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

Abstract

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.

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

“…This and other recent RPMD calculations [6][7][8]14,[20][21][22][23][24][25][26][27][28][29][30]61 firmly establish the 12 Page 12 of 23…”

“…17 RPMD provides reliable estimates for the correlation functions responsible for thermal rate coefficients in systems with various complex reaction paths and in different temperature regimes: [6][7][8]14,[18][19][20][21][22][23][24][25][26][27][28][29][30][31] RPMD rate coefficients are (i) exact in the high-temperature limit (ii) reliable at intermediate temperatures, (iii) more accurate than other approximate methods in the deep quantum tunnelling regime and close to the exact quantum results, (iv) able to capture ZPE effects perfectly. Unlike TST and QCT, RPMD treats the quantum Boltzmann operator accurately and automatically captures ZPE effects correctly along the entire reaction pathway; including throughout the transition-state and/or complex-formation regions.…”

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

“…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. 13,15,17,[23][24][25][26][28][29][30][31][32]34 Nevertheless, the level of accuracy that RPMD provides for the insertion reactions is indeed remarkable and suggests that it has the potential to be used for polyatomic reactions involving reaction intermediates, when high accuracy is desired.…”

“…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.…”

“…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. 15 Using two prototypical reactions of this type, namely X + H2  HX + H, (where X = N( 2 D),O( 1 D)) it has been shown that RPMD can provide very accurate results when compared to the exact quantum mechanical solution.…”