Condensed Phase Systems Research Articles

Reduced density matrix dynamics in multistate harmonic models via time-convolution and time-convolutionless quantum master equations with quantum-mechanical and semiclassical kernels.

In this work, we explore the electronic reduced density matrix (RDM) dynamics using time-convolution (TC) and time-convolutionless (TCL) quantum master equations (QMEs) that are based on perturbative electronic couplings within the framework of multistate harmonic (MSH) models. The MSH model Hamiltonian consistently incorporates the electronic-vibrational correlations between all pairs of states by satisfying the pairwise reorganization energies directly obtained from all-atom simulations, representing the globally heterogeneous environments that couple to the multiple states differently. We derive the exact quantum-mechanical and a hierarchy of semiclassical approximate expressions for the kernels in TC and TCL QMEs that project the full RDM for general shifted harmonic systems, including the MSH model. These QMEs are applied to simulate RDM dynamics of photoinduced charge transfer (PICT) in organic photovoltaic carotenoid-porphyrin-fullerene triad solvated in tetrahydrofuran solution and the excitation energy transfer (EET) dynamics in photosynthetic Fenna-Matthews-Olson complexes from C. tepidum and P. aestuarii. Our results show that while both TC and TCL QMEs capture similar phenomena in PICT and EET processes, TC QME generally provides more accurate results than TCL QME, particularly in the initial oscillation of EET population dynamics. This study highlights the effectiveness of the TC and TCL QMEs in modeling RDM dynamics of nonadiabatic processes, offering insights for realistic condensed phase systems.

Interatomic and intermolecular decay processes in quantum fluid clusters.

In this comprehensive review, we explore interatomic and intermolecular correlated electronic decay phenomena observed in superfluid helium nanodroplets subjected to extreme ultraviolet (XUV) radiation. Helium nanodroplets, known for their distinctive electronic and quantum fluid properties, provide an ideal environment for examining a variety of non-local electronic decay processes involving the transfer of energy, charge, or both between neighboring sites and resulting in ionization and the emission of low-kinetic energy electrons. Key processes include interatomic or intermolecular Coulombic decay (ICD) and its variants, such as electron transfer-mediated decay (ETMD). Insights gained from studying these light-matter interactions in helium nanodroplets enhance our understanding of the effects of ionizing radiation on other condensed-phase systems, including biological matter. We also emphasize the advanced experimental and computational techniques that make it possible to resolve electronic decay processes with high spectral and temporal precision. Utilizing ultrashort pulses from free-electron lasers, the temporal evolution of these processes can be
followed, significantly advancing our comprehension of the dynamics within quantum fluid clusters and non-local electronic interactions in nanoscale systems.

Reactivity of Atomic Oxygen Radical Anions in Metal Oxide Clusters.

Atomic oxygen radical anion (O⋅-) represents an important type of reactive centre that exists in both chemical and biological systems. Gas-phase atomic clusters can be studied under isolated and well controlled conditions. Studies of O⋅--containing clusters in the gas-phase provide a unique strategy to interpret the chemistry of O⋅- radicals at a strictly molecular level. This review summarizes the research progresses made since 2013 for the reactivity of O⋅- radicals in the atomically precise metal oxide clusters including negatively charged, nanosized, and neutral heteronuclear metal clusters benefitting from the development of advanced experimental techniques. New electronic and geometric factors to control the reactivity and product selectivity of O⋅- radicals under dark and photo-irradiation conditions have been revealed. The detailed mechanisms of O⋅- generation have been discussed for the reaction systems of nanosized and heteroatom-doped metal oxide clusters. The catalytic reactions mediated by the O⋅- radicals in metal clusters have also been successfully established and the microscopic mechanisms about the dynamic generation and depletion of O⋅- radicals have been clearly understood. The studies of O⋅- containing metal oxide clusters in the gas-phase provided new insights into the chemistry of reactive oxygen species in related condensed-phase systems.

Improved Gaussian basis sets for norm-conserving 4f-in-core pseudopotentials of trivalent lanthanides (Ln = Ce-Lu).

The first-principles quantum chemical computations often scale as Nk (N = basis sets; k = 1-4 for linear scaling, Hartree-Fock or density functional theory methods), which makes the development of accurate pseudopotentials and efficient basis sets necessary ingredients in modeling of heavy elements such as lanthanides and actinides. Recently, we have developed 4f-in-core norm-conserving pseudopotentials and associated basis sets for the trivalent lanthanides [Lu et al., J. Chem. Theory Comput. 19, 82-96 (2023)]. In the present paper, we present a unified approach to optimize high-quality Gaussian basis sets for modeling and simulations of condensed-phase systems. The newly generated basis sets not only capture the low total energy and fairly reasonable condition number of overlap matrix of lanthanide-containing systems, but also exhibit good transferability and reproducibility. These advantages ensure the accuracy of the basis sets while avoiding linear dependency concern of atom-centered basis sets. The performance of the basis sets is further illustrated in lanthanide molecular and condensed-phase systems by using Gaussian-plane wave density functional approach of CP2K. These new basis sets can be of particular interest to model structurally complicated lanthanide molecules, clusters, solutions, and solid systems.

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å−1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

Computing linear optical spectra in the presence of nonadiabatic effects on graphics processing units using molecular dynamics and tensor-network approaches.

We compare two recently developed strategies, implemented in open source software packages, for computing linear optical spectra in condensed phase environments in the presence of nonadiabatic effects. Both approaches rely on computing excitation energy and transition dipole fluctuations along molecular dynamics (MD) trajectories, treating molecular and environmental degrees of freedom on the same footing. Spectra are then generated in two ways: in the recently developed Gaussian non-Condon theory, the linear response functions are computed in terms of independent adiabatic excited states, with non-Condon effects described through spectral densities of transition dipole fluctuations. For strongly coupled excited states, we instead parameterize a linear vibronic coupling Hamiltonian directly from spectral densities of energy fluctuations and diabatic couplings computed along the MD trajectory. The optical spectrum is then calculated using powerful, numerically exact tensor-network approaches. Both the electronic structure calculations to sample system fluctuations and the quantum dynamics simulations using tensor-network methods are carried out on graphics processing units, enabling rapid calculations on complex condensed phase systems. We assess the performance of the approaches using model systems in the presence of a conical intersection and the pyrazine molecule in different solvent environments.

GPU-accelerated on-the-fly nonadiabatic semiclassical dynamics.

GPU-accelerated on-the-fly nonadiabatic dynamics is enabled by interfacing the linearized semiclassical dynamics approach with the TeraChem electronic structure program. We describe the computational workflow of the "PySCES" code interface, a Python code for semiclassical dynamics with on-the-fly electronic structure, including parallelization over multiple GPU nodes. We showcase the abilities of this code and present timings for two benchmark systems: fulvene solvated in acetonitrile and a charge transfer system in which a photoexcited zinc-phthalocyanine donor transfers charge to a fullerene acceptor through multiple electronic states on an ultrafast timescale. Our implementation paves the way for an efficient semiclassical approach to model the nonadiabatic excited state dynamics of complex molecules, materials, and condensed phase systems.

PyCTRAMER: A Python package for charge transfer rate constant of condensed-phase systems from Marcus theory to Fermi's golden rule.

In this work, we introduce PyCTRAMER, a comprehensive Python package designed for calculating charge transfer (CT) rate constants in disordered condensed-phase systems at finite temperatures, such as organic photovoltaic (OPV) materials. PyCTRAMER is a restructured and enriched version of the CTRAMER (Charge-Transfer RAtes from Molecular dynamics, Electronic structure, and Rate theory) package [Tinnin et al. J. Chem. Phys. 154, 214108 (2021)], enabling the computation of the Marcus CT rate constant and the six levels of the linearized semiclassical approximations of Fermi's golden rule (FGR) rate constant. It supports various types of intramolecular and intermolecular CT transitions from the excitonic states to CT state. Integrating quantum chemistry calculations, all-atom molecular dynamics (MD) simulations, spin-boson model construction, and rate constant calculations, PyCTRAMER offers an automatic workflow for handling photoinduced CT processes in explicit solvent environments and interfacial CT in amorphous donor/acceptor blends. The package also provides versatile tools for individual workflow steps, including electronic state analysis, state-specific force field construction, MD simulations, and spin-boson model construction from energy trajectories. We demonstrate the software's capabilities through two examples, highlighting both intramolecular and intermolecular CT processes in prototypical OPV systems.

(Invited) Disentangling the Nonequilibrium Dynamics of Excitations in 2D Material Interfaces Under Bias: Leveraging Theory, Electrochemistry, and Time-Resolved Spectroscopy

A fundamental challenge in elucidating, controlling, and exploiting nonequilibrium relaxation in condensed phase systems is the ability to find and employ physically transparent models. Through such models, one can develop a compelling assignment and interpretation of the spectral signatures of processes spanning charge and energy transfer, quasiparticle formation, and even chemical reactivity. Two-dimensional materials, such as transition metal dichalcogenides (TMDs), offer one such challenge, especially under applied fields. In this talk, I will describe our recent work combining theory, electrochemical measurements, and ultrafast spectroscopy to demonstrate hot carrier extraction in photoelectrochemical cells composed of monolayer MoS2 on an ITO electrode exposed to electrolyte solution. In addition, I will discuss our critical assessment of the ability of a physically intuitive Hamiltonian, consisting of an infinitely heavy exciton immersed in a fermi sea of conduction band electrons, to capture and offer an interpretation of the spectral features in the linear and transient absorption optical signals of this material under an applied bias. Importantly, we leverage our analysis to identify, physically, how trion formation moves, broadens, and resizes the “A exciton” absorption of our working device. We further unify the interpretation over various sources of such TMD spectral shifts: applied bias, fluence, and (TA) delay time. Our work thus demonstrates hot carrier extraction in 2D photoelectrochemical cells, outlines a path to exploit this phenomenon in semiconductor devices, delineates open questions that are only now becoming possible to address with theory and experiment, and identifies the underlying physical process responsible for previously misidentified spectral features in 2D materials that changed with applied voltage, fluence, and time.

(Invited) Machine Learning in Chemistry: Reactive Force Fields for Carbon Structure Formation

Machine learning (ML) became a premier tool for modeling chemical processes and materials properties. ML interatomic potentials have become an efficient alternative to computationally expensive quantum chemistry simulations. In the case of reactive chemistry designing high-quality training data sets is crucial to overall model accuracy. To address this challenge, we develop a general reactive ML interatomic potential through unbiased active learning with an atomic configuration sampler inspired by nanoreactor molecular dynamics. The resulting model is then applied to study five distinct condensed-phase reactive chemistry systems: carbon solid-phase nucleation, graphene ring formation from acetylene, biofuel additives, combustion of methane and the spontaneous formation of glycine from early-earth small molecules. In all cases, the results closely match experiment and/or previous studies using traditional model chemistry methods. Importantly, the model does not need to be refit for each application, enabling high throughput in silico reactive chemistry experimentation.

How Accurate Are Simulations and Experiments for the Lattice Energies of Molecular Crystals?

Molecular crystals play a central role in a wide range of scientific fields, including pharmaceuticals and organic semiconductor devices. However, they are challenging systems to model accurately with computational approaches because of a delicate interplay of intermolecular interactions such as hydrogen bonding and Van der Waals dispersion forces. Here, by exploiting recent algorithmic developments, we report the first set of diffusion MonteCarlo lattice energies for all 23molecular crystals in the popular and widely used X23 dataset. Comparisons with previous state-of-the-art lattice energy predictions (on a subset of the dataset) and a careful analysis of experimental sublimation enthalpies reveals that high-accuracy computational methods are now at least as reliable as (computationally derived) experiments for the lattice energies of molecular crystals. Overall, this work demonstrates the feasibility of high-level explicitly correlated electronic structure methods for broad benchmarking studies in complex condensed phase systems, and signposts a route towards closer agreement between experiment and simulation.

Enabling Ab Initio Molecular Dynamics under Bias: The CP2K+SMEAGOL Interface for Integrating Density Functional Theory and Non-Equilibrium Green Functions.

Density functional theory (DFT) combined with non-equilibrium Green's functions (NEGF) is a powerful approach to model quantum transport under external bias potentials at reasonable computational cost. In this work, we present a new interface between the popular mixed Gaussian/plane waves electronic structure package, CP2K, and the NEGF, code SMEAGOL, the most feature-rich implementation of DFT-NEGF available for CP2K to date. The CP2K+SMEAGOL interface includes the implementation of current induced forces. We verify this implementation for a variety of systems: an infinite 1D Au wire, a parallel-plate capacitor, and a Au-H2-Au junction. We find good agreement with SMEAGOL calculations performed with SIESTA for the same systems and with the example of a solvated Au wire demonstrating for the first time that DFT-NEGF can be used to perform molecular dynamics simulations under bias of large-scale condensed phase systems under realistic operating conditions.

Modification with lignin-based N-P flame retardant to improve the flame retardancy and smoke suppression of wood

The development of effective and eco-friendly wood-based functional composites is crucial for maximizing the value of forest resources. In this paper, we propose a novel method for preparing an aqueous-phase flame retardant (MPUC) using carboxymethylation alkali lignin, phytic acid, and melamine-urea-glyoxal resin. This approach aims to manufacture modified wood (MW/MPUC) with exceptional flame-retardant and smoke-suppressing properties. The results from the cone calorimeter test indicate that the modified wood achieved a remarkable reduction of up to 56.8 % in total heat release and an impressive 92.3 % decrease in total smoke production. Furthermore, the limiting oxygen index increased significantly from 23.6 % (natural wood) to 41.5 % (MW/MPUC-2). Notably, all modified wood successfully passed the V-1 test for UL-94 flammability rating. Further, our investigation into the gas-phase products formed during pyrolysis and the condensed-phase system created after combustion has led us to propose potential flame-retardant mechanisms for these flame retardants. Moreover, modified wood had improved mechanical properties and dimensional stability than natural wood. In addition, we extended the application of MPUC-2 flame-retardant to other flammable materials and demonstrated its excellent flame-retardant properties. Thus, the proposed strategy provided a new approach for preparing wood-based flame-retardant composites with lignin-based N-P flame retardants.

Instantaneous Marcus theory for photoinduced charge transfer dynamics in multistate harmonic model systems

Modeling the dynamics of photoinduced charge transfer (CT) in condensed phases presents challenges due to complicated many-body interactions and the quantum nature of electronic transitions. While traditional Marcus theory is a robust method for calculating CT rate constants between electronic states, it cannot account for the nonequilibrium effects arising from the initial nuclear state preparation. In this study, we employ the instantaneous Marcus theory (IMT) to simulate photoinduced CT dynamics. IMT incorporates nonequilibrium structural relaxation following a vertical photoexcitation from the equilibrated ground state, yielding a time-dependent rate coefficient. The multistate harmonic (MSH) model Hamiltonian characterizes an organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent, constructed by mapping all-atom inputs from molecular dynamics simulations. Our calculations reveal that the electronic population dynamics of the MSH models obtained with IMT agree with the more accurate quantum-mechanical nonequilibrium Fermi’s golden rule. This alignment suggests that IMT provides a practical approach to understanding nonadiabatic CT dynamics in condensed-phase systems.

Semiclassical approaches to perturbative time-convolution and time-convolutionless quantum master equations for electronic transitions in multistate systems.

Understanding the dynamics of photoinduced processes in complex systems is crucial for the development of advanced energy-conversion materials. In this study, we investigate the nonadiabatic dynamics using time-convolution (TC) and time-convolutionless (TCL) quantum master equations (QMEs) based on treating electronic couplings as perturbation within the framework of multistate harmonic (MSH) models. The MSH model Hamiltonians are mapped from all-atom simulations such that all pairwise reorganization energies are consistently incorporated, leading to a heterogeneous environment that couples to the multiple electronic states differently. Our exploration encompasses the photoinduced charge transfer dynamics in organic photovoltaic carotenoid-porphyrin-C60 triad dissolved in liquid solution and the excitation energy transfer (EET) dynamics in photosynthetic Fenna-Matthews-Olson complexes. By systematically comparing the perturbative TC and TCL QME approaches with exact quantum-mechanical and various semiclassical approximate kernels, we demonstrate their efficacy and accuracy in capturing the essential features of photoinduced dynamics. Our calculations show that TC QMEs generally yield more accurate results than TCL QMEs, especially in EET, although both methods offer versatile approaches adaptable across different systems. In addition, we investigate various semiclassical approximations featuring the Wigner-transformed and classical nuclear densities as well as the governing dynamics during the quantum coherence period, highlighting the trade-off between accuracy and computational cost. This work provides valuable insights into the applicability and performance of TC and TCL QME approaches via the MSH model, offering guidance for realistic applications to condensed-phase systems on the atomistic level.

Seamless integration of GEM, a density based-force field, for QM/MM simulations via LICHEM, Psi4, and Tinker-HP.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations have become an essential tool in computational chemistry, particularly for analyzing complex biological and condensed phase systems. Building on this foundation, our work presents a novel implementation of the Gaussian Electrostatic Model (GEM), a polarizable density-based force field, within the QM/MM framework. This advancement provides seamless integration, enabling efficient and optimized QM/GEM calculations in a single step using the LICHEM Code. We have successfully applied our implementation to water dimers and hexamers, demonstrating the ability to handle water systems with varying numbers of water molecules. Moreover, we have extended the application to describe the double proton transfer of the aspartic acid dimer in a box of water, which highlights the method's proficiency in investigating heterogeneous systems. Our implementation offers the flexibility to perform on-the-fly density fitting or to utilize pre-fitted coefficients to estimate exchange and Coulomb contributions. This flexibility enhances efficiency and accuracy in modeling molecular interactions, especially in systems where polarization effects are significant.

All-Atom Photoinduced Charge Transfer Dynamics in Condensed Phase via Multistate Nonlinear-Response Instantaneous Marcus Theory.

Photoinduced charge transfer (CT) in the condensed phase is an essential component in solar energy conversion, but it is challenging to simulate such a process on the all-atom level. The traditional Marcus theory has been utilized for obtaining CT rate constants between pairs of electronic states but cannot account for the nonequilibrium effects due to the initial nuclear preparation. The recently proposed instantaneous Marcus theory (IMT) and its nonlinear-response formulation allow for incorporating the nonequilibrium nuclear relaxation to electronic transition between two states after the photoexcitation from the equilibrium ground state and provide the time-dependent rate coefficient. In this work, we extend the nonlinear-response IMT method for treating photoinduced CT among general multiple electronic states and demonstrate it in the organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent. All-atom molecular dynamics simulations were employed to obtain the time correlation functions of energy gaps, which were used to generate the IMT-required time-dependent averages and variances of the relevant energy gaps. Our calculations show that the multistate IMT could capture the significant nonequilibrium effects due to the initial nuclear state preparation, and this is corroborated by the substantial differences between the population dynamics predicted by the multistate IMT and the Marcus theory, where the Marcus theory underestimates the population transfer. The population dynamics by multistate IMT is also shown to have a better agreement with the all-atom nonadiabatic mapping dynamics than the Marcus theory does. Because the multistate nonlinear-response IMT is straightforward and cost-effective in implementation and accounts for the nonequilibrium nuclear effects, we believe this method offers a practical strategy for studying charge transfer dynamics in complex condensed-phase systems.

Born-Oppenheimer Molecular Dynamics with a Linear Combination of Atomic Orbitals and Hybrid Functionals for Condensed Matter Simulations Made Possible. Theory and Performance for the Microcanonical and Canonical Ensembles.

The implementation of an original Born-Oppenheimer molecular dynamics module is presented, which is able to perform simulations of large and complex condensed phase systems for sufficiently long time scales at the level of density functional theory with hybrid functionals, in the microcanonical (NVE) and canonical (NVT) ensembles. The algorithm is fully integrated in the Crystal code, a program for quantum mechanical simulations of materials, whose peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals to describe the wave function. The corresponding efficiency in the evaluation of the exact Fock exchange series has led to the implementation of a rich variety of hybrid density functionals at a low computational cost. In addition, the molecular dynamics implementation benefits also from the effective MPI parallelization of the code, suited to exploit high-performance computing resources available on current generation supercomputer architectures. Furthermore, the information contained in the trajectory of the dynamics is extracted through a series of postprocessing algorithms that provide the radial distribution function, the diffusion coefficient and the vibrational density of states. In this work, we present a detailed description of the theoretical framework and the algorithmic implementation, followed by a critical evaluation of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach, when ice and liquid water simulations are performed in the microcanonical and canonical ensembles.

Taming the third order cumulant approximation to linear optical spectroscopy.

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

Generalized nonequilibrium Fermi's golden rule and its semiclassical approximations for electronic transitions between multiple states.

The nonequilibrium Fermi's golden rule (NE-FGR) approach is developed to simulate the electronic transitions between multiple excited states in complex condensed-phase systems described by the recently proposed multi-state harmonic (MSH) model Hamiltonian. The MSH models were constructed to faithfully capture the photoinduced charge transfer dynamics in a prototypical organic photovoltaic carotenoid-porphyrin-C60 molecular triad dissolved in tetrahydrofuran. A general expression of the fully quantum-mechanical NE-FGR rate coefficients for transitions between all pairs of states in the MSH model is obtained. Besides, the linearized semiclassical NE-FGR formula and a series of semiclassical approximations featuring Wigner and classical nuclear sampling choices and different dynamics during the quantum coherence period for the MSH model are derived. The current approach enables all the possible population transfer pathways between the excited states of the triad, in contrast to the previous applications that only addressed the donor-to-acceptor transition. Our simulations for two triad conformations serve as a demonstration for benchmarking different NE-FGR approximations and show that the difference between all levels of approximation is small for the current system, especially at room temperature. By comparing with nonadiabatic semiclassical dynamics, we observe similar timescales for the electronic population transfer predicted by NE-FGR. It is believed that the general formulation of NE-FGR for the MSH Hamiltonian enables a variety of applications in realistic systems.