Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

Theoretical H + O3 rate coefficients from ring polymer molecular dynamics on an accurate global potential energy surface: assessing experimental uncertainties

Thermal rate coefficients and kinetic isotope effects have been calculated for an important atmospheric reaction H/D + O3 → OH/OD + O2 based on an accurate permutation invariant polynomial-neural network potential energy surface, using ring polymer molecular dynamics (RPMD), quasi-classical trajectory (QCT) and variational transition-state theory (VTST) with multidimensional tunneling. The RPMD approach yielded results that are generally in better agreement with experimental rate coefficients than the VTST and QCT ones, especially at low temperatures, attributable to its capacity to capture quantum effects such as tunneling and zero-point energy. The theoretical results support one group of existing experiments over the other. In addition, rate coefficients for the D + O3 → OD + O2 reaction are also reported using the same methods, which will allow a stringent assessment of future experimental measurements, thus helping to reduce the uncertainty in the recommended rate coefficients of this reaction.

VTST and RPMD kinetics study of the nine-body X + C2H6 (X ≡ H, Cl, F) reactions based on analytical potential energy surfaces

Thermal rate constants of nine-atom hydrogen abstraction reactions, X + C2H6 → HX + C2H5 (X ≡ H, Cl, F) with qualitatively different reaction paths, have been investigated using two kinetics approaches - variational transition state theory with multidimensional tunnelling (VTST/MT) and ring polymer molecular dynamics (RPMD) - and full dimensional analytical potential energy surfaces. For the H + C2H6 reaction, which proceeds through a noticeable barrier height of 11.62 kcal mol-1, kinetics approaches showed excellent agreement between them (with differences less than 30%) and with the experiment (with differences less than 60%) in the wide temperature range of 200-2000 K. For X = Cl and F, however, the situation is very different. The barrier height is either low or very low, 2.44 and 0.23 kcal mol-1, respectively, and the presence of van der Waals complexes in the entrance channel leads to a very flat topography and, consequently, imposes theoretical challenges. For the Cl(2P) reaction, VTST/MT underestimates the experimental rate constants (with differences less than 86%), and RPMD demonstrates better agreement (with differences less than 47%), although the temperature dependence is opposite to the experiment at low temperatures. Finally, for the F(2P) reaction, available experimental information shows discrepancies, both in the absolute values of the rate constants and also in the temperature dependence. Unfortunately, kinetics theories did not resolve this discrepancy. Different possible causes of these theory/experiment discrepancies were analyzed.

An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH4→ HCl + CH3reaction

Thermal rate coefficients for the Cl + CH₄/CD₄reactions were studied on a new full-dimensional accurate potential energy surface with the spin–orbit corrections considered in the entrance channel.

New Stress Test for Ring Polymer Molecular Dynamics: Rate Coefficients of the O(3P) + HCl Reaction and Comparison with Quantum Mechanical and Quasiclassical Trajectory Results

In the past decade, ring polymer molecular dynamics (RPMD) has emerged as a very efficient method to determine thermal rate coefficients for a great variety of chemical reactions. This work presents the application of this methodology to study the O(³P) + HCl reaction, which constitutes a stringent test for any dynamical calculation due to rich resonant structure and other dynamical features. The rate coefficients, calculated on the ³A' and ³A″ potential energy surfaces (PESs) by Ramachandran and Peterson [ J. Chem. Phys. 2003 , 119 , 9590 ], using RPMD and quasiclassical trajectories (QCT) are compared with the existing experimental and the quantum mechanical (QM) results by Xie et al. [ J. Chem. Phys. 2005 122 , 014301 ]. The agreement is very good at T > 600 K, although RPMD underestimates rate coefficients by a factor between 4 and 2 in the 200-500 K interval. The origin of these discrepancies lies in the large contribution from tunneling on the ³A″ PES, which is enhanced by resonances due to quasibound states in the van der Waals wells. Although tunneling is fairly well accounted for by RPMD even below the crossover temperature, the effect of resonances, a long-time effect, is not included in the methodology. At the highest temperatures studied in this work, 2000-3300 K, the RPMD rate coefficients are somewhat larger than the QM ones, but this is shown to be due to limitations in the QM calculations and the RPMD are believed to be more reliable.

The low temperature D+ + H2→ HD + H+ reaction rate coefficient: a ring polymer molecular dynamics and quasi-classical trajectory study

The reaction between D⁺ and H₂ plays an important role in astrochemistry at low temperatures and also serves as a prototype for a simple ion-molecule reaction. Its ground X[combining tilde]¹A' state has a very small thermodynamic barrier (up to 1.8 × 10^-2 eV) and the reaction proceeds through the formation of an intermediate complex lying within the potential well with a depth of at least 0.2 eV, thus representing a challenge for dynamical studies. In the present work, we analyze the title reaction within the temperature range of 20-100 K by means of ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) methods over the full-dimensional global potential energy surface developed by Aguado et al. [A. Aguado, O. Roncero, C. Tablero, C. Sanz and M. Paniagua, J. Chem. Phys., 2000, 112, 1240]. The computed thermal RPMD and QCT rate coefficients are found to be almost independent of temperature and fall within the range of 1.34-2.01 × 10^-9 cm³ s^-1. They are also in very good agreement with previous time-independent quantum mechanical and statistical quantum method calculations. Furthermore, we observe that the choice of asymptotic separation distance between the reactants can markedly alter the rate coefficient in the low temperature regime (20-50 K). Therefore it is of utmost importance to correctly assign the value of this parameter for dynamical studies, particularly at very low temperatures of astrochemical importance. We finally conclude that the experimental rate measurements for the title reaction are highly desirable in future.

An experimental and theoretical investigation of the C(1D) + D2 reaction

Rate constants derived from ring polymer molecular dynamics calculations confirm the validity of this method for studying low-temperature complex-forming reactions

A ring polymer molecular dynamics study of the OH + H2(D2) reaction

Using ring polymer molecular dynamics we have calculated the rate coefficients for the OH + H₂ reaction.

Theoretical and experimental investigations of rate coefficients of O(1D) + CH4 at low temperature

The O(¹D) + CH₄ rates from RPMD and VUV-LIF are close to each other in the temperature range of the atmosphere.

Ring-Polymer Molecular Dynamics for the Prediction of Low-Temperature Rates: An Investigation of the C((1)D) + H2 Reaction

Quantum mechanical calculations are important tools for predicting the rates of elementary reactions, particularly for those involving hydrogen and at low temperatures where quantum effects become increasingly important. These approaches are computationally expensive, however, particularly when applied to complex polyatomic systems or processes characterized by deep potential wells. While several approximate techniques exist, many of these have issues with reliability. The ring-polymer molecular dynamics method was recently proposed as an accurate and efficient alternative. Here, we test this technique at low temperatures (300-50 K) by analyzing the behavior of the barrierless C((1)D) + H2 reaction over the two lowest singlet potential energy surfaces. To validate the theory, rate coefficients were measured using a supersonic flow reactor down to 50 K. The experimental and theoretical rates are in excellent agreement, supporting the future application of this method for determining the kinetics and dynamics of a wide range of low-temperature reactions.

The Cl + O3 reaction: a detailed QCT simulation of molecular beam experiments

QCT calculations have been carried out to determine angle–velocity differential cross-sections to simulate the results of molecular beam experiments.

Stress Test for Quantum Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H

Quantum effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a stress test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate quantum mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.

Quantum rate coefficients and kinetic isotope effect for the reaction Cl + CH4 → HCl + CH3 from ring polymer molecular dynamics

Thermal rate coefficients and kinetic isotope effect have been calculated for prototypical heavy-light-heavy polyatomic bimolecular reactions Cl + CH4/CD4 → HCl/DCl + CH3/CD3, using a recently proposed quantum dynamics approach: ring polymer molecular dynamics (RPMD). Agreement with experimental rate coefficients, which are quite scattered, is satisfactory. However, differences up to 50% have been found between the RPMD results and those obtained from the harmonic variational transition-state theory on one of the two full-dimensional potential energy surfaces used in the calculations. Possible reasons for such discrepancy are discussed. The present work is an important step in a series of benchmark studies aimed at assessing accuracy for RPMD for chemical reaction rates, which demonstrates that this novel method is a quite reliable alternative to previously developed techniques based on transition-state theory.

Ring-Polymer Molecular Dynamics Rate Coefficient Calculations for Insertion Reactions: X + H2 → HX + H (X = N, O)

The thermal rate constants of two prototypical insertion-type reactions, namely, N/O + H2 → NH/OH + H, are investigated with ring polymer molecular dynamics (RPMD) on full-dimensional potential energy surfaces using recently developed RPMDrate code. It is shown that the unique ability of the RPMD approach among the existing theoretical methods to capture the quantum effects, e.g., tunneling and zero-point energy, as well as recrossing dynamics quantum mechanically with ring-polymer trajectories leads to excellent agreement with rigorous quantum dynamics calculations. The present result is encouraging for future applications of the RPMD method and the RPMDrate code to complex-forming chemical reactions involving polyatomic reactants.