Global Potential Energy Surface Research Articles

Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer.

In this work, we present a full-dimensional potential energy surface for AlF-AlF. We apply a general machine learning approach for full-dimensional potential energy surfaces, employing an active learning scheme trained on abinitio points, whose size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As a result, it is possible to provide the full-dimensional AlF-AlF potential energy surface, requiring ≲0.01% of the configurations to be calculated abinitio. Furthermore, we analyze the general properties of the AlF-AlF system, finding critical differences with other reported results on CaF or bi-alkali dimers.

Reaction dynamics of P(4S) + O2(X3Σ−g) → O(3P) + PO(X2Π) on a global CHIPR potential energy surface of PO2(X2A1): implications for atmospheric modelling

Abstract. The reaction dynamics of P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are thought to be important in atmospheric and interstellar chemistry. Based on the state-of-the-art ab initio energy points, we analytically constructed a global potential energy surface (PES) for the ground-state PO2(X2A1) using the combined-hyperbolic-inverse-power-representation (CHIPR) method. A total of 6471 energy points were computed by the multireference configuration interaction method with the Davidson correction and aug-cc-pV5Z basis set. The analytical CHIPR PES reproduces ab initio energies accurately with a root-mean-square deviation of 91.5 cm−1 (or 0.262 kcal mol−1). The strongly bound valence region of the PES has complicated topographical features with multiple potential wells and barriers. The attributes of the important intermediates are carefully validated with our geometry optimization results, as well as previous experimental and computational results. Finally, the reaction probability, integral cross sections, and rate constants for P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are calculated using the quasi-classical trajectory and time-dependent wave packet methods. The trends of probability and integral cross section versus the collision energy can be divided into three stages, which are governed by the entrance barriers or exothermicity of the reaction. The rate constant demonstrates strong Arrhenius linear behaviour at relatively low temperatures but deviates from this pattern at high temperatures. The calculated cross sections and rate constants are helpful for modelling the phosphorus chemistry in atmospheric and interstellar media.

PotLib 2023: New version of a potential energy surface library for chemical systems

POTLIB is a library of global and semiglobal potential energy surface subprograms. The library currently features 410 entries, including both single-state entries and multi-state entries. When one calls the routine of a single-state entry, it returns the ground-electronic-state adiabatic potential energy surface at the input geometry. In addition, some entries also return the gradient of the surface. When one calls a multi-state entry, it returns a diabatic potential energy matrix (DPEM). If the entry also has the gradient of the DPEM, one can compute adiabatic surfaces, their gradients, and the nonadiabatic coupling vectors (NACs) from the DPEM and its gradient by diagonalization. Some but not all the routines conform to one of a set of standard interfaces. The goal is to facilitate chemical dynamics research by collecting and disseminating a comprehensive collection of state-of-the-art potential energy routines (developed by a wide, international group of researchers) with systematic and well-defined interfaces for use with chemical dynamics programs. Systems in the library include CHArO2, CHN2O+, CH2O, CH2O2, CH3N2, CH3O, CH4, CH4Br, CH4Cl, CH4F, CH4O, CH4OCl, CH4OF, CH4OH, CH5, CH5+, CH5N, CH5O2, CH8O2, C2H2N2O, C2H2O, C2H4N, C2H4O4, C2H6Cl, C2H6F, C2H6H, C2H6O, C2H6OH, C2H7, C2O2, C3H4O2, C3H7NO, C6H6O, C6H6S, C7H8S, HBrCl, HCl2, HF2, HI2, HLiF, HNaF, HO2, HO3, HOBr, HSiO, H2Br, H2ClO, H2F, H2F2, H2FO, H2Na, H2O, H2O2, H2OBr, H3, H3Cl, H3ClN, H3ClO, H3N, H3O, H3O2, H3+, H3S, H4ClSi, H4N, H4NO, H4O2, H5GeO, H5Si, H7+, AlmHn, Aln, ArNO, K2Rb2, NO2, N2O, N2O2, N3, N4, O3, and O4. New version program summaryProgram title: PotLib 2023CPC Library link to program files:https://doi.org/10.17632/chxxhnnt4p.1Licensing provisions: Apache 2.0Programming language: FortranDoes the new version supersede the previous version?: YesJournal references of previous versions: Comput. Phys. Comm. 144 (2002) 169–187 [1]; Erratum: Comput. Phys. Comm. 156 (2004) 319–32.Nature of problem: Within the Born–Oppenheimer approximation, the electronically adiabatic interactions of atoms and molecules can be represented by a potential energy surface (PES) that depends on the geometry of the reacting species [2-4]. An electronically nonadiabatic system can be approximately described by a diabatic potential energy matrix (DPEM) that also depends on molecular geometry [5,6]. The library contains Fortran subroutines of PESs and DPEMs for reactive and non-reactive systems.Solution method: The user can incorporate a PES, DPEM, or PES set from a DPEM into a chemical dynamics computer code to supply the needed potential or potentials and optionally the gradients (forces) and surface couplings.Summary of revisions: The new version includes many more potentials than the original version of the library.

Semiclassical Multistate Dynamics for Six Coupled 5A' States of O + O2.

Dynamics simulations of high-energy O2-O collisions play an important role in simulating thermal energy content and heat flux in flows around hypersonic vehicles. To carry out such dynamics simulations efficiently requires accurate global potential energy surfaces and (in most algorithms) state couplings for many energetically accessible electronic states. The ability to treat collisions involving many coupled electronic states has been a challenge for decades. Very recently, a new diabatization method, the parametrically managed diabatization by deep neural network (PM-DDNN), has been developed. The PM-DDNN method uses a deep neural network architecture with an activation function parametrically dependent on input data to discover and fit the diabatic potential energy matrix (DPEM) as a function of geometry, and the adiabatic potential energy surfaces are obtained by diagonalization of a small matrix with analytic matrix elements. Here, we applied the PM-DDNN method to the six lowest-energy potential energy surfaces in the 5A' manifold of O3 to perform simultaneous diabatization and fitting; the data are obtained by extended multistate complete-active-space second-order perturbation theory. We then used the adiabatic surfaces for dynamics calculations with three methods: coherent switching with decay of mixing (CSDM), curvature-driven CSDM (κCSDM), and electronically curvature-driven CSDM (eκCSDM). The κCSDM calculations require only adiabatic potential energies and gradients. The three dynamical methods are in good agreement. We then calculated electronically nonadiabatic, electronically inelastic, and dissociative cross sections for seven initial collision energies, five initial vibrational levels, and four initial rotational levels. Trends in the electronically inelastic cross sections as functions of the initial collision energy and vibrational level were rationalized in terms of the coordinate ranges where the gaps between the second and third potential energy surfaces are small.

An accurate many-body expansion potential energy surface for HO2 (X 2A″) by extrapolation to the complete basis set limit and quantum dynamics of the related reaction O(3P) + OH(2Π)

A new global many-body expansion potential energy surface (PES) for the ground electronic state of HO2 is constructed. All ab initio energy points are employed using aug-cc-pV(Q+ d)Z and aug-cc-pV(5+ d)Z basis sets at the multi-reference conformational interaction level and then extrapolated to the complete basis set limit. The topographic characteristics of the global PES for HO2 (X 2A″) are discussed in detail and compared with experimental results, showing good agreement. We subsequently consider the O(3P) + OH(2Π) → O2(3 ) + H(2S) reaction using the time-dependent wave packet method and calculate dynamics behaviors, including the vibration–rotation distribution and reaction probabilities. The results indicate that the new PES is suitable for dynamics investigations of O(3P) + OH(2Π) → O2(3 ) + H(2S) and can be used as a component for PESs to construct larger oxygen/hydrogen containing systems.

Global and Full-Dimensional Potential Energy Surfaces of the N2 + O2 Reaction for Hyperthermal Collisions.

The energy transfer, dissociations, and chemical reactions between O2 and N2 play an important role in the re-entry process of aircraft and many atmospheric, combustion, and plasma processes. Recently, Varga et al. (J. Chem. Phys., 2016, 144, 024310) developed a full-dimensional high-precision potential energy surface (PES) of the ground triplet electronic state for the O2 and N2 system based on ca. 55,000 data points, whose energies were calculated by multi-state complete-active-space second-order perturbation theory/minimally augmented correlation-consistent polarized valence triple-zeta electronic structure calculations plus dynamically scaled external correlation. The fitting function adopted the many-body expansion form with the four-body interactions fitted by the permutationally invariant polynomial in terms of bond-order functions of the six interatomic distances (MB-PIP). In this work, we refit the PES of the N2O2 system by two methods based on the same data set that was used by Varga et al. The first uses the permutation invariant polynomial-neural network (PIP-NN) method to fit the entire energy of the 55,000 data points. In the second approach, the PIP-NN method is used to fit only the four-body interaction component, a similar treatment in the MB-PIP method, and the resulting PES is named MB-PIP-NN. Then, the performances of these new PESs and the MB-PIP PES are comprehensively and systematically compared, such as comparisons of various scans, properties of stationary points, and dynamics simulations. Possible improvements for the PES of N2O2 are suggested. A more reliable PES of the system can be constructed in terms of data sampling range, electronic structure calculation level, and fitting method for high-temperature calculation and simulation in the future.

Beyond Born-Oppenheimer Constructed Diabatic Potential Energy Surfaces for HeH2.

First-principles based beyond Born-Oppenheimer theory has been employed to construct multistate global Potential-Energy Surfaces (PESs) for the HeH2+ system by explicitly incorporating the Nonadiabatic Coupling Terms (NACTs). Adiabatic PESs and NACTs for the lowest four electronic states (12A', 22A', 32A' and 42A') are evaluated as functions of hyperangles for a grid of fixed values of the hyperradius in hyperspherical coordinates. Conical intersection between different states are validated by integrating the NACTs along appropriately chosen contours. Subsequently, adiabatic-to-diabatic (ADT) transformation angles are determined by solving the ADT equations to construct the diabatic potential matrix for the HeH2+ system which are smooth, single-valued, continuous, and symmetric and are suitable for performing accurate scattering calculations for the titled system.

Reaction dynamics of C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) on a global CHIPR potential energy surface of the ground state Si2C(X 1A1)

ABSTRACT The dynamics of C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) on its ground state Si2C(X 1A1) are of great significance in carbon-rich interstellar chemistry. Using the combined-hyperbolic-inverse-power-representation method, we construct the first global potential energy surface (PES) for the electronic ground state Si2C(X 1A1) based on a total of 4080 ab initio energy points, which are obtained at the Davidson-corrected internally contracted multireference configuration interaction level of theory. The topographical features of the newly constructed PES are examined in detail and show good agreement with previous theoretical and experimental studies. Finally, we investigate the C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) reaction using the quasi-classical trajectory and time-dependent wave packet calculations, yielding reasonable integral cross sections and rate constants, which are expected to be useful for astrochemical modelling in carbon-rich interstellar environments.

The state-to-state dynamics of the N + NH(3Σ−) → N2(X1 Σg +) + H reaction: based on a new global potential energy surface

A new global potential energy surface (PES) of the ground state of the HN2 system is built using the neural network method. The aug-cc-pVQZ basis set for the H atom, cc-pwCVQZ basis set for the N atom and multi-reference configuration interaction method are employed in the ab initio calculations. The topographic features of the PES are discussed and compared with available theoretical studies. In addition, the initial state (v 0 = 0, j 0 = 0) dynamic studies of the N + NH(3Σ−) → N2(X1 ) + H reaction are performed using a time-dependent wave packet method, based on the newly constructed PES. The dynamics properties, such as reaction probabilities, integral cross-sections, differential cross-sections, the rovibrational state distribution of product and rate constants, are calculated at the state-to-state level of theory and compared with available theoretical and experimental results. The differential cross-section indicates that the forward abstraction mechanism dominates the reaction with the increase of collision energy. Highlights A new global potential energy surface of the ground state of the HN2 system was constructed using the neural network method. Quantum state-resolved dynamical calculations for the N + NH(3Σ−)(v 0 = 0, j 0 = 0) → N2(X1 ) + H reaction were carried out using a time-dependent wave packet method based on the newly constructed potential energy surface. Some meaningful dynamic properties were reported and compared with available theoretical and experimental data.

Accurate ab initio based global adiabatic potential energy surfaces for the 13A'', 13A' and 21A' states of SiH2.

Three accurate global adiabatic potential energy surfaces for the 13A'', 13A' and 21A' states of SiH2 are constructed by fitting numerous ab initio energies calculated at the aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets based on the multi-reference configuration interaction level with Davidson correction. It is worth noting that the potential energy surface of the 13A'' state is established for the first time. The topographic features of these novel potential energy surfaces are investigated in detail and are very consistent with those obtained in the available literature. Moreover, the integral cross-sections of the corresponding reaction are calculated for the first time using a quasi-classical trajectory method and time-dependent wave packet method, indicating that the 13A'' state makes a major contribution to the reaction of Si(3P) + H2(X1Σ+g) (v = 0, j = 0) → H(2S) + SiH(X2Π) at high collision energies. These new potential energy surfaces provide a reliable foundation for investigation of the dynamics and a component for constructing larger silicon-/hydrogen-containing systems.

Full-dimensional automated potential energy surface development and detailed dynamics for the CH2OO + NH3 reaction.

With the help of the ROBOSURFER program package, a global full-dimensional potential energy surface (PES) for the reaction of the Criegee intermediate, CH2OO, with the NH3 molecule is developed iteratively using different ab initio methods and the monomial symmetrization fitting approach. The final permutationally-invariant analytical PES is constructed based on 23447 geometries and the corresponding ManyHF-based CCSD(T)-F12b/cc-pVTZ-F12 energies. The accuracy of the PES is confirmed by the excellent agreement of its stationary-point properties and one-dimensional potential energy curves compared with the corresponding ab initio data. The reaction probabilities and integral cross sections are calculated for the ground-state and several vibrationally excited-state reactions by quasi-classical trajectory simulations. Remarkable is that the maximum impact parameter b where reactivity vanishes is almost independent of collision energy ranging from 1 to 40 kcal mol-1, and the reaction probability increases with increasing collision energy for this negative-barrier reaction. At the same time, a slight mode-specificity effect is observed. In addition, the deuterium effect is investigated and the sudden vector projection is discussed.

A highly accurate full-dimensional ab initio potential surface for the rearrangement of methylhydroxycarbene (H3C-C-OH).

We report here a full-dimensional machine learning global potential surface (PES) for the rearrangement of methylhydroxycarbene (H3C-C-OH, 1t). The PES is trained with the fundamental invariant neural network (FI-NN) method on 91 564 ab initio energies calculated at the UCCSD(T)-F12a/cc-pVTZ level of theory, covering three possible product channels. FI-NN PES has the correct symmetry properties with respect to permutation of four identical hydrogen atoms and is suitable for dynamics studies of the 1t rearrangement. The averaged root mean square error (RMSE) is 11.4 meV. Six important reaction pathways, as well as the energies and vibrational frequencies at the stationary geometries on these pathways are accurately preproduced by our FI-NN PES. To demonstrate the capacity of the PES, we calculated the rate coefficient of hydrogen migration in -CH3 (path A) and hydrogen migration of -OH (path B) with instanton theory on this PES. Our calculations predicted the half-life of 1t to be 95 min, which is excellent in agreement with experimental observations.

A pragmatic protocol for determining charge transfer states of molecules at metal surfaces by constrained density functional theory.

Electron transfer from a metal surface to a molecule is very important at the gas-surface interface, which can lead to electron-mediated energy transfer during molecular scattering from the surface, as evidenced by numerous state-to-state molecular beam experiments of NO and CO scattering from noble metal surfaces. However, it remains challenging to determine relevant charge-transfer states and their nonadiabatic couplings from first principles in such systems involving a continuum of metallic electronic states. In this work, we propose a pragmatic protocol for this purpose based on the constrained density functional theory (CDFT) approach. In particular, we discuss the influence of the charge partitioning algorithm used in CDFT to define the constraint property in molecule-metal systems. It is found that the widely used Bader charge analysis is adequate to define the physically sound CDFT diabatic states corresponding to a molecule with or without extra electron transferred from the metal. Numerical tests validate that the proposed CDFT scheme properly describes the electron transfer behaviors in several benchmark systems, namely, NO or CO interacting with Au(111) or Ag(111). The effects of the surface work function and the molecular electron affinity on electron transfer are discussed in detail by comparing the CDFT states of the four systems. This pragmatic CDFT protocol lays the foundation for constructing accurate global diabatic potential energy surfaces for these important systems and can be generalized to study other interfacial electron transfer related problems.

An analytic global potential energy surface of the CsH2 system and the dynamic calculations of the H + CsH reaction

ABSTRACT Based on 17,326 ab initio points, a global potential energy surface (PES) of the ground state of the CsH2 system was constructed using the neural network method. In ab initio calculations, the AVQZ basis set was used for the H atom, the def2-QZVP basis set was adopted for the Cs atom, and a multi-reference configuration interaction method was employed. The topographical characteristics of the newly developed PES were discussed in detail and no wells or barriers were detected. In addition, the dynamical calculations of the H + CsH reaction were performed using the time-dependent wave packet method, based on the new PES. Dynamics properties, such as reaction probability, integral cross section and differential cross-section were examined. The differential cross-section results indicated that the forward abstraction mechanism dominated the abstraction channel, and the ‘rebound' reaction mechanism played a primary role in the exchange channel. Highlights Using the PIP-NN method, A global potential energy surface for the ground state of the CsH2 system was built based on 17,326 ab initio points. Dynamic calculations for the abstraction and exchange channels of the H + CsH reaction were performed using the time-dependent wave packet method and the dynamic properties of these two channels were discussed in detail. The direct abstraction mechanism plays a dominant role in the abstraction channel and the ‘rebound' mechanism dominates the exchange channel.

Global Full-Dimensional Potential Energy Surface for the Reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 and the Formation Rate and Lifetime of the 23Na287Rb2 Collision Complex.

A full-dimensional global potential energy surface (PES) for the reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 was constructed based on high-level ab initio calculations. The short-range part was expressed as a permutation invariant polynomial-neural network (PIP-NN) fit of 22 003 ab initio points calculated using a coupled cluster method with the one-electron basis 5s5p5d2f plus effective core potentials and core polarizability potentials, while the long-range part was represented in an asymptotically correct form based on multipole expansion. The formation rate of the 23Na287Rb2 complex calculated using a quantum statistical method is in good agreement with experiment, while the estimated 19.20 μs lifetime of the complex from Rice-Ramsperger-Kassel-Marcus (RRKM) theory is significantly shorter than the measured millisecond decay rate, signaling either the inadequacy of RRKM theory or a yet unresolved loss mechanism.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory: The Lowest Doublet States Responsible for the N(4Su) + C2(a 3Πu) → CN(X 2Σ+) + C(3Pg) Reaction.

Global potential energy surfaces (PESs) for the 1 2A' and 1 2A″ states of the C2N system responsible for the N(4Su) + C2(a 3Πu) → CN(X 2Σ+) + C(3Pg) reaction are mapped using compressed-state multistate pair-density functional theory (CMS-PDFT), which is a multi-state version of multiconfiguration pair-density functional theory (MC-PDFT). Calculations are also performed at selected geometries by explicitly correlated multireference configuration interaction with quadruple corrections, MRCI-F12+Q, and the comparison of the two sets of calculations shows that CMS-PDFT describes the globally reactive PESs well, including the bond-breaking asymptotes. We conclude that CMS-PDFT is an efficient method for constructing PESs for strongly correlated reactive systems. The PESs for producing CN + C are found to be barrierless and proceed through intermediate complexes. The CMS-PDFT PESs were fitted with a neural network method, and quasiclassical trajectories were computed on the resulting analytic PESs. These trajectories predict that the reaction produces vibrationally excited CN.

Insights into the structural, electronic and spectral properties of gas-phase GaMgn+ (n = 2–12) clusters

A global potential energy surface search of the gas-phase GaMgn+ (n = 2–12) clusters was performed using CALYPSO, and they were comprehensively studied based on DFT. Specifically, the geometric growth of low-lying energy isomers, the relative stability of the ground state isomers, the electronic structure properties and the spectroscopic properties are fully studied. The results show that the structure of GaMgn+ (n = 3–12) clusters is based on tetrahedral and yurt-type patterns of growth. Calculations show that the ground state isomer of GaMg9+ is a relative special cluster due to it being the most locally stable. In addition, charge transfer studies show that all Ga atoms are electron receivers while most Mg atoms play the role of electron donor for GaMgn+ (n = 3–12) clusters. Electron configuration calculations confirm that the orbitals of the Mg and Ga atoms are sp hybridized in all the ground state isomers. Finally, to provide the corresponding data for possible future experimental validation, the present work also presents theoretical calculations of the IR, Raman and UV-Vis spectra of all the ground state isomers.

Inefficient intramolecular vibrational energy redistribution for the H + HO2 reaction and negative internal energy dependence for its rate constant

Quasiclassical trajectories (QCT) and newly constructed global potential energy surfaces are used to compute thermal and nonthermal rate constants for the H + HO2 reaction. The thermal QCTs rate constants are up to 50% smaller than transition state theory (TST) rate constants based on the same level of electronic structure theory. This reduction is demonstrated to result from inefficient intramolecular vibrational energy redistribution (IVR) in the transient H2O2 well, with a significant fraction of trajectories that reach the H2O2 well promptly dissociating back to reactants instead of via the heavily statistically favored 2OH channel. The nonstatistical reduction factor, κIVR, that quantifies this effect is shown to increase in importance with temperature, with κIVR = 0.81 at 300 K and 0.47 at 2500 K. Finally, we show that inefficient IVR causes H + HO2 rate constants mediated by H2O2 to depend inversely on the initial vibrational excitation of HO2.

Accurate time-dependent wave packet calculation for the reaction of Al(2P) + H2[formula omitted] on the AlH2(12A′) surface

The time-dependent wave packet calculation of the Al(2P) + H2X1∑g+ → H(2S) + AlHX1∑+(X1Σ+) reaction is studied on the precise global potential energy surface of AlH2(12A′). The collision energy dependence of reaction probabilities under different total angular momentum is discussed detailedly. The emphasis is on the exploration of different dynamical behaviors calculated by Coriolis coupling and centrifugal sudden approximation, which makes integral scattering cross section calculated by Coriolis coupling has a smaller oscillation intensity clearly. Moreover, the reaction is enhanced strongly by vibration excitation of H2 molecule but only weakly by rotation excitation due to the late barrier.

Dynamics of the proton transfer reaction O + H2 +(v = 0, j = 0) → OH+ + H on the ground 12A″ potential energy surface

The dynamics of the exothermic complex-forming reaction O + H2 +(v = 0, j = 0) → OH+ + H has been studied by the quasi-classical trajectory method on a global ab initio potential energy surface for the ground state 12A″ fitted by Miguel Paniagua et al. [Phys. Chem. Chem. Phys. 2014, 16, 23594]. The reaction probabilities and integral cross-section (ICS) were calculated and compared with available theoretical results in the collision energy range of 0–1.0 eV. Differential cross-section (DCS) exhibits forwardbackward symmetry, indicating the domination of indirect mechanism. The complex-forming reaction mechanism is investigated in detail. The results show that the contribution of indirect trajectories to ICS and the lifetime of the intermediate complex are strongly dependent on the collision energy. Another reaction mechanism, i.e. direct reaction, also exists. However, it is suppressed in the whole collision energy range; as a result, its contribution to the reaction is negligible.