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Manthe, Uwe

Publications and source records attributed to Manthe, Uwe.

12 records
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DOE OSTI2024

QuTree: A tree tensor network package

Here we present QuTree, a C++ library for tree tensor network approaches. QuTree provides class structures for tensors, tensor trees, and related linear algebra functions that facilitate the fast development of tree tensor network approaches such as the multilayer multiconfigurational time-dependent Hartree approach or the density matrix renormalization group approach and its various extensions. We investigate the efficiency of relevant tensor and tensor network operations and show that the overhead for managing the network structure is negligible, even in cases with a million leaves and small tensors. QuTree focuses on providing simple, high-level routines while retaining easy access to the backend to facilitate novel developments. We demonstrate the capabilities of the package by computing the eigenstates of coupled harmonic oscillator Hamiltonians and performing random circuit simulations on a virtual quantum computer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A non-hierarchical correlation discrete variable representation

The correlation discrete variable representation (CDVR) facilitates (multi-layer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. It employs a layered grid representation to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. The original CDVR approach and its multi-layer extension show a hierarchical structure: the size of the grids employed at the different layers increases when moving from an upper layer to a lower one. In this work, a non-hierarchical CDVR approach, which uses identically structured quadratures at all layers of the MCTDH wavefunction representation, is introduced. Here, the non-hierarchical CDVR approach crucially reduces the number of grid points required, compared to the hierarchical CDVR, shows superior scaling properties, and yields identical results for all three representations showing the same topology. Numerical tests studying the photodissociation of NOCl and the vibrational states of CH 3 demonstrate the accuracy of the non-hierarchical CDVR approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Vibrational control of the reaction pathway in the H + CHD 3 → H 2 + CD 3 reaction

An accurate full-dimensional quantum state-to-state simulation of the six-atom title reaction based on first-principles theory is reported. Counterintuitive effects are found: Increasing the energy in the reactant’s CD 3 umbrella vibration reduces the energy in the corresponding product vibration. An in-depth analysis reveals the crucial role of the effective dynamical transition state: Its geometry is controlled by the vibrational states of the reactants and subsequently controls the quantum state distribution of the products. This finding enables generalizing the concept of transition state control of chemical reactions to the quantum state–specific level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

S-matrix decomposition, natural reaction channels, and the quantum transition state approach to reactive scattering

A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH{sub 4} → H{sub 2} + CH{sub 3} reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Communication: Mode specific quantum dynamics of the F + CHD{sub 3} → HF + CD{sub 3} reaction

The mode specific reactivity of the F + CHD{sub 3} → HF + CD{sub 3} reaction is investigated using an eight-dimensional quantum dynamical model on a recently developed ab initio based full-dimensional potential energy surface. Our results indicate prominent resonance structures at low collision energies and absence of an energy threshold in reaction probabilities. It was also found that excitation of the C–D stretching or CD{sub 3} umbrella mode has a relatively small impact on reactivity. On the other hand, the excitation of the C–H vibration (v{sub 1}) in CHD{sub 3} is shown to significantly increase the reactivity, which, like several recent quasi-classical trajectory studies, is at odds with the available experimental data. Possible sources of the disagreement are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

The multi-configurational time-dependent Hartree approach revisited

The multi-configurational time-dependent Hartree (MCTDH) approach facilitates accurate high-dimensional quantum dynamics simulations. In the approach, the wavefunction is expanded in a direct product of self-adapting time-dependent single-particle functions (SPFs). The equations of motion for the expansion coefficients and the SPFs are obtained via the Dirac-Frenkel variational principle. While this derivation yields well-defined differential equations for the motion of occupied SPFs, singularities in the working equations resulting from unoccupied SPFs have to be removed by a regularization procedure. Here, an alternative derivation of the MCTDH equations of motion is presented. It employs an analysis of the time-dependence of the single-particle density matrices up to second order. While the analysis of the first order terms yields the known equations of motion for the occupied SPFs, the analysis of the second order terms provides new equations which allow one to identify optimal choices for the unoccupied SPFs. The effect of the optimal choice of the unoccupied SPFs on the structure of the MCTDH equations of motion and their regularization is discussed. Generalized equations applicable in the multi-layer MCTDH framework are presented. Finally, the effects resulting from the initial choice of the unoccupied SPFs are illustrated by a simple numerical example.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Full-dimensional and reduced-dimensional calculations of initial state-selected reaction probabilities studying the H + CH{sub 4} → H{sub 2} + CH{sub 3} reaction on a neural network PES

Initial state-selected reaction probabilities of the H + CH{sub 4} → H{sub 2} + CH{sub 3} reaction are calculated in full and reduced dimensionality on a recent neural network potential [X. Xu, J. Chen, and D. H. Zhang, Chin. J. Chem. Phys. 27, 373 (2014)]. The quantum dynamics calculation employs the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach and rigorously studies the reaction for vanishing total angular momentum (J = 0). The calculations investigate the accuracy of the neutral network potential and study the effect resulting from a reduced-dimensional treatment. Very good agreement is found between the present results obtained on the neural network potential and previous results obtained on a Shepard interpolated potential energy surface. The reduced-dimensional calculations only consider motion in eight degrees of freedom and retain the C{sub 3v} symmetry of the methyl fragment. Considering reaction starting from the vibrational ground state of methane, the reaction probabilities calculated in reduced dimensionality are moderately shifted in energy compared to the full-dimensional ones but otherwise agree rather well. Similar agreement is also found if reaction probabilities averaged over similar types of vibrational excitation of the methane reactant are considered. In contrast, significant differences between reduced and full-dimensional results are found for reaction probabilities starting specifically from symmetric stretching, asymmetric (f{sub 2}-symmetric) stretching, or e-symmetric bending excited states of methane.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The role of the transition state in polyatomic reactions: Initial state-selected reaction probabilities of the H + CH{sub 4} → H{sub 2} + CH{sub 3} reaction

Full-dimensional calculations of initial state-selected reaction probabilities on an accurate ab initio potential energy surface (PES) have been communicated recently [R. Welsch and U. Manthe, J. Chem. Phys. 141, 051102 (2014)]. These calculations use the quantum transition state concept, the multi-layer multi-configurational time-dependent Hartree approach, and graphics processing units to speed up the potential evaluation. Here further results of these calculations and an extended analysis are presented. State-selected reaction probabilities are given for many initial ro-vibrational states. The role of the vibrational states of the activated complex is analyzed in detail. It is found that rotationally cold methane mainly reacts via the ground state of the activated complex while rotationally excited methane mostly reacts via H–H–CH{sub 3}-bending excited states of the activated complex. Analyzing the different contributions to the reactivity of the vibrationally states of methane, a complex pattern is found. Comparison with initial state-selected reaction probabilities computed on the semi-empirical Jordan-Gilbert PES reveals the dependence of the results on the specific PES.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Communication: Ro-vibrational control of chemical reactivity in H+CH{sub 4}→ H{sub 2}+CH{sub 3} : Full-dimensional quantum dynamics calculations and a sudden model

The mode-selective chemistry of the title reaction is studied by full-dimensional quantum dynamics simulation on an accurate ab initio potential energy surface for vanishing total angular momentum. Using a rigorous transition state based approach and multi-configurational time-dependent Hartree wave packet propagation, initial state-selected reaction probabilities for many ro-vibrational states of methane are calculated. The theoretical results are compared with experimental trends seen in reactions of methane. An intuitive interpretation of the ro-vibrational control of the chemical reactivity provided by a sudden model based on the quantum transition state concept is discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Correlation functions for fully or partially state-resolved reactive scattering calculations

Flux correlation functions and the quantum transition state concept are important tools for the accurate description of polyatomic reaction processes. Combined with the multi-configurational time-dependent Hartree approach, they facilitate rigorous full-dimensional calculations of cumulative and initial-state selected reaction probabilities for six atom reactions. In recent work [R. Welsch, F. Huarte-Larrañaga, and U. Manthe, J. Chem. Phys. 136, 064117 (2012)], an approach which allows one to calculate also state-to-state reaction probabilities within the quantum transition state concept has been introduced. This article presents further developments. Alternative generalized flux correlation functions are introduced and discussed. Equations for the calculation of fully state-resolved differential cross section using arbitrary definitions of the body fixed frame are derived. An approach for the efficient calculation of partially state-resolved observables as a function of the collision energy is introduced. Finally, numerical test studying the D + H{sub 2} reaction illustrate important aspects of the formalism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗