Showing papers on "Potential energy surface published in 1973"

Ab initio potential energy surface for linear H3

Abstract: The configuration interaction (CI) method has been applied to determine an accurate potential energy surface for linear H3. The calculated surface is believed to lie no more than 0.8 kcal/mole and no less than 0.2 kcal/mole above the exact surface, a significant improvement over all previous calculations. The calculation yields a linear symmetric saddle point at an internuclear separation of 1.757 a.u. The saddle point energy is 9.8 kcal/mole above the calculated energy of an isolated hydrogen atom and a hydrogen molecule, and 10.28 kcal/mole above the exact energy of the isolated systems. An estimated lower bound for the barrier height is 9.5 kcal/mole. Comparison of the calculated H3 potential surface with the best semiempirical surface and the best previous ab initio surface shows good qualitative agreement. However, there are quantitative differences, whose effect can only be determined by accurate dynamical calculations. The method employed in the H3 calculation was designed to approach the complete ...

Study of the structure of molecular complexes. IV. The Hartree‐Fock potential for the water dimer and its application to the liquid state

Abstract: The Hartree‐Fock energy of the water dimer has been computed for 216 different nuclear configurations using the basis set given in the first paper of this series. Near the equilibrium configuration, a calculation was carried out using a large Gaussian basis set with optimized orbital exponents for the oxygen 3d ‐ and 4f ‐type and hydrogen 2p ‐ and 3d ‐type functions in order to get results close to the Hartree‐Fock limit. In the vicinity of the equilibrium configuration the mechanism for binding of the dimer is analyzed with the help of the bond energy analysis formalism. The importance of polarization (internal charge transfer), as pointed out previously by a number of authors, is clearly evident. The computed energies have been used to derive a simple analytical expression that reproduces the Hartree‐Fock potential energy surface to a high degree of accuracy. This analytical potential is compared with the empirical effective pair potentials proposed by Rowlinson and Ben‐Naim and Stillinger for the descr...

Diatomics‐in‐molecules potential energy surfaces. II. Nonadiabatic and spin‐orbit interactions

Abstract: A simple procedure is described for calculating spin‐orbit and nonadiabatic interactions by an extension of the diatomics‐in‐molecules approach. The method can be easily applied to a large number of polyatomic systems and will hopefully be of value in obtaining qualitative and quantitative descriptions of many important molecular collision processes which involve more than one potential energy surface. Results are presented for two such processes, the quenching of Li(2 2P) by H2 and the reaction of F atoms with H2.

Monte Carlo trajectories: Dynamics of the reaction F +D2 on a semiempirical valence-bond potential energy surface

Abstract: A semiempirical valence‐bond calculation was carried out for the potential energy surface of H2F treating explicitly seven valence electrons (2pF51sHa1sHb). The integrals were evaluated from diatomic potential energy curves using the Cashion‐Herschbach method. Using this potential energy surface, the chemical reaction F+D2→FD+D was studied by Monte Carlo calculations of quasiclassical trajectories. Cross‐section calculations were carried out for initial conditions in these ranges: relative translational energy, 1.56–19.3 kcal/mole; rotational angular momentum (in units of ℏ), 0–5; vibrational quantum number, 0–1. In addition, distributions of internal energy and scattering angles for the molecular product were calculated. The results were compared with those of previous theoretical studies and the comparison indicates that subtle features (not well understood) of the potential surface may be important for obtaining correct results. The results were also compared with molecular beam, chemical laser, and in...

Calculated frequencies and intensities associated with coupling of the proton motion with the hydrogen bond stretching vibration in a double minimum potential surface

Abstract: The influence of the coupling of the proton movement and the H bond stretching vibration in a double minimum potential energy surface on the energy levels, transitions, induced dipole moments and polarisabilities is calcualted ab initio as a function of an electric field for the H5O+2 system. The high polarisability of the hydrogen bonds remains to a large extent unchanged due to the coupling. New types of transitions occur, particularly when the tunnelling frequency and the frequency of the bond stretching vibration are comparable in size. Especially in this case numerous Fermi resonances occur due to the shift of the energy levels in the electric field, which leads to a considerable increase in the number of transitions. It is shown that the change of the frequencies of the transitions due to the induced dipole interaction of the bonds with fields from their environment is a decisive cause of the variety of energy level differences observed as a continuous absorption in the i.r. spectrum of such systems.

Quantum mechanical computational studies of chemical reactions : III. Collinear A BC reaction with some model potential energy surfaces

Abstract: The effects of the location of the energy barrier and of changing vibrational frequency along the reaction path on the reaction dynamics of a collinear A + BC → AB + C reaction were studied using a series of ‘diagnostic’ model potential energy surfaces. In accord with the classical trajectory study, vibration was found markedly more effective than translation in promoting reaction on a surface with a barrier located at the exit valley, and vice versa on a surface with a barrier placed in the entry valley. Considerable vibrational population inversion in the reaction product was found for an ‘early-down-hill’-type surface with a barrier placed in the entry valley. The energy release was exceedingly speecific, particularly so for the F + H2/F + D2 collinear collision on a realistic surface. Resonances in reactive molecular collisions were evident whenever the static effect of changing vibrational frequency along the reaction path gave rise to the potential wells necessary to support these quasibound states.

Monte Carlo calculations of reaction rates and energy distribution among reaction products. II. H+HF(v) → H2 (v′) + F and H+HF(v) → HF(v′) + H

Abstract: Rate constants are calculated for the reactions of atomic hydrogen with vibrationally excited hydrogen fluoride by analyzing the results of classical trajectories on a semiempirical London‐Eyring‐Polanyi‐Sato (LEPS) potential energy surface Monte Carlo procedures are used to start each collision trajectory Reaction rate constants are presented for direct reactions into specific vibrational states of the product H2 and HF molecules By means of this calculation, it is predicted for the reactant HF molecule in the ν = 3 state that 113% of the mean fraction of available energy will become vibrational energy in H2, 12% will become rotational energy in H2, and 875% will become translational energy in the products As the vibrational energy of the reactant HF molecule increases, the mean fraction of available energy which becomes vibrational energy of the product H2 molecule increases For example, if the reactant molecule HF is in the v = 6 state, it is found that the mean fraction of available energy that will become vibrational energy in H2 is 351%, 8% will become rotational in H2, and 569% will become translational energy in the products For the reactant HF molecule in the v = 3 state, 45% of the mean fraction of available energy will become vibrational energy in the product HF molecule, 04% will become rotational energy in HF, and 548% will become translational energy in the products The de‐excitation of HF by H atoms is due to vibration‐translation energy transfer Results of this trajectory calculation, indicate that (1) multiple quantum jumps are significant in the reactions of H atoms with vibrationally excited HF, and (2) chemical effects provide an important mechanism for the efficient relaxation of vibrationally excited HF by H atoms Both theory and experiment indicate that the rate of deactivation of vibrationally excited HF by H atoms is very fast Rate constants are provided for many reactions that have not been measured experimentally

Ab initio dynamics: HeH+ + H2 → He + H3+ (C2ν) classical trajectories using a quantum mechanical potential‐energy surface

Abstract: Tabular values of near‐Hartree‐Fock ab initio energies for the ground electronic state of HeH3+ were expressed in analytical form by fitting with spline interpolation functions. The interpolation functions were then used to provide the potential‐energy gradients necessary for dynamical calculations. General features of this method for representing potential‐energy surfaces are discussed. Classical trajectories have been computed for the ion‐molecule reaction HeH++H2 → He+H3++2.6 eV, constrained to follow C2ν symmetry reaction paths for which there is no energy barrier. Trajectories were run under the conditions: relative translational energies 0.001 and 0.1298 eV and internal vibrational states of reactants with quantum numbers 0 and 2; the initial vibrational phases of each trajectory were selected randomly. Analysis of the results revealed that most of the energy available to the products (including the exothermicity of the reaction) ends up as H3+ vibrational energy; more than half of the collisions pr...

Energy partitioning in photodissociation and photosensitization

Abstract: The molecular dynamics of photodissociation and of electronic vibrational/translational energy transfer have been investigated in terms of an impulsive ‘half-collision’ model, modified to accommodate the possibility of changes in the potential energy functions (force constants) of the separating fragments. The model, which is suitable for any system which is suddenly prepared on a repulsive potential energy surface (e.g. following electronic excitation or radiationless transition), has been applied to the quenching of Hg(63P1) by CO and NO and to the photodissociation of ICN. Experimental data and alternative theoretical treatments are available for each of these systems. The new model is able to achieve a remarkable agreement with observation in the Hg/CO and NO systems by assuming the intermediate formation of a Hg(63P0) - CO or NO complex in which the C-O or N-O bond order increases by ∼ 0·6. Model calculations for the quenching of Cd and Zn(3P0) suggest that the distributions over final states would b...

Reaction paths on the H4 potential energy surface

Abstract: Portions of the electronic potential energy surface corresponding to various nuclear geometries of the H4 molecular system have been studied. The variational calculations employed double‐zeta basis sets (1s and 1s′ Slater‐type orbitals on each center) to form configuration interaction wavefunctions. At selected points on the surface, the effects of exponent optimization and increased basis set size (1s, 1s′, and 2p orbitals per center) were assessed. A low energy reaction path allowing a bimolecular mechanism for exchange, requiring less energy than a single H2 dissociation, was not found. However, a path leading from trapezoidal to linear structures (and vice versa) was found to offer the possibility of exchange with less than 6 kcal/mole of energy above this dissociation limit.

On the H+F2→HF+F reaction. An ab initio potential energy surface

Abstract: Rigorous quantum mechanical calculations have been carried out to predict the H+F2→HF+F potential energy surface A double zeta basis set was used, and open‐shell self‐consistent‐field (SCF) calculations were carried out In addition, electron correlation was explicitly treated using first‐order wavefunctions, made up of 555 2A′ configurations Orbitals were optimized by the interative natural orbital method From the SCF calculations the barrier height and exothermicity are predicted to be 122 and 1324 kcal/mole, respectively The configuration interaction (CI) values are 10 and 883 kcal, in much better agreement with the experimental values, 12 and 1025 kcal The saddle point is predicted from the CI calculations to occur for a linear geometry, R(H–F)=205 A, R(F–F)=157 A This corresponds to an H–F separation more than twice as great as in the HF molecule but an F–F separation is only slightly (003 A) longer than in the isolated F2 molecule A substantial number of calculations were carried out

Variational theory of reaction rates: Application to F+H2⇄HF+H

Abstract: The classical variational theory of reaction rates is coupled with a Monte Carlo trajectory analysis to yield reaction rates and energy distributions of reactants and products for the forward and reverse reactions: F+H2⇄HF+H at 300°K. The results are compared with those of a standard quasiclassical trajectory analysis of the forward reaction using the same potential energy surface. Differences are attributed to the quantized distributions of reactants in the quasiclassical calculations. The combination of the two methods allows a substantial reduction in computation requirements for determining the characteristics of reactions in systems with reactants in thermal equilibrium.

Monte Carlo calculations of reaction rates and energy distributions among reaction products. IV. F+HF(ν) → HF(ν')+F and F+DF(ν) → DF(ν')+F

Abstract: Rate constants are calculated for the vibrational relaxation HF(ν) and DF(ν) molecules by F atoms with ν = 1, 2, 3, and 6. Three‐dimensional classical trajectories of the collision dynamics of these reactions were calculated by means of a modified London‐Eyring‐Polanyi‐Sato (LEPS) potential energy surface used to calculate rate constants for the reactions between H atoms and F2 molecules, and D atoms and F2 molecules. The Monte Carlo procedure is used to start each collision trajectory. By means of this calculation, it is predicted for the reactant HF molecule in the ν = 2, J = 8 state that 13.3% of the mean fraction of available energy will become rotation in the product HF, 80.7% will become vibrational energy in the product HF, and 6% will become relative translational energy of the products. As the vibrational energy of the reactant HF molecule increases the mean fraction of available energy that becomes rotational energy increases slightly. For example, if the reactant molecule HF is in the ν = 6, J ...

Classical trajectory studies of long‐lived collision complexes. I. Reaction of K atoms with NaCl molecules

Abstract: We have studied the reaction K+NaCl→KCl+Na using classical trajectory techniques on an analytic potential energy surface fit to the ground‐state semiempirical pseudopotential surface of Roach and Child. A total of 8000 trajectories were calculated in order to study product angular distributions, energy partitioning and complex lifetimes as a function of collision energy. The ``snarled'' trajectories, the shapes of the center‐of‐mass angular distributions, and the disposal of energy all provide evidence that reaction proceeds via the formation and subsequent decomposition of long‐lived complexes. The calculated laboratory angular distribution of KCl product and the magnitude of the reaction cross section are in reasonably good agreement with experimental results from molecular beam studies by Miller, Safron, and Herschbach. However, the predicted ratio of reactive‐to‐nonreactive complex decompositions is too large and, since the surface used has too weak a long‐range K–Na attraction, these results support ...

Potential energy surfaces for simple chemical reactions: Li+F2→LiF+F

Abstract: A potential energy surface is calculated for the Li+F2→LiF+F reaction using an ab initio multistructure valence-bond approach. The orthogonalized Moffit (OM) method is used to apply a correction for the large errors made by the ab initio calculation in representing the F- ion relative to the F atom. The lowest potential energy surface is predicted by the OM method to be of the highly ‘attractive’ or ‘early downhill’ type and possesses a substantial well with respect to dissociation to the products LiF+F. The ground state wavefunction and the charge distribution corresponding to it are analysed and the results contrasted with past expectations. The attributes of the surface predicted by the OM method are compared with those suggested by experiment and used in trajectory calculations for analogous systems. The surface is found to be in qualitative agreement with all the features deduced from experiments. The electron-jump region of the surface is examined and the electron-jump distance is plotted as a funct...

Monte Carlo calculations of reaction rates and energy distributions among reaction products. III. H+F2→ HF+F and D+F2→ DF+F

Abstract: A three‐dimensional classical trajectory calculation is made of the collision dynamics of the exothermic reactions H+F2(v, J)→ HF(v′, J′)+F and D+F2(v, J)→ DF(v′, J′)+F by means of a modified London‐Eyring‐Polanyi‐Sato (LEPS) potential energy surface. Trajectory calculations are used to establish the anti‐Morse parameters for a modified LEPS potential‐energy surface which produce the best agreement with previous experimental measurements of reaction rates and energy distributions among reaction products. Very good agreement is obtained with the experimental overall rate constant, the experimental prediction that the maximum vibrational level population of HF (v′) is achieved in v′ = 5, and the mean fraction of available energy entering vibration of the newly formed HF bond. The maximum vibrational level population of DF (v′) is achieved in v′ = 8. The mean fractions (fv′=Ev′/Etotal and fR′=EJ′/Etotal) of the total available energy entering vibration plus rotation are (1) for H+F2, fv′+fR′=(0.54+0.02)=...

Alkali-methyl iodide reactions

Abstract: Using empirical Monte Carlo trajectory procedures, we fitted a detailed 6-atom potential energy surface to molecular beam data for Rb + CH3I → RbI + CH3. Measurements at a single energy of product recoil velocity and scattering angle distributions, and of the effect of aligning the CH3I, were employed. We then used the potential surface to predict the energy dependence of the reactive cross-section, and to ascertain the consequences of omitting the CH3 hydrogens from the calculations. Experimental data with which to compare our results are expected to appear.

Trajectory study of reactions in HBr–Br2 systems

Abstract: A large number of trajectories have been calculated employing a semiempirical potential energy surface for H2Br2. Primary attention has focussed on reactions of H with HBr and Br2 and the isotopically substituted analogs. Cross sections have been determined for a large number of different relative velocities and initial vibration‐rotation states of the diatomic reactant. Center‐of‐mass angular scattering distributions and energy partitioning distributions were determined and compared with experimental data from molecular beam and infrared chemiluminescence data. Good agreement is found in the case of energy partitioning with about 80% of the available energy appearing as internal energy. Agreement is excellent in the case of angular scattering—the trajectory calculations predict a small amount of forward scattering, which increases and becomes fairly uniform in the backward hemisphere. Rate constants were computed from cross sections for both thermal and hot atom experiments. Absolute thermal rate coeffic...

The homogeneous gas phase H2 ? D2 metathesis at room temperature: Reaction induced by specific vibrational excitation

Abstract: We have demonstrated that reactions for which substantial activation energies are needed can be induced to occur at room temperature via specific vibrational excitation. Indeed, the indications are that the atom-switching reactions for which Ea > 25 kcal take place with high probability only when the activation energy is localized in the vibrational mode. In this preliminary report on the utilization of the stimulated Raman effect to generate substantial populations in the critical vibrational states required for the homogeneous atom exchange between H2 and D2, we first summarized the historical development of the concept. The experimental arrangement is then described and the analytical results tabulated; the observed dependence on relative concentrations is semiquantitatively rationalized on the basis of a model proposed in 1964. Independent shock tube and molecular beam investigations were similarly accounted for. Attention is called to the discrepancy between the generally concordant experimental results and the ab initio quantum mechanical calculations of the potential energy surface for 4H atoms.

Simplest halogen atom plus alkali dimer potential surface: F+Li2→LiF+Li

Abstract: Ab initio electronic structure calculations have been carried out to investigate some features of the potential energy surface for the chemical reaction F+Li2→LiF+Li. The basis set of contracted Gaussian functions was of ``double zeta plus polarization'' quality, with an additional set of p functions on F added to describe F−. Single‐configuration and two‐configuration self‐consistent‐field calculations are reported here. A minimum energy path was obtained for the collinear reaction, but the most important feature determined was the nature of the potential minimum due to the FLi2 complex. For linear F–Li–Li, this complex is bound by 4 kcal/mole relative to separated LiF + Li. The attraction is much stronger, 34 kcal, for C2v geometry, and this species is predicted to have a bond angle of 99° and Li–F bond distance of 1.79 A. Several excited electronic states of FLi2 are discussed briefly.

Collinear hydrogen atom transfer probabilities, O+HBr → OH+Br

Abstract: Quantum mechanical calculations of a collinear model of the reaction O+HBr→OH+Br have been performed using a semiempirical potential energy surface. At thermal energies this simple model predicts OH to be produced in its ground state and first excited state with population ratios 0.4 to 0.6, giving a moderate inversion over a considerable range of reactant kinetic energy.

Potential energy surface for the M2X+ ion and the ionization potential of M2X

Abstract: Potential energy surfaces for the M2X+ ions (M denotes alkali atom, X halogen atom) have been calculated by a classical ionic model based upon the Rittner model. In all cases M2X+ has substantial binding energy (∼1·5–2 eV) with respect of M+ + MX. The most stable configuration varies from linear for heavy M light X, to strongly bent for light M heavy X. The adiabatic ionization potential of the M2X molecule I ad (M2X) is found to be surprisingly low; less than that of the alkali atom I(M). The vertical ionization potential I v(M2X) is only slightly greater than the adiabatic value. This facilitates a second electron jump in the reactions of alkali dimers with polyhalide and alkyl halide molecules. The main implications of the M2X+ potential surface for the dynamics of the reaction M+ + M′X → MX + M′+ are briefly noted.

Dynamics of collinear A + BC systems

Abstract: A pair of coordinates, one along the minimum reaction path and one normal to it, is employed to treat the collinear dynamics of processes of the type A+B−C→A−B+C. Two potential‐energy surfaces are considered: Surface I in which the activated state lies in the approach portion of the reaction coordinate, and Surface II in which it lies in the retreat coordinate. It is shown analytically, in agreement with previous computer calculations, that for Surface I relative translational energy is effective in surmounting the barrier, and that vibration energy is ineffective. For Surface II vibrational energy is effective and relative translational energy ineffective. Consideration is also given to the effects of the relative masses of A, B, and C in determining the energy distribution of the products. Two cases are considered: (1) A light and B and C heavy (L+HH), and (2) A and B heavy and C light (H+HL). It is shown that Case (1) tends to lead to products of high translational and low vibrational energy, whereas C...

The methyl isocyanide isomerization: A CNDO/2 study with partitioning of energy

Abstract: CNDO/2 calculations together with a partitioning of the energy into various one- and two-centre components have been performed on CH3CN, CH3NC, and a large number of nuclear configurations formed by placing the methyl group at various positions with respect to the fixed CN group. A complete potential energy surface was obtained showing that a minimum in energy occurred for a pyramidal CH3 group placed at approximately 90° to the CN axis. The barrier to the reaction CH3NC→CH3CN is calculated as 32.9 kcal, in reasonable agreement with 38.4 kcal, the experimental value of Rabinovitch. A charge separation equivalent to [CH 3 +0.22 ][CN−0.22] is found for the intermediate compared to [CH 3 +0.08 ][CN−0.08] and [CH 3 +0.12 ][NC−0.22] for the cyanide and isocyanide, respectively.