This study deals with the understanding of hydrogen atom scattering from graphene, a process critical for exploring C-H bond formation and energy transfer during atom surface collision. In our previous work [Shi, L.; J. Chem. Phys. 2023, 159, 194102], starting from a cell with 24 carbon atoms treated periodically, we have achieved quantum dynamics (QD) simulations with a reduced-dimensional model (15D) and a simulation in full dimensionality (75D). In the former work, the H atom attacked the top of a single C atom, enabling a comparison of QD simulation results to classical molecular dynamics (cMD). Our approach required the use of sophisticated techniques such as Monte Carlo canonical polyadic decomposition (MCCPD) and multilayer multiconfiguration time-dependent Hartree (ML-MCTDH), as well as further development of quantum flux calculations. We could benchmark our calculations by comparison to cMD calculations. We now refined our method to better mimic experimental conditions. Specifically, rather than sending the H atom to a specific position on the surface, we employed a plane wave for the H atom in directions parallel to the surface. Key findings for these new simulations include the identification of discrepancies between classical molecular dynamics (cMD) simulations and experiments, which are attributed to both the potential energy surface (PES) and quantum effects. Additionally, this study sheds light on the role of classical collective normal modes during collisions, providing insights into energy transfer processes. The results validate the robustness of our simulation methodologies and highlight the importance of considering quantum mechanical effects in the study of hydrogen-graphene interactions.

We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin-orbitals. The algorithm for obtaining the canonical polyadic form starts from an exact sum-of-products, which is then optimally compactified using an alternating least squares procedure. We discuss the relation of this specific SOP with related forms, namely the Tucker format and the matrix product operator often used in conjunction with matrix product states. We benchmark the method on the electronic dynamics of an excited water molecule, trans-polyenes, and the charge migration in glycine upon inner-valence ionization. The quantum dynamics are performed with the multilayer multiconfiguration time-dependent Hartree method in second quantization representation. Other methods based on tree-tensor Ansätze may profit from this general approach.

This work presents systematic comparisons between classical molecular dynamics (cMD) and quantum dynamics (QD) simulations of 15-dimensional and 75-dimensional models in their description of H atom scattering from graphene. We use an experimentally validated full-dimensional neural network potential energy surface of a hydrogen atom interacting with a large cell of graphene containing 24 carbon atoms. For quantum dynamics simulations, we apply Monte Carlo canonical polyadic decomposition to transform the original potential energy surface (PES) into a sum of products form and use the multi-layer multi-configuration time-dependent Hartree method to simulate the quantum scattering of a hydrogen or deuterium atom with an initial kinetic energy of 1.96 or 0.96 eV and an incident angle of 0°, i.e., perpendicular to the graphene surface. The cMD and QD initial conditions have been carefully chosen in order to be as close as possible. Our results show little differences between cMD and QD simulations when the incident energy of the H atom is equal to 1.96 eV. However, a large difference in sticking probability is observed when the incident energy of the H atom is equal to 0.96 eV, indicating the predominance of quantum effects. To the best of our knowledge, our work provides the first benchmark of quantum against classical simulations for a system of this size with a realistic PES. Additionally, new projectors are implemented in the Heidelberg multi-configuration time-dependent Hartree package for the calculation of the atom scattering energy transfer distribution as a function of outgoing angles.

The Zundel ( H_5O_2^+ ) and Eigen ( H_9O_4^+ ) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit. Embedded in the static environment of the parent Eigen cation, this subunit reproduces the positions and broadenings of its main excess-proton bands. In isolation, its spectrum reverts to the well-known Zundel ion. Hence, the dynamics of this subunit polarized by an environment suffice to explain the spectral signatures and anharmonic couplings of the solvated proton in its first solvation shell.

The infrared (IR) spectra of protonated water clusters encode precise information on the dynamics and structure of the hydrated proton. However, the strong anharmonic coupling and quantum effects of these elusive species remain puzzling up to the present day. Here, we report unequivocal evidence that the interplay between the proton transfer and the water wagging motions in the protonated water dimer (Zundel ion) giving rise to the characteristic doublet peak is both more complex and more sensitive to subtle energetic changes than previously thought. In particular, hitherto overlooked low-intensity satellite peaks in the experimental spectrum are now unveiled and mechanistically assigned. Our findings rely on the comparison of IR spectra obtained using two highly accurate potential energy surfaces in conjunction with highly accurate state-resolved quantum simulations. We demonstrate that these high-accuracy simulations are important for providing definite assignments of the complex IR signals of fluxional molecules.

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.

In this work, high-dimensional (21D) quantum dynamics calculations on the mode-specific surface scattering of a carbon monoxide molecule on a copper(100) surface with lattice effects of a five-atom surface cell are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. We employ a surface model in which five surface atoms near the impact site are treated as fully flexible quantum particles, while all other more distant atoms are kept at fixed locations. To efficiently perform the 21D ML-MCTDH wave packet propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific sticking probabilities of CO on Cu(100) are computed, and lattice effects caused by the flexible surface atoms are demonstrated by comparison with sticking probabilities computed for a rigid surface. The dependence of the sticking probability of the initial state of the system is studied, and it is found that the sticking probability is reduced when the surface atom on the impact site is initially vibrationally excited.

We have implemented a Monte-Carlo version of a well-known alternating least squares algorithm to obtain a sum-of-products representation of potential energy surfaces, more precisely a so-called Canonical Polyadic Decomposition, for use in quantum-dynamical simulations. Our modification replaces exact integrals with Monte-Carlo integrals. The incorporation of correlated weights, and hence weighted integrals, is straight forward using importance sampling. Using Monte-Carlo methods allows to efficiently solve high-dimensional integrals that are needed in the original scheme and enables us to treat much larger systems than previously possible. We demonstrate the method with calculations on the 33-dimensional Eigen cation.

A Monte Carlo method is proposed for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Canonical Polyadic Decomposition form. To this end, a modified existing ansatz based on the alternating least squares method is used, in which numerically exact integrals are replaced with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows the treatment of surfaces with many degrees of freedom. Calculations on the 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form are presented and compared to the results obtained in a previous work [M. Schröder and H.-D. Meyer, J. Chem. Phys. 147, 064105 (2017)], where a sum-of-products form of the potential was obtained in the Tucker format.

We propose a Monte Carlo method, "Monte Carlo Potfit," for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.

Quantum dynamical simulations in full dimensionality play an essential role in the field of molecular dynamics. This is shown with the help of two examples: (1) the simulation of the infrared spectrum of the Zundel cation (H5OC2+) and (2) the investigation of the tunneling splitting in malonaldehyde (C3H4O2). For the Zundel cation, full, 15-dimensional dynamics calculations are presented for different isotopomers and experimental spectra are assigned to vibrational transitions. Furthermore, the internal proton transfer process within the Zundel cation is discussed. For malonaldehyde, full, 21-dimensional calculations of the ground state, the four lowest fundamentals, and their tunneling splittings are presented. The results are, along with assignments, compared to experimental data and findings of other researchers.

We report energies and tunneling splittings of vibrational excited states of malonaldehyde which have been obtained using full dimensional quantum mechanical calculations. To this end we employed the multi configuration time-dependent Hartree method. The results have been obtained using a recently published potential energy surface [Y. Wang, B. J. Braams, J. M. Bowman, S. Carter, and D. P. Tew, J. Chem. Phys. 128, 224314 (2008)] which has been brought into a suitable form by a modified version of the n-mode representation which was used with two different arrangements of coordinates. The relevant terms of the expansion have been identified with a Metropolis algorithm and a diffusion Monte-Carlo technique, respectively.

A detailed and accurate description of vibrations of molecules and chemical reactions in the field of physical chemistry often requires a full quantum mechanical treatment of the system of interest. This usually implies that the time-dependent or the time-independent Schrödinger equation of the nuclear degrees of freedom (DOF) has to be solved explicitly. For small systems (up to six internal DOF) this can be done with standard methods, i.e., by directly sampling the quantum mechanical wavefunction on a (product-) grid and solving the Schrödinger equation on these grid points. Numerically, within the standard method the multi-dimensional quantum mechanical wavefunction is stored as an f-way tensor, where f is the number of DOF. Due to the linearity of the Schrödinger equation the resulting numerical tasks then usually reduce to standard problems such as the calculation of eigenvalues or solving first order differential equations.

We discuss the role of the coordinates for the convergence of quantum dynamical simulations involving motions of large amplitude. We put special emphasis on the MCTDH algorithm and discuss several illustrative examples that are parametrized by polyspherical coordinates. Finally, new sets of curvilinear coordinates for malonaldehyde and benzopyran are proposed.

The ground state potential energy and dipole moment surfaces for CS2 have been determined at the CASPT2/C:cc-pVTZ,S:aug-cc-pV(T+d)Z level of theory. The potential energy surface has been fit to a sum-of-products form using the neural network method with exponential neurons. A generic interface between neural network potential energy surface fitting and the Heidelberg MCTDH software package is demonstrated. The potential energy surface has also been fit using the potfit procedure in MCTDH. For fits to the low-energy regions of the potential, the neural network method requires fewer parameters than potfit to achieve high accuracy; global fits are comparable between the two methods. Using these potential energy surfaces, the vibrational energies have been computed for the four most abundant CS2 isotopomers. These results are compared to experimental and previous theoretical data. The current potential energy surfaces are shown to accurately reproduce the low-lying vibrational energies within a few wavenumbers. Hence, the potential energy and dipole moments surfaces will be useful for future study on the control of quantum dynamics in CS2.

Full dimensional multi-configuration time-dependent Hartree calculations of the zero point energy and the tunneling splitting of malonaldehyde using a recently published potential energy surface [Y. Wang, B. J. Braams, J. M. Bowman, S. Carter, and D. P. Tew, J. Chem. Phys. 128, 224314 (2008)] are reported. The potential energy surface has been approximated by a modified version of the n-mode representation and careful convergence check has been performed to ensure accurate results. The obtained value for the splitting (23.4 cm(-1)) is in acceptable agreement with the experimental value of 21.583 cm(-1). The computed zero-point-energy is 14,670 cm(-1) which is lower than previous results of Wang et al., but likely to be about 4 cm(-1) too low because of shortcomings of the n-mode representation of the potential. The energies reported in this abstract contain a correction to account for neglected vibrational angular momentum terms.

Comparative studies of implementations of the controlled NOT quantum gate operation using vibrational states of ammonia as the qubit states are presented. The quantum gate operations are realized using tailored laser pulses, which are calculated using a combined approach of optimal control theory and the multiconfiguration time-dependent Hartree method. We compare results obtained with a reduced model of ammonia with three degrees of freedom (all N-H bond distances fixed) to those obtained with a full six-dimensional model. In our study, the optimal laser pulses of both models induce similar underlying physical mechanisms while the gate quality within the reduced model (>98%) is much higher than within the six-dimensional model (approximately 80%).