Algorithms for sampling a quantum microcanonical ensemble of harmonic oscillators at potential minima and conical intersections

Algorithms are presented for sampling quantum microcanonical ensembles for a potential energy minimum and for the conical intersection at the minimum energy crossing point of two coupled electronic states. These ensembles may be used to initialize trajectories for chemical dynamics simulations. The unimolecular dynamics of a microcanonical ensemble about a potential energy minimum may be compared with the dynamics predicted by quantum Rice-Ramsperger-Kassel-Marcus (RRKM) theory. If the dynamics is non-RRKM, it will be of particular interest to determine which states have particularly long lifetimes. Initializing a microcanonical ensemble for the electronically excited state at a conical intersection is a model for electronic nonadiabatic dynamics. The trajectory surface-hopping approach may be used to study the ensuing chemical dynamics. A strength of the model is that zero-point energy conditions are included for the initial nonadiabatic dynamics at the conical intersection.     

Post-transition state dynamics for propene ozonolysis: Intramolecular and unimolecular dynamics of molozonide

A direct chemical dynamics simulation, at the B3LYP6-31G(d) level of theory, was used to study the post-transition state intramolecular and unimolecular dynamics for the O3 + propene reaction. Comparisons of B3LYP6-31G(d) with CCSD(T)/cc-pVTZ and other levels of theory show that the former gives accurate structures and energies for the reaction's stationary points. The direct dynamics simulations are initiated at the anti and syn O3 + propene transition states (TSs) and the TS symmetries are preserved in forming the molozonide intermediates. Anti<-->syn molozonide isomerization has a very low barrier of 2-3 kcalmol and its Rice-Ramsperger-Kassel-Marcus (RRKM) lifetime is 0.3 ps. However, the trajectory isomerization is slower and it is unclear whether this anti<-->syn equilibration is complete when the trajectories are terminated at 1.6 ps. The syn (anti) molozonides dissociate to CH3CHO + H2COO and H2CO + syn (anti) CH3CHOO. The kinetics for the latter reactions are in overall good agreement with RRKM theory, but there is a symmetry preserving non-RRKM dynamical constraint for the former. Dissociation of anti molozonide to CH3CHO + H2COO is enhanced and suppressed, respectively, for the trajectory ensembles initiated at the anti and syn O3 + propene TSs. The dissociation of syn molozonide to CH3CHO + H2COO may also be enhanced for trajectories initiated at the syn O3 + propene TS. At the time the trajectories are terminated at 1.6 ps, the ratio of the trajectory and RRKM values of the CH3CHO + H2COO product yield is 1.6 if the symmetries of the initiation and dissociation TSs are the same and 0.6 if their symmetries are different. There are coherences in the intramolecular energy flow, which depend on molozonide's symmetry (i.e., anti or syn). This symmetry related dynamics is not completely understood, but it is clearly related to the non-RRKM dynamics for anti<-->syn isomerization and anti molozonide dissociation to CH3CHO + H2COO. Correlations are found between the stretching motions of molozonide, indicative of nonchaotic and non-RRKM dynamics. The non-RRKM dynamics of molozonide dissociation partitions vibration energy to H2COO that is larger than statistical partitioning. Though the direct dynamics simulations are classical, better agreement is obtained using quantum instead of classical harmonic RRKM theory. This may result from the neglect of anharmonicity in the RRKM calculations, the non-RRKM dynamics of the classical trajectories, or a combination of these two effects. The trajectories suggest that the equilibrium syn/anti molozonide ratio is approximately 1.1-1.2 times larger than that predicted by the harmonic densities of state, indicating an anharmonic correction.     

Anharmonic Effect of the Unimolecular Dissociation of HFCO and DFCO

The unimolecular reactions of HFCO and DFCO have been studied by RRKM theory. The harmonic and anharmonic rate constants of the HFCO and DFCO decompositions have been calculated. The harmonic and anharmonic rate constants increase with the increasing temperatures and total energies both in the canonical and microcanonical systems. The comparison shows that the rate constants of DFCO decomposition are lower than that of the HFCO decomposition. The anharmonic effect and isotope effect have also been investigated. It has been found that the anharmonic effect and isotope effect are not significant either in the canonical or microcanonical system for all the reactions.     

Non-RRKM dynamics in the CH3O2 + NO reaction system

Quasi-classical trajectory (QCT) calculations on a model potential energy surface (PES) show strong deviations from statistical Rice-Ramsperger-Kassel-Marcus (RRKM) rate theory for the decomposition reaction (1) CH3OONO* --> CH3O + NO2, where the highly excited CH3OONO* was formed by (2) CH3O2 + NO --> CH3OONO*. The model PES accurately describes the vibrational frequencies, structures, and thermochemistry of the cis- and trans-CH3OONO isomers; it includes cis-trans isomerization in addition to reactions 1 and 2 but does not include nitrate formation, which is too slow to affect the decay rate of CH3OONO*. The QCT results give a strongly time-dependent rate constant for decomposition and damped oscillations in the decomposition rate, not predicted by statistical rate theory. Anharmonicity is shown to play an important role in reducing the rate constant by a factor of 10 smaller than predicted using classical harmonic RRKM theory (microcanonical variational transition state theory). Master equation simulations of organic nitrate yields published previously by two groups assumed that RRKM theory is accurate for reactions 1 and 2 but required surprising parametrizations to fit experimental nitrate yield data. In the present work, it is hypothesized that the non-RRKM rate of reaction (1) and vibrational anharmonicity are at least partly responsible for the surprising parameters.     

Thermal decomposition of 1,5-dinitrobiuret (DNB): direct dynamics trajectory simulations and statistical modeling

A large set of quasi-classical, direct dynamics trajectory simulations were performed for decomposition of 1,5-dinitrobiuret (DNB) over a temperature range from 4000 to 6000 K, aimed at providing insight into DNB decomposition mechanisms. The trajectories revealed various decomposition paths and reproduced the products (including HNCO, N(2)O, NO(2), NO, and water) observed in DNB pyrolysis experiments. Using trajectory results as a guide, structures of intermediate complexes and transition states that might be important for decomposition were determined using density functional theory calculations. Rice-Ramsperger-Kassel-Marcus (RRKM) theory was then utilized to examine behaviors of the energized reactant and intermediates and to determine unimolecular rates for crossing various transition states. According to RRKM predictions, the dominant initial decomposition path of energized DNB corresponds to elimination of HNNO(2)H via a concerted mechanism where the molecular decomposition is accompanied with intramolecular H-atom transfer from the central nitrogen to the terminal nitro oxygen. Other important paths correspond to elimination of NO(2) and H(2)NNO(2). NO(2) elimination is a simple N-N bond scission process. Formation and elimination of nitramide is, however, dynamically complicated, requiring twisting a -NHNO(2) group out of the molecular plane, followed by an intramolecular reaction to form nitramide before its elimination. These two paths become significant at temperatures above 1500 K, accounting for >17% of DNB decomposition at 2000 K. This work demonstrates that quasi-classical trajectory simulations, in conjunction with electronic structure and RRKM calculations, are able to extract mechanisms, kinetics, dynamics and product branching ratios for the decomposition of complex energetic molecules and to predict how they vary with decomposition temperature.     

Anharmonic Effect of the Unimolecular Isomerization/Decomposition of Benzyne

The anharmonic and harmonic rate constants were calculated for the unimolecular decomposition of o‐benzyne, the isomerization of o‐benzyne to m‐benzyne, the isomerization of m‐benzyne to p‐benzyne and unimolecular decomposition of p‐benzyne by using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory respectively, in the canonical and microcanonical systems. The geometry and the vibrational frequencies were calculated by MP2 and B3LYP methods with 6‐311G(d,p) basis set and the barrier energies were corrected using CBS‐QB3 theory. The anharmonic effect on the reactions was also examined. Comparison of results for the decompositions of benzyne indicate that both in microcanonical and canonical cases, the anharmonic effect on the decomposition of the o‐C₆H₄ and p‐C₆H₄ are significant, while the anharmonic effect on the two isomerizations are not pronounced.     

Dynamics of ethyl radical decomposition. II. Applicability of classical mechanics to large-molecule unimolecular reaction dynamics

The classical trajectory method is used to investigate the unimolecular dynamics of ethyl radical dissociation. It is found that chaotic trajectories need not be backward integrable to yield accurate lifetime, and product energy and angular momenta distributions. This allows the use of large numerical integration step sizes in trajectory calculations. The product energy and angular momenta distributions are independent of the ethyl radical lifetime, and are obtained after only 50 dissociation events. Differences between classical and quantal unimolecular dynamics are discussed, and a prognosis for future trajectory studies of large-molecule unimolecular decompositions is given.     

On the statistical nature of collision and surface-induced dissociation: a theoretical investigation of aluminum clusters

The unimolecular dissociation dynamics of aluminum clusters following collision with either a rare gas atom or a surface is investigated by classical trajectory simulations with model potentials. Two conformers of Al(6) with very distinct shapes, i.e., the spherical O(h) and planar C(2)(h) clusters, are considered in this work. The initial vibrational energy and angular momentum distributions resulting from collision, as well as the energy and angular momentum resolved lifetime distributions, of excited clusters were determined for both collision-induced dissociation (CID) and surface-induced dissociation (SID) processes. The partitioning of excitation energy acquired upon collision was found to depend on the excitation mechanism (CID or SID), as well as on the cluster molecular shape, especially in the case of CID. For both types of processes, the energy and angular momentum resolved excited cluster lifetime distributions were found to decay exponentially, in agreement with statistical theories of chemical reactions, suggesting intrinsic Rice-Ramsperger-Kassel-Marcus (RRKM) behavior. Moreover, the simulated microcanonical rate constants determined from the cluster lifetime distributions are in good agreement with the predictions of the orbiting transition state model of phase space theory (OTS/PST), which further supports the statistical character of cluster CID and SID. Thus, in the CID and SID of highly fluxional systems such as aluminum clusters, the rate of intramolecular vibrational energy redistribution (IVR) is much faster than the dissociation rate, which validates one of the key assumptions, i.e., post-collision statistical behavior, underlying the models that are routinely used to determine cluster binding energies from experimental CID/SID cross sections.     

Implementation of a microcanonical variational transition state theory for direct dynamics calculations of rate constants

Calculation of microcanonical rate constants has been an important field in chemical dy-namic studies for many years because it can be used not only to give good prediction of rate con-stants in microcanonical assembly, but also to calculate rate constants with certain conserved quantum numbers such as the total angular momentum, and in turn, can be easily converted into thermal rate constants[1—3]. The widely used method for calculating microcanonical rate constants of unimolecular reac-tions…     

Simulating quantum dynamics in classical environments

Methods for simulating the dynamics of composite systems, where part of the system is treated quantum mechanically and its environment is treated classically, are discussed. Such quantum–classical systems arise in many physical contexts where certain degrees of freedom have an essential quantum character while the other degrees of freedom to which they are coupled may be treated classically to a good approximation. The dynamics of these composite systems are governed by a quantum–classical Liouville equation for either the density matrix or the dynamical variables which are operators in the Hilbert space of the quantum subsystem and functions of the classical phase space variables of the classical environment. Solutions of the evolution equations may be formulated in terms of surface-hopping dynamics involving ensembles of trajectory segments interspersed with quantum transitions. The surface-hopping schemes incorporate quantum coherence and account for energy exchanges between the quantum and classical degrees of freedom. Various simulation algorithms are discussed and illustrated with calculations on simple spin-boson models but the methods described here are applicable to realistic many-body environments.     

甲基肼自由基在高温燃烧分解反应下的非谐振效应

In this work, the harmonic and anharmonic rate constants of the decomposition reaction of monomethylhydrazine (MMH) radicals have been calculated by using transition state (TS) and Rice-Ramsperger-Kassel-Marcus (RRKM) theories with either MP2 or B3LYP method at 6-311++G (3df, 2p) basis set, respectively. The reaction mechanism and anharmonic effect of the MMH radicals are studied in detail and both of the harmonic and anharmonic rate constants increase sharply with increasing temperature in the canonical system. In the microcanonical system, these constants also show sharp increase with the energies. Overall, the anharmonic effect becomes more pronounced with the increasing temperature or energy in the canonical and microcanonical systems, respectively. These results indicate that the anharmonic effect of the decomposition reaction of MMH radicals is quite significant and cannot be ignored.     

Chemical dynamics simulations of X- + CH3Y → XCH3 + Y- gas-phase S(N)2 nucleophilic substitution reactions. Nonstatistical dynamics and nontraditional reaction mechanisms

Extensive classical chemical dynamics simulations of gas-phase X(-) + CH(3)Y → XCH(3) + Y(-) S(N)2 nucleophilic substitution reactions are reviewed and discussed and compared with experimental measurements and predictions of theoretical models. The primary emphasis is on reactions for which X and Y are halogen atoms. Both reactions with the traditional potential energy surface (PES), which include pre- and postreaction potential energy minima and a central barrier, and reactions with nontraditional PESs are considered. These S(N)2 reactions exhibit important nonstatistical atomic-level dynamics. The X(-) + CH(3)Y → X(-)---CH(3)Y association rate constant is less than the capture model as a result of inefficient energy transfer from X(-)+ CH(3)Y relative translation to CH(3)Y rotation and vibration. There is weak coupling between the low-frequency intermolecular modes of the X(-)---CH(3)Y complex and higher frequency CH(3)Y intramolecular modes, resulting in non-RRKM kinetics for X(-)---CH(3)Y unimolecular decomposition. Recrossings of the [X--CH(3)--Y](-) central barrier is important. As a result of the above dynamics, the relative translational energy and temperature dependencies of the S(N)2 rate constants are not accurately given by statistical theory. The nonstatistical dynamics results in nonstatistical partitioning of the available energy to XCH(3) +Y(-) reaction products. Besides the indirect, complex forming atomic-level mechanism for the S(N)2 reaction, direct mechanisms promoted by X(-) + CH(3)Y relative translational or CH(3)Y vibrational excitation are possible, e.g., the roundabout mechanism.     

丁酸甲酯单分子解离的非谐振效应

使用MP2/6-311++G（2d,2p）方法和基组,计算了丁酸甲酯单分子解离反应体系详细的势能面。应用RRKM理论,计算了在1000-5000 K的温度范围内的正则系综的速率常数。与此同时,在微正则系综下,我们计算了温度为1000-5000 K对应的能量从451.92到1519.52 kJ·mol^-1的速率常数。计算结果表明反应通道2、4和5的非谐振效应比较明显。因此对于丁酸甲酯单分子解离反应体系来说其非谐振效应是不能忽视的。     

Independent trajectory implementation of the semiclassical Liouville method: application to multidimensional reaction dynamics

We describe an independent trajectory implementation of semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, a single ensemble of trajectories describes all semiclassical density matrix elements of a coupled electronic state problem, with the ensemble evolving classically under a single reference Hamiltonian chosen on the basis of physical grounds. In this paper, we introduce an additional uncoupled trajectory approximation, allowing the members of the ensemble to evolve independently of one another and eliminating the major computational costs of our previous coupled trajectory implementation. The accuracy of the method is demonstrated for model one-dimensional problems. In addition, the approach is applied to the chemical reaction dynamics of a collinear triatomic system, yielding excellent agreement with exact calculations. This method allows molecular dynamics involving coupled electronic surfaces to be modeled with essentially the same effort as classical molecular dynamics and ensemble averaging.     

Vectorization of the general Monte Carlo classical trajectory program VENUS

The general chemical dynamics computer program VENUS is used to perform classical trajectory simulations for large polyatomic systems, with many atoms and complicated potential energy functions. To simulate an ensemble of many trajectories requires a large amount of CPU time. Since each trajectory is independent, it is possible to parallel process a large set of trajectories instead of processing the trajectories by the conventional sequential approach. This enhances the vectorizability of the VENUS program, since the integration of Hamilton's equations of motion and the gradient evaluation, which comprise 97.8% of the CPU, can each be parallel processed. In this article, the vectorization and ensuing optimization of VENUS on the CRAY-YMP and IBM-3090 are presented in terms of both global strategies and technical details. A switching algorithm is designed to enhance the vector performance and to minimize the memory storage. A performance of 140 MFLOPS and a vector/scalar execution rate ratio of 10.6 are observed when this new version of VENUS is used to study the association of CH₃ with the H(Ar)₁₂ cluster on the CRAY-YMP.     

Thermal decomposition of ethylene oxide: potential energy surface, master equation analysis, and detailed kinetic modeling

The unimolecular decomposition of ethylene oxide (oxirane) and the oxiranyl radial is examined by molecular orbital calculations, Rice-Ramsperger-Kassel-Marcus (RRKM)/Master Equation analysis, and detailed kinetic modeling of ethylene oxide pyrolysis in a single-pulse shock tube. It was found that the largest energy barrier to the decomposition of ethylene oxide lies in its initial isomerization to form acetaldehyde, and in agreement with previous studies, the isomerization was found to proceed through the *CH2CH2O* biradical. Because of the biradical nature of the transition states and intermediate, the energy barriers for the initial C-O rupture in ethylene oxide and the subsequent 1,2-H shift remain highly uncertain. An overall isomerization energy barrier of 59 +/- 2 kcal/mol was found to satisfactorily explain the available single pulse shock tube data. This barrier height is in line with the estimates made from an approximate spin-corrected procedure at the MP4/6-31+G(d) and QCISD(T)/6-31G(d) levels of theory. The dominant channel for the unimolecular decomposition of ethylene oxide was found to form CH3 + HCO at around the ambient pressure. It accounts for >90% of the total rate constant for T > 800 K. The high-pressure limit rate constant for the unimolecular decomposition of ethylene oxide was calculated as k(1,infinity)(s(-1)) = (3.74 x 10(10))T(1.298)e(-29990/T) for 600 < T < 2000 K.     

Trajectory studies of S(N)2 nucleophilic substitution. 8. Central barrier dynamics for gas phase Cl(-) + CH(3)Cl

Quasiclassical direct dynamics trajectories, calculated at the MP2/6-31G level of theory, are used to study the central barrier dynamics for the C1(-) + CH(3)Cl S(N)2 reaction. Extensive recrossings of the central barrier are observed in the trajectories. The dynamics of the Cl(-)-CH(3)Cl complex is non-RRKM and transition state theory (TST) is predicted to be an inaccurate model for calculating the Cl(-) + CH(3)Cl S(N)2 rate constant. Direct dynamics trajectories also show that Cl(-) + CH(3)Cl trajectories, which collide backside along the S(N)2 reaction path, do not form the Cl(-)-CH(3)Cl complex. This arises from weak coupling between the Cl(-)-CH(3)Cl intermolecular and CH(3)Cl intramolecular modes. The trajectory results are very similar to those of a previous trajectory study, based on a HF/6-31G* analytic potential energy function, which gives a less accurate representation of the central barrier region of the Cl(-) + CH(3)Cl reaction than does the MP2/6-31G* level of theory used here. Experiments are suggested for investigating the non-RRKM and non-TST dynamics predicted by the trajectories.