Operator Formulation of Feynman Path Centroid Dynamics for Rotations.

An operator formulation of centroid molecular dynamics (CMD) for rotational degrees of freedom is presented. The quasi-density operator concept was introduced by Jang and Voth [J. Chem. Phys 111, 2357 (1999)] and is used to obtain a phase-space mapping without the need for discretized path integrals. The approach allows the calculation of approximate Kubo-transformed time correlation functions. The particle on a ring is chosen as an illustrative example. Numerical results demonstrate that the proposed approach leads to accurate results when compared with exact diagonalization calculations for linear operators. At very low temperatures, it is found that rotational CMD yields results that are in exact agreement with the quantum dynamics of a spin-1 system.

A neural network-based four-body potential energy surface for parahydrogen.

We present an isotropic ab initio (para-H2)4 four-body interaction potential energy surface (PES). The electronic structure calculations are performed at the correlated coupled-cluster theory level, with single, double, and perturbative triple excitations. They use an atom-centered augmented correlation-consistent double zeta basis set, supplemented by a (3s3p2d) midbond function. We use a multilayer perceptron to construct the PES. We apply a rescaling transformation to the output energies during training to improve the prediction of weaker energies in the sample data. At long distances, the interaction energies are adjusted to match the empirically derived four-body dispersion interaction. The four-body interaction energy at short intermolecular separations is net repulsive. The use of this four-body PES, in combination with a first principles pair potential for para-H2 [J. Chem. Phys. 119, 12551 (2015)] and an isotropic ab initio three-body potential for para-H2 [J. Chem. Phys. 156, 044301 (2022)], is expected to provide closer agreement with experimental results.

Ground states of planar dipolar rotor chains with recurrent neural networks.

In this contribution, we employ a recurrent neural network (RNN) architecture in a variational optimization to obtain the ground state of linear chains of planar, dipolar rotors. We test different local basis sets and discuss their impact on the sign structure of the many-body ground state wavefunction. It is demonstrated that the RNN ansatz we employ is able to treat systems with and without a sign problem in the ground state. For larger chains with up to 50 rotors, accurate properties, such as correlation functions and Binder parameters, are calculated. By employing quantum annealing, we show that precise entanglement properties can be obtained. All these properties allow one to identify a quantum phase transition between a paraelectric and a ferroelectric quantum phase.

Quantum criticality in chains of planar rotors with dipolar interactions.

In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model.

Optimized basis sets for DMRG calculations of quantum chains of rotating water molecules.

In this contribution, we employ a density matrix-based optimization procedure to obtain customized basis functions to describe chains of rotating water molecules in interaction regimes associated with different intermolecular distances. This procedure is shown to yield a very compact basis with a clear truncation criterion based on the population of the single particle basis functions. For the water trimer, we discuss the convergence behavior of several properties and show it to be superior when compared to an energy-based truncated basis. It is demonstrated that the optimized basis reduces the necessary number of basis functions by at least an order of magnitude. Finally, the optimization procedure is employed to study larger chains of up to ten water molecules. The formation of hydrogen bonds as well as its impact on the net polarization of the chain is discussed.

On the nature of the Schottky anomaly in endohedral water.

In this work, we study the heat capacity contribution of a rigid water molecule encapsulated in C60 by performing six-dimensional eigenstate calculations with the inclusion of its quantized rotational and translational degrees of freedom. Two confinement model potentials are considered: in the first, confinement is described using distributed pairwise Lennard-Jones interactions, while in the second, the water molecule is trapped within an eccentric but isotropic 3D harmonic effective confinement potential [Wespiser et al., J. Chem. Phys. 156, 074304 (2022)]. Contributions to the heat capacity from both the ortho and para nuclear spin isomers of water are considered to enable the effects of their interconversion to be assessed. By including a symmetry-breaking quadrupolar potential energy term in the Hamiltonian, we can reproduce the experimentally observed Schottky anomaly at ∼2 K [Suzuki et al., J. Phys. Chem. Lett. 10, 1306 (2019)]. Furthermore, our calculations predict a second Schottky anomaly at ∼0.1 K resulting from the H configuration, a different orientational arrangement of the fullerene cages in crystalline solid C60. Contributions from the H configuration to CV also explain the second peak observed at ∼7 K in the experimentally measured heat capacity.

ROESY and 13C NMR to distinguish between D- and L-rhamnose in the α-D-Manp-(1 → 4)-ß-Rhap-(1 → 3) repeating motif.

Many children suffering from autism spectrum disorder (ASD) experience gastrointestinal (GI) conditions. Enterocloster bolteae has been regularly detected in the stool of individuals suffering from GI symptoms and autism. Literature has suggested that E. bolteae strains WAL 16351 and WAL 14578 produce an immunogenic capsular polysaccharide (CPS) comprised of disaccharide repeating units: α-D-Man-(1 → 4)-ß-Rha-(1 → 3) that could be used for the development of an immunotherapeutic vaccine. Ambiguity in the configuration of rhamnose led to the synthesis of tri- and disaccharide analogues containing D-rhamnose and L-rhamnose, respectively. ROESY-NMR spectra showed that CH3-6 of rhamnose and H-2 of mannose in the L-Rha containing disaccharide gave correlation. No such correlation was seen between the CH3-6 of rhamnose and the H-2 of mannose in the D-Rha containing trisaccharide. Molecular dynamics studies on hexasaccharide containing L-Rha or D-Rha confirmed that these structures adopt conformations resulting in different distances between the C6-rhamnose and the H-2 mannose of the preceding residue. We also demonstrate that assignment of the absolute configuration of the rhamnosyl residue in the ß-Rhap-(1 → 3)-D-Man linkage can be determined using the 13C chemical shift of C-2 in of D-Mannose. While ß-D-Rha will lead to an upfield shift of C-2 due to γ-gauche interaction between H-1 Rha and H-2 Man, ß-L-Rha will not. Our results provide insights to distinguish between D- and L-rhamnose in the α-D-Manp-(1 → 4)-ß-Rhap-(1 → 3) repeating motif.

Reaction-intermediate-induced atomic mobility in heterogeneous metal catalysts for electrochemical reduction of CO2.

Improving the activity and selectivity of heterogeneous metal electrocatalysts has been the primary focus of CO2 electroreduction studies, however, the stability of these materials crucial for practical application remains less understood. In our work, the impact of the reaction intermediates (RIs) on the energetics and mechanism of metal-atom migration is studied with a combination of density functional theory (DFT) and ab initio molecular dynamics (AIMD) on pure transition metals Cu, Ag, Au, Pd, as well as three Cu4-xPdx (x = 1,2, and 3) alloys. Reaction intermediates (RIs) for the CO2 reduction reaction, H2 evolution, and O2 reduction were considered. The effect of adsorbed RIs was observed to facilitate metal atom migration generally by decreasing the kinetic barriers for migration. The atomic mobility trends in the commonly used CO2RR metal electrocatalysts in the course of electrolysis conditions were established. This study provides theoretical insight into understanding how the electrocatalyst may undergo promoted restructuring in the presence of RIs under realistic electrochemical conditions.

Equation of state of solid parahydrogen using ab initio two-body and three-body interaction potentials.

We present the equation of state of solid parahydrogen between 0.024 and 0.1 Å-3 at T = 4.2 K, calculated using path integral Monte Carlo simulations, with ab initio two-body and three-body interaction potentials. We correct for finite size simulation errors using potential tail corrections. Trotter factorization errors are accounted for either via extrapolation or by using a suitably small imaginary time step. We incorporate the three-body interaction using two methods: (1) the full inclusion method, where pair and three-body interactions are used in both Monte Carlo sampling and in the energy estimators, and (2) the perturbative method, where three-body interactions are omitted from sampling but are still present in energy estimations. Both treatments of the three-body interaction return very similar total energies and pressures. The presence of three-body interactions has only minor effects on the structural properties of the solid. Whereas the pair interaction, on its own, significantly overestimates the pressure of solid parahydrogen, the additional presence of the three-body interaction causes a severe underestimation of the pressure. Our findings suggest that accurate simulations of solid parahydrogen require four-body and possibly higher-order many-body interactions. It may also be the case that static interaction potentials are entirely unsuitable for simulations of solid parahydrogen at high densities.

Ferroelectric water chains in carbon nanotubes: Creation and manipulation of ordered quantum phases.

Systems composed of molecular rotors are promising candidates as quantum devices. In this work, we employ our recently developed density matrix renormalization group approach to study such a rotor system, namely, linear chains of rotating para-water molecules encapsulated in a (6,5)-carbon nanotube. We show that the anisotropic environment provided by the nanotube breaks the inversion symmetry of the chain. This symmetry breaking lifts the degeneracy of the ground state and leads to a splitting between the left- and right-polarized states. In turn, a ferroelectric phase in nanoscopic systems is created, with a polarization that can be switched in a manner analogous to that of a supramolecular qubit. We present results for a few low-lying states and discuss the effect of external electric fields on the energy splitting and the occurrence of a quantum phase transition.

Ground state chemical potential of parahydrogen clusters of size N = 21-40.

We report the ground state chemical potential of parahydrogen clusters between N = 21-40 calculated using the Langevin equation Path Integral Ground State method. There has been much debate in the past whether the chemical potential size evolution in this region is jagged (indicating magic number cluster sizes) or if it is smooth (indicating some quantum melting below 1 K). We compare to previous diffusion Monte Carlo and Path Integral Ground State (PIGS) results, including very recent Variational Path Integral Molecular Dynamics (VPIMD) calculations [S. Miura, J. Chem. Phys. 148, 102333 (2018)]. We find that the ground state chemical potential is not a smooth curve and that magic number clusters are present, consistent with VPIMD and PIGS Monte Carlo results.

Ground state of asymmetric tops with DMRG: Water in one dimension.

We propose an approach to compute the ground state properties of collections of interacting asymmetric top molecules based on the density matrix renormalization group method. Linear chains of rigid water molecules of varying sizes and density are used to illustrate the method. A primitive computational basis of asymmetric top eigenstates with nuclear spin symmetry is used, and the many-body wave function is represented as a matrix product state. We introduce a singular value decomposition approach in order to represent general interaction potentials as matrix product operators. The method can be used to describe linear chains containing up to 50 water molecules. Properties such as the ground state energy, the von-Neumann entanglement entropy, and orientational correlation functions are computed. The effect of basis set truncation on the convergence of ground state properties is assessed. It is shown that specific intermolecular distance regions can be grouped by their von-Neumann entanglement entropy, which in turn can be associated with electric dipole-dipole alignment and hydrogen bond formation. Additionally, by assuming conservation of local spin states, we present our approach to be capable of calculating chains with different arrangements of the para and ortho spin isomers of water and demonstrate that for the water dimer.

Three-body potential energy surface for para-hydrogen.

We present a 3D isotropic ab initio three-body (para-H2)3 interaction potential energy surface (PES). The electronic structure calculations are carried out at the correlated coupled-cluster theory level, with single, double, and perturbative triple excitations. The calculations use an augmented correlation-consistent triple zeta basis set and a supplementary midbond function. We construct the PES using the reproducing-kernel Hilbert space toolkit [O. T. Unke and M. Meuwly, J. Chem. Inf. Model. 57, 1923 (2017)] with phenomenological and empirical adjustments to account for short-range and long-range behaviors. The (para-H2)3 interaction energies deviate drastically from the Axilrod-Teller-Muto (ATM) potential at short intermolecular separations. We find that the configuration of three para-H2 molecules at the corners of an equilateral triangle is responsible for the majority of the (para-H2)3 interaction energy contribution in a hexagonal-close-packed lattice. In cases where two para-H2 molecules are close to one another while the third is far away, the (para-H2)3 interaction PES takes the form of a modified version of the ATM potential. We expect the combination of this PES together with a first-principles para-H2-para-H2 adiabatic hindered rotor potential to outperform a widely used effective pair potential for condensed many-body systems of para-H2.

On the accuracy and efficiency of different methods to calculate Raman vibrational shifts of parahydrogen clusters.

The Raman vibrational frequency shifts of pure parahydrogen and orthodeuterium clusters of sizes N = 4-9 are calculated using the Langevin equation path integral ground state method. The shifts are calculated using three different methods; the results obtained from each are compared to experiment and variance properties are assessed. The first method requires the direct calculation of energies from two simulations: one when the cluster is in the v = 0 vibrational state and one when the cluster has v = 1 total quantum of vibration. The shift is directly calculated from the difference in those two energies. The second method requires only a v = 0 simulation to be performed. The ground state energy is calculated as usual and the excited state energy is calculated by using the distribution of the v = 0 simulation and the ratio of the density matrices between the v = 1 state and the v = 0 state. The shift is calculated from the difference in those two energies. These first two are both exact methods. The final method is based on perturbation theory where the shift is calculated by averaging the pairwise difference potential over the pair distribution function. However, this is an approximate approach. It is found that for large enough system sizes, despite the approximations, the perturbation theory method has the strongest balance between accuracy and precision when weighing against computational cost.

Path integral simulations of confined parahydrogen molecules within clathrate hydrates: Merging low temperature dynamics with the zero-temperature limit.

Clathrate hydrates, or cages comprised solely of water molecules, have long been investigated as a clean storage facility for hydrogen molecules. A breakthrough occurred when hydrogen molecules were experimentally placed within a structure-II clathrate hydrate, which sparked much interest to determine their feasibility for energy storage [Mao et al., Science 297, 2247-2249 (2002)]. We use Path Integral Molecular Dynamics (PIMD) and Langevin equation Path Integral Ground State (LePIGS) for finite temperature and zero-temperature studies, respectively, to determine parahydrogen occupancy properties in the small dodecahedral (512) and large hexakaidecahedral (51264) sized cages that comprise the structure-II unit cell. We look at energetic and structural properties of small clusters of hydrogen, treated as point-like particles, confined within each of the different sized clathrates, and treated as rigid, to determine energetic and structural properties in the zero-temperature limit. Our predicted hydrogen occupancy within these two cage sizes is consistent with previous literature values. We then calculate the energies as a function of temperature and merge the low temperature results calculated using finite temperature PIMD with the zero-temperature results using LePIGS, demonstrating that the two methods are compatible.

Ro-translational dynamics of confined water. I. The confined asymmetric rotor model.

Confinement effects on the ro-translational (RT) dynamics of water, trapped in rare gas matrices or within endofullerenes (i.e., H2O@C60), can be experimentally assessed using rotationally resolved far-infrared, or mid-infrared, spectroscopy [Putaud et al., J. Chem. Phys. 156, 074305 (2022) (Paper II)]. The confined rotor model is used here to reveal how the quantized rotational and frustrated translational energy levels of confined water interact and mix by way of the confinement-induced rotation-translation coupling (RTC). An eccentric but otherwise isotropic 3D harmonic effective potential is used to account for confinement effects, thereby allowing the dependence of the magnitude of the RTC on the topology of the model confinement potential, the resulting intricate mixing schemes, and their impact on the RT energy levels to be examined in detail. The confined rotor model thus provides a convenient framework to investigate the matrix and isotope effects on the RT dynamics of water under extreme confinement probed spectroscopically, thereby potentially providing insight into the mechanisms and rates for ortho-H2O ↔ para-H2O nuclear spin isomer interconversion in confined water.

A path integral ground state approach for asymmetric top rotors with nuclear spin symmetry: Application to water chains.

A path integral ground state (PIGS) approach for the simulation of asymmetric top rotors is presented. The method is based on Monte Carlo sampling of angular degrees of freedom. A symmetry-adapted rotational density matrix is used to account for nuclear spin statistics. To illustrate the method, ground-state properties of collections of para-water molecules confined to a one-dimensional lattice are computed. Those include energetic and structural observables. An advantage of the PIGS method is that expectation values can be obtained directly since the square of the wavefunction is sampled during a simulation. To benchmark the method, ground state energies and orientational distributions are computed using exact diagonalization for a single para-water molecule in an external field using a finite basis of symmetric top eigenfunctions. Benchmark results are also provided for N = 2 para-water molecules pinned to lattice sites at various distances to sample the crossover from hydrogen bonding to the dipole-dipole interaction regime. Excellent agreement between the PIGS results and the finite basis set calculations is observed. A thorough analysis of the convergence in terms of the imaginary time propagation length and systematic Trotter error is performed. The PIGS approach is then applied to a chain of N = 11 water molecules, and an equation of state is constructed in terms of the intermolecular separation. Ordering effects are also studied, and a transition between hydrogen bonding to dipole-dipole alignment is observed. The method is scalable and can also be applied in higher dimensions.

Comparison of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) for ground state properties of linear rotor chains.

We demonstrate the applicability of the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method to the problem of computing ground states of one-dimensional chains of linear rotors with dipolar interactions. Specifically, we successfully obtain energies, entanglement entropies, and orientational correlations that are in agreement with the Density Matrix Renormalization Group (DMRG), which has been previously used for this system. We find that the entropies calculated by ML-MCTDH for larger system sizes contain nonmonotonicity, as expected in the vicinity of a second-order quantum phase transition between ordered and disordered rotor states. We observe that this effect remains when all couplings besides nearest-neighbor are omitted from the Hamiltonian, which suggests that it is not sensitive to the rate of decay of the interactions. In contrast to DMRG, which is tailored to the one-dimensional case, ML-MCTDH (as implemented in the Heidelberg MCTDH package) requires more computational time and memory, although the requirements are still within reach of commodity hardware. The numerical convergence and computational demand of two practical implementations of ML-MCTDH and DMRG are presented in detail for various combinations of system parameters.

Vibrational Raman Shifts of Spin Isomer Combinations of Hydrogen Dimers and Isotopologues.

Binding energies for para-para, ortho-para, and ortho-ortho hydrogen dimers (H2)2 are calculated using the six-dimensional (6D) interaction potential developed by Hinde [ J. Chem. Phys. 2008, 128, 154308]. The eigenstates of the dimers are computed by diagonalization using, as a basis, products of the rovibrational states of the monomers, a radial grid for the distance between the monomers, and spherical harmonics for the end-over-end rotation of the dimer. We describe the overall nuclear spin symmetry and use these properties to determine the relative population of various states, making use of a Boltzmann factor for each spin isomer to assess the effect of temperature. A predicted Raman spectrum in the Q(0) and Q(1) region of the hydrogen dimer is produced. To assess the accuracy of our model, we verify our produced shifts with experimental results obtained previously by Montero et al. [ Eur. Phys. J. D 2009, 52, 31-34] and find good agreement. These results are extended to other cases involving the deuterium (D2)2 and tritium dimer (T2)2 isotopologues, to predict Raman shifts.

A path integral ground state replica trick approach for the computation of entanglement entropy of dipolar linear rotors.

We calculate the second Rényi entanglement entropy for systems of interacting linear rotors in their ground state as a measure of entanglement for continuous rotational degrees of freedom. The entropy is defined in relation to the purity of a subsystem in a bipartite quantum system, and to compute it, we compare two sampling ensembles based on the path integral ground state (PIGS) formalism. This scheme centers on the replica trick and is aided by the ratio trick, both developed in this context by Hastings et al. [Phys. Rev. Lett. 104, 157201 (2010)]. We study a system composed of linear quantum rotors on a lattice in one dimension, interacting via an anisotropic dipole-dipole potential. The ground state second Rényi entropies estimated by PIGS are benchmarked against those from the density matrix renormalization group for various interaction strengths and system sizes. We find that the entropy grows with an increase in interaction strength, and for large enough systems, it appears to plateau near log(2). We posit that the limiting case of many strongly interacting rotors behaves akin to a lattice of two-level particles in a cat state, in which one naturally finds an entanglement entropy of log(2).