Showing papers on "Potential energy surface published in 1975"
TL;DR: In this article, the authors derived the semiclassical limit of quantum mechanical transition state theory by invoking the classical path approximation for the Boltzmann density operator and making use of the stationary phase approximation; separability of motion along a reaction coordinate is not assumed.
Abstract: The semiclassical limit of quantum mechanical transition state theory is derived by invoking the classical path approximation for the Boltzmann density operator and making use of the stationary phase approximation; separability of motion along a reaction coordinate is not assumed. The resulting expression for the rate constant bears an interesting similarity to that of conventional transition state theory, although all quantities in it refer to the full classical dynamics on the potential energy surface. In place of the vibrational frequencies of the ’’activated complex’’ which appear in the conventional theory, for example, the semiclassical expression contains characteristic frequencies related to the stability properties of a periodic classical trajectory. Conservation of total angular momentum is easily accounted for in a rigorous manner so that the semiclassical model can be applied to three−dimensional dynamical systems.
606 citations
TL;DR: In this paper, a theory for the statistical emission of large fragments is developed, where a ridge line in the potential energy surface is defined which controls the decay width of the system into any two given fragments.
219 citations
TL;DR: In this article, extended basis sets were used in conjunction with both self-consistent−field (SCF) and configuration interaction (CI) wavefunctions to determine the more important features of the potential energy surface for the simple isomerization reaction HNC → HCN.
Abstract: Ab initio electronic structure theory has been used to determine the more important features of the potential energy surface for the simple isomerization reaction HNC → HCN. Extended basis sets were used in conjunction with both self−consistent−field (SCF) and configuration interaction (CI) wavefunctions. For nonlinear or Cs geometrical arrangements of the three atoms, the CI included 11735 configurations, i.e., all single and double excitations. This large scale CI reproduces the HCN ground state geometry quite accurately and has been used to tentatively identify HNC in the interstellar medium. The SCF calculations predict HNC to lie 9.5 kcal/mole above HCN, while CI yields 14.6 kcal/mole. Similarly, barrier heights of 40.2 and 34.9 kcal/mole are predicted by SCF and CI. Thus, the SCF approximation is qualitatively reasonable for HNC → HCN. If HNC is designated by a reaction angle of 180° and HCN by 0°, then the saddle point or transition state is predicted to lie at 73.7°, significantly closer to HCN. A...
174 citations
TL;DR: In this paper, the first 3D-quantum-mechanical calculations of differential and total cross sections for the H + H2 exchange reaction on the Porter and Karplus potential energy surface have been performed.
Abstract: Accurate three–dimensional (3–D) quantum–mechanical calculations of differential and total cross sections for the H + H2 exchange reaction on the Porter and Karplus potential energy surface have been performed. These are the first such calculations which are vibrationally and rotationally converged, and the results are believed to be accurate to 5% or better. They can serve as a comparison standard against which approximate methods can be tested.
162 citations
TL;DR: In this article, an empirically calibrated potential energy surface was used in a trajectory study of the effect of reactant energy partitioning on cross section for CH3 + H2 → CH4 + H. The relationship of these results to experimental ones was discussed.
Abstract: An empirically calibrated potential energy surface, obtained previously [J. Chem. Phys. 61, 21 (1974)], was used in a trajectory study of the effect of reactant energy partitioning on cross section for CH3 + H2 → CH4 + H. Artificial variations in the barrier position, and artificial and naturally occuring changes in the H masses, were also made. For natural CH3 + H2, H2 vibration enhances and CH3 out‐of‐plane bending depresses the cross section, at constant (25 kcal) translational energy of approach. The isotope substitution and barrier position effects are more complex and not predictable from triatomic A + BC generalizations. The relationship of these results to experimental ones is discussed.
145 citations
TL;DR: In this paper, integral and differential cross sections for pure rotational and simultaneous rotational−vibrational excitation of H2 by Li+ impact have been computed following the coupled−channel formalism using two different SCF potential energy hypersurfaces and a CI hypersurface at 0.6 and 1.2 eV.
Abstract: Integral and differential cross sections for pure rotational and simultaneous rotational−vibrational excitation of H2 by Li+ impact have been computed following the coupled−channel formalism using two different SCF potential energy hypersurfaces and a CI hypersurface at 0.6 and 1.2 eV. Sensitivity of integral cross sections to (a) choice of ab initio potential energy surface and (b) expansion length of a Legendre polynomial representation of one of the energy surfaces is examined. It is seen that preparation of H2 in the v = 0, j = 2 state leads to four− and fivefold increases in excitation cross sections to the v′ = 1, j′ = i, i = 0,2,4 states relative to excitation of ground state (v = 0, j = 0) H2. Differential cross sections are reported at 1.2 eV for up to five quantum rotational and for vibrational transitions on one of the energy hypersurfaces. All angular distributions required for determining ratios (inelastic : elastic) of differential cross sections needed for comparison with recent time−of−fli...
97 citations
TL;DR: In this article, the authors examined two realistic potential energy surfaces for atom−diatomic molecule reactions for two reaction attributes: (1) vibrational energy of the products of a thermal energy exothermic reaction; (2) threshold energy for endothermic reactions of ground−state reagents.
Abstract: Collinear quasiclassical trajectories are examined for two realistic potential energy surfaces for atom−diatomic molecule reactions for two reaction attributes: (1) vibrational energy of the products of a thermal−energy exothermic reaction; (2) threshold energy for endothermic reaction of ground−state reagents. Eight different mass combinations are studied. The potential energy surfaces differ primarily in the amount of potential energy released in an exothermic reaction before and in the region of large curvature of the minimum−energy path and in the curvature of the repulsive potential energy contours when all three atoms are close. For attribute (1), we find the results are qualitatively correlated by the theory of Hofacker and Levine although, contrary to previous work, one potential energy surface shows high mixed energy release (in the language of Polanyi and co−workers) but low excitation to product vibration for five different mass combinations. For reaction attribute (2), we find one surface has a high translational threshold (or no reaction at any energy) for six mass combinations, while the other surface shows this behavior in only three cases. Thus, this type of surface provides an exception to previous generalizations that extra vibrational energy is required for very endothermic reactions with late barriers. This demonstrates the importance of the location of the curvature of the reaction channel for such reaction attributes. Very accurate determinations of potential energy surfaces will be required to make reliable predictions of reaction attributes such as (1) and (2) for real systems. Analysis of the details of the trajectories shows that the high threshold can generally be attributed to reflection before the saddle point of the surface rather than to recrossing the saddle point region. The vibrational excitation of reagents in nonreactive collisions is also strongly effected by curvature of the minimum−energy path.
86 citations
TL;DR: In this paper, a simple model of solvation within the molecular orbital method is proposed whereby the effect of solvent molecules is simulated by the inclusion of fractional point charges at the solvent atomic centers.
77 citations
TL;DR: In this paper, the potential energy surface used is based on the ab initio SCF CI surface of Bender et al. for the collinear F + H2 →H + HF reaction by the State Path Sum method.
Abstract: Exact quantum mechanical transition probabilities have been calculated for the collinear F + H2 →H + HF reaction by the State Path Sum method. The potential energy surface used is based on the ab initio SCF CI surface of Bender et al. For the energy range considered, four product channels are open. Pronounced level inversion is found. The dominant transition is the 3 ←0 one. It has a resonance-like energy dependence which is similar to that for the 2 ←0 transition. The 1 ←0 and 0 ←0 transition probabilities are negligible. These results are compared with those of Wu et al. and Schatz et al. who use semi-empirical LEPS surfaces.
74 citations
TL;DR: In this article, the effect of intrinsic barrier asymmetry on BEBO calculated Bronsted plots is investigated, and contributions to work terms are also considered, making use of classical trajectories, semiclassical concepts, and a previous quantum study.
Abstract: Several energetic and dynamical aspects of proton transfers are treated. The effect of intrinsic barrier asymmetry on BEBO calculated Bronsted plots is investigated, and contributions to work terms are also considered. The dynamics of transfer of a light particle between two heavier ones is discussed for a particular potential energy surface, making use of classical trajectories, semiclassical concepts, and a previous quantum study. The question of nonequilibrium polarization of solvent is also considered.
58 citations
01 Jan 1975
TL;DR: In this paper, the results of ab initio SCF calculations for the potential energy surface of the system Li + /CO are presented, and two minima have been found, both of them with linear configurations: the minimum corresponding to CO⋯Li + is slightly deeper (V O = −0.63 eV) and has a shorter equilibrium distance R e = 4.5 α 0 between Li + and the center of mass of CO than the one corresponding to Li + ⋯CO (V C = − 0.53 eV, R e
Abstract: The results of ab initio SCF calculations for the potential energy surface of the system Li + /CO are presented. Two minima have been found, both of them with linear configurations: The minimum corresponding to CO⋯Li + is slightly deeper ( V O = −0.63 eV) and has a shorter equilibrium distance R e = 4.5 α 0 between Li + and the center of mass of CO than the one corresponding to Li + ⋯CO ( V C = −0.53 eV, R e = 5.5 α 0 ). Inclusion of electron correlation does not change the equilibrium distances appreciably, but leads to a slightly more favorable approach of Li + to the C-atom in CO ( V O = −0.54 eV, V C = −0.62 eV). The anisotropy of the potential surface is discussed as well as the change of the equilibrium distance r e and force constant k e of CO during appoach of Li + . From these properties a qualitative explanation of the similarities and differences in the inelastic scattering cross sections between Li + /N 2 and Li + /CO is attempted.
TL;DR: In this paper, a contract Gaussian basis set was employed to determine the HLi2 potential energy surface, which was then used to calculate the dissociation energy of the diatomic molecules Li2 and LiH.
Abstract: Ab initio electronic structure calculations have been performed to determine the HLi2 potential energy surface. A contracted Gaussian basis set was employed: H(5s 1p/3s 1p), Li(8s 3p/4s 3p). In addition to selfconsistent‐field (SCF) wavefunctions, full configuration interaction (CI) was carried out for the three valence electrons. For general geometry (point group Cs), the CI included 5175 configurations. For the diatomic molecules Li2 and LiH, these methods yield dissociation energies within 5 kcal/mole of experiment, and accurate spectroscopic constants are also predicted. The minimum on the HLi2 CI potential surface occurs for an isosceles triangle structure with r (H–Li) = 1.72 A and on LiHLi bond angle of 95°. This minimum lies 22.4 kcal/mole below the separated products LiH + Li. The linear HLiLi minimum is much shallower, lying only 4.2 kcal/mole below the products. The much simpler single configuration SCF calculations yield qualitatively similar results. Furthermore, these features of the surface...
TL;DR: In this article, a simple rule for estimating the low energy reaction efficiency is described and the integrated reaction cross section ratios for the tritium atom reactions are found to be in good agreement with observed experimental isotope effects.
Abstract: Classical trajectory studies have been performed using an empirical potential energy surface for the interactions H + H2, D + D2, T + H2, T + D2, H + T2 and T + HD. Reaction and dissociation cross sections in each system are examined and a simple rule of thumb for estimating the low energy reaction efficiency is described. The integrated reaction cross section ratios for the tritium atom reactions are found to be in good agreement with observed experimental isotope effects. The vibrational excitation of the product molecule and the centre of mass scattering distributions are also discussed.
TL;DR: In this paper, the authors used the high-resolution photoelectron spectrum of H 2 O + to predict an equilibrium angle of about 60° for the 2 B 2 state of the ion.
TL;DR: In this paper, a large number of geometrical configurations (250) are computed with a large Gaussian basis set in the Hartree-Fock approximation for the H2O-Li-F complex.
Abstract: A large number of geometrical configurations (250) are computed with a large Gaussian basis set in the Hartree–Fock approximation for the H2O–Li–F complex. The many‐dimensional potential energy surface has been sampled by keeping the molecule of water at a fixed position and by allowing the lithium and the fluorine to assume many positions in space. Because of the symmetry (C2v) of the water molecule, the 250 computations correspond to a sampling of about 600 configurations. The sampling includes a few highly repulsive configurations (up to about 300 kcal/mole in repulsion); the remaining points are either in the strongly attractive regions or in the weakly attractive regions of the surface. The stabilization energy of the complex reveals the existence of at least three possible structures: the Li–F–H2O structure (with C2v symmetry), with a stabilization energy (relative to H2O, F−, and Li+) of about −186 kcal/mole; a second Li–F–H2O structure with the fluorine forming a hydrogen bond (with one of the H–O...
IBM1
TL;DR: In this paper, the authors discuss the coupled channel studies of rotational and vibrational energy transfer by collision and examine the dependence of computed cross sections on selected computational and physical parameters.
Abstract: Publisher Summary The chapter discusses the coupled-channel studies of rotational and vibrational energy transfer by collision. For nonreactive collisions of closed-shell molecules at energies below the threshold of electronic excitation, nuclear motion is determined by a single potential energy surface. Under these conditions, the physical processes possible are elastic scattering and energy exchange between the translational (T), rotational (R), and vibrational (V) degrees of freedom. Almost all non-empirical potential energy surfaces determined over a range of coordinate space to be usable for scattering applications have been computed following the Hartree-Fock (HF) and configuration interaction (CI) models. A method that, in principle, can yield the exact solution of the collision dynamics on a specified potential energy surface is the ‘coupled channel’ or ‘close-coupling’ (CC) method. Applications of CC methods have been restricted almost exclusively to collisions of H, He, and Li + with H 2 because of the lack of availability of accurate ab initio and reliable semi-empirical potential energy surfaces for larger systems. The H 2 molecule provides a particularly useful scattering target because of its large energy level spacing, which greatly reduces the range of excitations possible at specified collision energy. This chapter examines the dependence of computed cross sections on selected computational and physical parameters.
TL;DR: The reliability of these semiclassical calculations allows one to determine the region of the potential energy surface which is sufficient for calculation of vibrational excitation probabilities for strongly classically forbidden single and two-quantum transitions as mentioned in this paper.
Abstract: Vibrational transition probabilities for strongly classically forbidden single‐quantum and two‐quantum transitions calculated by two semiclassical methods involving real‐valued trajectories are compared to quantum mechanical close coupling for various analytic fits to the ab initio interaction potential for the He–H2 system. The final‐value‐representation integral expression from classical S matrix theory and the classical‐trajectory forced‐quantum‐oscillator method are found to be in semiquantitative agreement with the quantum mechanical calculation even for transition probabilities as small as about 10−6. Further, the semiclassical methods reproduce the important trends in the results as functions of the interaction potential. The reliability of these semiclassical calculations allows one to determine the region of the potential energy surface which is sufficient for calculation of vibrational excitation probabilities. The important region for the present calculations is in the classically allowed regio...
TL;DR: In this article, the existence of reactive and unreactive regions on the collinear SSMK potential energy surface has been investigated and the relationship between trajectory times and band positions is shown.
TL;DR: In this article, an ab initio calculation of the Ne-H-H potential energy hypersurface for a wide range of H2 internuclear separation (0.8⩽R⌽5.0 bohr) and Ne-Ne-H2 separation (2.5⎆X⌆6.0bohr), for both the collinear and perpendicular bisector geometries, is reported.
Abstract: An ab initio calculation of the Ne–H–H potential energy hypersurface for a wide range of H2 internuclear separation (0.8⩽R⩽5.0 bohr) and Ne–H2 separation (2.5⩽X⩽6.0 bohr) is reported. Calculations were carried out for both the collinear and perpendicular bisector geometries. For the perpendicular bisector geometry, the potential surface has the property previously found for He–H2 of exerting a contractive force on the H2 molecule as the noble gas atom approaches. The surface demonstrates a crossover point near 3.0 bohr where the contractive force changes to a stretching force. Analytic fits to the potential energy surface are presented and discussed in detail. In particular, the ’’dumbbell’’ model was not found to provide a good description of the potential surface. Because of the wide range in values of X and R for which points were calculated, the surface reported here should be useful for trajectory studies of diatomic dissociation and atom recombination.
TL;DR: In this article, the rate coefficients for the reactions of H and D-atoms with vibrationally excited HF and DF molecules were calculated by means of the London-Eyring-Polanyi-Sato (LEPS) potential energy surface.
Abstract: Rate coefficients are calculated for the reactions of H and D-atoms with vibrationally excited HF and DF molecules. Three-dimensional classical trajectories of the collision dynamics of these reactions have been calculated by means of the London-Eyring-Polanyi-Sato (LEPS) potential energy surface. The Monte Carlo procedure is used to start each collision trajectory. Results of this study indicate that (a) chemical exchange provides an efficient mechanism for relaxing vibrationally excited HF and DF molecules by H and D-atoms; (b) multiple-quantum transitions are important in the deactivation processes; and (c) both vibration-translation and vibration-rotation energy transfers contribute to vibrational relaxation of vibrationally excited HF and DF molecules by H and D-atoms. The vibrational relaxation of HF (v = 1) by H-atoms is faster than the vibrational relaxation of DF (v = 1) by H-atoms. A similar effect is indicated for D-atoms; i.e. the vibrational relaxation of DF (v = 1) by D-atoms is faster than ...
TL;DR: In this paper, the potential energy surface of H+H2 has been calculated and the hydrogen molecule bond length was kept at 1.4 a0.1 a0, which is in good agreement with the experimentally determined V0 reported by Gengenbach, Hahn and Toennies.
Abstract: Valence bond calculations of the potential energy surface of H+H2 have been done. In all the calculations the hydrogen molecule bond length was kept at 1.4 a0. The isotropic potential V0(r) and the leading anisotropic potential V2(R) were obtained. Our caclulated V0 is in good agreement with the experimentally determined V0 reported by Gengenbach, Hahn, and Toennies. Our calculations predict that the triangular arrangement of H2+H is favored over the linear configuration at long distances of R with alignment to the linear geometry at approximately 3.1 a0. A populaion analysis of our wavefunction is also presented.
TL;DR: In this article, the authors discussed previous estimates of the anisotropy of the surface, and presented new calculated results for the leading anisotropic dependence for the H2 system.
Abstract: There have been numerous attempts to calculate the potential energy of the H–H2 system. In this communication, we discuss previous estimates of the anisotropy of the surface, and present new calculated results for the leading anisotropic dependence.
TL;DR: In this article, preliminary results of ab initio unrestricted Hartree-Fock calculations for the potential energy surface for the reaction N+ + H 2 → NH + + H are reported.
TL;DR: Several points on the potential energy surface of penta-1,4-diene as a function of the two torsional angles around the C-C single bonds have been computed using a SCF MO LCAO scheme with a basis of contracted gaussian functions as discussed by the authors.
Abstract: Several points on the potential energy surface of penta-1,4-diene as a function of the two torsional angles around the C—C single bonds have been computed using a SCF MO LCAO scheme with a basis of contracted gaussian functions. Three stable conformations are predicted for the molecule at very similar total energies and a fourth metastable form is found at a higher energy. The stable isomers belong to the point groups Cs, C2 and C1; the metastable conformation has C1 symmetry. Following a very simple mechanism suggested by the analysis of the theoretical results, the isomerization paths are also investigated, and estimates of the appropriate barrier heights obtained.The Raman spectra of the liquid and of the solid phase have been recorded and show the existence of three conformers. The results prove that the three isomers have Cs, C2 and C1 symmetry, and have nearly equal enthalpies.
TL;DR: In this article, a new type of seniority quantum number, related to the number of nucleons in time-reversal-conjugate states, is proposed as an explanation for the occurrence of rotational-type quadrupole moments in deformed as well as spherical nuclei.
Abstract: The magnetic moments of the first 3/2+ states of 203, 205, 207Tl are discussed in terms of mesonic-exchange and configuration-mixing corrections. The gyromagnetic ratios of two fission isomeric states of 237Pu are discussed in terms of Nilsson states for the second well in the potential energy surface. The gyromagnetic ratios of high spin states of 164Er and 160Dy are discussed in terms of Coriolis-Anti-Pairing and Rotation-Alignment theories. A new type of seniority quantum number, related to the number of nucleons in time-reversal-conjugate states, is proposed as an explanation for the occurrence of rotational-type quadrupole moments in deformed as well as spherical nuclei. Further tests of this seniority classification are suggested on the basis of the quadrupole moments of high-spin states and first 3+ states.
TL;DR: In this article, the potential energy surface for isomerization of unsymmetrical olefins A2CCB2 in strongly polar solvents is shown to possess a remarkable double-well form.
Abstract: The potential energy surface for isomerization of unsymmetrical olefins A2CCB2 in strongly polar solvents is shown to possess a remarkable double-well form.
01 Jan 1975
TL;DR: In this paper, the authors define the concept of Tunnelling as a barrier separating two stable situations, and show that a system with insufficient energy initially at one side of a barrier can be discovered on the other side of the barrier.
Abstract: Tunnelling is defined in terms of a barrier separating two stable situations. If the system acquires energy equal to or greater than the height of the barrier, then it can cross the barrier and get from one side to another. If the energy is less than that of the top of the barrier then classically it cannot get from one side to another. According to quantum mechanics, however, there is a perceptible chance that a system with insufficient energy initially at one side of the barrier can be discovered on the other side of the barrier. This process has been called ‘tunnelling’, by analogy to the only classical way to cheat a geographical energy barrier.
01 Jun 1975
TL;DR: In this paper, an extensive literature review on the potential energy surfaces of fifteen atmospheric triatomic molecular systems has been made, including water, nitrogen dioxide, ozone, carbon dioxide, nitrous oxide, and their singly charged positive and negative ions.
Abstract: : An extensive literature review on the potential energy surfaces of fifteen atmospheric triatomic molecular systems has been made. The systems are water, nitrogen dioxide, ozone, carbon dioxide, nitrous oxide, and their singly charged positive and negative ions. The potential energy surface characteristics for each molecular system are summarized in the form of adiabatic correlation diagrams between the electronic states of the triatomic molecule and those of the atom, diatomic asymptotes. Where available information allows, such correlation diagrams are constructed not only for the equilibrium symmetry and geometry of the triatomic ground state, but also for other symmetries and geometries as appropriate to the clear indication of the three-dimensional surface characteristics and the general adiabatic asymptotic correlations. The correlation diagrams for each system are discussed in connection with some of its triatomic and atom-diatomic processes.
TL;DR: In this paper, an empirically calibrated potential energy surface was used in a trajectory study of the effect of reactant energy partitioning on cross section for CH3 + H2 → CH4 + H. The relationship of these results to experimental ones was discussed.
Abstract: An empirically calibrated potential energy surface, obtained previously [J. Chem. Phys. 61, 21 (1974)], was used in a trajectory study of the effect of reactant energy partitioning on cross section for CH3 + H2 → CH4 + H. Artificial variations in the barrier position, and artificial and naturally occuring changes in the H masses, were also made. For natural CH3 + H2, H2 vibration enhances and CH3 out‐of‐plane bending depresses the cross section, at constant (25 kcal) translational energy of approach. The isotope substitution and barrier position effects are more complex and not predictable from triatomic A + BC generalizations. The relationship of these results to experimental ones is discussed.