Model Potential Energy Surfaces Research Articles

Compensation States Approach in the Hybrid Diabatization Scheme: Extension to Multidimensional Data and Properties.

The diabatization of reactive systems for more than just a couple of states is a very demanding problem and generally requires advanced diabatization techniques. Especially for dissociative processes, the drastic changes in the adiabatic wave functions often would require large diabatic state bases, which quickly become impractical. Recently, we addressed this problem by the compensation states approach developed in the context of our hybrid diabatization scheme. This scheme utilizes wave function as well as energy data in combination with a diabatic potential model. In regions where the initial diabatic state basis becomes insufficient for an appropriate representation of the adiabatic states, new model states are generated. The new model states compensate for the state space not spanned by the initial diabatic basis. Such a compensation state is obtained by projecting the initial diabatic state space out of the adiabatic wave function. This yields a very efficient basis representation of the electronic Hamiltonian. The present work presents two new aspects. First, it is shown how other operators like the spin-orbit operator in the framework of the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) can be evaluated in this compact model state space without losing the correct wave function information and accuracy. Second, the extension of the approach to multidimensional potential energy surface models is presented for methyl iodide including the C-I dissociation coordinate and the angular H3C-I bending coordinates.

Automated learning data-driven potential models for spectroscopic characterization of astrophysical interest noble gas-containing [formula omitted] molecules

The choice of a proper machine learning (ML) algorithm for constructing potential energy surface (PES) models has become a crucial tool in the fields of quantum chemistry and computational modeling. These algorithms offer the ability to make reliable and accurate predictions at a reasonable computational cost, and thus they can be then used in various molecular dynamics and spectroscopic studies. For that, it is not surprising that much of the current research focuses on the development of software that generates machine learning models using precalculated ab initio data points. This study is primarily dedicated to the application and assessment of various automated learning models. These models are trained and tested using datasets derived from CCSD(T)/CBS[56] calculations, aiming to represent intermolecular interactions in small molecules, such as the NgH2+ complexes, where Ng represents helium (He), neon (Ne), and argon (Ar) atoms. These noble gas-containing molecules have gained increasing significance in the field of molecular astrochemistry, due to the recent discovery of HeH+ and ArH+ molecular cations in the interstellar medium (ISM), thereby opening up a wide range of possibilities in this scientific area. Consequently, the ML-generated PESs are employed to compute vibrational bound states for these molecular cations, with the goal of characterizing all their known isotopologues. Furthermore, the results are compared with spectroscopic data, when available, from previous studies in the literature. Our findings have the potential to provide valuable guidance for future ML-PES development and benchmarking studies involving noble gas-containing cations of astrophysical importance.

Nuclear quantum effects in gas-phase ethylene glycol.

Path integral molecular simulations are used to explore the nuclear quantum effects (NQEs) on the structure, dihedral landscape and infrared spectrum of ethylene glycol. The simulations are carried out on a new reaction surface Hamiltonian-based model potential energy surface, with special focus on the role of the OCCO and HOCC dihedrals. In contrast with classical simulations, we analyse how the intramolecular interactions between the OH groups change due to zero-point effects as well as temperature. These are found to be weak. The NQEs on the free energy profile along the OCCO dihedral are analysed, where notable effects are seen at low temperatures and found to be correlated with the radii of gyration of the atoms. Finally, the power spectrum of the molecule from path integral simulations is compared with the experimental infrared spectrum, yielding a good agreement of band positions.

Optical and theoretical study of NaCr(P2O7): a look through the Neuhauser model and Racah theory.

A sample of NaCr(P2O7) was synthesized using the solid-state reaction method. X-ray diffraction and Rietveld refinement confirmed the formation of a monoclinic structure with the P21/a space group. Scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) analysis identified the morphology and homogeneity of the chemical composition. The optical absorption spectrum revealed a direct optical band gap of 2.9 eV and an Urbach energy of 0.44 eV. Notably, the absorption spectrum showed an interference dip on the lowest energy band 4T2g(4F), attributed to spin-orbit coupling between states 2Eg(2G) and 4T2g(4F). This phenomenon was analyzed using the Neuhauser model based on coupled potential energy surfaces. From this analysis, the electronic structure of Cr3+ (3d3) ions in the NaCr(P2O7) sample was determined, enabling a reliable calculation of Racah and crystal-field parameters. The results showed good agreement between experimental and theoretical energy levels. The study demonstrates the impact of spin-orbit interactions using the coupled potential energy surface model.

Hydrogen-iodine scattering. I. Development of an accurate spin-orbit coupled diabatic potential energy model.

The scattering of H by I is a prototypical model system for light-heavy scattering in which relativistic coupling effects must be taken into account. Scattering calculations depend strongly on the accuracy of the potential energy surface (PES) model. The methodology to obtain such an accurate PES model suitable for scattering calculations is presented, which includes spin-orbit (SO) coupling within the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) approach. In this approach, the SO coupling is determined only for the atomic states of the heavy atom, and the geometry dependence of the SO effect is accounted for by a diabatization with respect to asymptotic states. The accuracy of the full model, composed of a Coulomb part and the SO model, is achieved in the following ways. For the SO model, the extended ERCAR approach is applied, which accounts for both intra-state and inter-state SO coupling, and an extended number of diabatic states are included. The corresponding coupling constants for the SO operator are obtained from experiments, which are more accurate than computed values. In the Coulomb Hamiltonian model, special attention is paid to the long range behavior and accurate c6 dispersion coefficients. The flexibility and accuracy of this Coulomb model are achieved by combining partial models for three different regions. These are merged via artificial neural networks, which also refine the model further. In this way, an extremely accurate PES model for hydrogen iodide is obtained, suitable for accurate scattering calculations.

Significance of Nonadiabatic Effects on Efficient Triplet Generation in Lumazines.

The photophysics of lumazines leading to triplet formation and the effect of thionation are explored in the presence of near-degenerate electronic states. Wave packet simulations are performed on model potential energy surfaces to understand the nonadiabatic population transfer among close-lying excited states. Ultrafast population transfer among singlets opens up new intersystem crossing channels from the higher states. An increased spin-orbit coupling strength originating from thionation enhances intersystem crossing and populates the higher triplets first. The rapid internal conversion in the triplet manifold eventually brings the molecules to their respective low-lying long-lived triplet state.

Quantum Chemical Studies on Possible Molecular Devices Based on Electric Field-Induced Intramolecular Charge Transfer.

We report quantum chemical studies on possible molecular devices working based on electric field-induced intramolecular charge transfer (EFIMCT). In the case of donor-acceptor (DA)-type molecular systems, intramolecular charge transfer (IMCT) can be induced by applying the external electric field to molecular systems along the charge transport direction, providing a possible switching mechanism which does not depend upon the electron-phonon coupling effect and is different from the negative differential resistance mechanism observed in the well-known NO2-substituted phenylene ethynylene oligomers. When the EFIMCT proceeds, the molecular systems have strong static electron correlation effects, where the standard nonequilibrium Green's function-density functional theory (DFT) approach cannot be applied to the molecular junction. As a first step toward practical switching devices, we do quantum chemical studies on the EFIMCT in such molecular systems as an isolated molecule, instead of using the electrode-junction-electrode open quantum system model. A prototype molecule P1 is designed as a tentative candidate molecule where the EFIMCT can proceed. The complete active space self-consistent field (CASSCF) molecular orbital calculations on P1 indicate that the EFIMCT can proceed at the external electric field intensity of 0.003 au, corresponding to about 2.25 V bias voltage. This calculated result strongly suggests that the development of this type of switching devices working at practically low bias voltage is feasible if the molecular system is properly designed. Broken symmetry unrestricted Hartree-Fock and spin-polarized Kohn-Sham DFT calculations also qualitatively reproduce the CASSCF results on P1, to some extent, indicating that these approaches can be employed for rough estimations on the EFIMCT such as the first screening of a large quantity of candidate molecules for this type of molecular devices. The possibility of molecular memory devices based on the EFIMCT is also discussed by analyzing the ground and excited potential energy surface model. Remaining challenges to develop practical molecular devices are discussed.

Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations.

Defining a theoretical model systematically delivering accurate ab initio predictions of the fluorescence quantum yields of organic dyes is highly desirable for designing improved fluorophores in a systematic rather than trial-and-error way. To this end, the first required step is to obtain reliable radiative rates (kr), as low kr typically precludes effective emission. In the present contribution, using a series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol on the kr determined through the thermal vibration correlation function (TVCF) approach on the basis of time-dependent density functional theory (TD-DFT) calculations of the energies, structures, and vibrational parameters. Both the electronic structure (selected exchange-correlation functional, application or not of the Tamm-Dancoff approximation) and the vibronic parameters (line-shape formalism, coordinate system, potential energy surface model, and dipole expansion) are tackled. Considering all possible combinations yields more than 3500 cases, allowing to extract statistically-relevant information regarding the impact of each computational parameter on the magnitude of the estimated kr. It turns out that the selected vibronic model can have a significant impact on the computed kr, especially the potential energy surface model. This effect is of the same order of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates. For the treated compounds, all evaluated functionals do deliver reasonable trends, fitting the experimental values.

A minimal model of potential energy surface for H2OHCl

AbstractIn this paper, we present a model of potential energy surface for the H2OHCl system, consisting in the exact transformation of quantum chemical input data related to a minimal number of significant configurations. Both molecules are assumed as rigid. The interaction potential is given by an expansion in real spherical harmonics depending on the distance between the two centers of mass of the molecules and on four angles that define their mutual orientation. The main target of this work is the construction of a model of potential energy surface that requires a limited number of single energy points, which is suitable for applications to classical and quantum molecular dynamics simulations, permitting interpolation and further implementation of different sets of input data.

Large scale and quantum accurate molecular dynamics simulation: Liquid iron under extreme condition

Liquid iron is the major component of planetary cores. Its structure and dynamics under high pressure and temperature is of great significance in studying geophysics and planetary science. However, for experimental techniques, it is still difficult to generate and probe such a state of matter under extreme conditions, while for theoretical method like molecular dynamics simulation, the reliable estimation of dynamic properties requires both large simulation size and <i>ab initio</i> accuracy, resulting in unaffordable computational costs for traditional method. Owing to the technical limitation, the understanding of such matters remains limited. In this work, combining molecular dynamics simulation, we establish a neural network potential energy surface model to study the static and dynamic properties of liquid iron at its extreme thermodynamic state close to core-mantle boundary. The implementation of deep neural network extends the simulation scales from one hundred atoms to millions of atoms within quantum accuracy. The estimated static and dynamic structure factor show good consistency with all available X-ray diffraction and inelastic X-ray scattering experimental observations, while the empirical potential based on embedding-atom-method fails to give a unified description of liquid iron across a wide range of thermodynamic conditions. We also demonstrate that the transport property like diffusion coefficient exhibits a strong size effect, which requires more than at least ten thousands of atoms to give a converged value. Our results show that the combination of deep learning technology and molecular modelling provides a way to describe matter realistically under extreme conditions.

FCclasses3: Vibrationally-resolved spectra simulated at the edge of the harmonic approximation.

We introduce FCclasses3, a code to carry out vibronic simulations of electronic spectra and nonradiative rates, based on the harmonic approximation. Key new features are: implementation of the full family of vertical and adiabatic harmonic models, vibrational analysis in curvilinear coordinates, extension to several electronic spectroscopies and implementation of time-dependent approaches. The use of curvilinear valence internal coordinates allows the adoption of quadratic model potential energy surfaces (PES) of the initial and final states expanded at arbitrary configurations. Moreover, the implementation of suitable projectors provides a robust framework for defining reduced-dimensionality models by sorting flexible coordinates out of the harmonic subset, so that they can then be treated at anharmonic level, or with mixed quantum classical approaches. A set of tools to facilitate input preparation and output analysis is also provided. We show the program at work in the simulation of different spectra (one and two-photon absorption, emission and resonance Raman) and internal conversion rate of a typical rigid molecule, anthracene. Then, we focus on absorption and emission spectra of a series of flexible polyphenyl molecules, highlighting the relevance of some of the newly implemented features. The code is freely available at http://www.iccom.cnr.it/en/fcclasses/.

DP Compress: A Model Compression Scheme for Generating Efficient Deep Potential Models.

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning-based PES model. This scheme, we call DP Compress, is an efficient postprocessing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, H2O, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online.

Exploring Potential Energy Surfaces Using Reinforcement Machine Learning.

Reinforcement machine learning is implemented to survey a series of model potential energy surfaces and ultimately identify the global minima point. Through sophisticated reward function design, the introduction of an optimizing target, and incorporating physically motivated actions, the reinforcement learning agent is capable of demonstrating advanced decision making. These improved actions allow the agent to successfully converge to an optimal solution more rapidly when compared to an agent trained without the aforementioned modifications. This study showcases the conceptual feasibility of using reinforcement machine learning to solve difficult environments, namely, potential energy surfaces, with multiple, seemingly, correct solutions in the form of local minima regions. Through these results, we hope to encourage extending reinforcement learning to more complicated optimization problems and using these novel techniques to efficiently solve traditionally challenging problems in chemistry.

Molecular Conformer Search with Low-Energy Latent Space.

Identifying low-energy conformers with quantum mechanical accuracy for molecules with many degrees of freedom is challenging. In this work, we use the molecular dihedral angles as features and explore the possibility of performing molecular conformer search in a latent space with a generative model named variational auto-encoder (VAE). We bias the VAE towards low-energy molecular configurations to generate more informative data. In this way, we can effectively build a reliable energy model for the low-energy potential energy surface. After the energy model has been built, we extract local-minimum conformations and refine them with structure optimization. We have tested and benchmarked our low-energy latent-space (LOLS) structure search method on organic molecules with 5–9 searching dimensions. Our results agree with previous studies.

Development of a fully coupled diabatic spin-orbit model for the photodissociation of phenyl iodide.

The theoretical treatment of the quantum dynamics of the phenyl iodide photodissociation requires an accurate analytical potential energy surface (PES) model. This model must also account for spin-orbit (SO) coupling. This study is the first step to construct accurate SO coupled PESs, namely, for the C-I dissociation coordinate. The model is based on the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) method developed over the past ten years. The SO-free Hamiltonian is represented in an asymptotic diabatic basis and then combined with an atomic effective relativistic coupling operator determined analytically. In contrast to the previously studied cases (HI, CH3I), the diabatic basis states are due to excitations in the phenyl fragment rather than the iodine atom. An accurate analytical model of the abinitio reference data is determined in two steps. The first step is a simple reference model describing the data qualitatively. This reference model is corrected through a trained artificial neural-network to achieve high accuracy. The SO-free and the fine structure states resulting from this ERCAR model are discussed extensively in the context of the photodissociation.

Q-AQUA: A Many-Body CCSD(T) Water Potential, Including Four-Body Interactions, Demonstrates the Quantum Nature of Water from Clusters to the Liquid Phase.

Many model potential energy surfaces (PESs) have been reported for water; however, none are strictly from "first-principles". Here we report such a potential, based on a many-body representation at the CCSD(T) level of theory up to the four-body interaction. The new PES is benchmarked for the isomers of the water hexamer for dissociation energies, harmonic frequencies, and unrestricted diffusion Monte Carlo (DMC) calculations of the zero-point energies of the Prism, Book, and Cage isomers. Dissociation energies of several isomers of the 20-mer agree well with recent benchmark energies. Exploratory DMC calculations on this cluster verify the robustness of the new PES for quantum simulations. The accuracy and speed of the new PES are demonstrated for standard condensed phase properties, i.e., the radial distribution function and the self-diffusion constant. Quantum effects are shown to be substantial for these observables and also needed to bring theory into excellent agreement with experiment.

Quantum Gaussian process model of potential energy surface for a polyatomic molecule.

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain.

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface.

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

BEP-Like Correction of Nonequilibrium Thermodynamic Parameters of the Solvent-Assisted Reactions: The DFT and Ab Initio Study of Hydration, Peroxidation, and Enolization of Acetone and 1,1,1-Trifluoroacetone in Aqueous Solutions.

The mechanisms of enolization and reactions of nucleophilic addition to carbonyl compounds were analyzed by density functional theory (DFT) (PBE1PBE) and ab initio (DLPNO-CCSD(T)) level of theory using the interaction of water and hydrogen peroxide with acetone and 1,1,1-trifluoroacetone (TFA) as the reference reactions. The transition states of the studied reactions were localized within the integrated approach that includes both the dielectric continuum theory (polarizable continuum model (PCM)) and the cyclic or two-cluster explicit solvation models. The considered models provide proton transfer in the enolization, hydration, and peroxidation reactions by the Grotthuss mechanism. It is shown that the calculated activation parameters at a sufficiently high level of theory and a sufficiently flexible solvation model can be additionally refined using the Bell-Evans-Polanyi (BEP)-like correction (in a form of the Bell-Evans-Polanyi equation), which is linear scaling of the model potential energy surface according to the equilibrium parameters of the reference reaction (experiment or high-level calculation). Quite good correspondence of the corrected and reference activation parameters and the lower sensitivity of the calculation results to the choice of the solvation model indicate the high reliability of the proposed BEP-like correction technique.

Effective active sites of triangular Mo-S Nano-catalysts from first-principle calculations

High density of effective active sites (EASs) is critical for efficient catalysis of hydrogen evolution. Basis on the first-principle calculations, the potential energy surface model was used to explore the mechanism determining the proportion of EASs on the edge of Mo-S nanoparticles. It is found that the large proton affinity of Mo-S nanoparticles leads to the high onset overpotential, while the small electron affinity that attenuates rapidly with increasing hydrogen coverage accounts for the scarce EASs. Substituting S with Se reduces the proton affinity and retards the attenuation of electron affinity. Substituting Mo with Nb increazes the electron affinity and decreaze the proton affinity significantly since the d1 configuration of Nb ions. By substituting all Mo ions with Nb and the edge S ions with Se, the proportion of EASs increazes significantly from 25% to more than 62.5% and the catalytic rate increazes by more than 2 orders of magnitude.