Effective Potential Energy Surface Research Articles

A K-dependent adiabatic approximation to the Renner–Teller effect for triatomic molecules

A K-dependent adiabatic approach is suggested to study the Renner–Teller effect in triatomic molecules using a two-dimensional Hilbert space approximation in the electronic degree of freedom. The theory is developed in hyperspherical coordinates, and approximately includes the electronic spin–orbit interaction. The adiabatic Hamiltonians are expressed in terms of a K-dependent effective potential energy surface. Eigenpairs are calculated by solving the time-independent Schrödinger equation, which is represented in a mixed grid/basis set. The method is applied to the Ã←X̃ band system of bromomethylene (H/DCBr). The results obtained show that the Renner–Teller effect in this molecule is pronounced, particularly in the excited à 1A″ state. The results are compared to recent experimental measurements and good agreement is found.

Rotationally induced transitions in small clusters

The dynamics of an Ar6 cluster held together by Lennard-Jones forces is studied classically. The development of chaotic dynamics is mainly followed by a calculation of the maximum Lyapunov exponent (MLE). Initial momentum vectors are chosen from the eigenvectors of the Hessian of the potential energy so that rotating and nonrotating clusters can be studied systematically. It is found that the dependence of MLE on the total energy is considerably different for rotational and vibrational excitations. As the magnitude of the angular momentum increases, sharp transitions in MLE are observed. These transitions are explained in terms of the changes of the topology of the effective rovibrational potential energy surface and the dynamic equilibration between the global and local minima.

Translation-to-rotational energy transfer in scattering of H 2 molecules from Cu(111) surfaces

This work investigates rotational transitions of H 2 scattering from Cu(111). A notable feature of this study is the application of simple classical dynamics to reveal mechanisms of rotational transitions. This methodology is justified for the H 2/Cu system by remarkable agreement between quantum wavepacket calculations and classical trajectory simulations for both dissociation and ro-vibrational transitions. A vibrational sudden approximation is proposed which interprets rotational transitions in terms of an effective gas-surface potential energy surface for a molecule having a distended bond. The validity of the approximation is verified by the close correlation between molecular trajectories and this effective potential. The vibrational sudden analysis comprehensively explains the mechanism of strong translation-to-rotational energy transfer for H 2 scattering from Cu(111), observed experimentally.

Large Thermal Expansivity of Clathrate Hydrates

The free energies of clathrates are calculated over a wide range of temperatures in order to explain a large thermal expansivity of clathrate hydrates compared with that of ice. Several proton-disordered configurations for hexagonal ice and type I chathrate hydrates are generated. The free energy is approximated to the sum of the minimum potential energy, the harmonic free energy, and the configurational entropy arising from the disordered nature of protons. The free energy at a given temperature is minimized with respect to the volume of the system. This enables us to evaluate the thermal expansivity from only intermolecular interaction potentials. The larger thermal expansivity of clathrate hydrates than ice is successfully reproduced. It is found that the large expansivity of clathrate hydrate structure I stems from the existence of guest molecules and that a difference in oxygen atom arrangement between clathrate hydrates and ice plays a minor role. The effective potential energy surface of a guest molecule becomes harmonic with an increase in temperature. This seems to undermine the large difference in the thermal expansivity between clathrate hydrates and ice.

Calculations on ground and excited state potential energy surfaces of floppy free radicals: HC 4H 2, HC 3NH, and HC 3O

Ab initio calculations using the 6-311G(d, p) basis set at the QCISD and CCSD(T) levels were undertaken on the ground and lowest excited electronic states of the isoelectronic carbon-chain free radicals, HC 4H 2, HC 3NH and HC 3O. The equilibrium geometry for each molecule is a C s structure with four electrons in a″ orbitals, and the lowest excited states are characterized by configurations with three, five, and six a″ electrons. The effective vibrational potential energy surfaces of these states along the two lowest frequency in-plane bending coordinates were investigated in order to assess the trend in large-amplitude motions and isomerization across different electronic configurations in a series of isoelectronic molecules. The (4- a″) ground state potential surfaces of HC 3NH and HC 3O are subject to the Renner-Teller effect, and intersect the (5- a″) excited state surfaces at linear 2π states of at 2300 cm −1 and 8400 cm −1, respectively, above the energy of the equilibrium geometries. The (3- a″) states of HC 3O and HC 3NH lie 27 000 cm −1 and 24 000 cm −1 above the (4- a″) equilibrium states, respectively, and form Renner-Teller pairs with the (6- a″) tates. Although two minima are found for HC 3O and HC 3NH on the (3- a″) surface, none of these minima is stable with respect to planarity. The (5- a″) surface of HC 4H 2 has a single minimum at a C 2v structure, which is unstable with respect to the ground state. The (3- a″) surface has two minima, both of which are stable. Equilibrium structures, excitation energies, and potential surface properties for these structures are reported.

The role of solute - solvent interactions in the dynamics of unimolecular reactions in compressed solvents

The role of the solvent in the liquid phase dynamics of unimolecular processes involving small energy barriers is studied by ultrafast laser spectroscopy. Different regions of the interaction potential between the solvent environment and the reactant are characterized by investigating photoisomerization reactions of trans-stilbene and related compounds in liquid n-alkanes and n-alkanols over a wide pressure range. By varying the physical properties of the solvent environment in such a controlled way, aspects of the reactant - solvent interaction which dominate the different density regimes are identified. In particular, the kind of friction acting along the reaction path, the role of solvent-induced changes of the effective potential energy surface for reaction, and the coupling of dielectric solvent shell relaxation and motion along the reaction coordinate are addressed.

Structure, rearrangements and evaporation of rotating atomic clusters

Eigenvector-following techniques are used to explore the classical effective potential energy surface of rotating clusters composed of identical rare gas atoms. Precise determination of transition states reveals the mechanisms for atomic rearrangements and allows us to calculate rate constants for the evaporation of an atom from the cluster surface using RRK theory. We examine the variation in the effective potential energy surface with the magnitude of the angular momentum, with particular reference to centrifugal distortion and the resulting spectroscopic constants, the Hessian index of the stationary points, and the centrifugal barriers to evaporation. Most of the calculations are performed using a pairwise additive Lennard-Jones potential, but comparisons are made with the accurate Aziz potential augmented by a three-body Axilrod-Teller term.

Electron and ion transfer reactions on metal electrodes

An extended Anderson model is used as a unifying framework for both ion and electron transfer reactions. The model allows the construction of effective potential energy surfaces as functions of the solvent coordinates and the separation of the reactant from the electrode surface. For electron transfer the reaction coordinate is mainly in the direction of the solvent coordinates; for ion transfer the partial loss of the solvation sheath and the encompanying solvent displacement is the rate determining step, and the reaction coordinate is mainly determined by the separation from the metal surface. Further differences and similarities between the two types of reactions are discussed.

Simulated annealing using coarse grained classical dynamics: Smoluchowski dynamics in the Gaussian density approximation

A dynamical annealing algorithm for global optimization based on approximate solution of the Smoluchowski equation is presented. The equations of motion in the Gaussian density approximation are interpreted as a steepest descent quench on a time dependent effective potential energy surface. A relation between the convexity condition for the effective potential surface and the size of thermal fluctuations provides a definition of the critical temperature above which the distribution is delocalized and the effective potential is smooth and convex during an annealing run. This critical temperature may be significantly less than the temperature characteristic of escape from a local energy minimum.

Asymmetric adiabatic correction to the rotation–vibration levels of H2D+ and D2H+

Calculations on H2D+ and D2H+ have shown that the energy levels of these asymmetric isotopomers of H3+ cannot be reproduced using effective potential energy surfaces with D3h symmetry. It is shown that for these ions the adiabatic correction to the Born–Oppenheimer approximation has an asymmetric component which can be expressed as a mass-independent surface multiplied by a mass factor. An expression for this function is obtained from ab initio calculations. Use of this adiabatic correction is found to resolve the discrepancy with the levels of H2D+ and D2H+. The ab initio calculations reported reproduce the observed H2D+ transitions with an average error (obs−calc) of −8 MHz for the rotational transitions, −0.06 cm−1 for the ν1 band, −0.13 cm−1 for ν2, and −0.19 cm−1 for ν3. These errors are nearly constant for all transitions within a vibrational band. This gives a very accurate ab initio framework for predicting unobserved transition frequencies.

A unified model for electrochemical electron and ion transfer reactions

Electron and ion transfer reactions on metal electrodes are considered in an extended Anderson model, in which the interactions of the reactant with the metal and with the solvent depend on the separation from the interface. The model allows the construction of effective potential energy surfaces. Explicit calculations are performed for the transfer of an iodide ion and for the electron transfer reaction of the Fe 2+/Fe 3+ couple.

Quantum scattering studies of vibrational excitation in collisions of NO(X 2Π) with a Ag(111) surface

We report the results of fully quantum close-coupled studies of vibrational excitation in collisions of NO(X 2Π) with a Ag(111) surface. The interaction potentials used were an extension, to include the dependence on the NO bond distance, of the recent corrected effective medium potential energy surfaces (PES) of Depristo and Alexander. [J. Chem. Phys. 94, 8454 (1991)]. The final state rotational distributions show evidence of at least four rotational rainbows, corresponding to scattering on (and interference between) the two PES which arise when the degeneracy of the NO molecule is lifted upon approach to the surface. A strong tendency is seen to populate the lower spin–orbit manifold at low to moderate final J, which disappears as J rises beyond 30.5 and the final states are better described in Hund’s case (b). Simultaneously, there exists a propensity to populate those Λ-doublet levels in which the electronic-rotational wave function is symmetric (ΠA′) with respect to reflection of the electronic coordinates in the plane of rotation of the scattered NO molecule. This feature is similar to what has been seen experimentally.

Solution conformation of laminaribioside and (1 → 3)‐β‐D‐glucan from optical rotation

AbstractA chiroptical method of conformational analysis is applied to linear (1 → 3)‐β‐D‐glucans and the dimeric analogues β‐ and α‐laminaribioside. The method is based on a recently developed semiempirical calculational model for saccharide optical activity. We conclude that disaccharide conformational energy maps in the literature represent the effective potential energy surface in aqueous solution well. The positive optical rotation observed with long chains in dilute alkaline solution is not characteristic of any single–chain conformation, and must reflect chain association.

Far-infrared vibration–rotation-tunneling spectroscopy of Ar–NH3: Intermolecular vibrations and effective angular potential energy surface

Two new intermolecular vibration–rotation-tunneling (VRT) bands of Ar–NH3 have been measured using tunable far infrared laser spectroscopy. We have unambiguously assigned these and a previously measured FIR band [Gwo et al., Mol. Phys. 71, 453 (1990)] as Π(10, n=0)←Σ(00, n=0), Σ(10, n=0)←Σ(00, n=0), and Σ(00, n=1)←Σ(00, n=0). The three upper states of these are found to be strongly mixed by anisotropy and Coriolis effects. A simultaneous least squares fit of all transitions has yielded vibrational frequencies, rotational and centrifugal distortion constants, and a Coriolis parameter as well as quadrupole hyperfine coupling constants for the upper states. An effective angular potential energy surface for Ar–NH3 in its lowest stretching state has been determined from these data, after explicitly accounting for the effects of bend stretch interactions. Features of the surface include a global minimum at the near T-shaped configuration (θ=90°), a 30 cm−1 to 60 cm−1 barrier to rotation at θ=180° (or 0°), and a very low barrier or possibly a secondary minimum at θ=0° (or 180°). Both attractive and repulsive interactions are shown to contribute significantly to the anisotropic forces in the complex. Comparison with ab initio calculations are presented.

Collisions of NO(X 2Π) with a Ag(111) surface: New quantum scattering studies based on a semiempirical potential energy surface

We report the results of fully quantum close-coupled studies of collisions of NO(X 2Π) with a Ag(111) surface. The recent corrected effective medium potential energy surfaces (PES) of DePristo and Alexander [J. Chem. Phys. 94, 8454 (1991)] were used. The final state rotational distributions show evidence of at least four rotational rainbows, corresponding to scattering on (and interference between) the two PES which arise when the degeneracy of the NO molecule is lifted upon approach to the surface. A strong tendency is seen to populate the lower spin–orbit manifold at low to moderate final J, which disappears as J rises beyond 30.5 and the final states are better described in Hund’s case (b). Simultaneously, there exists a propensity to populate those Λ-doublet levels in which the electronic–rotational wave function is antisymmetric (ΠA″) with respect to reflection of the electronic coordinates in the plane of rotation of the scattered NO molecule. This feature is opposite to what has been seen experimentally. An approximate averaging over the lateral position of the NO molecule above the surface showed that although the rainbow oscillations are strongly sensitive to surface corrugation, the fine-structure propensities are not. This suggests that these latter are reflective of some fundamental characteristic of the NO–Ag interaction which is independent of the position of the NO molecule above the Ag(111) unit cell.

Tunable far infrared laser spectroscopy of van der Waals bonds: The intermolecular stretching vibration and effective radial potentials for Ar–H2O

Measurements of the fundamental van der Waals stretching vibration Σ(000,vs=1) ←Σ(000,vs=0) of Ar–H2O [ν0=907 322.08(94) MHz] and a transition from the lowest excited internal rotor state Σ(101,vs=0) to the Σ(101,vs=1) level [ν0=1019 239.4(1.0) MHz] are presented. A simultaneous rotational analysis of the new stretching data with the internal rotor bands observed by us previously [J. Chem. Phys. 89, 4494 (1988)], including the effects of Coriolis interactions, provides experimental evidence for the new assignment of the internal rotor transitions suggested by Hutson in the accompanying paper. Fits to the rotational term values for the vs=0 states are used to derive effective radial potential energy surfaces for each of the Σ internal rotor states. The results show the well depth (153.4 cm−1) of the effective radial potential for the Σ(101,vs=0) level to be approximately 25 cm−1 deeper than that for the Σ(000,vs=0) ground state of the complex, indicating that the former is stabilized considerably more by the anisotropic intermolecular potential energy surface than is the ground state.

Reaction dynamics for O(3P)+HD. V. Reduced dimensionality quantum and quasiclassical reaction probabilities and rate constants with an adiabatic incorporation of the bending motion

Reduced dimensionality exact quantum and quasiclassical reaction probabilities and rate constants are presented for the O(3P)+HD(ν=0,1)→OH+D and OD+H reactions. The effective potential energy surface used is the ab initio collinear MODPOLCI surface with the ground state adiabatic bending energy added in, as in the previous paper in this series. The rate constants are compared with the recent experiments of Gordon et al.

Theory of absorption and emission of radiation in molecular collisions: Semiclassical model

A semiclassical transition amplitude is derived for electronically inelastic molecular collisions in the presence of an intense electromagnetic field. The calculation of this amplitude involves the integration of classical trajectories for nuclei moving on effective potential energy surfaces. These surfaces, which exhibit an avoided crossing due to the coupling through the dipole interaction around the resonance nuclear configuration, are analytically continued to their complex intersection points, where trajectories switch surfaces. Other parts of these surfaces are similar to the field-free adiabatic surfaces, where one is shifted by ħω. Metastable states, formed at some collision energies, are suggested in the field which are absent in the field-free system.