Cumulative Reaction Probability Research Articles

Advanced software for the calculation of thermochemistry, kinetics, and dynamics

Recent results are presented for the efficient computation of matrix eigenvalue and eigenvector equations, the fitting of discrete sets of energy points using interpolating moving least squares methods, and time-dependent and time-independent calculations of molecular dynamics and cumulative reaction probabilities.

Cumulative reaction probabilities for the unimolecular dissociation and isomerization reactions of formaldehyde

The cumulative reaction probabilities are calculated for the dissociation and isomerization reactions of formaldehyde in the ground state by the use of the Watson Hamiltonian. We devise an efficient computational procedure for treating the vibrational angular momentum operator. We employ an improved global potential function at the CCSD(T) level derived from the MP2 level one. The resultant cumulative reaction probability for the dissociation channel is ∼1.5 times larger than that for the isomerization one at the energy region of interest. It is also found that the transition state theory reproduces the result with the full Watson Hamiltonian within 10% error.

Influence of van der Waals wells on the quantum scattering dynamics of the Cl(2P)+HCl→ClH+Cl(2P) reaction

We investigate the influence of van der Waals wells on the quantum scattering dynamics of the Cl + HCl → ClH + Cl reaction in which the three electronic states that correlate asymptotically to the ground state of Cl(2P) + HCl(1Σ+) are included in the dynamical calculations. The short range region of the potential energy surfaces is taken from recent restricted open-shell coupled-cluster singles doubles with perturbative triples and multireference configuration-interaction ab initio computations of Dobbyn et al. [Phys. Chem. Chem. Phys. 1 (1999) 957], as refined by Whiteley et al. [Phys. Chem. Chem. Phys. 2 (2000) 549]. The long range van der Waals region of the potential surfaces is derived from multisurface empirical potentials due to Dubernet and Hutson [J. Phys. Chem. 98 (1994) 5844]. We manipulate the van der Waals portions of the global potential surfaces by scaling the interaction of the Cl quadrupole with the HCl multipoles. This results in van der Waals wells that are either deeper or shallower than the unscaled reference case. Spin–orbit coupling is included using a spin–orbit parameter that is assumed to be independent of nuclear geometry, and Coriolis interactions are calculated accurately. Reactive scattering calculations have been performed for total angular momentum quantum number, J=1/2, using a hyperspherical-coordinate coupled-channel method in full dimensionality. We investigate how the cumulative reaction probability and the fine-structure-resolved cumulative reaction probabilities are influenced by variations in the van der Waals wells.

A reduced dimensionality quasiclassical and quantum study of the proton transfer reaction H3O(+)+H2O-->H2O+H3O(+).

We report quantum and quasiclassical calculations of proton transfer in the reaction H(3)O(+)+H(2)O in three degrees of freedom, the two OH(+) bond lengths and the OH(+)O angle. The reduced dimensional potential energy surface is obtained from the full dimensional OSS3(p) energy function of H(5)O(2) (+) [L. Ojamae, I. Shavitt, and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)], with an additional long-range correction to reproduce the correct ion-molecule interaction. This surface is used to perform both quasiclassical trajectory and quantum reactive scattering calculations of the zero total angular momentum cumulative reaction probability and cross sections for initial rotational states 0, 1, and 2. Comparison of these quantities are made to assess the importance of quantum effects in this reduced dimensional reaction. Additional quasiclassical cross sections are calculated to obtain the thermal rate constant for the reaction.

Quantum stereodynamics of the F+H2→HF+H reaction by the stereodirected S-matrix approach

Reaction stereodynamics can be studied in quantum mechanics using alternative representations of the S matrix. In this paper we employ the equations for the orthogonal transformations (expressed in terms of Wigner 3j symbols) that convert the S matrix from the body fixed (|jΩ〉) representation into the stereodirected one (|νΩ〉). This representation is characterized by the introduction of the steric quantum number ν, which in the vector model of quantum mechanics is put into correspondence with given precession cones of attack of the incoming atom on the diatomic molecule for the reactants' channels, and of cones of escape for the departing atom away from the diatomic molecule for the products' channels. The angles of aperture of such cones are determined from the uncertainty principle. As the ν quantum number increases (semiclassical limit), the grid of discrete values of the precession cones more finely scans the angle between the Jacobi vectors. Using a time-independent hyperspherical coordinate method we have generated the full S matrix including all open reactive and inelastic channels for two potential energy surfaces corresponding to the F + H2 → HF + H reaction and they have been used to calculate, via |jΩ〉→|νΩ〉 matrix transformations, the attack and exit cumulative reaction probabilities. During the calculations, we have distinguished between ortho-H2 and para-H2. Clear stereodynamical effects have being identified, in particular, regarding the reaction entrance channel, that F-atom attacks are preferred at the transition state (bent) geometry, while for the exit channel the H-atom departs in a collinear geometry by the H-end side of HF.

Cumulative reaction probability N( E) as estimated from empirical bimolecular rate constant k( T)

Approximate cumulative reaction probabilities have been calculated from two empirical rate equations: one is the 3-parameter rate equation, AT n exp(− E/ k B T), and the other is the modified Arrhenius equation, A ′ exp(−E 0/k B T 2+T 0 2 ) proposed in Chem. Phys. Lett. 160 (1989) 295, for expressing the rate constants at low temperatures. Numerical calculations were made for the D + H 2 → DH + H reaction. It is shown that this reaction occurs mainly through tunneling at 200 K, and that the 3-parameter rate equation involves the tunneling effect along with the correction at high temperatures.

Influence of Spin−Orbit Effects on Chemical Reactions: Quantum Scattering Studies for the Cl(2P) + HCl → ClH + Cl(2P) Reaction Using Coupled ab Initio Potential Energy Surfaces

We present converged quantum scattering results for the Cl + HCl → ClH + Cl reaction in which the three electronic states that correlate asymptotically to the ground state of Cl(2P) + HCl(1Σ+) are included in the dynamical calculations. The potential energy surfaces are taken from recent restricted open-shell coupled-cluster singles doubles with perturbative triples and multireference configuration interaction ab initio computations of A. J. Dobbyn, J. N. L. Connor, N. A. Besley, P. J. Knowles, and G. C. Schatz [Phys. Chem. Chem. Phys. 1999, 1, 957], as refined by T. W. J. Whiteley, A. J. Dobbyn, J. N. L. Connor, and G. C. Schatz [Phys. Chem. Chem. Phys. 2000, 2, 549]. The long-range van der Waals portions of the potential surfaces are derived from multisurface empirical potentials due to M.-L. Dubernet and J. M. Hutson [J. Phys. Chem. 1994, 98, 5844]. Spin−orbit coupling has been included using a spin−orbit parameter that is assumed to be independent of nuclear geometry, and Coriolis interactions are calculated accurately. Reactive scattering calculations have been performed for total angular momentum quantum number J = 1/2 using a hyperspherical-coordinate coupled-channel method in full dimensionality. The scattering calculations are used to study the influence of the spin−orbit coupling parameter λ on the fine-structure-resolved cumulative reaction probabilities and transition-state resonance energies with λ varying from −150% to +150% of the true Cl value. The results show the expected dominance of the 2P3/2 state to overall reactivity for λ close to the true Cl value and the dominance of the 2P1/2 state for λ close to −1 times the true Cl value. Between these two limits, the fine-structure-resolved cumulative reaction probabilities show oscillations as λ varies, statistical behavior being recovered for λ = 0. We present a two-state model that roughly matches these oscillations and which suggests that the reactivity oscillations are due to coherent mixing of the Ωj = 1/2 components of the 2Σ and 2Π states that are derived from the 2P states in the van der Waals regions of the potential surfaces. This mixing leads to inverted spin−orbit propensities (i.e., the upper spin−orbit state is more reactive than the lower one) for certain values of λ. Our analysis of resonance energies indicates significant variation in resonance stability with the value of λ, a general trend being that narrower resonances occur when |λ| is smaller than about 50% of the absolute value of the true Cl value, suggesting that narrow resonances occur when there is significant coherent mixing. In addition, we find evidence for Stueckelberg interference oscillations in the total cumulative reaction probabilities due to a conical intersection between the 1 2A‘ and 2 2A‘ potential surfaces.

Quantum mechanical investigation of the O+H2→OH+H reaction

We report quantum mechanical calculations of cross sections and rate coefficients for the O+H2→OH+H reaction using the chemically accurate potential energy surfaces of A'3 and A"3 geometry by Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)]. Calculations were performed for total angular momentum quantum number J=0 and the J-shifting approximation was applied to obtain cumulative reaction probabilities, initial state selected reaction cross sections, and thermal rate coefficients. The reliability of the J-shifting approximation was tested by performing accurate calculations for selected values of nonzero J. We obtain thermal rate coefficients in good agreement with experimental data at temperatures lower than 500 K but our calculations predict rate coefficients that are smaller than the experimental values at higher temperatures.

Narrow Subthreshold Quantum Mechanical Resonances in the Li + HF → H + LiF Reaction

State-to-state, state-specific, and cumulative reaction probabilities are presented for the bimolecular scattering process Li + HF → H + LiF in the ground electronic state. Calculations were performed for zero total angular momentum at total energies from 0.26 to 0.50 eV (relative to HF at its classical equilibrium bond distance and infinitely far from Li). The energy dependence of the state-to-state, initial-state-selected, and cumulative reaction probabilities for LiFH in the low-energy regime displays a pronounced resonance structure due to quasibound states associated with a Li...FH van der Waals well in the entrance valley of the potential energy surface. The lifetimes of the long-lived resonances are obtained by fitting the calculated eigenphase sum to the multichannel Breit-Wigner formula. The final rotational state distributions of the LiF product fragment resulting from decay of the resonance state complexes are presented for two resonances. Quantum numbers are assigned to the resonances using bound-state and quasibound-state calculations in the Li...FH van der Waals well, and possible decay mechanisms are discussed. The lifetimes show a systematic dependence on the translational vibrational quantum number.

Quantal study of the exchange reaction for N+N2 using an ab initio potential energy surface

The N+N2 exchange rate is calculated using a time-dependent quantum dynamics method on a newly determined ab initio potential energy surface (PES) for the ground A″4 state. This ab initio PES shows a double barrier feature in the interaction region with the barrier height at 47.2 kcal/mol, and a shallow well between these two barriers, with the minimum at 43.7 kcal/mol. A quantum dynamics wave packet calculation has been carried out using the fitted PES to compute the cumulative reaction probability for the exchange reaction of N+N2(J=0). The J–K shift method is then employed to obtain the rate constant for this reaction. The calculated rate constant is compared with experimental data and a recent quasiclassical calculation using a London–Eyring–Polanyi–Sato PES. Significant differences are found between the present and quasiclassical results. The present rate calculation is the first accurate three-dimensional quantal dynamics study for the N+N2 reaction system and the ab initio PES reported here is the first such surface for N3.

Quantum dynamics study of the isotopic effect on capture reactions: HD, D2+CH3

Time-dependent wave-packet-propagation calculations are reported for the isotopic reactions, HD+CH3 and D2+CH3, in six degrees of freedom and for zero total angular momentum. Initial-state-selected reaction probabilities for different initial rotational-vibrational states are presented in this study. This study shows that excitations of the HD(D2) enhances the reactivities, whereas the excitations of the CH3 umbrella mode have the opposite effects. This is consistent with the reaction of H2+CH3. The comparison of these three isotopic reactions also shows the isotopic effects in the initial-state-selected reaction probabilities. The cumulative reaction probabilities (CRPs) are obtained by summing over initial-state-selected reaction probabilities. Theenergy-shift approximation to account for the contribution of degrees of freedom missing in the six dimensionality calculation is employed to obtain approximate full dimensional CRPs. The rate constant comparison shows the H2+CH3 reaction has the biggest reactivity, then HD+CH3, and D2+CH3 has the smallest.

A time-dependent quantum dynamics study of the H2+CH3→H+CH4 reaction

We present a time-dependent wave-packet propagation calculation for the H2+CH3→H+CH4 reaction in six degrees of freedom and for zero total angular momentum. Initial state selected reaction probabilities for different initial rotational–vibrational states are presented in this study. Excitation of the H2 stretch enhances the reaction probability, whereas the excitation of the CH3 umbrella mode has the opposite effect. The cumulative reaction probability (CRP) is obtained by summing over initial-state-selected reaction probabilities. The energy-shift approximation to account for the contribution of degrees of freedom missing in the six-dimensional calculation is employed to obtain an approximate full-dimensional CRP. Thermal rate constant is compared with different experiment results.

Chebyshev real wave packet propagation: H+O2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith et al. [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrödinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrödinger equation is different from that obtained using the standard Schrödinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined.

A quantum dynamics study of H2+OH→H2O+H employing the Wu–Schatz–Lendvay–Fang–Harding potential function and a four-atom implementation of the real wave packet method

We carry out numerous six-dimensional wave packet propagations for H2+OH→H2O+H on the ab initio based, Wu–Schatz–Lendvay–Fang–Harding potential energy function. For comparison, some calculations are also carried out on the older but more widely studied potential function of Walch, Dunning, Schatz, and Elgersma. The energy dependence of the total angular momentum J=0 cumulative reaction probability is obtained and J-shifting is used to estimate the bimolecular rate constant as a function of temperature. Some J>0 calculations are also carried out. A novel J-shifting procedure, designed to more accurately describe the effects of angular momentum, is introduced. We compare our results with transition state theory calculations and experiment. An important feature of our work is the development of an efficient, four-atom, parallel implementation of the real wave packet method, augmented with a recently developed finite difference method.

REACTION RATES: ACCURATE QUANTUM DYNAMICAL CALCULATIONS FOR POLYATOMIC SYSTEMS

Rate constants of chemical reactions can be computed directly: employing flux correlation functions, no scattering calculations are required. If the reaction is direct, the dynamical simulation can be restricted to the vicinity of the reaction barrier. Therefore accurate thermal rate constants and cumulative reaction probabilities can be calculated for rather large systems. Recent calculations have studied systems with up to six atoms, e.g., H + CH 4 → H 2 + CH 3. The calculations provide a full-dimensional quantum description of the reaction process. In the article, an introduction to the theory of flux correlation functions is given. Methods for the efficient computation of accurate thermal rate constants and cumulative reaction probabilities are reviewed. Connections to transition state ideas are highlighted. The multi-configurational time-dependent Hartree (MCTDH) approach, which facilitates efficient multi-dimensional wave packet propagation, is described and its use in reaction rate calculation is discussed. As examples, recent results for the prototypical polyatomic reaction H + CH 4 → H 2 + CH 3 are presented and rotational effects on the reaction rates of H 2 + OH → H + H 2 O , O + HCl → OH + Cl , and H 2 + Cl → H + HCl are discussed.

Cumulative reaction probability by constrained dynamics: H transfer in HCN, H2CO, and H3CO

A strategy to obtain quantum corrections to the cumulative reaction probability from a subspace of active coordinates is analyzed. The kinetic energy operator exactly takes into account the constraints due to inactive coordinates. The geometry of the inactive skeleton is adiabatically adjusted to the dynamical variables or simply frozen according to the coupling to the active space. Dynamics is carried out using the curvilinear coordinates of the Z-matrix so that computation of the potential energy surface and dynamics are coupled. The cumulative reaction probability N(E) is obtained directly in a large range of energy by a time independent formulation of the Zhang and Light transition state wave packet method. NnD(E) is first computed in the active n-dimensional space and then convoluted with a bath. The efficiency of the Chebyshev expansion of the microcanonical projection operator δ(E−ĤnD) appearing in the quantum expression of NnD(E) is checked. The method is implemented for the study of tunneling effect in H transfer. The coordinates are three spherical coordinates referred to the frozen or adiabatic skeleton. We compare the quantum corrections brought about by different 2D groups of internal coordinates.

Lanczos Subspace Time-Independent Wave Packet Calculations of S (1D) + H2 Reactive Scattering

In this paper. we present the results of quantum dynamical simulations of the S (D-1) + H-2 insertion reaction on a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). State-to-state reaction probabilities. product state distributions, and initial-state resolved cumulative reaction probabilities from a given incoming reactant channel are obtained from a time-independent wave packet analysis, performed within a single Lanczos subspace. Integral reaction cross sections are then estimated by J-shifting method and compared with the results from molecular beam experiment and QCT calculations.

Resonances in the O(3P)+HCl reaction due to van der Waals minima

We present extensive exact quantum calculations of the cumulative reaction probability (CRP) for the O(3P)+HCl→OH+Cl reaction for a large range of total angular momentum, using the most recent ab initio potential energy surface of Ramachandran et al. This surface contains van der Waals minima in both the entrance and exit channels that are shown to be responsible for a number of prominent resonances in the CRP in the tunneling region. The evidence for this claim is based on an analysis of the quasibound states of the van der Waals minima and a simple overlap of these states with the region of the saddle point of the reaction. The shift of the CRP with total angular momentum is analyzed in detail, with a focus on the resonances. A rigorous test of the simple J–K shifting approximation is also made both for the total CRP and the thermal rate constant.

A quantum reactive scattering study of the spin-forbidden CH(X 2Π)+N2(X 1Σg+)→HCN(X 1Σ+)+N(4S) reaction

The dynamics of the spin-forbidden CH(X 2Π)+N2(X 1Σg+)→HCN(X 1Σ+)+N(4S) reaction has been studied theoretically using the reduced dimensionality quantum scattering method. Three degrees of freedom have been considered in the dynamics calculations by treating CH as a united atom. The problem is thus reduced to the usual atom–diatom scattering calculation. Three-dimensional potential energy surfaces for both the doublet and quartet states were constructed using ab initio electronic structure calculations while the spin–orbit coupling element was taken from previous work. Time-independent quantum reactive scattering calculations have been performed using the hyperspherical close-coupling method. The calculated cumulative reaction probabilities show that the reaction dynamics is exclusively resonance-dominated. The thermal rate constants calculated using the reduced dimensionality cumulative reaction probabilities with the energy shifting and J-shifting approximations were found to be much smaller than experimental measurements and previous reduced-dimensionality results of Seideman [J. Chem. Phys. 101, 3662 (1994)] by a factor of more than two orders of magnitude. In order to understand this serious disagreement, we have carried out the scattering calculations with the use of modified potential energy surfaces and spin–orbit couplings but found that the calculated rate constants were still much smaller than experimental data. The present computational study strongly suggests that further experimental studies including direct detection of N(4S) and/or any other mechanism for the “prompt-NO” formation will be necessary.

Direct calculation of cumulative reaction probabilities from Chebyshev correlation functions

The transition-state wave packet method of Zhang and Light [J. Chem. Phys. 104, 6184 (1996)] for the direct calculation of cumulative reaction probabilities is implemented in the Chebyshev order domain to take advantage of exactness and efficiency of the Chebyshev propagator. Numerical testing for three-dimensional H+H2 reactive scattering (J=0) confirms the accuracy and efficiency of the proposed algorithm. This new implementation is then used to compute the cumulative reaction probability of the Li+HF→LiF+H reaction (J=0) up to 0.65 eV. It is found that the latter reaction is dominated in low energy region by numerous narrow resonances.