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The Dynamics of the S ( 1 D ) + H 2 / D 2 Reactions at Low Temperature via Statistical Simulations

Two different statistical approaches, the statistical quantum model (SQM) and the mean potential phase space theory (MPPST), have been employed to calculate the integral cross sections for the reactive collisions between S(1D) and H2/ D2 in the low energy regime (below 0.3 eV collisional energy). The rate constant for the S(1D) + H2 → SH + H reaction has been also obtained and compared with previously reported experimental and theoretical results. The good agreement shows the capability of these two methods to study the dynamics of these complex-forming atom-diatom processes in the present energy regime.


Following the pioneering experiments by
Lee and Liu [1][2][3], the dynamics of the S( 1 D)+H2 → SH+H reaction and its corresponding isotopic variants, with substitutions of H atoms by D, have been investigated in some detail by means of kinetics and crossed molecular beam (CMB) experiments [4][5][6][7] at very low temperature (down to states. In fact, many authors have concluded that the overall dynamics of the reaction is ruled by this complex-forming mechanism [3,9,10], which warrants the use of statistical techniques to investigate the process [3,7,[11][12][13][14][15][16][17]. In this sense, we present in this work results of calculations performed with the statistical quantum model (SQM) [13,14,18] and the mean potential phase space theory (MPPST) [19,20]. This combined theoretical investigation at the low energy regime is in-line with the recently reported study on the C( 1 D)+H2 reaction and isotopic variant [21].
Integral cross sections (ICS) below 10 meV both results are presented and discussed and finally, in Section 4 we present the conclusions.

Statistical Quantum Method
The theoretical basis of the SQM have been presented elsewhere before [13,14]

Mean Potential Phase Space Theory
The MPPST is a semi-classical technique to tackle the study of barrierless reactions [19,20] assuming as well the formation of an intermediate complex.
In this case, the individual probabilities for the asymptotic semiclassically quantized (v; j) states are calculated following an approximate two-body capture model [22] which accounts for tunnelling by means of the WKB model [23] through the radial effective potential. The interaction potential is averaged over the Jacobi angle to implicitly account for moderate anisotropies involved in complex-formation dynamics for barrierless processes at low collision energies. Here, a rigid rotor anharmonic oscillator approximation is considered to treat internal states of both reactant and product channels. The capture cross sections resulting from the isotropic assumption for the inter-fragment (averaged) potential do not depend on the initial rotational state of the reactant diatom.
The SQM calculations are performed using the PES by Ho et al. [8]. MPPST predictions have been obtained, in turn, considering also the matching with long range terms described in Ref. [24]. All calculations have been performed for the ground rovibrational states, H2(v = 0, j = 0) and D2(v = 0, j = 0), respectively.

Results and Discussion
The SQM and MPPST methods described in Excitation functions for S( 1 D)+D2 reported in Ref. [2] have been scaled with the same factor employed in Figure 1 for the case of S( 1 D)+H2 and compared with the present theoretical results.
Differences between theory and experiment are noticeable at this larger energy range.
Nevertheless, it is worth mentioning that some of the conclusions extracted from the isotopic investigations of the title reaction by Lee  In Table 1 Table 1. Ratio between the ICSs for the S( 1 D)+H2 and S( 1 D)+D2 reactions at specific values of the collision energy (in eV) obtained with the SQM (second column) and MPPST (third column) approaches in comparison with those adapted from the EQM cross sections of Ref. [7] (in fourth column) and the experimental values of Ref. [2] (in the last column). Recent studies on the S( 1 D)+H2 reaction [5,6] also included the calculation of the rate constant at temperatures between 5.8 and 298

Energy
K. In Figure 3 we show the actual comparison of present SQM and MPPST rates with those reported in Ref. [5] and rates obtained in a ring polymer molecular dynamics (RPMD) calculation [27]. Both the SQM and MPPST approaches yield predictions in a remarkably good agreement with the measured rates at 23 and 49 K [5]. Ref. [24] included in the MPPST calculation.   [5], RPMD (blue circles) [27], MPCT (black dashed line) [12] and experimental (red squares) [5] results.

Conclusions
The