbiased procedures and procedures heavily biased toward the saddle point region of the surface are investigated. Collinear quasiclassical trajectory calculations of the reaction rate constant and one and three dimensional transition state theory rate constant calculations are performed and compared for selected fits and the exact DIM test surface. Fitting functions based on BEBO and RMO forms are found to give quite accurate results.

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

Abstract: 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 49 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)

Potential Energy Characteristics for Chemical Reactions

Abstract: Ab initio molecular orbital (MO) methods can provide accurate descriptions of potential energy surfaces for chemical reactions For triatomic systems such as H3 and H2F extensive calculations of very accurate potential surfaces have been carried out For systems having four atoms or more, however, the accomplishment so far has been rather limited One of the reasons for this is that the full potential energy surface is a function of 3N-6 coordinates where N is the number of atoms, and this is too many degrees of freedom for the full surface to be mapped Even to optimize the geometrical parameters for all the degrees of freedom to determine the reactant and saddle point geometries is very difficult However, a revolution is taking place in the way quantum chemists probe a potential surface It is based on the development of new theoretical methods and computer programs for analytically calculating the gradient of the energy with respect to the nuclear coordinates1 Quantum chemists are now learning how to use this energy gradient, a concept more familiar in the context of collision theory, to study the characteristics of potential energy surfaces In this review we will first summarize briefly how to calculate the energy gradient analytically Then we will discuss methods of determining geometries, force constants, and normal vibrations for both equilibrium configurations and saddle points, and we will show several examples of such calculations we have recently carried out

Rotational excitation of OH by H2 at thermal energies

Abstract: Using a recently computed potential energy surface, the authors calculate cross sections for the rotational excitation of OH by para-H2 (in its rotational ground state) over the range of energies believed to be relevant to the interstellar OH emission. Results are obtained in Hund's case b coupling scheme (neglecting the spin-orbit interaction) and the significance of departures from case b coupling are considered. The authors results indicate that collisions with H2 molecules may be expected to invert the populations of the ground rotational state and of certain excited-state Lambda doublets. At low temperatures (T

A model study of the intermolecular interactions of amino acids in aqueous solution: The glycine-water system

Abstract: We have performed calculations of the glycine zwitterion surrounded by water molecules with the help of the mutually consistent field (MCF) method and perturbation theoretical expressions. Two different models for the hydration shell have been chosen, the glycine·6H2O and glycine·12H2O complexes, representing the most probable first and second solvation shell, respectively. To calculate the exchange and charge transfer energy contributions we have applied approximative expressions derived from perturbation theory for weakly overlapping subunits. For the sake of comparison we also calculated the interaction energy in the supermolecule approach for the smaller of the two solvation complexes. Furthermore, we have investigated the part of the potential energy surface which is determined by varying the lengths of the hydrogen bonds between glycine and water in the complex glycine·12H2O using the electrostatic approach. The exchange energy contribution to the interaction energy for different points on the surface was approximated with the help of an analytical expression fitted to three directly calculated points. For the charge transfer energy a polynomial expansion of second order was established on the basis of five values, computed with the aid of the perturbation theoretical expression. To get a more detailed insight in the relatively strong hydrogen bonds between the water molecules and the ionic hydrophilic parts of glycineab initio model studies on NH 4 + ·3H2O and HCOO−·3H2O systems are reported.

Reactive Scattering Resonances and their Physical Interpretation: The Vibrational Structure of the Transition State

Abstract: Quantum mechanical structure in reaction-probability-versus-energy curves for a realistic potential energy surface was first observed about a decade ago,1,2 for the collinear H + H2 system. Such structure had been previously found for a potential energy surface having sharp edges,3 made of piecewise-constant potentials, but in one-mathematical-dimensional (1MD) barrier problems, structure in transmission-probability-versus-energy curves4 is known to disappear when a rectangular barrier is replaced by one which is sufficiently “rounded”, such as parabolic5,6 or Eckart6,7 barriers, and is attributed to edge diffraction effects. The structure in the collinear H + H2 results on a smoothly varying surface, at energies above the vibrational excitation threshold of reaction products, was guessed1b as being due to interference effects between different reaction paths, a guess subsequently confirmed by a quantum mechanical lifetime analysis8 and a semiclassical calculation.9 The former indicated the concomitant presence of and interference between direct and dynamic resonance (Feshbach10) processes. The mechanism of such resonances was attributed to the existence of wells in the vibrationally adiabatic potentials along the minimum energy path.2b

A quantum mechanical study of the collinear Li+FH reaction

Abstract: 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.