Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering

Computing Excited States of Molecules Using Normalizing Flows

Calculations of highly excited and delocalized molecular vibrational states are computationally challenging tasks, which strongly depend on the choice of coordinates for describing vibrational motions. We introduce a new method that leverages normalizing flows, i.e, parametrized invertible functions, to learn optimal vibrational coordinates that satisfy the variational principle. This approach produces coordinates tailored to the vibrational problem at hand, significantly increasing the accuracy and enhancing the basis set convergence of the calculated energy spectrum. The efficiency of the method is demonstrated in calculations of the 100 lowest excited vibrational states of H2S, H2CO, and HCN/HNC. The method effectively captures the essential vibrational behavior of molecules by enhancing the separability of the Hamiltonian and hence allows for an effective assignment of approximate quantum numbers. We demonstrate that the optimized coordinates are transferable across different levels of basis set truncation, enabling a cost-efficient protocol for computing vibrational spectra of high-dimensional systems.

Full Quantum Dynamics Study for H Atom Scattering from Graphene

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.

ML-MCTDH-Aid: An auxiliary package for multilayer multiconfiguration time-dependent Hartree calculations

The multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method has garnered significant attention in the realm of theoretical chemistry owing to its powerful ability to perform numerically exact descriptions of multi-dimensional quantum dynamics and exhibit the remarkable performance in simulating the nonadiabatic dynamics of complex systems. Despite the availability of computational packages within the ML-MCTDH framework, executing these calculations seamlessly is not a straightforward task. Typically, substantial efforts are necessitated to configure the correct inputs for ML-MCTDH calculations, which require to correctly define several non-trivial parameters, to reasonably setup the optimal tree expansion of wavefunctions, and to properly select basis function numbers. To address these challenges, we have developed an auxiliary package named ML-MCTDH-Aid, which facilitates the setup of ML-MCTDH calculations using the Heidelberg MCTDH package in a user-friendly manner. This package is primarily tailored to handle the high-dimensional nonadiabatic dynamics governed by the Hamiltonian composed of several electronic states, several vibrational modes and their linear vibronic coupling terms. It automatically generates multiple essential input files, and all the calculations can be performed in an all-in-one black-box easy-to-use manner. To show the utility of the ML-MCTDH-Aid package, we provide a step-by-step tutorial that demonstrates running ML-MCTDH studies on three models. These examples illuminate how the utilization of the ML-MCTDH-Aid package significantly enhances the efficiency and effectiveness of ML-MCTDH calculations. This substantially boosts the accessibility of ML-MCTDH calculations in tackling the high-dimensional quantum dynamics of complex systems.

Vibrational Entanglement through the Lens of Quantum Information Measures

We introduce a quantum information analysis of vibrational wave functions to understand complex vibrational spectra of molecules with strong anharmonic couplings and vibrational resonances. For this purpose, we define one- and two-modal entropies to guide the identification of strongly coupled vibrational modes and to characterize correlations within modal basis sets. We evaluate these descriptors for multiconfigurational vibrational wave functions which we calculate with the n-mode vibrational density matrix renormalization group algorithm. Based on the quantum information measures, we present a vibrational entanglement analysis of the vibrational ground and excited states of CO2, which display strong anharmonic effects due to the symmetry-induced and accidental (near-) degeneracies. We investigate the entanglement signature of the Fermi resonance and discuss the maximally entangled state arising from the two degenerate bending modes.

Determining internal coordinate sets for optimal representation of molecular vibration

Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced.

Molecular Dynamics of Artificially Pair-Decoupled Systems: An Accurate Tool for Investigating the Importance of Intramolecular Couplings

We propose a numerical technique to accurately simulate the vibrations of organic molecules in the gas phase, when pairs of atoms (or, in general, groups of degrees of freedom) are artificially decoupled, so that their motion is instantaneously decorrelated. The numerical technique we have developed is a symplectic integration algorithm that never requires computation of the force but requires estimates of the Hessian matrix. The theory we present to support our technique postulates a pair-decoupling Hamiltonian function, which parametrically depends on a decoupling coefficient α ∈ [0, 1]. The closer α is to 0, the more decoupled the selected atoms. We test the correctness of our numerical method on small molecular systems, and we apply it to study the vibrational spectroscopic features of salicylic acid at the Density Functional Theory ab initio level on a fitted potential. Our pair-decoupled simulations of salicylic acid show that decoupling hydrogen-bonded atoms do not significantly influence the frequencies of stretching modes, but enhance enormously the out-of-plane wagging and twisting motions of the hydroxyl and carboxyl groups to the point that the carboxyl and hydroxyl groups may overcome high potential energy barriers and change the salicylic acid conformation after a short simulation time. In addition, we found that the acidity of salicylic acid is more influenced by the dynamical couplings of the proton of the carboxylic group with the carbon ring than with the hydroxyl group.