Fast Shepard interpolation on graphics processing units: Potential energy surfaces and dynamics for H + CH4 → H2 + CH3

Abstract

A strategy for the fast evaluation of Shepard interpolated potential energy surfaces (PESs) utilizing graphics processing units (GPUs) is presented. Speed ups of several orders of magnitude are gained for the title reaction on the ZFWCZ PES [Y. Zhou, B. Fu, C. Wang, M. A. Collins, and D. H. Zhang, J. Chem. Phys. 134, 064323 (2011)]. Thermal rate constants are calculated employing the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach. Results for the ZFWCZ PES are compared to rate constants obtained for other ab initio PESs and problems are discussed. A revised PES is presented. Thermal rate constants obtained for the revised PES indicate that an accurate description of the anharmonicity around the transition state is crucial.

Rigorous close-coupling quantum dynamics calculation of thermal rate constants for the water formation reaction of H2 + OH on a high-level PES

“…Additionally, full-dimensional quantum dynamics calculations of rate constants employing the J-shifting approximation are only available for a few polyatomic reactions. [21][22][23][24][25][26][27] a) Electronic mail: ralph.welsch@desy.de Most accurate thermal rate constant calculations for polyatomic molecules employ the quantum transition state concept [28][29][30][31][32][33][34][35] and the multi-configurational time-dependent Hartree (MCTDH) approach. 36,37 The quantum transition state concept has been proven as the most efficient method to treat the reaction dynamics of polyatomic systems rigorously.…”

Multi-layer Potfit: An accurate potential representation for efficient high-dimensional quantum dynamics

“…This is due to the difficulties encountered when evaluating matrix elements of the potential energy operator. The CDVR approach 35,36 has been successful in overcoming these difficulties 23,[37][38][39][40][41][42] , though its use requires an enormous amount of PES evaluations, which may require a large amount of computational resources. The alternative to CDVR is to represent (or fit) the PES in a form that is compatible with ML-MCTDH, in the sense that it allows efficient evaluation of the matrix elements.…”

“…In a similar manner, one may estimate the computational effort for the H-terms (39) and for the RHS of the EOMs (40)(41)(42). In case of the latter, the effort for multiplying with the inverse density matrix and for applying the projector can usually be neglected, as these need to be done only once so that their cost doesn't depend on s. In summary, for a non-leaf node z with p z = p, n z =n, and n z,κ = n, one obtains: cost(h (z) ) = snn p (n + pn) (B2) cost (H (z,1) ) + · · · + cost(H (z,p) ) = snn p (n + p 2 n) (B3) cost(RHS (z) ) ≈ snn p (n + pn) (B4) For leaf nodes, the computational effort depends on the sparsity of the matrix representations of the primitive mode operators, χ [f ] α |ĥ…”

“…(39), and finally the RHS of Eqs. (40)(41)(42). To illustrate how to estimate the numerical effort of these computations, take as an example the h-terms for a nonleaf node z with p z = 3, n z =n, and n z,κ = n, so that Eq.…”

“…But first it should be noted that the quadrature problem may alternatively be solved by employing time-dependent grids, as in Manthe's CDVR method 35 which also works in conjunction with ML-MCTDH 36 , where it has been successfully used to treat a 189D system-bath problem which involved a 9D PES 23 as well as systems with global PES up to 21D [37][38][39][40][41] . The drawback of this approach is that it requires an extreme amount of PES function evaluations, which can easily become a bottleneck for the calculation, and massively parallel architectures (like GPUs) may be needed to overcome this problem 42 .…”