Erratum: “Rotational excitations in para-H2+para-H2 collisions: Full- and reduced-dimensional quantum wave packet studies comparing different potential energy surfaces” [J. Chem. Phys. 128, 064305 (2008)]

State resolved densities of high rovibrationally excited hydrogen isotopologues H 2 , HD, and D 2 in the electronic ground state have been measured in a supersonically expanding plasma jet. The obtained state distributions differ substantially from thermal equilibrium. Moreover, the distributions are not the same for H 2 , HD, and D 2 indicating different formation and relaxation rates for each isotopologue. Mechanisms for this deviation from a Boltzmann distribution are given and compared to hydrogen reactions in other environments. The difference between the measured highest occupied rovibrational states in H 2 , HD, and D 2 is ascribed to an isotope effect in the dissociation process.

Section: Relaxation Of Molecular Hydrogenmentioning

confidence: 99%

Nonequilibrium rovibrational energy distributions of hydrogen isotopologues in an expanding plasma jet

Gabriel

Dungen

Schram

et al. 2010

“…MCTDH was initially formulated with molecular quantum dynamics in mind, where the degrees of freedom (DOFs) are distinguishable and the potential operator correlates in principle all vibrational degrees of freedom of the system. Many successful applications over the years deal with the spectroscopy of molecules, [6][7][8][9][10] isomerization and intramolecular vibrational energy redistribution (IVR), 11,12 inelastic and reactive scattering calculations, [13][14][15][16][17] scattering of atoms or molecules at surfaces, [18][19][20] etc. More recently, the potential of the MCTDH method for the treatment of systems of indistinguishable particles, either fermions or bosons, has been realized as well, and many applications can be counted nowadays in such new directions.…”

Section: Introductionmentioning

confidence: 99%

Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine

Vendrell¹,

Meyer

2011

Self Cite

357

388

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. 128, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) Hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH Hamiltonian using a seven-layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D Hamiltonian of Raab et al. [J. Chem. Phys. 110, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with 4.6 × 10 7 time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only 4.5 × 10 5 coefficients and requiring a shorter computation time.

“…Again, the overall strategy is to first evaluate the U-terms (57,56), then the W-terms (58), and finally the RHS contributions (60)(61)(62). Naturally, the analysis of the computational costs for these expressions is now more involved.…”

Section: Ml-mctdh With Multi-layer Operatorsmentioning

confidence: 99%

“…After propagating for 250 fs, the method of Tannor and Weeks 62 was used to extract energy-resolved transition probabilities P i→f (E) for rotational excitations of the molecules from the time-dependent wavefunction (see Ref. 57 for details of this analysis procedure). Here, only the four strongest rotational transitions from i = (j 1 , j 2 ) = (0, 0) to f = (j 1 , j 2 ) = (2, 0), (2, 2), (4, 0), (4, 2) were considered (the j i are the rotational quantum numbers of the molecules; changes Table II. in the vibrational states were not considered).…”

Section: A Computational Examplementioning

confidence: 99%

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

Otto

2014

Self Cite

The multi-layer multi-configuration time-dependent Hartree method (ML-MCTDH) is a highly efficient scheme for studying the dynamics of high-dimensional quantum systems. Its use is greatly facilitated if the Hamiltonian of the system possesses a particular structure through which the multi-dimensional matrix elements can be computed efficiently. In the field of quantum molecular dynamics, the effective interaction between the atoms is often described by potential energy surfaces (PES), and it is necessary to fit such PES into the desired structure. For high-dimensional systems, the current approaches for this fitting process either lead to fits that are too large to be practical, or their accuracy is difficult to predict and control.This article introduces multi-layer Potfit (MLPF), a novel fitting scheme that results in a PES representation in the hierarchical tensor (HT) format. The scheme is based on the hierarchical singular value decomposition, which can yield a near-optimal fit and give strict bounds for the obtained accuracy. Here, a recursive scheme for using the HT-format PES within ML-MCTDH is derived, and theoretical estimates as well as a computational example show that the use of MLPF can reduce the numerical effort for ML-MCTDH by orders of magnitude, compared to the traditionally used Potfit representation of the PES. Moreover, it is shown that MLPF is especially beneficial for high-accuracy PES representations, and it turns out that MLPF leads to computational savings already for comparatively small systems with just four modes.