Construction Of Potential Energy Surfaces Research Articles

Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction.

We present a new quasi-direct quantum molecular dynamics computational method which offers a compromise between quantum dynamics using a precomputed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for constructing a PES on the fly during a dynamics simulation. This is achieved by acquisition of new single-point (SP) calculations and refitting of the PES, depending on the need of the dynamics. The TD-ADGA is a further development of the adaptive density-guided approach (ADGA) for PES construction where the placement of SPs is guided by the density of the nuclear wave function. In TD-ADGA, the ADGA framework has been integrated into the time propagation of the time-dependent nuclear wave function and we use the reduced one-mode density of this wave function to guide when and where new SPs are placed. The PES is thus extended or updated if the wave function moves into new areas or if a certain area becomes more important. Here, we derive equations for the reduced one-mode density for the time-dependent Hartree (TDH) method and for multiconfiguration time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used with any time-dependent wave function method as long as a density is available. The TD-ADGA method has been investigated on molecular systems containing single- and double-minimum potentials and on single-mode and multi-mode systems. We explore different approaches to handle the fact that the TD-ADGA involves a PES that changes during the computation and show how results can be obtained that are in very good agreement with results obtained by using an accurate reference PES. Dynamics with TD-ADGA is essentially a black box procedure, where only the initialization of the system and how to compute SPs must be provided. The TD-ADGA thus makes it easier to carry out quantum molecular dynamics and the quasi-direct framework opens up the possibility to compute quantum dynamics accurately for larger molecular systems.

Efficient vibrationally correlated calculations using n-mode expansion-based kinetic energy operators.

Due to its efficiency and flexibility, the n-mode expansion is a frequently used tool for representing molecular potential energy surfaces in quantum chemical simulations. In this work, we investigate the performance of n-mode expansion-based models of kinetic energy operators in general polyspherical coordinate systems. In particular, we assess the operators with respect to accuracy in vibrationally correlated calculations and their effect on potential energy surface construction with the adaptive density guided approach. Our results show that the n-mode expansion-based operator variants are reliable and systematically improvable approximations of the full kinetic energy operator. Moreover, we introduce a workflow to generate the n-mode expanded kinetic energy operators on-the-fly within the adaptive density guided approach. This scheme can be applied in studies of species and coordinate systems, for which an analytical form of the kinetic energy operator is not available.

Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules.

We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm-1. A much higher accuracy with errors below 1 cm-1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations.

Temperature Dependence of the Electronic Absorption Spectrum of NO2.

The nitrogen dioxide (NO2) radical is composed of the two most abundant elements in the atmosphere, where it can be formed in a variety of ways including combustion, detonation of energetic materials, and lightning. Relevant also to smog and ozone cycles, together these processes span a wide range of temperatures. Remarkably, high-resolution NO2 electronic absorption spectra have only been reported in a narrow range below about 300 K. Previously, we reported [ J. Phys. Chem. A 2021, 125, 5519-5533] the construction of quasi-diabatic potential energy surfaces (PESs) for the lowest four electronic states (X̃, Ã, B̃, and C̃) of NO2. In addition to three-dimensional PESs based on explicitly correlated MRCI(Q)-F12/VTZ-F12 ab initio data, the geometry dependence of each component of the dipoles and transition dipoles was also mapped into fitted surfaces. The multiconfigurational time-dependent Hartree (MCTDH) method was then used to compute the 0 K electronic absorption spectrum (from the ground rovibrational initial state) employing those energy and transition dipole surfaces. Here, in an extension of that work, we report an investigation into the effects of elevated temperature on the spectrum, considering the effects of the population of rotationally and vibrationally excited initial states. The calculations are complemented by new experimental measurements. Spectral contributions from hundreds of rotational states up to N = 20 and from 200 individually-characterized vibrational states were computed. A spectral simulation tool was developed that enables modeling the spectrum at various temperatures─by weighting individual spectral contributions via the partition function, or for pure excited initial states, which can be probed via transient absorption spectroscopy. We validate these results against experimental absorption spectroscopy data at high temperatures, as well as via a new measurement from the (1,0,1) initial vibrational state.

MLRNet: Combining the Physics-Motivated Potential Models with Neural Networks for Intermolecular Potential Energy Surface Construction.

A physics-based machine learning model called MLRNet has been developed to construct the high-accuracy two-body intermolecular potential energy surface (IPES). The outputs of the neural network are integrated into the physically realistic Morse/long-range (MLR) function, which ensures that the MLRNet has meaningful extrapolation at both short and long ranges and solves the asymptotic problem in common neural network potential (NNP) models. The neural network representation of the MLR parameters is more flexible and more efficient than the polynomial expansion in the conventional mdMLR model, especially for systems containing nonrigid monomer(s). The present work illustrates the basic framework of the current MLRNet model, including (i) how to combine the physically meaningful MLR function with different possible NN structures, (ii) the preservation of permutation symmetry, and (iii) the predetermination of the long-range function uLR. We choose two realistic systems to demonstrate the performance of MLRNet: the three-dimensional IPES of CO2-He including the CO2 antisymmetric vibration Q3 and the six-dimensional IPES of the H2O-Ar system. In both cases, the fitting errors of the MLRNet are several times smaller than those of the conventional mdMLR model. Both short-range and long-range extrapolation tests were performed to illustrate the extrapolation ability of the MLRNet and its damping function version. Moreover, for the 6-D H2O-Ar system, the MLRNet only needs 1596 trainable parameters, which is almost equal to the number needed for the 5-D mdMLR model (1509) and half that needed for the PIP-NN model (3501) within similar accuracy, which illustrates the model efficiency in high-dimensional IPES fitting.

Formation and fragmentation of 2-hydroxyethylhydrazinium nitrate (HEHN) cluster ions: a combined electrospray ionization mass spectrometry, molecular dynamics and reaction potential surface study.

The 2-hydroxyethylhydrazinium nitrate ([HOCH2CH2NH2NH2]+NO3-, HEHN) ionic liquid has the potential to power both electric and chemical thrusters and provide a wider range of specific impulse needs. To characterize its capabilities as an electrospray propellant, we report the formation of HEHN cluster ions in positive electrospray ionization (ESI) and their collision-induced dissociation. The experiment was carried out using ESI guided-ion beam mass spectrometry which mimics an electrospray thruster in terms of ion emission, injection into a vacuum and fragmentation in space. Measurements include compositions of primary ions in the electrospray plume and their individual dissociation product ion cross sections and threshold energies. The results were interpreted in light of theoretical modeling. To determine cluster structures that are comprised of [HE + H]+ and NO3- constituents, classical mechanics simulations were used to create initial guesses; and for clusters that are formed by reactions between ionic constituents, quasi-classical direct dynamics trajectory simulations were used to mimic covalent bond formation and structures. All candidate structures were subject to density functional theory optimization, from which global minimum structures were identified and used for construction of reaction potential energy surface. The comparison between experimental values and calculated dissociation thermodynamics was used to verify the structures for the emitted species [(HEHN)nHE + H]+, [(HEHN)n(HE)2 + H]+, [(HE)n+1 + H]+ and [(HE)nC2H4OH]+ (n = 0-2), of which [(HE)1-2 + H]+ dominates. Due to the protic nature of HEHN, cluster fragmentation can be rationalized by proton transfer-mediated elimination of HNO3, HE and HE·HNO3, and the latter two become dominant in larger clusters. [(HE)2 + H]+ and [(HE)nC2H4OH]+ contain H-bonded water and consequently are featured by water elimination in fragmentation. These findings help to evaluate ion formation and fragmentation efficiencies and their impacts on electrospray propulsion.

Ab initio relativistic potential energy surface with analytical long-range part of benzene-Rn complex and its application to intermolecular vibrations

We study the benzene-Rn (BzRn) complex in its electronic ground state using an ab initio scalar relativistic method in the framework of the coupled-cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)]. Two different approaches to treat the scalar relativistic effects have been tested — the small-core pseudopotential (PP) and the Douglas–Kroll–Hess (DKH) Hamiltonian. These methods were used with the augmented Dunning’s double zeta basis set for C and H atoms, and the augmented triple PP basis set for Rn supplemented by midbond functions. Additionally, the effects of the basis extension for C and H atoms and the extension of the correlation space to include the internal orbitals of Rn and C have been tested. The comparison of the binding energy De and the equilibrium coordinate ze found with different methods has allowed to choose the optimal one based on PP for the construction of the analytical potential energy surface (PES). The long-range part of the potential has been fitted separately and the obtained long-range coefficients have been compared to their counterparts calculated from the first principles using the CCSD polarization propagator. The vibrational energy level pattern of BzRn has been studied, and the revealed polyad structure of the complex has been compared to the previously studied benzene-Kr and benzene-Xe complexes. A Python code that yields the interaction energy at any Rn position is provided.

An accurate many-body expansion potential energy surface for SiH2 (11 A') using a switching function formalism.

An accurate many-body expansion potential energy surface for the ground state of SiH2 is reported. To warrant the correct behavior at the Si (1D) + H2 (X1Σ+g) dissociation channels involving silicon in the first excited Si (1D) and ground Si (3P) states, a switching function formalism has been utilized. A great deal of ab initio points based on aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets are utilized at the multi-reference configuration interaction level using the full-valence-complete-active-space wave function as the reference. Subsequently the calculated energies are corrected via a many-body expansion method to extrapolate to the complete basis set limit. The topographic features of the novel many-body expansion global potential energy surface are studied in detail, showing a good agreement with the theoretical and experimental results in the literature. Moreover, the integral cross-section of the Si (1D) + H2 (X1Σ+g) → H (2S) + SiH (X2Π) reaction has been calculated using the time-dependent wave packet method, which provides support for the reliability of the title potential energy surface. This work can serve as the foundation for the study of Si (1D) + H2 (X1Σ+g) reaction kinetics, and for the construction of the larger multibody expansion potential energy surface of silicon/hydrogen containing systems.

Predicting third-body collision efficiencies for water and other polyatomic baths.

Low-pressure-limit microcanonical (collisional activation) and thermal rate constants are predicted using a combination of automated ab initio potential energy surface construction, classical trajectories, transition state theory, and a detailed energy- and angular-momentum-resolved collision kernel. Several systems are considered, including CH4 (+M) and HO2 (+M), with an emphasis on systems where experimental information is available for comparison. The a priori approach involves no adjustable parameters, and we show that the predicted thermal rate constants are in excellent agreement with experiments, with average deviations of less than 25%. Notably, the a priori approach is shown to perform equally well for atomic, diatomic, and polyatomic baths, including M = H2O, CO2, and "fuel" baths like M = CH4 and NH3. Finally, the utility of microcanonical rate constants for interpreting trends and inferring mechanistic details in the thermal kinetics is demonstrated.

Automated Construction of Neural Network Potential Energy Surface: The Enhanced Self-Organizing Incremental Neural Network Deep Potential Method.

In recent years, the use of deep learning (neural network) potential energy surface (NNPES) in molecular dynamics simulation has experienced explosive growth as it can be as accurate as quantum chemistry methods while being as efficient as classical mechanic methods. However, the development of NNPES is highly nontrivial. In particular, it has been troubling to construct a dataset that is as small as possible yet can cover the target chemical space. In this work, an ESOINN-DP method is developed, which has the enhanced self-organizing incremental neural network (ESOINN) and a newly proposed error indicator at its core. With ESOINN-DP, one can construct the NNPES with little human intervention, and this method ensures that the constructed reference dataset covers the target chemical space with minimum redundancy. The performance of the ESOINN-DP method has been well validated by developing neural network potential energy surfaces for water clusters, tripeptides, and by de-redundancy of a sub-dataset of the ANI-1 database. We believe that the ESOINN-DP method provides a novel idea for the construction of NNPES and, especially, the reference datasets, and it can be used for molecular dynamics (MD) simulations of various gas-phase and condensed-phase chemical systems.

Interpolation Methods for Molecular Potential Energy Surface Construction.

The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system's energy and its geometry (i.e., atom positions) and can provide useful information about the system's chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.

Electron-nuclear quantum dynamics of diatomic molecules: nonadiabatic signatures in molecular spectra

The Born–Oppenheimer approximation is the fundamental approximation in the quantum-mechanical description of molecules, and holds true in most applications for ground-state properties and to a lesser extent for excited states. In situations where the coupling of electronic and nuclear motion becomes significant, for example, in strong-field induced time-dependent processes, the electron-nuclear interaction must be described beyond the Born–Oppenheimer picture. Presented here are multiconfiguration electron-nuclear dynamics simulations with and without a laser pulse excitation for the diatomic molecules H, HeH, LiH, BeH, Li, and N, taking into account electron-nuclear coupling. The computational approach allows a direct propagation of the electron-nuclear wave function, thus avoiding the construction of potential energy surfaces. With this approach, ground-state and time-dependent properties, including equilibrium bond lengths, dipole moments, and electronic, vibrational, and high-harmonic spectra are obtained. For some of the diatomics, manifestations of nonadiabatic effects are observed in the high-harmonic spectra, where both an uptake of nuclear motion and electronic excitation into higher-lying excited states can occur, resulting in an effective driving force that displaces the nuclei from the equilibrium position. Isotope effects can also be observed in electronic excitation spectra.

Deciphering Spectroscopic and Structural Insights into the Photophysical Behavior of 2,2'-Dipyridylamine: An Efficient Environment Sensitive Fluorescence Probe.

Excited state deactivation properties and the effects of solvent hydrogen bonding (HB) on the photophysical behavior of 2,2'-dypyridylamine (DPyA) were investigated by steady state and time-resolved fluorescence experiments, molecular docking, and density functional theory (DFT) calculations. In addition to the polarity effect, the contributions of solvent HB donation (HBD) acidity and HB acceptance (HBA) basicity to modulate the solvatochromic spectral properties were estimated from multiparametric linear regression analysis using Kamlet-Taft (KT) and Catalán formalisms. The importance of C-N bond torsion, leading to the trans → cis conversion, was manifested by substantial increase in DPyA fluorescence yield in the presence of cyclodextrin (CD) and glycerol. The unusually low fluorescence yield in aqueous medium was explained on the basis of synergistic effect of solvent hydrogen bonding combined with excited state conformational isomerization, which renders DPyA to be an excellent environment sensitive fluorescence reporter. The experimental results were verified with structural insights obtained from DFT calculations at B3LYP/6-311++G(d,p) level and construction of potential energy surface (PES) in the ground state as well as in the excited states.

Atom-Diatom Reactive Scattering Collisions in Protonated Rare Gas Systems.

The study of the dynamics of atom–diatom reactions involving two rare gas (Rg) atoms and protons is of crucial importance given the astrophysical relevance of these processes. In a series of previous studies, we have been investigating a number of such Rg RgH Rg RgH reactions by means of different numerical approaches. These investigations comprised the construction of accurate potential energy surfaces by means of ab initio calculations. In this work, we review the state-of-art of the study of these protonated Rg systems making special emphasis on the most relevant features regarding the dynamical mechanisms which govern these reactive collisions. The aim of this work therefore is to provide an as complete as possible description of the existing information regarding these processes.

The quantum and quasi-classical dynamics calculations of the Au++HD → AuH+/AuD++D/H reaction

The dynamics studies of the Au+ + HD (v 0 = 0, j 0 = 0) → AuH+/AuD+ + D/H reaction are carried out using time-dependent quantum wave packet and quasi-classical trajectory (QCT) methods. Some meaningful dynamics properties are reported at state-to-state level of theory, such as reaction probability, integral cross section (ICS), and differential cross section (DCS). Furthermore, the ICSs of the two channels of the Au+ + HD reaction are compared with experimental data. Large discrepancies between theory and experiment are observed near the threshold, which can be attributed to the pseudopotential basis set used in the construction of potential energy surface. However, present QCT values are in general good agreement with experimental results as the collision energy above 4.0 eV. The DCSs results indicated that the insert complex-forming reaction mechanism dominates the reaction for these two channels.

Rapid enthalpy prediction of transition states using molecular graph convolutional network

AbstractThe rapid development of machine learning has provided low‐cost and high‐throughput molecular energy prediction methods; however, the direct energy prediction of transition states (TSs) in radical reactions has received little attention, which can facilitate the rapid construction of potential energy surface (PES) and chemical reactivity inference. Here, we present a generic descriptor of TSs, molecules and radicals to realize the simultaneous prediction of their enthalpy of formation through the augmented molecular graph convolutional network (MGCN). It is proved that the network can rapidly (within milliseconds per prediction) and accurately predict the enthalpy of various types of samples, of which the mean absolute error (MAE) of the held‐out test set is 1.44 kcal/mol (>50% samples less than 1.0 kcal/mol) with high R2 (0.925–0.998) among all categories. The PES constructed from predictions is close to the calculated results by density functional theory (DFT) and conforms to the trend of chemical reactivity.

Direct laser cooling schemes for the triatomic SOH and SeOH molecules based on ab initio electronic properties.

Direct laser cooling is a very promising method to obtain cold molecules for various applications. However, a molecule with satisfactory electronic and optical properties for the optical scheme is difficult to identify. By suggesting criteria for the qualified molecules, we develop a method to identify the suitable polyatomic molecules for direct laser cooling. The new criteria from the equilibrium geometrical structures and fundamental frequencies of the ground and low-lying excited states are used to replace the past ones based on Franck-Condon factors. The new method can rapidly identify the preferable one among many candidate polyatomic molecules based on ab initio calculations because the new criteria are free from the construction of potential energy surfaces. The method is testified by using triatomic molecules containing OH. All the reported and two new molecules suitable for direct laser cooling are identified by comparing 168 electronic states of 28 molecules with the new criteria. The newly found molecules have been confirmed using the Franck-Condon factors from the construction of potential energy surfaces. Finally, the optical schemes for the direct laser cooling of the SOH and SeOH molecules are established.

A unified cost-effective method for the construction of reliable potential energy surfaces for H2S and H2O clusters.

A DFT-based methodology has been used to construct the potential energy surface of H2S clusters up to pentamers. Geometrical parameters and energetics show very good agreement with the existing experimental and high-level theoretical results. Distinct stable conformers of three dimers, six trimers, eleven tetramers and twenty-three pentamers have been identified. Both S-HS H-bond and SS interactions are identified in dimers, trimers and pentamers, while no SS interactions could be found in any of the 11 tetramer conformers. The binding energies of the most stable dimer, trimer, tetramer and pentamer are -1.66, -5.21, -8.57 and -12.54 kcal mol-1, respectively. The PES has been found to be exceedingly flat and the energy gap between the most and the least stable conformers was found to be only 0.09, 2.13, 1.65 and 1.13 kcal mol-1, from the dimer to the pentamer, respectively. The proposed method has also been used for water clusters up to the pentamer. The results obtained were found to agree closely with the existing results. Only one conformer was found for the water dimer, whereas four, five and fifteen conformers were obtained for the trimer, tetramer and pentamer, respectively. Atoms in molecular calculations were found to corroborate with the geometric and energetic results for both clusters.

Physically inspired atom-centered symmetry functions for the construction of high dimensional neural network potential energy surfaces

Among different atomistic neural network (AtNN) potential energy surfaces (PESs), the Behler-Parrinello neural network (BPNN) based on atom-centered symmetry functions (ACSFs) has been proved to be capable of constructing accurate PESs for various crystals. A judicious setting of the parameters of the ACSFs largely determines the accuracy of a BPNN PES. However, this is typically an ad hoc and tedious task requiring highly acute chemical intuition. To address this issue, we derived a set of physically inspired ACSFs from the effective densities of atoms, in which the radii of atoms are naturally incorporated. Therefore, the parameters of the physically inspired ACSFs can be directly chosen based on the types of chemical bonds within a target system. Compared with the original ones, the physically inspired ACSFs are more suitable for complex systems based on its better performance on predicting the formation enthalpies of molecules in QM9 database. Moreover, the physically inspired ACSFs can also effectively accelerate the convergence of the atomic forces during the training of an AtNN PES. With the physically inspired ACSFs, we constructed a highly accurate AtNN PES for a solid electrolyte Li10GeP2S12. Based on the AtNN PES, we studied the bulk Li ion diffusion within Li10GeP2S12 by molecular dynamics (MD) simulations. The MD results well reproduced the experimental results, indicating the high accuracy of the AtNN PES constructed with the physically inspired ACSFs.

A Gaussian process regression adaptive density guided approach for potential energy surface construction.

We present a new iterative scheme for potential energy surface (PES) construction, which relies on both physical information and information obtained through statistical analysis. The adaptive density guided approach (ADGA) is combined with a machine learning technique, namely, the Gaussian process regression (GPR), in order to obtain the iterative GPR-ADGA for PES construction. The ADGA provides an average density of vibrational states as a physically motivated importance-weighting and an algorithm for choosing points for electronic structure computations employing this information. The GPR provides an approximation to the full PES given a set of data points, while the statistical variance associated with the GPR predictions is used to select the most important among the points suggested by the ADGA. The combination of these two methods, resulting in the GPR-ADGA, can thereby iteratively determine the PES. Our implementation, additionally, allows for incorporating derivative information in the GPR. The iterative process commences from an initial Hessian and does not require any presampling of configurations prior to the PES construction. We assess the performance on the basis of a test set of nine small molecules and fundamental frequencies computed at the full vibrational configuration interaction level. The GPR-ADGA, with appropriate settings, is shown to provide fundamental excitation frequencies of an root mean square deviation (RMSD) below 2 cm-1, when compared to those obtained based on a PES constructed with the standard ADGA. This can be achieved with substantial savings of 65%-90% in the number of single point calculations.