A ring polymer molecular dynamics study of the isotopologues of the H + H2 reaction

Abstract

The inclusion of Quantum Mechanical (QM) effects such as zero point energy (ZPE) and tunneling in simulations of chemical reactions, especially in the case of light atom transfer, is an important problem in computational chemistry. In this respect, the hydrogen exchange reaction and its isotopic variants constitute an excellent benchmark for the assessment of approximate QM methods. In particular, the recently developed ring polymer molecular dynamics (RPMD) technique has been demonstrated to give very good results for bimolecular chemical reactions in the gas phase. In this work, we have performed a detailed RPMD study of the H + H(2) reaction and its isotopologues Mu + H(2), D + H(2) and Heμ + H(2), at temperatures ranging from 200 to 1000 K. Thermal rate coefficients and kinetic isotope effects have been computed and compared with exact QM calculations as well as with quasiclassical trajectories and experiment. The agreement with the QM results is good for the heaviest isotopologues, with errors ranging from 15% to 45%, and excellent for Mu + H(2), with errors below 15%. We have seen that RPMD is able to capture the ZPE effect very accurately, a desirable feature of any method based on molecular dynamics. We have also verified Richardson and Althorpe's prediction [J. O. Richardson and S. C. Althorpe, J. Chem. Phys., 2009, 131, 214106] that RPMD will overestimate thermal rates for asymmetric reactions and underestimate them for symmetric reactions in the deep tunneling regime. The ZPE effect along the reaction coordinate must be taken into account when assigning the reaction symmetry in the multidimensional case.

Ring-polymer molecular dynamics: Rate coefficient calculations for energetically symmetric (near thermoneutral) insertion reactions (X + H2) → HX + H(X = C(1D), S(1D))

“…This is not surprising as this prediction was developed for reactions dominated by a significant barrier, where tunneling was significant. 26,27 The present (and previous 15 ) RPMD calculations for prototypical insertion-type reactions suggest that RPMD slightly overestimates the rates for this class of reactions. However, such conclusion is rather speculative and more extensive accuracy assessment of RPMD for barrierless reactions is required, similar to numerous recent studies of thermally-activated chemical reactions.…”

“…The present results suggest less sensitivity of RPMD to the energetics of insertion-type chemical reactions compared to the previously studied thermallyactivated ones. 26 The two title reactions feature relatively small energy differences between reactants and products -0.17 eV and 0.30 eV for C( 1 D) + H2 and S( 1 D) + H2, respectively (see Fig. 1).…”

“…At low temperatures, the RPMD rate theory exhibits systematic behavior: it consistently underestimates rates for energetically symmetric (thermoneutral) reactions, and conversely overestimates rates for significantly asymmetric (endo or exothermic) reactions. 26,27 A recent comprehensive test of various quantum transition-state theories and other ratecalculation methods suggested that the RPMD approach is the most accurate and well behaved. 32,33 More recently, the RPMD method was applied to insertion chemical reactions.…”

“…In a series of recent studies 13,15,17,20,21,[23][24][25][26][28][29][30][31][32]34 it has been shown that the RPMD method provides accurate rate coefficients when applied to systems with various dimensionalities starting from one-dimensional Eckhart barriers, 20,21 atomdiatom 13,15,26,32 to more complex polyatomic reactions. 17, [23][24][25][28][29][30][31] The RPMD rate coefficient captures the ZPE effect almost perfectly, and is within a factor of 2-3 of the exact rate at low temperatures in the so-called deep tunneling regimes, where tunneling dominates.…”

“…In the previous studies of thermally-activated chemical reactions, it has been well established that RPMD provides over-and underestimations of rate coefficients depending on the reaction energy symmetry. 26 It is therefore important to assess the accuracy of RPMD for energetically symmetric (or thermoneutral) chemical reactions of the insertion type, which represent the main purpose of this work. To this end, we employ two prototypical complexforming reactions, namely X + H2  HX + H, where the difference in energies between reactants and products is 0.2 and 0.3 eV for X = C( 1 D) and S( 1 D), respectively (see Fig.…”