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The use of Δ-self-consistent field (SCF) approaches for studying excited electronic states has received a renewed interest in recent years. In this work, the use of this scheme for calculating excited-state vibrational frequencies is examined. Results from Δ-SCF calculations for a set of representative molecules are compared with those obtained using configuration interaction with single substitutions (CIS) and time-dependent density functional theory (TD-DFT) methods. The use of an approximate spin purification model is also considered for cases where the excited-state SCF solution is spin-contaminated. The results of this work demonstrate that an SCF-based description of an excited-state potential energy surface can be an accurate and cost-effective alternative to CIS and TD-DFT methods.

The excited-state (ES) geometry optimization and electronic emission (fluorescence and phosphorescence) spectra and the ES vibrational spectra of large systems are great challenges in quantum chemistry. In this work, we develop a generalized energy-based fragmentation (GEBF) approach to compute the localized ES structures and vibrational frequencies of large systems. In this approach, the ES energy derivatives (gradients or Hessians) for a localized ES of a large system can be obtained by combining the ES energy derivatives of the corresponding active subsystems (including local excitation center) and the ground-state energy derivatives of inactive subsystems. Two strategies are adopted to overcome two difficulties from state-classification and state-tracking for treating specific ESs. First, for state-classification, we develop an improved density-based spatial clustering applied with noise algorithm with a modified transition orbital projection (TOP) algorithm, which allow a certain ES energy and energy derivatives of the whole system to be calculated with different ES energies and energy derivatives of active subsystems. Furthermore, we also employ the TOP algorithm for tracking the ESs in their geometry optimizations at the time-dependent density functional theory (TDDFT) level. Then, the GEBF approach is applied to investigate the optimized ES geometries or ES vibrational frequencies for two typical systems. Our results show that the cost-effective GEBF approach can accurately reproduce the TDDFT fluorescence spectra of the cytosine derivative and the experimental phosphorescence spectra of the β-cyclodextrin derivative. The GEBF approach is expected to be routinely applied to investigate the electronic emission spectra of very large systems with local chromophores.

We discuss the general features of the time-evolving reduced density matrix (RDM) of multistate systems coupled to dissipative environments and show that many important aspects of the dynamics are visualized effectively and transparently through coherence maps, defined as snapshots of the real and imaginary components of the RDM on the square grid of system sites. In particular, the spread, signs, and shapes of the coherence maps collectively characterize the state of the system and the nature of the dynamics, as well as the equilibrium state. The topology of the system is readily reflected in its coherence map. Rows and columns show the composition of quantum superpositions, and their filling indicates the extent of the surviving coherence. Linear combinations of imaginary RDM elements specify instantaneous population derivatives. The main diagonal comprises the incoherent component of the dynamics, while the upper/lower triangular areas give rise to coherent contributions that increase the purity of the RDM. In open systems, the coherence map evolves to a band surrounding the principal diagonal whose width decreases with increasing temperature and dissipation strength. We illustrate these behaviors with examples of 10-site model molecular aggregates with Frenkel exciton couplings, where the electronic states of each monomer are coupled to harmonic vibrational baths.

The mixed quantum-classical dynamical simulation is essential to study nonadiabatic phenomena in photophysics and photochemistry. In recent years, many machine learning models have been developed to accelerate the time evolution of the nuclear subsystem. Herein, we implement long short-term memory (LSTM) networks as a propagator to accelerate the time evolution of the electronic subsystem during the fewest-switches surface hopping (FSSH) simulations. A small number of reference trajectories are generated using the original FSSH method, and then the LSTM networks can be built, accompanied by careful examination of typical LSTM-FSSH trajectories that employ the same initial condition and random numbers as the corresponding reference. The constructed network is applied to FSSH to further produce a trajectory ensemble to reveal the mechanism of nonadiabatic processes. Taking Tully's three models as test systems, the collective results can be reproduced qualitatively. This work demonstrates that LSTM is applicable to the most popular surface hopping simulations., Comment: 32 pages, 7 figures in Article; 28 pages, 20 figures, 5 tables in SI

Excitation-energy transfer is a key step in processes such as photosynthesis that convert light into other forms of energy. Time-dependent density functional theory (DFT) in real time is ideal for the first-principles simulation of such processes due to its computational efficiency. We here demonstrate how real-time DFT can be used for analyzing excitation-energy transfer from first-principles. We discuss several measures of energy transfer that are based solely on the time-dependent density, are well founded in the DFT framework, allow for intuitive understanding and visualization, and reproduce important limiting cases of an analytical model. We demonstrate their usefulness in calculations for model systems, both with static nuclei and in the context of DFT-based Ehrenfest dynamics.

We utilize ab initio quantum mechanics calculations to evaluate a range of plausible mechanistic pathways for the unexpected formation of a [6-4-4] ring system from an enone-olefin photocycloaddition in the synthesis of (-)-scabrolide A, previously reported by our group. We present a mechanistic analysis that is consistent with all current experimental observations, including the photoexcitation, the C-C bond formation, and the associated chemo- and diastereoselectivity.

The CC2 and ADC(2) wave function models and their spin-component scaled modifications are adopted for predicting vertical ionization potentials (VIPs) and electron affinities (VEAs). The ionic solutions are obtained as electronic excitations in the continuum orbital formalism, making possible the use of existing, widespread quantum chemistry codes with minimal modifications, in full consistency with the treatment of charge transfer excitations. The performance of different variants is evaluated via benchmark calculations on various sets from previous works, containing small and medium-sized systems, including the nucleobases. It is shown that with the spin-scaled approximate methods, in particular the scaled opposite-spin variant of the ADC(2) method the accuracy of EOM-CCSD is achievable at a fraction of the computational cost, also outperforming many common electron propagator approaches.

A common strategy to exploring the properties and reactivity of complex systems is to use quantum mechanics/molecular mechanics (QM/MM) embedding, wherein a QM region is defined and treated with electronic structure theory and the remainder of the system is treated with a forcefield. Of equal importance to the level of quantum chemical theory used for the QM region and the quality of the forcefield is the treatment of the coupling between the QM and MM subsystems. The state-of-the-art is to use a polarizable forcefield for the MM region and mutually couple the QM wavefunction and MM induced dipoles, in addition to the usual electrostatic embedding, yielding a polarizable embedding (QM/MM-Pol) approach. However, extensions to electronic excited states are less well developed, and we showed previously that current popular QM/MM-Pol approaches exhibit issues of root flipping and/or incorrect descriptions of electronic crossings in multistate calculations.[J. Chem. Theory Comput. 14, 2137 (2018)] Here we demonstrate a solution to these problems with an integral-exact reformulation of the Direct Reaction Field approach of Thole and Van Duijnen (QM/MM-IEDRF). The resulting embedding potential includes one- and two-electron operators, and many-body dipole-induced dipole interactions, and thus includes a natural description of the screening of electron-electron interactions by the MM induced dipoles. Pauli repulsion from the environment is mimicked by effective core potentials on the MM atoms. Inherent to the DRF approach is the assumption that MM dipoles respond instantaneously to the positions of the QM electrons, therefore dispersion interactions are captured approximately. All electronic states are eigenfunctions of the same Hamiltonian while the polarization induced in the environment and the associated energetic stabilization are unique to each state. This allows for a consistent definition of transition properties and state crossings. We demonstrate QM/MM-IEDRF by exploring the influence of a (polarizable) inert xenon matrix environment on the conical intersection underlying cis-trans isomerization of ethylene.

Weighting methods applied to systems with many conformers have been broadly employed to calculate thermodynamic properties, structural characteristics, and populations. To better understand and test the sensitivity of conventional weighting methods, the conformational distributions of nicotine and its phosphorus-substituted derivatives are investigated. The weighting schemes used for this are all based on Boltzmann statistics. Classical Boltzmann factors based on the electronic energy and the Gibbs free energy are calculated at different quantum chemical levels of theory and compared to cluster weights obtained by the quantum cluster equilibrium method. Furthermore, the influence of the modified rigid-rotor-harmonic-oscillator (mRRHO) approximation on the cluster weights is investigated. The substitution of the nitrogen atom in the methylpyrrolidine ring by a phosphorus atom results in more monomer conformers and clusters being populated. The conformational distribution of the monomers remained stable at different levels of theory and weighting methods. However, going to dimers and trimers, we observe a significant influence of the level of theory, weighting method, and mRRHO cutoff on the populations of these clusters. We show that mRRHO cutoff values of 50 and 100 cm

In this study, the interaction energy (

The ongoing integration of quantum chemistry, statistical mechanics, and artificial intelligence is paving the route toward more effective and accurate strategies for the investigation of the spectroscopic properties of medium-to-large size chromo- phores in condensed phases. In this context we are developing a novel workflow aimed at improving the generality, reliability, and ease of use of the available computational tools. In this paper we report our latest developments with specific reference to unsupervised atomistic simulations employing non periodic boundary conditions (NPBC) followed by clustering of the trajectories employing optimized feature spaces. Next accurate variational computations are performed for a representative point of each cluster, whereas intracluster fluctuations are taken into account by a cheap yet reliable perturbative approach. A number of methodological improvements have been introduced including, e.g., more realistic reaction field effects at the outer boundary of the simulation sphere, automatic definition of the feature space by continuous perception of solute−solvent interactions, full account of polarization and charge transfer in the first solvation shell, and inclusion of vibronic contributions. After its validation, this new approach has been applied to the challenging case of solvatochromic effects on the UV−vis spectra of a prototypical nitroxide radical (TEMPO) in different solvents. The reliability, effectiveness, and robustness of the new platform is demonstrated by the remarkable agreement with experiment of the results obtained through an unsupervised approach characterized by a strongly reduced computational cost as compared to that of conventional quantum mechanics and molecular mechanics models without any accuracy reduction.

The computationally very demanding evaluation of the 4-center-2-electron (4c2e) integrals and their respective integral derivatives typically represents the major bottleneck within hybrid Kohn-Sham density functional theory molecular dynamics simulations. Building upon our previous works on seminumerical exact-exchange (sn-LinK) [Laqua, H., Thompsons, T. H., Kussmann, J., Ochsenfeld, C.

Parametrization of the bonded part of molecular mechanics (MM) force fields (FFs) is typically done by fitting reference quantum mechanical (QM) energies or forces of representative structures. FFs for small molecules are constructed in incremental parametrization procedures, where parameters developed previously are retained for novel molecules, followed by optimization of missing, not previously optimized parameters. Equilibrium QM and MM geometries of molecules can deviate due to parameters transferred from existing molecules in the FF. In this work, we demonstrate that conventional parametrization methods based on fitting QM energies and/or forces to derive parameters for bond and angle terms produce largely suboptimal force constants when MM and QM equilibrium structures deviate. We further developed and tested a new method to derive CHARMM FF parameters based on the potential energy surface scans where a structural deviation between QM and MM optimized geometries is explicitly allowed during parametrization. The test of the new method was performed on a diverse set of 32 molecules. The results show that without any need for additional restraints, the new method produces robust and largely transferable parameters for bond and angle terms. The new method also improves the agreement for the normal modes for all molecules in the test set, reducing the average error in the reproduction of QM normal mode frequencies from 9.5% computed with CGenFF parameters to 6.8% computed with the new parameters. The new method will allow parametrization of molecules under structural deviations, common for force fields for small molecules, producing robust and transferable parameters.

For nearly the past 30 years, Centroid Molecular Dynamics (CMD) has proven to be a viable classical-like phase space formulation for the calculation of quantum dynamical properties. However, calculation of the centroid effective force remains a significant computational cost and limits the ability of CMD to be an efficient approach to study condensed phase quantum dynamics. In this paper we introduce a neural network-based methodology for first learning the centroid effective force from path integral molecular dynamics data, which is subsequently used as an effective force field to evolve the centroids directly with the CMD algorithm. This method, called Machine-Learned Centroid Molecular Dynamics (ML-CMD) is faster and far less costly than both standard on the fly CMD and ring polymer molecular dynamics (RPMD). The training aspect of ML-CMD is also straightforwardly implemented utilizing the DeepMD software kit. ML-CMD is then applied to two model systems to illustrate the approach: liquid para-hydrogen and water. The results show comparable accuracy to both CMD and RPMD in the estimation of quantum dynamical properties, including the self-diffusion constant and velocity time correlation function, but for significantly reduced overall computational cost., 29 pages, 6 figures

Nonadiabatic excited state dynamics are important in a variety of processes. Theoretical and experimental developments have allowed for a great progress in this area, while combining the two is often necessary and the best approach to obtain insight into the photophysical behavior of molecules. In this Feature Article we use examples of our recent work combining time-resolved photoelectron spectroscopy with theoretical nonadiabatic dynamics to highlight important lessons we learned. We compare the nonadiabatic excited state dynamics of three different organic molecules with the aim of elucidating connections between structure and dynamics. Calculations and measurements are compared for uracil, 1,3-cyclooctadiene, and 1,3-cyclohexadiene. The comparison highlights the role of rigidity in influencing the dynamics and the difficulty of capturing the dynamics accurately with calculations.

We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of subsystems and have been previously used for ab initio molecular dynamics (AIMD) calculations and for computing multidimensional potential energy surfaces. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at density functional theory cost. The approach has been demonstrated for gas-phase studies, for condensed phase electronic structure, and also for basis set extrapolation-based AIMD. Recently, this approach has also been used to derive new quantum-computing algorithms that enormously reduce the quantum circuit depth in a circuit-based computation of correlated electronic structure. In this publication, we introduce (a) a

Excited-state absorption (ESA) spectra of π-conjugated compounds are frequently calculated by (quadratic response) time-dependent density functional theory, (QR) TD-DFT, often giving a reasonable representation of the experimental results despite the (known) incomplete electronic description. To investigate whether this is inherent to the method, we calculate here the ESA spectra of small-to-medium-sized oligophenylenevinylenes (

Thionation of carbonyl groups of known dyes is a rapidly emerging strategy to propose an advance toward heavy-atom-free photosensitizers to be used in photodynamic therapy (PDT). The sulfur-for-oxygen replacement has recently proved to enhance the singlet oxygen quantum yield of some existing fluorophores and to shift the absorption band at longer wavelengths. Drawing inspiration from this challenging evidence, the effect of both sulfur- and selenium-for-oxygen replacement in the skeleton of the oxo-4-dimethylamino-1,8-naphthalimide molecule (DMN) has been analyzed by means of a DFT study. The thio- and seleno-derivatives (SDMN and SeDMN, respectively) have been shown to offer the possibility to access a multitude of ISC (intersystem crossing) pathways involved in the triplet deactivation mechanisms with a consequent enhancement of the singlet oxygen production, also arising from the change of orbital type involved in the radiationless

We assessed enzyme:substrate conformational dynamics and the rate-limiting glycosylation step of a human pancreatic α-amylase:maltopentose complex. Microsecond molecular dynamics simulations suggested that the distance of the catalytic Asp197 nucleophile to the anomeric carbon of the buried glucoside is responsible for most of the enzyme active site fluctuations and that both Asp197 and Asp300 interact the most with the buried glucoside unit. The buried glucoside binds either in a

The interaction between light and multichromophoric assemblies (MCAs) is the primary event of many fundamental processes, from photosynthesis to organic photovoltaics, and it triggers dynamical processes that share remarkable similarities at the molecular scale: light absorption, energy and charge transfer, internal conversions, emission, and so on. Those events often involve many chromophores and different excited electronic states that are coupled on an ultrafast time scale. This Account aims to discuss some of the chemical physical effects ruling these processes, a fundamental step toward their control, based on our experience on nucleic acids.In the last 15 years, we have, indeed, studied the photophysics and photochemistry of DNA and its components. By combining different quantum mechanical methods, we investigated the molecular processes responsible for the damage of the genetic code or, on the contrary, those preventing it by dissipating the excess energy deposited in the system by UV absorption. Independently of its fundamental biological role, DNA, with its fluctuating closely stacked bases stabilized by weak nonbonding interactions, can be considered a prototypical MCA. Therefore, it allows one to tackle within a single system many of the conceptual and methodological challenges involved in the study of photoinduced processes in MCA.In this Account, by using the outcome of our studies on oligonucleotides as a guideline, we thus highlight the most critical modellistic issues to be faced when studying, either experimentally or computationally, the interaction between UV light and DNA and, at the same time, bring out their general relevance for the study of MCAs.We first discuss the rich photoactivated dynamics of nucleobases (the chromophores), highlighting the main effects modulating the interplay between their excited states and how the latter can affect the photoactivated dynamics of the polynucleotides, either providing effective monomer-like nonradiative decay routes or triggering reactive processes (e.g., triplet generation).We then tackle the reaction paths involving multiple bases, showing that in the DNA duplex the most important ones involve two stacked bases, forming a neutral excimer or a charge transfer (CT) state, which exhibit different spectral signatures and photochemical reactivity. In particular, we analyze the factors affecting the dynamic equilibrium between the excimer and CT, such as the fluctuations of the backbone or the rearrangement of the solvent.Next, we highlight the importance of the effects not directly connected to the chromophores, such as the flexibility of the backbone or the solvent effect. The former, affecting the stacking geometry of the bases, can determine the preference between different deactivation paths. The latter is particularly influential for CT states, making very important an accurate treatment of dynamical solvation effects, involving both the solvent bulk and specific solute-solvent interactions.In the last section, we describe the main methodological challenges related to the study of polynucleotide excited states and stress the benefits derived by the integration of complementary approaches, both computational and experimental. Only exploiting different point of views, in our opinion, it is possible to shed light on the complex phenomena triggered by light absorption in DNA, as in every MCA.

Photochemical reactions are of great importance in chemistry, biology, and materials science because they take advantage of a renewable energy source, mild reaction conditions, and high atom economy. Light absorption can excite molecules to a higher energy electronic state of the same spin multiplicity. The following nonadiabatic processes induce molecular transformations that afford exotic molecular architectures and high-energy-isomers that are inaccessible by thermal means. Computational simulations now complement time-resolved instrumentation to reveal ultrafast excited-state mechanistic information for photochemical reactions that is essential in disentangling elusive spectroscopic features, excited-state lifetimes, and excited-state mechanistic critical points. Nonadiabatic molecular dynamics (NAMD), powered by surface hopping techniques, is among the most widely applied techniques to model the photochemical reactions of medium-sized molecules. However, the computational efficiency is limited because of the requisite thousands of multiconfigurational quantum-chemical calculations multiplied by hundreds of trajectories. Machine learning (ML) has emerged as a revolutionary force in computational chemistry to predict the outcome of the resource-intensive multiconfigurational calculations on the fly. An ML potential trained with a substantial set of quantum-chemical calculations can predict the energies and forces with errors under chemical accuracy at a negligible cost. The integration of ML potentials in NAMD dramatically extends the maximum simulation time scale by ∼10 000-fold to the nanosecond regime.In this Account, we present a comprehensive demonstration of ML photodynamics simulations and summarize our most recent applications in resolving complex photochemical reactions. First, we address three fundamental components of ML techniques for photodynamics simulations: the quantum-chemical data set, the ML potential, and NAMD. Second, we describe best practices in building training data and our procedure toward training the ML photodynamics model with our recent literature contributions. We introduce a convenient training data generation scheme combining Wigner sampling and geometrical interpolation. It trains reliable and effective ML potentials suitable for subsequent active learning to detect undersampled data. We demonstrate how active learning automatically discovers new mechanistic pathways and reproduces experimental results. We point out that atomic permutation is an essential data augmentation approach to improve the learnability of distance-based molecular descriptors for highly symmetric molecules. Third, we demonstrate the utility of ML-photodynamics by showing the results of ML photodynamics simulations of (1) photo-torquoselective 4π disrotatory electrocyclic ring closing of norbornyl cyclohexadiene, which reveals a thermal conversion from experimentally unobserved intermediates to the reactant in 1 ns; (2) [2 + 2] photocycloaddition of substituted [3]

We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2'-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce

Iron(II) porphyrins play critical roles in enzymes and synthetic catalysts. Computationally determining the spin-state ordering for even the unsubstituted iron(II) porphyrin (FeP) is challenging due to its large size. Multiconfiguration pair-density functional theory (MC-PDFT), a method capable of accurately capturing correlation with lower cost than comparably accurate methods, was previously used to predict a triplet ground state for FeP across a wide range of active spaces up to (34e, 35o). The purpose of this present MC-PDFT study is to determine the effects of including nonlocal exchange in the energy calculation and of using a larger active space size [DMRG(40e, 42o) and RAS(40, 2, 2; 16, 6, 20)] on the calculated FeP spin-state ordering. The recently developed hybrid MC-PDFT method, which uses a weighted average of the MC-PDFT energy and the energy expectation value of the reference wave function, is applied with a weight of the reference wave function energy of λ. We find that increasing λ stabilizes the quintet relative to the triplets. The hybrid tPBE0 functional (tPBE with λ set to 0.25) consistently predicts a triplet ground state with the quintet lying above by 0.10-0.16 eV, depending on the reference wave function. These values are particularly interesting in light of tPBE0's very strong performance for a diverse set of other systems.

A family of Pt(II) complexes bearing monoanionic C^N^N ligands as luminophoric units as well as a set of monodentate ligands derived from allenylidene and carbene species were synthesized and characterized in terms of structure and photophysical properties. In addition, we present the extraordinary molecular structure of a phosphorescent complex carrying an allenylidene ligand. Depending on the co-ligand, an effect can be observed in the photoluminescence lifetimes and quantum yields as well as in the radiative and radiation less deactivation rate constants. Their correlation with the substitution pattern was analyzed by comparing the photoluminescence in fluid solution at room temperature and in frozen glassy matrices at 77 K. Moreover, in order to gain a deeper understanding of the electronic states responsible for the optical properties, density functional theory calculations were performed. Finally, the cytotoxicity of the complexes was evaluated

We address the problem of intermolecular interaction energy calculations in molecular complexes with localized excitons. Our focus is on the correct representation of the dispersion energy. We derive an extended Casimir-Polder formula for direct computation of this contribution through second order in the intermolecular interaction operator

Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [Grimme, S.

A new tool, ML-J-DP4, provides an efficient and accurate method for determining the most likely structure of complex molecules within minutes using standard computational resources. The workflow involves combining fast Karplus-type J calculations with NMR chemical shifts predictions at the cheapest HF/STO-3G level enhanced using machine learning (ML), all embedded in the J-DP4 formalism. Our ML provides accurate predictions, which compare favorably alongside with other ML methods., This research was supported by UNR (BIO 500 and 567), ANPCyT (PICT-2016-0116, PICT-2017-1524 and PICT-2019-4052), MICIIN (PID2019-109476RB-C21) and ACIISI-FEDER (ProID2021010118).

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations have advanced the field of computational chemistry tremendously. However, they require the partitioning of a system into two different regions that are treated at different levels of theory, which can cause artefacts at the interface. Furthermore, they are still limited by high computational costs of quantum chemical calculations. In this work, we develop BuRNN, an alternative approach to existing QM/MM schemes, which introduces a buffer region that experiences full electronic polarization by the inner QM region to minimize artefacts. The interactions between the QM and the buffer region are described by deep neural networks (NNs), which leads to high computational efficiency of this hybrid NN/MM scheme while retaining quantum chemical accuracy. We demonstrate the BuRNN approach by performing NN/MM simulations of the hexa-aqua iron complex., 37 pages, 9 figures

International audience; Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

A fragmentation approach referred to as a simple overlapping region method for force matching (SORForM) is presented. SORForM is designed to enable efficient computation of quantum mechanical (QM) forces for large molecules and is validated in the framework of adaptive force matching (AFM) to develop solute models in water. The SORForM method divides a molecule into overlapping QM regions with each region containing a gradient zone and a buffer zone. The buffer zone ensures that the atoms in the gradient zone have their surroundings unchanged with fragmentation. The performance of the method is validated with mefenamic acid and linalyl acetate by comparing the hydration free energies of AFM models developed with and without SORForM. The AFM hydration free energies are also compared with that of the experiments. The models developed with B3LYP-D3(BJ) and def2-TZVP are in excellent agreement with experiments. Our work shows that PBE-D3(BJ) provides less satisfactory results when compared to B3LYP-D3(BJ). The def2-TZVP basis set is found to greatly improve the agreement with experiments when compared to a double-zeta quality basis set.

A key step during indirect alchemical free energy simulations using quantum mechanical/molecular mechanical (QM/MM) hybrid potential energy functions is the calculation of the free energy difference Δ

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the over-structuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

We show that combining the linearized semiclasscial approximation with Fermi's golden rule (FGR) rate theory gives rise to a general-purpose cost-effective and scalable computational framework that can accurately capture the cavity-induced rate enhancement of charge transfer reactions that occurs when the molecular system is placed inside a microcavity. Both partial linearization with respect to the nuclear and photonic degrees of freedom and full linerization with respect to nuclear, photonic, and electronic degrees of freedom (the latter within the mapping Hamiltonian approach) are shown to be highly accurate, provided that the Wigner transforms of the product (WoP) of operators at the initial time is not replaced by the product of their Wigner transforms. We also show that the partial linearization method yields the quantum-mechanically exact cavity-modified FGR rate constant for a model system in which the donor and acceptor potential energy surfaces are harmonic and identical except for a shift in the equilibrium energy and geometry, if WoP is applied.

Urease catalyzes the hydrolysis of urea to form ammonia and carbamate, inducing an overall pH increase that affects both human health and agriculture. Inhibition, mutagenesis, and kinetic studies have provided insights into its enzymatic role, but there have been debates on the substrate binding mode as well as the reaction mechanism. In the present study, we report quatum mechanics-only (QM-only) and quantum mechanics/molecular mechanics molecular dynamics (QM/MM MD) calculations on urease that mainly investigate the binding mode of urea and the mechanism of the urease-catalyzed hydrolysis reaction. Comparison between the experimental data and our QM(GFN2-xTB)/MM metadynamics results demonstrates that urea hydrolysis via a complex with bidentate-bound urea is much more favorable than via that with monodentate-bound urea for both nucleophilic attack and the subsequent proton transfer steps. We also indicate that the bidentate coordination of urea fits the active site with a closed conformation of the mobile flap and can facilitate the stabilization of transition states and intermediates by forming multiple hydrogen bonds with certain active site residues.

To analyze the impact of various technical details on the results of QM/MM enzyme simulations, including the QM region size, catechol-O-methyltransferase (COMT) is studied as a model system using an approximate QM/MM method (DFTB3/CHARMM). The results show that key equilibrium and kinetic properties for methyl transfer in COMT exhibit limited variations with respect to the size of the QM region, which ranges from ~100 to ~500 atoms in this study. With extensive sampling, local and global structural characteristics of the enzyme are largely conserved across the studied QM regions, while the nature of the transition state (e.g., secondary kinetic isotope effect) and reaction exergonicity are largely maintained. Deviations in the free energy profile with different QM region sizes are similar in magnitude to those observed with changes in other simulation protocols, such as different initial enzyme conformations and boundary conditions. Electronic structural properties, such as the covariance matrix of residual charge fluctuations, appear to exhibit rather long-range correlations, especially when the peptide backbone is included in the QM region; this observation holds when a range-separated DFT approach is used as the QM region, suggesting that delocalization error is unlikely the origin. Overall, the analyses suggest that multiple simulation details determine the results of QM/MM enzyme simulations with comparable contributions.

The London dispersion interactions between systems undergoing bond breaking, twisting, or compression are not well studied due to the scarcity and the high computational cost of methods being able to describe both the dynamic correlation and the multireference character of the system. Recently developed methods based on the Generalized Valence Bond wave function, such as EERPA-GVB and SAPT(GVB) (SAPT = symmetry-adapted perturbation theory), allow one to accurately compute and analyze noncovalent interactions between multireference systems. Here, we augment this analysis by introducing a local indicator for dispersion interactions inspired by Mata and Wuttke's Dispersion Interaction Density [

Fast and accurate assessment of small-molecule dihedral energetics is crucial for molecular design and optimization in medicinal chemistry. Yet, accurate prediction of torsion energy profiles remains challenging as the current molecular mechanics (MM) methods are limited by insufficient coverage of drug-like chemical space and accurate quantum mechanical (QM) methods are too expensive. To address this limitation, we introduce TorsionNet, a deep neural network (DNN) model specifically developed to predict small-molecule torsion energy profiles with QM-level accuracy. We applied active learning to identify nearly 50k fragments (with elements H, C, N, O, F, S, and Cl) that maximized the coverage of our corporate compound library and leveraged massively parallel cloud computing resources for density functional theory (DFT) torsion scans of these fragments, generating a training data set of 1.2 million DFT energies. After training TorsionNet on this data set, we obtain a model that can rapidly predict the torsion energy profile of typical drug-like fragments with DFT-level accuracy. Importantly, our method also provides an uncertainty estimate for the predicted profiles without any additional calculations. In this report, we show that TorsionNet can accurately identify the preferred dihedral geometries observed in crystal structures. Our TorsionNet-based analysis of a diverse set of protein-ligand complexes with measured binding affinity shows a strong association between high ligand strain and low potency. We also present practical applications of TorsionNet that demonstrate how consideration of DNN-based strain energy leads to substantial improvement in existing lead discovery and design workflows. TorsionNet500, a benchmark data set comprising 500 chemically diverse fragments with DFT torsion profiles (12k MM- and DFT-optimized geometries and energies), has been created and is made publicly available.

Quantum and molecular mechanics (QM/MM) and QM-only (cluster model) modeling techniques represent the two workhorses in mechanistic understanding of enzyme catalysis. One of the stringent tests for QM/MM and/or QM approaches is to provide quantitative answers to real-world biochemical questions, such as the effect of single-point mutations on enzyme kinetics. This translates into predicting the

Color centers in diamond are widely explored as qubits in quantum technologies. However, challenges remain in the effective and efficient integration of these diamond-hosted qubits in device heterostructures. Here, nanoscale-thick uniform diamond membranes are synthesized via "smart-cut" and isotopically (12C) purified overgrowth. These membranes have tunable thicknesses (demonstrated 50 nm to 250 nm), are deterministically transferable, have bilaterally atomically flat surfaces (Rq, 50 pages, 13 figures

Flavins are central to countless enzymes but display different reactivities depending on their environments. This is understood to reflect modulation of the flavin electronic structure. To understand changes in orbital natures, energies, and correlation over the ring system, we begin by comparing seven flavin variants differing at C8, exploiting their different electronic spectra to validate quantum chemical calculations. Ground state calculations replicate a Hammett trend and reveal the significance of the flavin π-system. Comparison of higher-level theories establishes CC2 and ACD(2) as methods of choice for characterization of electronic transitions. Charge transfer character and electron correlation prove responsive to the identity of the substituent at C8. Indeed, bond length alternation analysis demonstrates extensive conjugation and delocalization from the C8 position throughout the ring system. Moreover, we succeed in replicating a particularly challenging UV/Vis spectrum by implementing hybrid QM/MM in explicit solvents. Our calculations reveal that the presence of nonbonding lone pairs correlates with the change in the UV/Vis spectrum observed when the 8-methyl is replaced by NH

Carbon monoxide (CO) is a well-known inhibitor of nitrogenase activity. Under turnover conditions, CO binds to FeMoco, the active site of Mo nitrogenase. Time-resolved IR measurements suggest an initial terminal CO at 1904 cm–1 that converts to a bridging CO at 1715 cm–1, and an X-ray structure shows that CO can displace one of the bridging belt sulfides of FeMoco. However, the CO-binding redox state(s) of FeMoco (En) and the role of the protein environment in stabilizing specific CO-bound intermediates remain elusive. In this work, we carry out an in-depth analysis of the CO–FeMoco interaction based on quantum chemical calculations addressing different aspects of the electronic structure. (1) The local electronic structure of the Fe–CO bond is studied through diamagnetically substituted FeMoco. (2) A cluster model of FeMoco within a polarizable continuum illustrates how CO binding may affect the spin-coupling between the metal centers. (3) A QM/MM model incorporates the explicit influence of the amino acid residues surrounding FeMoco in the MoFe protein. The QM/MM model predicts both a terminal and a bridging CO in the E1 redox state. The scaled calculated CO frequencies (1922 and 1716 cm–1, respectively) are in good agreement with the experimentally observed IR bands supporting CO binding to the E1 state. Alternatively, an E2 state QM/MM model, which has the same atomic structure as the CO-bound X-ray structure, features a semi-bridging CO with a scaled calculated frequency (1718 cm–1) similar to the bridging CO in the E1 model., The MoFe protein of wild-type nitrogenase has been shown to bind CO during enzymatic turnover. According to our QM/MM model, the protein environment plays a pivotal role during the binding event. A detailed analysis of the electronic structure reveals that CO modulates the spin-coupling between Fe centers and therefore an atypical set of broken-symmetry determinants has to be considered in the DFT calculations.

Zinc metalloproteins are ubiquitous, with protein zinc centers of structural and functional importance, involved in interactions with ligands and substrates and often of pharmacological interest. Biomolecular simulations are increasingly prominent in investigations of protein structure, dynamics, ligand interactions, and catalysis, but zinc poses a particular challenge, in part because of its versatile, flexible coordination. A computational workflow generating reliable models of ligand complexes of biological zinc centers would find broad application. Here, we evaluate the ability of alternative treatments, using (nonbonded) molecular mechanics (MM) and quantum mechanics/molecular mechanics (QM/MM) at semiempirical (DFTB3) and density functional theory (DFT) levels of theory, to describe the zinc centers of ligand complexes of six metalloenzyme systems differing in coordination geometries, zinc stoichiometries (mono- and dinuclear), and the nature of interacting groups (specifically the presence of zinc-sulfur interactions). MM molecular dynamics (MD) simulations can overfavor octahedral geometries, introducing additional water molecules to the zinc coordination shell, but this can be rectified by subsequent semiempirical (DFTB3) QM/MM MD simulations. B3LYP/MM geometry optimization further improved the accuracy of the description of coordination distances, with the overall effectiveness of the approach depending upon factors, including the presence of zinc-sulfur interactions that are less well described by semiempirical methods. We describe a workflow comprising QM/MM MD using DFTB3 followed by QM/MM geometry optimization using DFT (e.g., B3LYP) that well describes our set of zinc metalloenzyme complexes and is likely to be suitable for creating accurate models of zinc protein complexes when structural information is more limited.

The lone-pair…π (lp…π) (deoxy)ribose…nucleobase stacking is a recurring structural motif in Z DNA and RNAs that is characterized by sub-van der Waals lp…π contacts (

Structural DNA nanotechnology is a promising approach to create chromophore networks with modular structures and Hamiltonians to control the material's functions. The functional behaviors of these systems depend on the interactions of the chromophores' vibronic states, as well as interactions with their environment. To optimize their functions, it is necessary to characterize the chromophore network's structural and energetic properties, including the electronic delocalization in some cases. In this study, parameters of interest are deduced in DNA-scaffolded Cyanine 3 and Cyanine 5 dimers. The methods include steady-state optical measurements, physical modeling, and a genetic algorithm approach. The parameters include the chromophore network's vibronic Hamiltonian, molecular positions, transition dipole orientations, and environmentally induced energy broadening. Additionally, the study uses temperature-dependent optical measurements to characterize the spectral broadening further. These combined results reveal the quantum mechanical delocalization, which is important for functions like coherent energy transport and quantum information applications.

Diabatization of one-electron states in flexible molecular aggregates is a great challenge due to the presence of surface crossings between molecular orbital (MO) levels and the complex interaction between MOs of neighboring molecules. In this work, we present an efficient machine learning approach to calculate electronic couplings between quasi-diabatic MOs without the need of nonadiabatic coupling calculations. Using MOs of rigid molecules as references, the MOs that can be directly regarded to be quasi-diabatic in molecular dynamics are selected out, state tracked, and phase corrected. On the basis of this information, artificial neural networks are trained to characterize the structure-dependent onsite energies of quasi-diabatic MOs and the intermolecular electronic couplings. A representative sequence of DNA is systematically studied as an illustration. Smooth time evolution of electronic couplings in all base pairs is obtained with quasi-diabatic MOs. In particular, our method can calculate electronic couplings between different quasi-diabatic MOs independently, and thus, this possesses unique advantages in many applications.

The role of pigment-protein coupling in the dynamics of photosynthetic energy transport in chromophoric complexes has not been fully understood. The excitation energy transfer in the photosynthetic system is tremendously efficient. In particular, we investigate the excitation energy transport in the Fenna-Matthews-Olson (FMO) complex. The exciton dynamics and excitation energy transfer (EET) depend on the interaction between the excited chromophores and their environment. Most theoretical models believe that all bacteriochlorophyll-a (BChla) sites are surrounded by the same local protein environment, which is contradicted by the structural analysis of the FMO complex. Based on different values of pigment-protein coupling for different sites, measured in the adiabatic limit, we have theoretically investigated the effect of the heterogeneous local protein environment on the EET process. By the realistic and site-dependent model of the system-bath couplings, the results show that this interaction may have a critical value for the coherent energy-transfer process. Furthermore, we verify that the two transport pathways are coherent and stable to the important parameter reorganization energy of environmental interactions. The quantum dynamical simulations show that the correlation fluctuation keeps the oscillation of the coherent excitation on a long timescale. In addition, due to the inhomogeneous pigment-protein coupling, different BChl sites have asymmetric excitation oscillation timescales.

The determination of accurate equilibrium molecular structures plays a fundamental role for understanding many physical-chemical properties of molecules, ranging from the precise evaluation of the electronic structure to the analysis of the role played by dynamical and environmental effects in tuning their overall behavior. For small semi-rigid systems in the gas phase, state-of-the-art quantum chemical computations rival the most sophisticated experimental (from, for example, high-resolution spectroscopy) results. For larger molecules, more effective computational approaches must be devised. To this end, we have further enlarged the compilation of available semi-experimental (SE) equilibrium structures, now covering the most important fragments containing H, B, C, N, O, F, P, S, and Cl atoms collected in the new SE100 database. Next, comparison with geometries optimized by methods rooted in the density functional theory showed that the already remarkable results delivered by PW6B95 and, especially, rev-DSDPBEP86 functionals can be further improved by a linear regression (LR) approach. Use of template fragments (taken from the SE100 library) together with LR estimates for the missing interfragment parameters paves the route toward accurate structures of large molecules, as witnessed by the very small deviations between computed and experimental rotational constants. The whole approach has been implemented in a user-friendly tool, termed nano-LEGO, and applied to a number of demanding case studies.

Quantum chemical calculations have successfully predicted the stereoselectivities of many BINOL phosphoric acid catalyzed reactions over the past 10-15 years. Herein we report a contrasting example: a reaction for which standard quantum chemistry techniques have proven unexpectedly ineffective at explaining the stereoselectivity. The Nazarov cyclizations of a divinyl ketone catalyzed by a BINOL phosphoric acid or H8-BINOL dithiophosphoric acid were studied with a conventional contemporary quantum chemical approach, consisting of transition state optimizations with B3LYP-D3(BJ) and single-point calculations with several functionals in implicit solvent. Unexpectedly, different functionals gave widely different predictions of the level of enantioselectivity and were unable even to agree on which enantiomer of the product would predominate. Molecular dynamics simulations with the OPLS-AA force field provided evidence that the transition state geometries optimized with DFT in the gas phase or in implicit solvent are not good representations of the true transition states of these reactions in solution. One possible reason for this, which may also explain the failure of quantum chemical techniques to reliably predict the enantioselectivity, is the fact that the transition states contain ion pairs which are not highly organized and do not contain any strongly directional noncovalent interactions between the substrate and the catalyst.