Jorge M. C. Marques

Method for quasiclassical trajectory calculations on potential energy surfaces defined from gradients and Hessians, and model to constrain the energy in vibrational modes

A method for calculating quasiclassical trajectories on potential energy surfaces defined using a sequence of model quadratic surfaces (QCT/GH) is suggested, and tested for atom–diatom collisions against the traditional quasiclassical trajectory approach. A simple model is also suggested to constrain the classical energy of a bound vibrational mode to be greater than a specified amount, namely, its zero‐point energy value. Essentially the model consists of assuming that the sum of the energies in the nonrelevant vibrational modes (typically unbound modes) of the supermolecular complex acts as a pool from which energy may be taken to compensate any leak of vibrational energy in the relevant bound modes, hence preventing the latter from falling below zero‐point value. Extensive QCT/GH trajectory calculations carried out for the H+H2 exchange reaction, which occurs over an energy barrier, as well as exploratory trajectories for the reaction O+OH→O2+H, which occurs on a potential energy surface with a deep chemical well, have shown that the total energy and total angular momentum are conserved within a small numerical tolerance. Correcting for the leak of zero‐point vibrational energy still leaves the total energy rigorously conserved but the total angular momentum is then only approximately kept constant. For H+H2(v=0, j=0)→H2(v’, j’)+H, the calculated state‐to‐state QCT/GH cross sections show reasonably good agreement with those of converged quantum results reported in the literature for the same H3 potential energy surface. This agreement does not deteriorate after correction of zero‐point energy leak. For both H3 and HO2, accurate global analytical potential energy surfaces based on the double many‐body expansion method have been utilized. Using these prototype systems, an assessment is made of the difficulties encountered on direct reaction dynamics using the novel QCT/GH method.A method for calculating quasiclassical trajectories on potential energy surfaces defined using a sequence of model quadratic surfaces (QCT/GH) is suggested, and tested for atom–diatom collisions against the traditional quasiclassical trajectory approach. A simple model is also suggested to constrain the classical energy of a bound vibrational mode to be greater than a specified amount, namely, its zero‐point energy value. Essentially the model consists of assuming that the sum of the energies in the nonrelevant vibrational modes (typically unbound modes) of the supermolecular complex acts as a pool from which energy may be taken to compensate any leak of vibrational energy in the relevant bound modes, hence preventing the latter from falling below zero‐point value. Extensive QCT/GH trajectory calculations carried out for the H+H2 exchange reaction, which occurs over an energy barrier, as well as exploratory trajectories for the reaction O+OH→O2+H, which occurs on a potential energy surface with a deep ch...

An Evolutionary Algorithm for the Global Optimization of Molecular Clusters: Application to Water, Benzene, and Benzene Cation

We have developed an evolutionary algorithm (EA) for the global minimum search of molecular clusters. The EA is able to discover all the putative global minima of water clusters up to (H(2)O)(20) and benzene clusters up to (C(6)H(6))(30). Then, the EA was applied to search for the global minima structures of (C(6)H(6))(n)(+) with n = 2-20, some of which were theoretically studied for the first time. Our results for n = 2-6 are consistent with previous theoretical work that uses a similar interaction potential. Excluding the very symmetric global minimum structure for n = 9, the growth pattern of (C(6)H(6))(n)(+) with n ≥ 7 involves the (C(6)H(6))(2)(+) dimer motif, which is placed off-center in the cluster. Such observation indicates that potentials commonly used in the literature for (C(6)H(6))(n)(+) cannot reproduce the icosahedral-type packing suggested by the available experimental data.

A detailed state‐to‐state low‐energy dynamics study of the reaction O(3P)+OH(2Π)→O2(X̃ 3Σg−)+H(2S) using a quasiclassical trajectory–internal‐energy quantum‐mechanical‐threshold method

The quasiclassical trajectory (QCT) method has been used for a detailed study of the state‐to‐state dynamics of the reaction O(3P) + OH(2Π)→O2(X33Σ−g) + H(2S) over the range of translational energies 0.125 ≤ Etr/kcal mol−1≤2.0, corresponding to the temperature range 40≤T/K≤680. A novel variant of this method insuring that trajectory calculations properly account for the zero‐point energy of the diatomic molecules, the so‐called quasiclassical trajectory–internal‐energy quantum‐mechanical‐threshold method, is also suggested and applied to the title reaction. The most recent and accurate double many‐body expansion potential‐energy surface for the ground doublet state of the hydroperoxyl radical has been employed in all calculations. The computed reactive cross sections for initial quantum rotational states of OH varying from J=0 to J=10 (the vibrational quantum number is kept fixed at v=0) are shown to have a marked decreasing dependence on translational energy, thus suggesting that long‐range forces play ...

On the chaperon mechanism for association rate constants: the formation of HO2 and O3

Abstract We report rate constants for the formation of HO2 and O3 using the chaperon mechanism, and with Ar as scattering partner. The ArHO2 and ArO3 potential energy surfaces have been written as a pairwise summation of realistic EHFACE2-type potentials for interactions involving Ar and reliable global DMBE potential surfaces for chemically stable triatomic species. The calculations have been carried out using the quasiclassical trajectory approach.

Quasiclassical dynamics simulation of the collision-induced dissociation of Cr(CO)6+ with Xe

Quasiclassical trajectory calculations are employed to investigate the dynamics of collision-induced dissociation (CID) of Cr(CO)6 + with Xe atoms at collision energies ranging from 1.3 to 5.0 eV. The trajectory simulations show that direct elimination of CO ligands, during the collision, becomes increasingly important as the collision energy increases. In a significant number of cases, this shattering mechanism is accompanied with a concomitant formation of a transient Xe-Cr(CO)x +(x<6) complex. The calculated results are in very good agreement with the experimental results presented previously [F. Muntean and P. B. Armentrout, J. Chem. Phys. 115, 1213 (2001)]. In particular, the computed cross sections and scattering maps for the product ions Cr(CO)x +(x=3-5) compare very favorably with the reported experimental data. However, in contrast with the conclusions of the previous study, the present calculations suggest that CID dynamics for this system exhibits a significant impulsive character rather than proceeding via a complex surviving more than a rotational period.

A study on diversity for cluster geometry optimization

Diversity is a key issue to consider when designing evolutionary approaches for difficult optimization problems. In this paper, we address the development of an effective hybrid algorithm for cluster geometry optimization. The proposed approach combines a steady-state evolutionary algorithm and a straightforward local method that uses derivative information to guide search into the nearest local optimum. The optimization method incorporates a mechanism to ensure that the diversity of the population does not drop below a pre-specified threshold. Three alternative distance measures to estimate the dissimilarity between solutions are evaluated. Results show that diversity is crucial to increase the effectiveness of the hybrid evolutionary algorithm, as it enables it to discover all putative global optima for Morse clusters up to 80 atoms. A comprehensive analysis is presented to gain insight about the most important strengths and weaknesses of the proposed approach. The study shows why distance measures that consider structural information for estimating the dissimilarity between solutions are more suited to this problem than those that take into account fitness values. A detailed explanation for this differentiation is provided.

A new genetic algorithm to be used in the direct fit of potential energy curves to ab initio and spectroscopic data

We propose a two-step genetic algorithm (GA) to fit potential energy curves to both ab initio and spectroscopic data. In the first step, the GA is applied to fit only the ab initio points; the parameters of the potential so obtained are then used in the second-step GA optimization, where both ab initio and spectroscopic data are included in the fitting procedure. We have tested this methodology for the extended-Rydberg function, but it can be applied to other functions providing they are sufficiently flexible to fit the data. The results for NaLi and Ar2 diatomic molecules show that the present method provides an efficient way to obtain diatomic potentials with spectroscopic accuracy.

On the Use of Different Potential Energy Functions in Rare-Gas Cluster Optimization by Genetic Algorithms: Application to Argon Clusters

We study the effect of the potential energy function on the global minimum structures of argon clusters arising in the optimization performed by genetic algorithms (GAs). We propose a robust and efficient GA which allows for the calculation of all of the putative global minima of Ar(N) (N = 3-78) clusters modeled with four different potentials. Both energetic and structural properties of such minima are compared among each other and with those previously obtained for the Lennard-Jones function. In addition, the possibility of obtaining global minima of one potential through local optimization over the corresponding cluster geometry given by other potentials was associated with some structural parameters. The influence of the contribution from the three-body (Axilrod-Teller-Muto) triple-dipole potential (including or not a damping function to describe its correct behavior at smaller interatomic distances) has also been analyzed.

Designing Efficient Evolutionary Algorithms for Cluster Optimization: A Study on Locality

Cluster geometry optimization is an important problem from the Chemistry area. Hybrid approaches combining evolutionary algorithms and gradient-driven local search methods are one of the most efficient techniques to perform a meaningful exploration of the solution space to ensure the discovery of low energy geometries. Here we performa comprehensive study on the locality properties of this approach to gain insight to the algorithm’s strengths andweaknesses.Theanalysis is accomplished through the application of several static measures to randomly generated solutions in order to establish the main properties of an extended set of mutation and crossover operators. Locality analysis is complemented with additional results obtained from optimization runs. The combination of the outcomes allows us to propose a robust hybrid algorithm that is able to quickly discover the arrangement of the cluster’s particles that correspond to optimal or near-optimal solutions.

Analysis of Locality in Hybrid Evolutionary Cluster Optimization

State of the art algorithms for cluster geometry optimization rely on hybrid approaches that combine the global exploration performed by evolutionary methods with local search procedures. These methods use derivative information to discover the nearest local optimum. In this paper we analyze the locality properties of this approach to gain insight on the algorithms strengths and weaknesses and to determine the role played by each of its components. Results show that there are important differences in what concerns the locality of different mutation operators commonly used in this problem.