The method of Gaussian weighted trajectories. V. On the 1GB procedure for polyatomic processes

Abstract

In recent years, many chemical reactions have been studied by means of the quasiclassical trajectory (QCT) method within the Gaussian binning (GB) procedure. The latter consists of "quantizing" the final vibrational actions in Bohr spirit by putting strong emphasis on the trajectories reaching the products with vibrational actions close to integer values. A major drawback of this procedure is that if N is the number of product vibrational modes, the amount of trajectories necessary to converge the calculations is ∼10(N)×larger than with the standard QCT method. Applying it to polyatomic processes is thus problematic. In a recent paper, however, Czakó and Bowman propose to quantize the total vibrational energy instead of the vibrational actions [G. Czakó and J. M. Bowman, J. Chem. Phys. 131, 244302 (2009)], a procedure called 1GB here. The calculations are then only ∼10 times more time consuming than with the standard QCT method, allowing thereby for considerable numerical saving. In this paper, we propose some theoretical arguments supporting the 1GB procedure and check its validity on model test cases as well as the prototype four-atom reaction OH+D(2)→HOD+D.

Classical versus quantum vibrational state distributions for the benchmark polyatomic reaction OH+D2: Checking the validity of the QCT method

“…Let us briefly recall that QCT-SB results are obtained by assuming that a trajectory ending with x 1 , x 2 and x 3 contributes to the quantum state ðx 1 , x 2 and x 3 Þ [13,14]. However, a major limitation of QCT-GB is that, as far as the title reaction is concerned, the number of reactive trajectories required to obtain statistically meaningful results is about 1000 times the one required in standard QCT-SB calculations [28]. As an alternative, Czáko and Bowman recently proposed to quantize the vibrational energy itself rather than the actions [27], a procedure involving only one Gaussian whatever the number of vibrational modes.…”

“…The computational saving of this 1GB procedure may thus be huge. However, it makes only sense to apply it when the distribution in the action space is sufficiently smooth [28]. The statistical weight is given by…”

“…To deal with vibrational quantization in the products within the QCT method, we used the GB procedure [17][18][19][20][21][22][23][24][25][26][27][28] which can be summarized as follows: Bohr's basic idea is that only the classical paths corresponding to integer actions of the final products should be permitted. This is also an idea to which the classical S matrix theory (CSMT) of Miller and Marcus leads [32][33][34][35][36][37][38].…”

“…We do not aim here to perform an analysis of the different PESs developed for this system, which can be found elsewhere [15,16]. QCT results within the standard binning (SB) procedure are also considered, as well as those quantization of the overall vibrational energy is taken into account, rather than the quantization of the energy of each of the vibrational normal modes [27,28]. It is important to check the ability of the QCT method to describe chemical reaction dynamics for polyatomic processes, since there is hardly any other alternative for the time being.…”

“…When in the QCT calculations the standard binning (SB) procedure (which amounts to attribute the same statistical weight to each trajectory) was used, the experimental product vibrational state populations were not reproduced [6][7][8][9]. However, using the Gaussian binning (GB) procedure, which takes into account Bohr quantization principle for vibrational energies [17][18][19][20][21][22][23][24][25][26][27][28], made the expected product state spectrum appear, for the first time as far as polyatomic processes are concerned [10]. However, this method (QCT-GB) gives a population of the (1, 1) state of 3%, much lower than the experimental value, 11% [10].…”