Adiabatic Potential Energy Surfaces Research Articles

Charge-Transfer Steps in Density Functional Theory from the Perspective of the Exact Electron Factorization.

When a molecule dissociates, the exact Kohn-Sham (KS) and Pauli potentials may form step structures. Reproducing these steps correctly is central for the description of dissociation and charge-transfer processes in density functional theory (DFT): The steps align the KS eigenvalues of the dissociating subsystems relative to each other and determine where electrons localize. While the step height can be calculated from the asymptotic behavior of the KS orbitals, this provides limited insight into what causes the steps. We give an explanation of the steps with an exact mapping of the many-electron problem to a one-electron problem, the exact electron factorization (EEF). The potentials appearing in the EEF have a clear physical meaning that translates to the DFT potentials by replacing the interacting many-electron system with the KS system. With a simple model of a diatomic, we illustrate that the steps are a consequence of spatial electron entanglement and are the result of a charge transfer. From this mechanism, the step height can immediately be deduced. Moreover, two methods to approximately reproduce the potentials during dissociation are proposed. One is based on the states of the dissociated system, while the other one is based on an analogy to the Born-Oppenheimer treatment of a molecule. The latter method also shows that the steps connect adiabatic potential energy surfaces. The view of DFT from the EEF thus provides a better understanding of how many-electron effects are encoded in a one-electron theory and how they can be modeled.

NO+ + H2: Potential energy surface and bound state calculations

The first four-dimensional (4D) adiabatic potential energy surface (PES) for the interaction of NO+ cation with the H2 molecule has been accurately determined using the CCSD(T)-F12a method with cc-pVTZ-F12 basis set augmented with mid-bond functions. A detailed characterization of the PES and lowest bound states of the H2–NO+ complex have been provided. The H2–NO+ PES exhibits a single global minimum with a well depth of −824.63 cm−1 corresponding to off-planar structure with the H2 molecule in a perpendicular orientation to the NO+ cation. The solution of the nuclear Schrödinger equation for the bound states gives a zero-point energy corrected dissociation energy of D0 = 498.15 cm−1 for para-H2–NO+ complex, and of 541.35 cm−1 for ortho-H2–NO+.

A beyond Born-Oppenheimer treatment of C6H6 + radical cation for diabatic surfaces: Photoelectron spectra of its neutral analog using time-dependent discrete variable representation.

We employ theoretically "exact" and numerically "accurate" Beyond Born-Oppenheimer (BBO) treatment to construct diabatic potential energy surfaces (PESs) of the benzene radical cation (C6H6 +) for the first time and explore the workability of the time-dependent discrete variable representation (TDDVR) method for carrying out dynamical calculations to evaluate the photoelectron (PE) spectra of its neutral analog. Ab initio adiabatic PESs and nonadiabatic coupling terms are computed over a series of pairwise normal modes, which exhibit rich nonadiabatic interactions starting from Jahn-Teller interactions and accidental conical intersections/seams to pseudo Jahn-Teller couplings. Once the electronic structure calculation is completed on the low-lying five doublet electronic states (X̃2E1g, B̃2E2g, and C̃2A2u) of the cationic species, diabatization is carried out employing the adiabatic-to-diabatic transformation (ADT) equations for the five-state sub-Hilbert space to compute highly accurate ADT angles, and thereby, single-valued, smooth, symmetric, and continuous diabatic PESs and couplings are constructed. Subsequently, such surface matrices are used to perform multi-state multi-mode nuclear dynamics for simulating PE spectra of benzene. Our theoretical findings clearly depict that the spectra for X̃2E1g and B̃2E2g-C̃2A2u states obtained from BBO treatment and TDDVR dynamics exhibit reasonably good agreement with the experimental results as well as with the findings of other theoretical approaches.

Unravelling the Origin of the Linear Structures Distortions of the Acetylene Isoelectronic Compounds (Disilyne, Digermyne, and Distannyne)

The role and contributions of the effective factors on the structural properties of acetylene (1), disilyne (2), digermyne (3), and distannyne (4) were examined by means of LC-ωPBE long-range corrected density functional method with TZP basis set on all atoms. Although the ground state structure of acetylene (1) is linear (D∞h-symmetry), the trans-bent (C2h, as a local minimum) and di-bridged structures (C2v, as a global minimum) were found for compounds 2–4. Plotted electronic energies of the ground and excited states versus the nuclear displacement (by considering the symmetries of the normal modes) revealed that the negative curvatures of the ground state electronic configurations and the positive curvatures of the excited states of the adiabatic potential energy surfaces (APESs) result from mixing of the ground $$^{1}\Sigma _{{\text{g}}}^{ + }$$ and excited 1Πg states, revealing the presence of the strong pseudo Jahn–Teller effect (i.e., PJT ( $$^{1}\Sigma _{{\text{g}}}^{ + }$$ + 1Πg) ⊗ πg problem). The weak PJTE in acetylene (1) does not distort its linear configurations. The distortions of the linear (D∞h) configurations of compounds 2–4 to their corresponding trans-bent structures (C2h) are due to the PJTE associated with the mixing of the ground $$^{1}\Sigma _{{\text{g}}}^{ + }$$ state and third excited Πg states through the mixing of their HOMOs(πu) with their corresponding LUMOs+2(σu) ([HOMO(πu)] + [LUMO+1(σu)]) in compound 2, the mixing of the ground $$^{1}\Sigma _{{\text{g}}}^{ + }$$ state and second excited Πg states ([HOMO(πu)] + [LUMO(σu)]) in compound 3 and the ground $$^{1}\Sigma _{{\text{g}}}^{ + }$$ state and second excited Πg states ([HOMO(πu)] – [LUMO+1(σu)]) in compound 4. The higher- and lower-lying $$^{1}\Sigma _{{\text{u}}}^{ - }$$ , $$^{1}\Sigma _{{\text{u}}}^{ - }$$ , 1Δu, and 1Πu states are not involved in the PJT interactions. The trans-bent local minimum structures could be converted to their corresponding global minimum structures (di-bridge, C2v) by passing from axial symmetrical (C2) transition state geometries. The energy gaps between reference states (∆) in the linear (D∞h) configurations decrease from disilyne (2) to distannyne (4) while the energy difference between the linear (D∞h) and trans-bent (C2h) configurations increases from compound 2 to 3 but decreases from compound to compound 4, revealing the determining impacts of their corresponding vibronic coupling constants (F) which may control their corresponding D∞h → C2h distortion PJT stabilization energies. Importantly, the variations of the M–M-bond length differences in the linear (D∞h) and trans-bent (C2h) structures of compounds 2–4, Δ(rM–M) D∞h–C2h, correlate well with their corresponding PJT-stabilization energies.

Pseudo–Jahn-Teller interaction among electronic resonant states of H3

We study the electronic resonant states of H3 with energies above the potential energy surface of the H3+ ground state. These resonant states are important for the dissociative recombination of H3+ at higher collision energies, and previous studies have indicated that these resonant states exhibit a triple intersection. We introduce a complex generalization of the pseudo-Jahn-Teller model to describe these resonant states. The potential energies and the autoionization widths of the resonant states are computed with electron scattering calculations using the complex Kohn variational method, and the complex model parameters are extracted by a least-square fit to the results. This treatment results in a non-Hermitian pseudo-Jahn-Teller Hamiltonian describing the system. The non-adiabatic coupling and geometric phase are further calculated and used to characterize the enriched topology of the complex adiabatic potential energy surfaces.

Strong Electronic Coupling-Induced Ultrafast Charge Transfer in Donor-Pyrene-Acceptor Systems.

In this study, we decipher the charge transfer (CT) processes in donor-pyrene-acceptor (DPA) molecules via various time-resolved spectroscopic measurements. It has been challenging to unravel the ultrafast CT dynamics in DPA molecules because they exhibit an initial CT emission in the same spectral range as the locally excited (LE) emission. However, we finally observed the CT rate of ∼200 fs in DPA molecules from the time-resolved fluorescence anisotropy decay profiles. Our measurements allow us to suggest that the LE and CT states of DPA systems have isoenergetic potential surfaces and that the introduction of the acceptor to the pyrene moiety gives rise to strong electronic coupling between the LE and CT states. Therefore, we determined that this solvent-independent ultrafast CT occurs through the adiabatic potential energy surface and that the CT characteristics are enhanced in DPA compared to the donor-pyrene-donor system.

Electric-field-induced wave-packet dynamics and geometrical rearrangement of trilobite Rydberg molecules

We investigate the quantum dynamics of ultra-long-range trilobite molecules exposed to homogeneous electric fields. A trilobite molecule consists of a Rydberg atom and a ground-state atom, which is trapped at large internuclear distances in an oscillatory potential due to scattering of the Rydberg electron off the ground-state atom. Within the Born-Oppenheimer approximation, we derive an analytic expression for the two-dimensional adiabatic electronic potential energy surface in weak electric fields valid up to 500 V/m. This is used to unravel the molecular quantum dynamics employing the Multi-Configurational Time-Dependent Hartree method. Quenches of the electric field are performed to trigger the wave packet dynamics including the case of field inversion. Depending on the initial wave packet, we observe radial intra-well and inter-well oscillations as well as angular oscillations and rotations of the respective one-body probability densities. Opportunities to control the molecular configuration are identified, a specific example being the possibility to superimpose different molecular bond lengths by a series of periodic quenches of the electric field.

Towards photoassociation processes of ultracold rubidium trimers

We theoretically investigate the prospects for photoassociation (PA) of Rb$_3$, in particular at close range. We provide an overview of accessible states and possible transitions. The major focus is placed on the calculation of equilibrium structures, the survey of spin-orbit effects and the investigation of transition dipole moments. Furthermore we discuss Franck-Condon overlaps and special aspects of trimers including the (pseudo) Jahn-Teller effect and the resulting topology of adiabatic potential-energy surfaces. With this we identify concrete and suitable PA transitions to potentially produce long-lived trimer bound states. Calculations are performed using the multireference configuration-interaction method together with a large-core effective core potential and a core-polarization potential with a large uncontracted even-tempered basis set.

The Connection between Pseudo-Jahn–Teller Effect and Electron Delocalization for Proving the Origin of Equilibrium Geometry of Nitrosyl Halides (Halides = Cl, Br, and I)

The theoretical calculations on triplet linear and non-linear structures of nitrosyl halides XNO (X = Cl, Br, and I) confirm that the origin of instability and symmetry breaking of XNO linear structures is a pseudo-Jahn–Teller effect (PJTE). However, the PJTE associated with electron delocalization may prove the stability of XNO non-linear structures best. The distortion of high-symmetry (C∞v) configurations in XNOs emerges from mixing the PJT with ground 3Σ– and the excited 3Π states in the Qπ direction, which consequently make the ground state unstable. The PJT problem is formulated in the form (3Σ– + 3Π) $$ \otimes $$ π. The energy difference between high-symmetry C∞v geometries and low-symmetry Cs geometries energy gap between the ground and excited states decreases from ClNO to INO. Also, ΔEPJT (i.e., the difference of energy between the highest occupied molecular orbital (HOMO; LPX), and the lowest unoccupied molecular orbital (LUMO; $$\pi _{{{\text{NO}}}}^{*}$$ )) plays an important role in the instability of structures. Electron delocalization decreases and PJT instability increases from ClNO to INO in high-symmetry C∞v geometries. According to the results of the canonical molecular orbital (CMO) analysis, the contribution of the LPX non-bonding orbitals in the vibronic coupling constant (F) increases from ClNO to INO. Also, the NBODEL results indicate that the instability of compounds increases from ClNO to INO. Because the primary force constant is positive, the curvature of ground electronic state configuration curves in adiabatic potential energy surfaces (APESs) decreases from ClNO to INO. The variations of the chemical hardness differences between the non-linear (Cs) and linear (C∞v) structures decrease from ClNO to INO and of chemical potential differences increase from ClNO to INO, justifying the variation trend of ΔEPJT. Furthermore, based on the obtained results, Δ[η(Cs) – η(C∞v)] obeys the maximum hardness principle.

Modeling of the thermal migration mechanisms of atomic oxygen in Ar, Kr, and Xe crystals.

Accommodation and migration of the ground-state (2s22p4 3P) oxygen atom in the ideal Ar, Kr, and Xe rare gas crystals are investigated using the classical model. The model accounts for anisotropy of interaction between guest and host atoms, spin-orbit coupling, and lattice relaxation. Interstitial and substitutional accommodations are found to be the only thermodynamically stable sites for trapping atomic oxygen. Mixing of electronic states coupled to lattice distortions justifies that its long-range thermal migration follows the adiabatic ground-state potential energy surface. Search for the migration paths reveals a common direct mechanism for interstitial diffusion. Substitutional atoms are activated by the point lattice defects, whereas the direct guest-host exchange meets a higher activation barrier. These three low-energy migration mechanisms provide plausible interpretation for multiple migration activation thresholds observed in Kr and Xe free-standing crystals, confirmed by reasonable agreement between calculated and measured activation energies. An important effect of interaction anisotropy and a minor role of spin-orbit coupling are emphasized.

Permutationally Restrained Diabatization by Machine Intelligence.

Simulations of electronically nonadiabatic processes may employ either the adiabatic or diabatic representation. Direct dynamics calculations are usually carried out in the adiabatic basis because the energy, force, and state coupling can be evaluated directly by many electronic structure methods. However, although its straightforwardness is appealing, direct dynamics is expensive when combined with quantitatively accurate electronic structure theories. This generates interest in analytically fitted surfaces to cut the expense, but the cuspidal ridges of the potentials and the singularities and vector nature of the couplings at high-dimensional, nonsymmetry-determined intersections in the adiabatic representation make accurate fitting almost impossible. This motivates using diabatic representations, where the surfaces are smooth and the couplings are also smooth and-importantly-scalar. In a recent previous work, we have developed a method called diabatization by deep neural network (DDNN) that takes advantage of the smoothness and nonuniqueness of diabatic bases to obtain them by machine learning. The diabatic potential energy matrices (DPEMs) learned by the DDNN method yield not only diabatic potential energy surfaces (PESs) and couplings in an analytic form useful for dynamics calculations, but also adiabatic surfaces and couplings in the adiabatic representation can be calculated inexpensively from the transformation. In the present work, we show how to extend the DDNN method to produce good approximations to global permutationally invariant adiabatic PESs simultaneously with DPEMs. The extended method is called permutationally restrained DDNN.

Manifestation of descent symmetry phenomena in tetrahedral structure of M42+ (M = P, As, Sb) analogues

Manifestation of descent symmetry phenomena induced by pseudo Jahn–Teller interactions is reported for the P4 dicationic tetrahedral structure and its As4 and Sb4 analogues. The symmetry descent phenomena in the dicationic tetrahedral structure for the series is caused by the pseudo Jahn–Teller effect (PJTE) where the unstable (high Td symmetry) configuration distorts to the equilibrium geometry with a lower, C2 symmetry. State averaging six low-lying electronic states via CASSCF(8,8)/cc-pVTZ–(PP) computations determined the adiabatic potential energy surfaces along the distorting normal coordinate. The (E(I) + A1 + E(II)) ⊗ e for the M42+ (M = P, As, Sb) series has been formulated accordingly. Subsequently, the coupling constants were estimated by fitting energies obtained from the PJTE equations. Moreover, to understand how removing or adding electrons affects the PJTE in the M42+ series, electronic configurations were analysed for M4(0,2+,4+) analogues in which the M4(0,4+) are stable in their tetrahedral structure.

QCT calculations of O2 + O collisions: Comparison to molecular beam experiments

We present quasiclassical trajectory simulations of O2 + O collisions under conditions representative of a crossed molecular beam experiment [Lahankar et al., J. Phys. Chem. A 120, 5348-5359 (2016)]. These calculations are compared to experimental data in order to further validate Potential Energy Surfaces (PESs) recently developed at the University of Minnesota [Z. Varga, Y. Paukku, and D. G. Truhlar, J. Chem. Phys. 147, 154312 (2017)]. Spin and spatial symmetries allow nine adiabatic PESs to represent the ground state interactions of O2 + O. We simulate trajectories adiabatically on all nine surfaces and perform analysis on data from each surface separately and the combined set of nine. It is shown that aggregated adiabatic calculations from nine surfaces agree better with the experiment for both inelastic and exchange collisions than a previous study that used a single surface and lie within the reported experimental uncertainty at almost all points. Distributions for exchange reactions using all nine PESs are interpreted using each surface's opacity function and activation energy for exchange. Rovibrationally resolved product distributions are then studied for a better understanding of energy relaxation in exchange collisions and may prove useful for further quasiclassical trajectory study and new experiments that use rovibrational spectroscopy to resolve the internal energy of the scattered products.

Beyond Born-Oppenheimer constructed diabatic potential energy surfaces for F + H2 reaction.

First principles based beyond Born-Oppenheimer theory has been implemented on the F + H2 system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin-orbit (SO) coupling effect on the collision process of the F + H2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (12A', 22A', and 12A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn-Teller (JT) type conical intersections between the two A' states translate along C2v and linear geometries in F + H2. In addition, A' and A″ states undergo Renner-Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H2, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H2 system.

Perovskite Crystals: Unique Pseudo-Jahn–Teller Origin of Ferroelectricity, Multiferroicity, Permittivity, Flexoelectricity, and Polar Nanoregions

In a semi-review paper, we show that the local pseudo-Jahn–Teller effect (PJTE) in transition metal B ion center of ABO3 perovskite crystals, notably BaTiO3, is the basis of all their main properties. The vibronic coupling between the ground and excited electronic states of the local BO6 center results in dipolar distortions, leading to an eight-well adiabatic potential energy surface with local tunneling or over-the-barrier transitions between them. The intercenter interaction between these dipolar dynamic units results in the formation of the temperature-dependent three ferroelectric and one paraelectric phases with order–disorder phase transitions. The local PJTE dipolar distortion is subject to the presence of sufficiently close in energy local electronic states with opposite parity but the same spin multiplicity, thus limiting the electronic structure and spin of the B(dn) ions that can trigger ferroelectricity. This allowed us to formulate the necessary conditions for the transition metal perovskites to possess both ferroelectric and magnetic (multiferroic) properties simultaneously. It clarifies the role of spin in the spontaneous polarization. We also show that the interaction between the independently rotating dipoles in the paraelectric phase may lead to a self-assembly process resulting in polar nanoregions and relaxor properties. Exploring interactions of PJTE ferroelectrics with external perturbations, we revealed a completely novel property—orientational polarization in solids—a phenomenon first noticed by P. Debye in 1912 as a possibility, which was never found till now. The hindered rotation of the local dipole moments and their ordering along an external field is qualitatively similar to the behavior of polar molecules in liquids, thus adding a new dimension to the properties of solids—notably, the perovskite ferroelectrics. We estimated the contribution of the orientational polarization to the permittivity and flexoelectricity of perovskite crystals in different limiting conditions.

An efficient way to incorporate the geometric phase in the time-dependent wave packet calculations in a diabatic representation.

We present a new approach to incorporate the geometric phase in the time-dependent wave packet calculations based on the analytic diabatic potential energy matrices for two-state systems connecting via a conical intersection. The approach only requires information on the location of the conical intersection and the adiabatic potential energy surface of the ground electronic state and merely takes the same computational cost as a diabatic calculation. Demonstrations of the benchmark H + H2/HD reactions show that the new approach can accurately include the geometric phase in dynamics calculation and can be easily extended to the cold regime where the GP effects become more pronounced. Due to its simplicity and numerical efficiency, the new approach has the potential to extend the dynamics study of the geometric effects to a wide range of reaction systems.

Efficient quantum theory for studying cold charge-transfer state dissociations in donor–acceptor heterojunction organic solar cells

In donor–acceptor (D–A) heterojunction organic solar cells, hot and cold charge transfer (CT) states are formed at the interface as the precursor for subsequent charge separations. Hot CT states dissociate easily because they are loosely bound, while for cold CT states, the origin of their high-efficiency charge separations still remains heavily debated. Here, we propose a simple but effective methodology that can be used to simulate the cold CT dissociation process and, thereby, the multiple factors which may essentially affect the charge separation efficiency and can be conveniently investigated. The energy barriers on the path from cold CT to the separated charges are analyzed by calculating the adiabatic potential energy surfaces of the lowest-energy excitonic state. The calculation results indicate that the D–A molecular coupling strength and coupling area, D–A energetic offset, charge carrier delocalizations, interfacial Coulomb screening strength, and interfacial disorders can essentially affect the charge separation efficiency of a cold CT state.

A general code for fitting global potential energy surfaces via CHIPR method: Direct-Fit Diatomic and tetratomic molecules

A general program to fit global adiabatic potential energy surfaces of up to tetratomic molecules to ab initio points and available spectroscopic data for simple diatomics is reported. It is based on the Combined-Hyperbolic-Inverse-Power-Representation (CHIPR) method. The final form describes all dissociating fragments and long-range/valence interactions, while obeying the system permutational symmetry. The code yields as output a Fortran 90 subroutine that readily evaluates the potential and gradient at any arbitrary geometry. Program summaryProgram title: CHIPR-4.0CPC Library link to program files:http://dx.doi.org/10.17632/8wdv87gt5x.2Licensing provisions: GPLv3Programming language: Fortran 90Journal reference of previous version: C. M. R. Rocha, A. J. C. Varandas, Comput. Phys. Commun. 247 (2020) 106913Does the new version supersede the previous version?: YesReasons for the new version: CHIPR-4.0 is a major extension of the previous CHIPR-3.0 code [1] which, besides diatomics and triatomics, also includes the possibility of fitting global adiabatic potential energy surfaces (PESs) of A4-, AB3-, A2B2-, ABC2- and ABCD-type tetratomic molecules [3]. Additionally, a new feature is that it allows the user to fine-tune ab initio diatomic curves using available spectroscopic data.Summary of revisions:• Implementation of CHIPR’s polynomial form and permutation operators for tetratomic molecules• Implementation of a direct-fit module to fine-tune ab initio potential energy curves using spectroscopic data• Automatic global minimum search on the diatomic, triatomic or tetratomic final PESs• Automatic harmonic vibrational analysis at the optimum molecular geometriesNature of problem: This version of the CHIPR code, CHIPR-4.0, provides a set of subroutines to fit global adiabatic potential energy surfaces of up to tetratomic molecules using ab initio and (for diatomics) optional fine-tuning experimental data.Solution method: CHIPR-4.0 uses the Combined-Hyperbolic-Inverse-Power-Representation (CHIPR) [2] method to interpolate and extrapolate ab initio data points.Additional comments including restrictions and unusual features: For triatomic and tetratomic fits, the user must supply subroutines containing the analytic forms defining the sum of two- and two-plus-three-bodies, respectively. These are utilized internally to calculate (from ab initio data) the corresponding three- and four-body energies to be fitted. The current version of this code is strictly based on single-sheeted analytical PESs. High-accuracy in diatomic refinements is currently limited to the 1Σ single-curve case.

First Principles Nonadiabatic Excited-State Molecular Dynamics in NWChem.

Computational simulation of nonadiabatic molecular dynamics is an indispensable tool for understanding complex photoinduced processes such as internal conversion, energy transfer, charge separation, and spatial localization of excitons, to name a few. We report an implementation of the fewest-switches surface-hopping algorithm in the NWChem computational chemistry program. The surface-hopping method is combined with linear-response time-dependent density functional theory calculations of adiabatic excited-state potential energy surfaces. To treat quantum transitions between arbitrary electronic Born-Oppenheimer states, we have implemented both numerical and analytical differentiation schemes for derivative nonadiabatic couplings. A numerical approach for the time-derivative nonadiabatic couplings together with an analytical method for calculating nonadiabatic coupling vectors is an efficient combination for surface-hopping approaches. Additionally, electronic decoherence schemes and a state reassigned unavoided crossings algorithm are implemented to improve the accuracy of the simulated dynamics and to handle trivial unavoided crossings. We apply our code to study the ultrafast decay of photoexcited benzene, including a detailed analysis of the potential energy surface, population decay timescales, and vibrational coordinates coupled to the excitation dynamics. We also study the photoinduced dynamics in trans-distyrylbenzene. This study provides a baseline for future implementations of higher-level frameworks for simulating nonadiabatic molecular dynamics in NWChem.

Complete Nuclear Permutation Inversion Invariant Artificial Neural Network (CNPI-ANN) Diabatization for the Accurate Treatment of Vibronic Coupling Problems.

A recently developed scheme to produce accurate high-dimensional coupled diabatic potential energy surfaces (PESs) based on artificial neural networks (ANNs) [ J. Chem. Phys. 2018, 149, 204106 and J. Chem. Phys. 2019, 151, 164118] is modified to account for the proper complete nuclear permutation inversion (CNPI) invariance. This new approach cures the problem intrinsic to the highly flexible ANN representation of diabatic PESs to account for the proper molecular symmetry accurately. It turns out that the use of CNPI invariants as coordinates for the input layer of the ANN leads to a much more compact and thus more efficient representation of the diabatic PES model without any loss of accuracy. In connection with a properly symmetrized vibronic coupling reference model, which is modified by the output neurons of the CNPI-ANN, the resulting adiabatic PESs show perfect symmetry and high accuracy. In the present paper, the new approach will be described and thoroughly tested. The test case is the representation and corresponding vibrational/vibronic nuclear dynamics of the low-lying electronic states of planar NO3 for which a large number of ab initio data is available. Thus, the present results can be compared directly with the previous studies.