Diabatic Potential Energy Matrix Research Articles

Accurate diabatization based on combined-hyperbolic-inverse-power-representation: 1,2 2A' states of BeH2.

A diabatic potential energy matrix (DPEM) for the two lowest states of BeH2+ has been constructed using the combined-hyperbolic-inverse-power-representation (CHIPR) method. By imposing symmetry constraints on the coefficients of polynomials, the complete nuclear permutation inversion symmetry is correctly preserved in the CHIPR functional form. The symmetrized CHIPR functional form is then used in the diabatization by ansatz procedure. The abinitio energies are reproduced with satisfactory accuracy. In addition, the CHIPR-based DPEM also reproduces the local topology of a conical intersection. Future work will focus on a complete four-state diabatic representation with emphasis on the long-range interactions and spin-orbit couplings, which will enable accurate quantum scattering calculations for the Be+(2P) + H2 → BeH+(X1Σ+) + H(2S) reaction.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2.

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π) → H + NO+(X1Σ+): Influence of ro-vibrational excitation of NO

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π, vi = 1, 3, ji = 0, 1) → H + NO+(X1Σ+) has been studied based on the recently constructed diabatic potential energy matrix. It was found that the vibrational excitation of reactant NO inhibits the reactivity, while the rotational excitation of reactant NO has little effect on the reaction probability. These attributes were also observed in the semi-classical trajectory calculations employed in the adiabatic representation. Such an inhibitory effect of the vibrational excitation of reactant NO was owing to lower accessibility of the conical intersection and avoided crossing regions, which are located in the wells with respect to the Π diabat, as evidenced by the analysis of the population of the time-independent wave functions. Calculated vibrational state distributions of the product show that the decrease of the reaction mainly leads to the less formation of low vibrational states (vf < 6), and the product vibrational state distributions are more evenly populated for vi = 1 and 3, suggesting a non-statistical behavior. However, the overall shapes of the product rotational distributions remain unchanged, indicating that the redistribution of energy into the rotation of product NO is sufficient in the charge transfer process between H+ and NO. While the reaction is dominated by the forward and backward scattering in differential cross sections (DCSs), consistent with the complex-forming mechanism, a clear forward bias in the DCSs appears, indicating that the occurrence of the reaction is not sufficiently long to undergo the whole phase space of the interaction configurations.

A diabatization method based upon integrating the diabatic potential gradient difference.

In this work we develop a new scheme to construct a diabatic potential energy matrix (DPEM). We propose a diabatization method which is based on integrating the diabatic potential gradient difference to diabatize adiabatic ab initio energies. This method is capable of performing high-precision adiabatic-to-diabatic transformations, with a unique advantage in effectively handling the significant fluctuations in derivative-couplings caused by conical intersection (CI) seams. The above scheme is applied to the DPEM construction of the Na(3p) + H2 → NaH + H reaction. The fitting data including adiabatic energies, energy gradients and derivative-couplings obtained from a previous benchmark DPEM are diabatized and fitted using a general neural network fitting procedure to generate the DPEM. The produced DPEM can effectively describe nonadiabatic processes involving different electronic states. We further perform quantum dynamical calculations on the new DPEM and the previous benchmark DPEM, and the obtained results demonstrate the effectiveness of our scheme.

New diabatic potential energy surfaces of KH2 system constructed using neural network method

New diabatic potential energy surfaces (PESs) for the KH2 system, related to both ground and first excited states, were constructed using only adiabatic electronic energies. The elements of the diabatic potential energy matrix were determined using neural network (NN) method. Prior to calculation, the symmetry constraints of the coupling term were incorporated into the NN code. A comprehensive comparison was undertaken between the topographic characteristics of the newly constructed diabatic PESs and those previously developed using the molecular properties method. To validate the accuracy of the new diabatic PESs, the dynamics calculations of K(4p2P) + H2 (v 0 = 1, j 0 = 0) reaction were performed based on both new and old diabatic PESs with same parameters. The results indicate that the values based on the new diabatic PESs generally agree well with those from the old ones. In addition, compared with the previous diabatic PESs, the new diabatic PESs can accurately describe the geometric phase effect.

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.

Toward a Unified Analytical Description of Internal Conversion and Intersystem Crossing in the Photodissociation of Thioformaldehyde. I. Diabatic Singlet States.

The photodissociation of thioformaldehyde is an archetypal system for the study of competition between internal conversion and intersystem crossing, which involves its two singlet states (S0 and S1) and two triplet states (T1 and T2). In order to perform accurate dynamic simulations, either quantum or quasi-classical, it is essential to construct an analytical representation for all necessary electronic structure data. In this work, a diabatic potential energy matrix (DPEM), Hd, for the two singlet states (S0 and S1) is reported. The analytical form of DPEM is symmetrized and constructed to reproduce adiabatic energies, energy gradients, and derivative couplings obtained from high-level multireference configuration interaction wave functions. The Hd is fully saturated in the molecular configuration space with a trajectory-guided point sampling approach. This Hd can provide the accurate description of the photodissociation of thioformaldehyde on its singlet states and is also a necessary part for incorporating the spin-orbit couplings into a unified diabatic framework. Preliminary quasi-classical trajectory simulations show that a roaming mechanism also exists in the molecular dissociation channel of thioformaldehyde.

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.

Accurate Full-Dimensional Global Diabatic Potential Energy Matrix for the Two Lowest-Lying Electronic States of the H + O2 ↔ HO + O Reaction.

A new and more accurate diabatic potential energy matrix (DPEM) is developed for the two lowest-lying electronic states of HO2, covering both the strong interaction region and reaction asymptotes. The ab initio calculations were performed at the Davidson corrected multireference configuration interaction level with the augmented correlation-consistent polarized valence quintuple-zeta basis set (MRCI+Q/AV5Z). The accuracy of the electronic structure calculations is validated by excellent agreement with the experimental HO2 equilibrium geometry, fundamental vibrational frequencies, and H + O2 ↔ OH + O reaction energy. Through the combination of an electronic angular momentum-method and a configuration interaction vector-based method, the mixing angle between the first two 2A″ states of HO2 was successfully determined. Elements of the 2×2 DPEM were fit to neural networks with a proper account of the complete nuclear permutation inversion symmetry of HO2. The DPEM correctly predicted the properties of conical intersection seams at linear and T-shape geometries, thus providing a reliable platform for studying both the spectroscopy of HO2 and the nonadiabatic dynamics for the H + O2 ↔ OH + O reaction.

Quantum and Semiclassical Dynamics of Nonadiabatic Electronic Excitation of C(3P) to C1D) by Hyperthermal Collisions with N2.

The dynamics and kinetics of nonadiabatic excitation of C(3P) to C(1D) induced by hyperthermal collisions with N2 molecules are investigated using a quantum mechanical and two semiclassical nonadiabatic methods. The full-dimensional interaction potential energy surfaces and spin-orbit coupling, which facilitates the spin-forbidden process, are represented by a recently constructed diabatic potential energy matrix. The multistate quantum dynamics for selected partial waves found small transition probabilities due to the weak spin-orbit coupling. The spin-flip transition is the most favored near the threshold due to effective curve crossing. Strong oscillations are also found in the probabilities, which are attributable to resonances supported by the deep well in the singlet-state potential. Vibrational state-specified rate coefficients are reported from J-shifted quantum dynamics calculations, and they follow the Arrhenius form. Vibrational excitation in the N2 collision partner is found to increase the excitation rate at low temperatures, but the trend is reversed at high temperatures. The two semiclassical methods qualitatively reproduce the quantum rate coefficients.

Simulating the HeI photoelectron spectrum of Cl2O with new full-dimensional adiabatic potential energy surfaces of Cl2O(X̃1A1), Cl2O+(X̃2B1), and Cl2O+(C̃2A2) and a three-state diabatic potential energy matrix of Cl2O+(Ã2B2, B̃2A1, and 22A1): a quantum mechanical study.

To interpret the HeI photoelectron spectrum of Cl2O (involving four lowest electronic states of Cl2O+), in this work we first constructed the associated adiabatic full-dimensional potential energy surfaces (PESs) of Cl2O(X̃1A1), Cl2O+(X̃2B1), and Cl2O+(C̃2A2) and a diabatic potential energy matrix (PEM) of Cl2O+(Ã2B2, B̃2A1, and 22A1) using the explicitly correlated internally contracted multi-reference configurational interaction with Davidson correction (MRCI-F12+Q) and neural network methods. Particularly for the Ã2B2, B̃2A1, and 22A1 states of Cl2O+ coupled in terms of conical intersection, their diabatization is achieved by the neural network approach based merely on the associated adiabatic energies. With the help of newly constructed adiabatic PESs and the diabatic PEM, the HeI photoelectron spectrum of Cl2O is further computed quantum mechanically. The calculated photoelectron spectrum is found to be in good accord with experiment. The mode specificity in the HeI photoelectron bands of Cl2O is analyzed in detail.

Nonadiabatic quantum dynamics of the charge transfer reaction H+ + NO(X2Π) → H + NO+(X1Σ+).

Nonadiabatic quantum dynamics of the charge transfer (CT) reaction H+ + NO(X2Π) → H + NO+(X1Σ+) is investigated on a new diabatic potential energy matrix (PEM) including the 12A' and 22A' states of HNO+/HON+ at the multireference configuration interaction level with Davidson correction using a large basis set. The diabatization of the two coupled states was achieved by the adiabatic-to-diabatic transformation with a mixing angle and the final diabatic PEM was obtained by fitting each matrix element separately using a three-dimensional cubic spline interpolation including more than 22 000 ab initio points. The reaction was found to be dominated by the resonances supported by the double well associated with HNO+ and HON+ species, manifested by the oscillatory structures in the reaction probabilities and product rotational distributions. The product vibrational states were highly excited due to the large exothermicity of the reaction. Consistent with the complex-forming mechanism, the differential cross sections (DCSs) were found to be dominated by the forward and backward scatterings. A clear forward bias in the vibrational state resolved DCSs suggests that the non-statistical behavior of the reaction mainly comes from the low vibrational states of the product. In addition, the rate constants of the reaction in the temperature range from 50 to 500 K were computed for the first time and found to be in fairly good agreement with the available experimental results at 300 K. In particular, compared to other reactions involving neutral species in this system including N, O, and H atoms, such a CT reaction was found to be much more reactive, which has rate constants more than thirty times larger.

Nonadiabatic heavy atom tunneling in 1nσ*-mediated photodissociation of thioanisole.

The 1nσ*-mediated photodissociation dynamics of thioanisole is investigated quantum mechanically using a three-dimensional model based on a newly constructed diabatic potential energy matrix. The lifetimes of the low-lying S1(1ππ*) resonances are determined and found to accord well with available experimental data. Specifically, our theoretical results demonstrate that the photodissociation of thioanisole at the low-lying S1(1ππ*) levels takes place via the heavy atom tunneling due to the higher S1/S2 conical intersection and two equivalent out-of-plane saddle points appearing on the dissociation path. The isotopic effect on the lifetimes is found to be pronounced, manifesting the nature of the tunneling process. Moreover, the geometric phase effect around the S1/S2 conical intersection is found to slightly impact the lifetimes due to the weak destructive or constructive interferences in this heavy atom tunneling, which differs significantly from the scenario in the nonadiabatic hydrogen atom tunneling. Importantly, the quantum mechanical treatment is essentially required to accurately describe the 1nσ*-mediated photodissociation dynamics of thioanisole owing to involving quantum tunneling and geometric phase effects near the conical intersection.

Diabatic potential energy surfaces and semiclassical multi-state dynamics for fourteen coupled 3 A′ states of O3

Dissociation and energy transfer in high-energy collisions of O2 play important roles in simulating thermal energy content and heat flux in flows around hypersonic vehicles. Furthermore, atomic oxygen reactions on the vehicle surface are an important contributor to heat shield erosion. Molecular dynamics modeling is needed to better understand the relevant rate processes. Because it is necessary to model the gas flows in high-temperature shock waves, electronically excited states of O2 and O can be populated, and molecular dynamics simulations should include collisions of electronically excited species and electronically nonadiabatic collisions. This requires potential energy surfaces and state couplings for many energetically accessible electronic states. Here we report a systematic strategy to calculate such surfaces and couplings. We have applied this method to the fourteen lowest-energy potential energy surfaces in the 3 A′ manifold of O3, and we report a neural-network fit to diabatic potential energy matrix (DPEM). We illustrate the use of the resulting DPEM by carrying out semiclassical dynamics calculations of cross sections for excitation of O2 in 3 A′ collisions with O at two collision energies; these dynamics calculations are carried out by the curvature-driven coherent switching with decay of mixing method.

Nonadiabatic Reactive Quenching of OH(A2Σ+) by H2: Origin of High Vibrational Excitation in the H2O Product.

The nonadiabatic dynamics of the reactive quenching channel of the OH(A2Σ+) + H2/D2 collisions is investigated with a semiclassical surface hopping method, using a recently developed four-state diabatic potential energy matrix (DPEM). In agreement with experimental observations, the H2O/HOD products are found to have significant vibrational excitation. Using a Gaussian binning method, the H2O vibrational state distribution is determined. The preferential energy disposal into the product vibrational modes is rationalized by an extended Sudden Vector Projection model, in which the h and g vectors associated with the conical intersection are found to have large projections with the product normal modes. However, our calculations did not find significant insertion trajectories, suggesting the need for further improvement of the DPEM.

Electronically Nonadiabatic Effects on the Quantum Dynamics of the Ha + BeHb+ → Be+ + HaHb; Hb + BeHa+ Reactions.

Nonadiabatic effects are ubiquitous and play an important role in many chemical processes. Here, the adiabatic and nonadiabatic quantum scattering calculations of the H + BeH+ reaction are performed using the time-dependent wave packet method based on an accurate diabatic potential energy matrix that includes the lowest two electronic states and their couplings. The resulting integral cross sections reveal that the nonadiabatic effect significantly inhibits the reactivity of the BeH+-depletion channel but enhances that of the H-exchange channel. The vibrational excitation is suppressed, but the translational excitation is promoted for the H2 product in the BeH+-depletion channel when the nonadiabatic coupling is included. However, the nonadiabatic coupling has a mild effect on the H-exchange product-state distribution. When the nonadiabatic effect is considered, the differential cross sections of the H2 product become less polarized because of the formation of an excited-state complex, whereas the corresponding results of the H-exchange channel only present an increase in the magnitude at the backward region.

Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics.

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.

Semiclassical Trajectory Studies of Reactive and Nonreactive Scattering of OH(A 2 Σ+ ) by H2 Based on an Improved Full-Dimensional Ab Initio Diabatic Potential Energy Matrix.

We present a new full-dimensional diabatic potential energy matrix (DPEM) for electronically nonadiabatic collisions of OH(A 2 Σ+ ) with H2 , and we calculate the probabilities of electronically adiabatic inelastic collisions, nonreactive quenching, and reactive quenching to form H2 O+H. The DPEM was fitted using a many-body expansion with permutationally invariant polynomials in bond-order functions to represent the many-body part. The dynamics calculations were carried out with the fewest-switches with time uncertainty and stochastic decoherence (FSTU/SD) semiclassical trajectory method. We present results both for head-on collisions (impact parameter b equal to zero) and for a full range of impact parameters. The results are compared to experiment and to earlier FSTU/SD and quantum dynamics calculations with a previously published DPEM. The various theoretical results all agree that nonreactive quenching dominates reactive quenching, but there are quantitative differences between the two DPEMs and between the b=0 results and the all-b results, especially for the probability of reactive quenching.

Accurate description of the nonadiabatic proton-coupled electron-transfer process in a diabatic representation: A model study

Using a two-dimensional model system for the proton-coupled electron-transfer process, the eigenvalues and nonadiabatic dynamics have been notably investigated by means of diabatic representation in the Born-Oppenheimer picture. Different from a previously reported diabatic model, which was approximately determined by the eigenstates of the differently defined electronic Hamiltonians, the rigorous diabatization was achieved by a fitting method based on the adiabatic energies and derivative couplings. As expected, the rigorous diabatic models were found to be able to accurately reproduce the eigenvalues or nonadiabatic dynamics in the adiabatic representation for three different models. Furthermore, we proposed an approximate diabatic scheme, which was built from fitting the adiabatic energies solely but with a fixed form for the off-diagonal terms in the diabatic potential energy matrix. This approximate diabatic model without the aid of the derivative coupling is shown to be as accurate as the rigorous one, which provides a simple and efficient way to accurately describe the complex proton-coupled electron-transfer processes due to accurately computing derivative couplings that are quite challenging for realistic systems.

EOM-CCSD-based neural network diabatic potential energy matrix for 1πσ*-mediated photodissociation of thiophenol

A new diabatic potential energy matrix (PEM) of the coupled 1ππ* and 1πσ* states for the 1πσ*-mediated photodissociation of thiophenol was constructed using a neural network (NN) approach. The diabatization of the PEM was specifically achieved by our recent method [Chin. J. Chem. Phys. 34, 825 (2021)], which was based on adiabatic energies without the associated costly derivative couplings. The equation of motion coupled cluster with single and double excitations (EOM-CCSD) method was employed to compute adiabatic energies of two excited states in this work due to its high accuracy, simplicity, and efficiency. The PEM includes three dimensionalities, namely the S−H stretch, C−S−H bend, and C−C−S−H torsional coordinates. The root mean square errors of the NN fitting for the S1 and S2 states are 0.89 and 1.33 meV, respectively, suggesting the high accuracy of the NN method as expected. The calculated lifetimes of the S1 vibronic 00 and 31 states are found to be in reasonably good agreement with available theoretical and experimental results, which validates the new EOM-CCSD-based PEM fitted by the NN approach. The combination of the diabatization scheme solely based on the adiabatic energies and the use of EOM-CCSD method makes the construction of reliable diabatic PEM quite simple and efficient.