Semiempirical Surface Research Articles

Collisional deactivation of Br(4 2P1/2) by hydrogen isotopes

The quenching of electronically excited bromine atoms Br(4 2P1/2) upon collision with H2, HD, and D2 has been studied at 300 °K. The temporal profile of the Br(4 2P1/2) concentration was monitored by observation of the time-resolved attenuation of bromine resonance radiation at 153.2 nm. The probabilities of deactivation by the hydrogen isotopes are presented and compared to theoretical treatments based either upon long-range coupling via mulitpolar interactions or explicit treatment of the nonadiabatic crossing probabilities computed using semiempirical potential surfaces. These results are then examined with a view toward assessing the importance of near-resonant electronic–vibrational energy transfer in such an elementary system.

Angular distributions in the elastic scattering and rotational excitation of molecular hydrogen by atomic hydrogen

view Abstract Citations (24) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Angular distributions in the elastic scattering and rotational excitation of molecular hydrogen by atomic hydrogen. Chu, S. -I. ; Dalgarno, A. Abstract The effective close-coupling method of Rabitz is tested and used to calculate the angular distributions of the elastic and inelastic scattering of molecular hydrogen in collision with atomic hydrogen when rotational transitions may occur. The interaction potential adopted is the Porter-Karplus semi-empirical potential surface, which was joined smoothly to the correct long-range potentials. Explicit calculations are reported for the differential elastic and total inelastic cross sections in the energy range from 0.1 to 1.5 eV. Publication: The Astrophysical Journal Pub Date: August 1975 DOI: 10.1086/153731 Bibcode: 1975ApJ...199..637C Keywords: Angular Distribution; Atomic Collisions; Hydrogen; Interstellar Matter; Molecular Excitation; Scattering Cross Sections; Elastic Scattering; Graphs (Charts); Hydrogen Atoms; Inelastic Scattering; Quantum Mechanics; Tables (Data); Wave Functions; Astrophysics full text sources ADS |

Molecular beam kinetics: Exchange reactions of deuterium atoms with hydrogen halides

A crossed-beam study finds the reactions of D atoms with HCl, HBr, and HI give large yields of DCl, DBr, and DI, corresponding to reaction cross sections of the order 1–10 Å2. This demonstrates that the exceptionally small steric factors or transmission coefficients previously inferred from analysis of chain reaction mechanisms are low by several orders of magnitude. The reactively scattered deuterium halides recoil predominantly into the backward hemisphere with respect to the incident D atoms. In each case, the reaction exoergicity is ∼1 kcal/mole and the mean initial collision energy is 9 kcal/mole (with the D beam at 2800 °K, the hydrogen halide at 250 °K). The most probable final relative translational energy of the products is ≳4 kcal/mole for the HCl and HBr reactions and 7 kcal/mole for the HI reaction. The magnitude of the reaction cross sections and the predominant backward recoil and translational energy of the products are consistent with recent classical trajectory calculations based on semiempirical potential surfaces.

Three-dimensional quantum mechanical studies of D+H2 → HD+H reactive scattering

A three-dimensional quantum mechanical study is made on the reactive scattering of D+H2 → DH+H. The differential and total cross sections as well as the S-matrix elements are obtained from the adiabatic distorted wave model. With the initial molecule H2 in the ground rotational state, we calculated the cross sections for reactions to all possible rotational states of the product molecule DH. The potential used is that of the Porter and Karplus semiempirical surface. The reactive scattering is predominantly backward. However, the peak in the differential cross sections gradually shifts away from ϑ=π as the energy is increased, with higher rotational states shifting more. In the thermal energy region, there is virtually no scattering in forward directions. The reaction is endothermic but only slightly so. Although the 0→0 rotational transition contributes only a small fraction to the total reactive cross section, most product molecules prefer rotational states that are considerably lower than the highest one allowed by energy conservation. Differential cross sections summed over all possible final rotational states are significantly different from that of any one state. Previous three-dimensional quantum mechanical studies on this system are all limited to one final rotational state; these previous results are compared with the result of the corresponding case in the present study. The present results are also compared with the corresponding classical trajectory calculations on the same potential surface. Finally, the experimental measurements of Geddes, Kraus, and Fite are compared with the present results. Qualitatively, there are general agreements. but quantitatively the calculated cross sections are definitely too large as compared with the experimental ones. The most likely cause for this difference is that the potential surface used is ’’too reactive.’’

Exact quantum transition probabilities by the state path sum method: Collinear F + H2reaction

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.

The collinear Cl + XY system (X,Y=H,D,T). A comparison between quantum mechanical, classical, and transition state theory results

In this work, exact quantum mechanical (QM) and classical (CL) transition probabilities for the Cl+XY (X,Y=H,D,T) collinear system are compared. The calculations were performed using a semiempirical LEPS surface. The main features discussed are tunneling and threshold behavior for both the ground state and the first excited state of the hydrogen molecule. In the second part, kinetic isotope effects are presented and discussed. Those were calculated in three different ways, using (i) QM transition probabilities, (ii) CL transition probabilities, and (iii) transition state theory (TST-1D). Tunneling coefficients kQM/kCL and kQM/kTST were calculated and discussed. Finally, a brief comparison with experimental data was performed.

Distribution of reaction products (theory). Investigation of an ab initio energy-surface for F + H 2 ⇀ HF + H

Bender, O'Neil, Pearson and Schaefer (BOPS) have computed ab initio energies for 232 collinear configurations of FHH, using extensive configuration interaction. We have fitted these points using an LEPS-type function. Comparison with semi-empirical surfaces for FHH shows that the general form of these surfaces is in good accord with the ab initio findings. Evidence is presented which indicates that the BOPS ab initio surface exhibits too great a drop in energy along the favoured route into the exit valley.

Collinear quantum mechanical calculations of the He + H +2 proton transfer reactions

Exact quantum mechanical results for collinear He + H + 2 → H + HeH + reactive collisions are presented for the (total) energy range of 0.93 cV to 1.4 eV. The H + 2 initial vibrational states include ν = 0 through ν = 5. The diatomics-in-molecules semi-empirical surface of Kuntz is used in the computations. Except for a short range of energies, the calculated reaction probabilities of H + 2 (ν = 0) are larger than those of excited H + 2.

Classical trajectory study of the K + CH3I reaction

Classical trajectory calculations have been carried out in an attempt to simulate the reactive scattering of K by RI (R≡CH3). Several semiempirical three-body potential surfaces have been explored. An electron-jump surface of the covalent-ionic type, with considerable ``repulsive energy release,'' accounts for most of the gross features of the scattering behavior. In particular, it has provided an understanding of the maximum in the reactive cross section σR (E) for the exchange reaction, which can be attributed to recrossing from the ionic to the covalent region of the potential. The present calculations also predict the onset (above 2.5 eV) of collision-induced dissociation (CID), and show the conservation of total reaction cross section as CID takes over from the exchange reaction.

Thermal dissociation and recombination of hydrogen according to the reactions H2+H⇄ H+H+H

Three-body recombination and dissociation rate coefficients (kr and kd, respectively) for the reactions H2+H⇄ H+H+H have been evaluated for temperatures ranging between 300 and 10 000°K on the basis of the modified phase-space theory of reaction rates and Monte Carlo trajectory calculations. The semiempirical Porter-Karplus surface for H3 was used in the calculations. Good agreement was obtained between the theoretical estimates of kd and the bulk of the dissociation rate measurements. However, in contradistinction to some of the recent experimental investigations, neither the extremely steep temperature decay ([inverted lazy s] T−6) of kr at high temperatures nor the existence of a pronounced maximum in kr at moderate temperatures are supported by this theoretical work. Possible reasons for these differences are suggested. A simple ratio was deduced which relates kr(H) and the corresponding rate coefficients of the isotopes of hydrogen. The result is in good agreement with available experimental measurements and enables one to predict the latter rate coefficients without additional trajectory calculations. An example is given to illustrate the capability of the present Monte Carlo method in obtaining other useful information about atomic and molecular collision processes.

Classical dynamical investigations of reaction mechanism in three-body hydrogen-halogen systems

A theoretical investigation of the reaction mechanisms in eight different three-body hydrogen-halogen reactions has been accomplished by means of Monte Carlo averages over classical trajectories computed on reasonable semiempirical potential-energy surfaces. Two of the surfaces employed contain a single adjustable parameter characteristic of a halogen core charge while six others result from unadjusted computations. The analysis shows that dynamic effects resulting from momentum transfer require the reactions M2+X=MX+M (M=H,D, or T; X=Br or I) to proceed through excited vibrational states of M2. Reaction of the ground vibrational state is dynamically forbidden in each case. Reaction rate coefficients, associated activation energies, pre-exponential factors, and kinetic isotope effects calculated from rotationally averaged reaction cross sections are in reasonable agreement with experiment. The computations further suggest an origin for the isotope effect that is significantly different from that derived from statistical mechanical theory. A comparison of the relative magnitudes of the experimental activation energy and vibrational level spacing can be used to qualitatively predict the importance of dynamic effects in homogeneous gas-phase reactions of diatomic species.

Ab initio potential energy surface for linear H3

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 CI result with a severely truncated CI expansion. It attempts to establish, computationally, convergence patterns that can be reliably extrapolated to the complete CI limit. Thus, the calculations reported here also serve the purpose of evaluating a computational method applicable to more complicated systems.

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

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 the earlier suggestion that many nonreactive decompositions result from linear complexes formed with the wrong orientation. Comparison with other trajectory calculations reemphasize the importance of the height and shape of the entrance and exit-channel barriers in determining both complex formation and reaction dynamics.

Monte Carlo Classical Trajectory Calculation of the Rates of H- and D-Atom Vibrational Relaxation of HF and DF

Monte Carlo classical trajectory methods have been used to investigate H- and D-atom vibrational relaxation of HF and DF. A semi-empirical valence-bond interaction surface was employed for the calculation of three-dimensional collision trajectories. Both vibration-rotation and vibration-translation are found to contribute to the vibration de-excitation. Multiple-quantum jumps contribute to the relaxation for initial excitation levels greater than v=1.

Monte Carlo Classical Trajectory Calculation of the Rates of F-Atom Vibrational Relaxation of HF and DF

Rates of F-atom vibrational relaxation of HF and DF have been calculated for the temperature range 600–2000°K using Monte Carlo classical trajectory methods. The processes F+(D)HF(v)→ F+(D)HF(v−1), where v=1, 3, and 5 and F+HF(0)→ F+HF(1) were investigated. Agreement with available experimental data is excellent. The calculations show that vibrational de-excitation is due to vibration-rotation transfer and that excitation is due to translation-vibration transfer. Multiple-quantum transfers are found to occur in de-excitation of higher vibrational levels. A semiempirical valence-bond potential-energy surface was used. No adjustments were made to the surface to cause agreement between calculated and experimental energy-transfer results.

Hot Atom Reactions in the HBr–Br2, DBr–Br2 Systems

Reactions of photochemically generated hot hydrogen atoms have been studied in HBr–Br2 systems at 185 and 229 nm and in DBr–Br2 systems at 185 nm. Kinetic analysis furnishes k3/k2—the rate coefficient ratio for the reactions H*+Br2← lim 3HBr+Brand H*+HBr← lim 2H2+Br.At 185 nm for HBr, k3/k2=4.11± 0.16, while at 229 nm k3/k2=5.48± 0.22. For DBr at 185 nm the ratio is 5.07± 0.12. Complementary trajectory calculations have been performed on a semiempirical potential-energy surface. The results of these calculations suggest that the observed variations in k3/k2 arise primarily because the reaction cross section for Process (3) varies strongly with energy in the hot atom regime and is different for the HBr and DBr systems.

Theoretical Studies of H + H2 Rotationally Inelastic Scattering

Rotationally inelastic H,H2 scattering, without rearrangement, was studied quantum mechanically in three dimensions. A close-coupling technique was employed with a basis set consisting of unperturbed molecular functions. The resulting coupled differential equations were solved numerically by a technique recently developed by Gordon. The Porter-Karplus semi-empirical potential surface was used to represent the H3 system. Cross sections were calculated for relative kinetic energies of 0.05 to 0.50 eV. Various approximations were investigated and their effect on the inelastic cross sections were computed; they include variation of the number of terms in the expansion of the exact wavefunction, exclusion of high-order asymmetry contributions to the potential surface, treating the H2 target as a rigid rotor fixed at some specified internuclear distance, and modifying the long-range behavior of the Porter-Karplus surface. Differential cross sections in the helicity representation were also computed for various energies.

Parameterization in the H2I2 potential surface

Five types of parameters were found effective in producing a reasonable semi-empirical four-electron valence-bond potential-energy surface for the H2I2 system. They were (a) the Slater exponents, (b) hybridization of the I orbital, (c) a space scale factor, (d) the I-core penetration energy, and to a more limited extent (e) the ionization potentials. Insignificant or non-physical changes in the surface resulted from alterations in (a) the integral approximations, (b) values of the electron affinities, and (c) orientation dependence of the p orbitals.

Semiempirical Energy Surface for H3

A semiempirical potential-energy surface has been generated from the London equation by evaluating the Coulomb and exchange integrals using a method which takes into account the effective orbital overlap as a function of internuclear distance. A single adjustable parameter is used to fit the calculated activation energy to the observed value. The surface is symmetrical and very flat over the saddle-point region, which leads to much lower values for the probability of H-atom tunneling through the barrier.

Symmetric H3: A Semiempirical and Ab Initio Study of a Simple Jahn–Teller System

Semiempirical and multiconfiguration ab initio results for the potential energy of H3 are used to obtain a detailed description of the potential-energy surface in the region of interest for the Jahn–Teller problem. Topographical properties of truncated perturbation expansions of the potential-energy function about the D3h minimum are compared with those of the complete semiempirical contour map; six symmetric dissociation “troughs” are found in the complete semiempirical surface, in contrast to three stable basins in the second-order surface and three dissociative troughs in the third-order surface. The relationships among the various parts of the complete three-dimensional H3 potential-energy hypersurface are discussed and illustrated by means of a single compact diagram. A convenient matrix-projection method for identifying normal-mode coordinate and electronic wavefunction partners associated with degenerate representations is discussed in an appendix.