Nonadiabatic Coupling Terms Research Articles

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Nonadiabatic Dynamics Simulations for Photoinduced Processes in Molecules and Semiconductors: Methodologies and Applications.

Nonadiabatic dynamics (NAMD) simulations have become powerful tools for elucidating complicated photoinduced processes in various systems from molecules to semiconductor materials. In this review, we present an overview of our recent research on photophysics of molecular systems and periodic semiconductor materials with the aid of ab initio NAMD simulation methods implemented in the generalized trajectory surface-hopping (GTSH) package. Both theoretical backgrounds and applications of the developed NAMD methods are presented in detail. For molecular systems, the linear-response time-dependent density functional theory (LR-TDDFT) method is primarily used to model electronic structures in NAMD simulations owing to its balanced efficiency and accuracy. Moreover, the efficient algorithms for calculating nonadiabatic coupling terms (NACTs) and spin-orbit couplings (SOCs) have been coded into the package to increase the simulation efficiency. In combination with various analysis techniques, we can explore the mechanistic details of the photoinduced dynamics of a range of molecular systems, including charge separation and energy transfer processes in organic donor-acceptor structures, ultrafast intersystem crossing (ISC) processes in transition metal complexes (TMCs), and exciton dynamics in molecular aggregates. For semiconductor materials, we developed the NAMD methods for simulating the photoinduced carrier dynamics within the framework of the Kohn-Sham density functional theory (KS-DFT), in which SOC effects are explicitly accounted for using the two-component, noncollinear DFT method. Using this method, we have investigated the photoinduced carrier dynamics at the interface of a variety of van der Waals (vdW) heterojunctions, such as two-dimensional transition metal dichalcogenides (TMDs), carbon nanotubes (CNTs), and perovskites-related systems. Recently, we extended the LR-TDDFT-based NAMD method for semiconductor materials, allowing us to study the excitonic effects in the photoinduced energy transfer process. These results demonstrate that the NAMD simulations are powerful tools for exploring the photodynamics of molecular systems and semiconductor materials. In future studies, the NAMD simulation methods can be employed to elucidate experimental phenomena and reveal microscopic details as well as rationally design novel photofunctional materials with desired properties.

Coupled three-dimensional quantum mechanical wave packet study of proton transfer in H2+ + He collisions on accurate abinitio two-state diabatic potential energy surfaces.

We have carried out fully close-coupled three dimensional quantum mechanical wave packet dynamical calculations for the reaction He+H2+→HeH++H on the ground electronic adiabatic potential energy surface and on the lowest two electronic states of newly constructed abinitio calculated diabatic potential energy surfaces for the system [Naskar et al., J. Phys. Chem. A 127, 3832 (2023)]. With the reactant diatom (H2+) in its roto-vibrational ground state (v = 0, j = 0), the calculations have been carried out in hyperspherical coordinates to obtain the reaction attributes. Convergence profiles of the reaction probability with respect to the total angular momentum quantum number at different collision energies are presented for the title reaction. State-to-state as well as initial state selected integral reaction cross sections are calculated from the fully converged reaction probabilities over a range of collision energies. The integral cross section values computed using the two-state diabatic potential energy surfaces are significantly lower than those obtained using the ground electronic state adiabatic potential energy surface and are in much better agreement with the available experimental results than the latter for total energy greater than 1.1eV. Therefore, it becomes clear that it is important to include the nonadiabatic coupling terms for a quantitative prediction of the dynamical observables.

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.

Semiclassical Dynamics on Machine-Learned Coupled Multireference Potential Energy Surfaces: Application to the Photodissociation of the Simplest Criegee Intermediate.

Determination of high-dimensional potential energy surfaces (PESs) and nonadiabatic couplings have always been quite challenging. To this end, machine learning (ML) models, trained with a finite set of ab initio data, allow accurate prediction of such properties. To express the PESs in terms of atomic contributions is the cornerstone of any ML based technique because it can be easily scaled to large systems. In this work, we have constructed high fidelity PESs and nonadiabatic coupling terms at the CASSCF level of ab initio data using a machine learning technique, namely, kernel-ridge regression. Additional MRCI-level calculations were carried out to assess the quality of the PESs. We use these machine-learned PESs and nonadiabatic couplings to simulate excited-state molecular dynamics based on Tully's fewest-switches surface hopping method (FSSH). FSSH is a semiclassical method in which nuclei move on the PESs due to the electrons according to the laws of classical mechanics. Nonadiabatic effects are taken into account in terms of transitions between PESs. We apply this scheme to study the O-O photodissociation of the simplest Criegee intermediate (CH2OO). The FSSH trajectories were initiated on the lowest optically bright singlet excited state (S2) and propagated along the three most important internal coordinates, namely, O-O and C-O bond distances and the COO bond angle. Some of the trajectories end up on energetically lower PESs as a result of radiationless transfer through conical intersections. All of the trajectories lead to the dissociation of the O-O bond due to the dissociative nature of the excited PESs through one of the two dissociative channels. The simulation reveals that there is about 88.4% probability of dissociation through the lower channel leading to the H2CO (X1A1) and O (1D) products, whereas there is only 11.6% probability of dissociation through the upper channel leading to H2CO (a3A″) and O (3P) products.

Non-adiabatic coupling in the potential energy surfaces of SO2 molecule.

To investigate the potential energy surfaces and the coupling between the adiabatic states of SO2 molecules, it is necessary to consider the non-adiabatic coupling terms (NACTs), where the Born-Oppenheimer approximation breaks down. In this work, we analyze the conical intersections between 1 1A1 and 1 1B2 states (the A' states in Cs symmetry) and 1 1A2 and 1 1B1 states (the A'' states in Cs symmetry) using NACTs and adiabatic-to-diabatic transformation (ADT) angles. Our results confirm reasonable interaction between 1 1A1 and 1 1B2 states and strong interaction between 1 1A2 and 1 1B1 states.

Construction of Beyond Born-Oppenheimer Based Diabatic Surfaces and Generation of Photoabsorption Spectra: The Touchstone Pyrazine (C4 N2 H4 ).

We construct theoretically "exact" and numerically "accurate" Beyond Born-Oppenheimer (BBO) based diabatic potential energy surfaces (PESs) of pyrazine (C4 N2 H4 ) molecule involving lowest four excited adiabatic PESs (S1 to S4 ) and nonadiabatic coupling terms (NACTs) among those surfaces as functions of nonadiabatically active normal modes (Q1 , Q6a , Q9a and Q10a ) to compute its photoabsorption (PA) spectra. Those adiabatic PESs are calculated using CASSCF as well as MRCI based methodologies, where NACTs are obtained from CP-MCSCF approach. Employing ab initio quantities (adiabatic PESs and NACTs), it is possible to depict the conical intersections (CIs) and develop matrices of diabatic PESs over six normal mode planes. Once single-valued, smooth, symmetric and continuous 2×2 and 4×4 diabatic surface matrices are in hand for the first time, such matrices are used to perform multi-state multi-mode nuclear dynamics with the aid of Time-Dependent Discrete Variable Representation (TDDVR) methodology initializing the product type wavefunction on (S1 ) and (S2 ) states to obtain the corresponding PA spectra. TDDVR calculated spectra for those states (S1 and S2 ) obtained from BBO based 2×2 and 4×4 diabatic surface matrices show good and better agreement with the experimental results, respectively. Both of these calculated results depict better peak progression over the existing profiles of Multi-Configuration Time-Dependent Hartree (MCTDH) dynamics over 2×2 Vibronic Coupling Model (VCM) Hamiltonian.

Trajectory surface hopping vs. quantum scattering calculations on D+ + H2 and H + [formula omitted] reactions using ab initio surfaces and couplings

We employ trajectory surface hopping (TSH) formalism [Chem. Phys. 349 (2008) 334, J. Chem. Phys. 142 (2015) 144307] to compute cross-sections or/and rate constants of D+ + H2 (v=0,j=0) and H + H2+ (v=0,j=0) reactions initiating from ground and first excited electronic state of H3+, respectively. While solving Hamilton’s equations over adiabatic potential energy surfaces (PESs), switching probabilities are calculated by ab initio nonadiabatic coupling terms for the first time. During hopping, momenta are adjusted to fulfil total energy conservation, where a scaling factor is introduced to explore the conservation of linear momentum. For non-charge transfer process, quasi-classical cross-sections match well with quantum results obtained from diabatic PESs of H3+ and experimental findings, but deviations are observed at the energy domain of conical intersection driven hopping for charge-transfer processes. Calculated results indicate the origin of limitations of TSH algorithm as well as depict computational advantage with respect to quantum dynamics.

Jahn-Teller Effect in Orthorhombic Manganites: Ab Initio Hamiltonian and Roto-vibrational Spectrum.

For the first time, using three different electronic structure methodologies, namely, CASSCF, RS2c, and MRCI(SD), we construct ab initio adiabatic potential energy surfaces (APESs) and nonadiabatic coupling term (NACT) of two electronic states (5Eg) of MnO69- unit, where eight such units share one La atom in LaMnO3 crystal. While fitting those APESs with analytic functions of normal modes (Qx, Qy), an empirical scaling factor is introduced considering the mass ratio of eight MnO69- units with and without one La atom to explore the environmental (mass) effect on MnO69- unit. When the roto-vibrational levels of MnO69- Hamiltonian are calculated, peak positions computed from ab initio constructed excited APESs are found to be enough close with the experimental satellite transitions [ J. Exp. Theor. Phys. 2016, 122, 890-901] endorsing our earlier model results [ J. Chem. Phys. 2019, 150, 064703]. In order to explore the electron-nuclear coupling in an alternate way, theoretically "exact" and numerically "accurate" beyond Born-Oppenheimer (BBO) theory based diabatic potential energy surfaces (PESs) of MnO69- are constructed to generate the photoelectron (PE) spectra. The PE spectral band also exhibits good peak by peak correspondence with the higher satellite transitions in the dielectric function spectra of the LaMnO3 complex.

Singularity-free internal conversion golden-rule rate with application to correlated triplet pair recombination in bipentacenes.

We introduce a singularity-free golden-rule rate expression for internal conversion (IC), a spin-conserved radiationless relaxation process, expressed as the product of a nonadiabatic coupling term and the time integral of a vibration correlation function. For a set of small polyatomic molecules (acenes and azulene), we show that our calculated rates are in near quantitative agreement with the rates derived from experiments. Interestingly, we find that our rates do not agree with previous golden-rule-based theoretical efforts; detailed analysis shows that while the level of electronic structure theory can play a role, the more significant error is from not fully converging the numerical time integral over the oscillatory vibration correlation function. We then use our singularity-free IC rate expression to compute the rate of recombination of the correlated triplet pair state generated by intramolecular singlet fission in a trio of bipentacenes. We show that the recombination rates are in good agreement with experimentally observed trends-specifically, the rates are robust to temperature changes and decrease rapidly with increasing inter-monomer dihedral angle. Finally, we use a pair-wise breakdown of normal mode contributions to the rate to identify the key vibrational modes that drive recombination in bipentacenes.

Surface hopping simulations on photoexcitation dynamics of conjugated polymer

Surface hopping is a very active research area in the recent decades of years. In this work, we derive all necessary equations for a surface hopping method based on Pariser-Parr-Pople (PPP) Hamiltonian and configuration interaction singles (CIS). The surface hopping method is then used to study the dynamics of a cis-polyacetylene chain after it is photoexcited to a high-lying excited state. We find that an excited state may be falsely populated because it is impossible to detect the trivial crossings between noninteracting excited states at time zero using the traditional Min-Cost method.This problem can be solved by screening the initial lattice geometries that do not match a certain condition. By comparison, we discuss the contribution of molecular orbital response with respect to atom displacements (Z matrix) to the nonadiabatic coupling terms and forces, and find that the contribution of Z matrix can be neglected, to some degree. This can greatly save the computational cost.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections.

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

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.

Non-adiabatic coupling as a frictional force in the formation of H3+: a model dynamical study

By treating the non-adiabatic coupling terms (NACTs) in a molecular system as equivalent to a frictional force, the classical equation of motion is solved for a test case of quasi-H3+ along the C2v axis and axes parallel to it, and it is shown that the singular NACTs between the first two excited electronic states slow down the relative motion of the three quasi-ions (H,H,H)+ while approaching each other.

Study of non‐adiabatic interactions among low‐lying electronic states of HeH2+ with its implication in its dissociation into various species

AbstractPossible interplay of various atomic and molecular systems like He+, He, H+, H, H2+, H2, HeH+, HeH2+ in the interstellar spaces in various phases of the creation and development of the universe as well as in the present interstellar spaces have been the subject of experimental and theoretical investigations for quite a long period. A chemical network involving these species has been considered. The molecular system HeH2+, being a weakly bound species, may readily give the dissociation products (H, HeH+), (He, H2+), (He+, H2) and (He, H, H+) through different dissociation channels, as has been argued from the contour diagram of the ground as well as non‐adiabatically interacting excited electronic state. A seam of Conical Intersections (CI) between two lowest excited states of linear HeH2+, as a result of non‐adiabatic interactions, has been demonstrated for the first time, through calculation and plot of non‐adiabatic coupling term (NACT) between these two states. Calculations of NACT's, followed by construction of the adiabatic‐to‐diabatic transformation (ADT) angles, ADT matrix and calculation of topological (Berry) phases have been presented to confirm the presence of Jahn‐Teller(JT) CI in two representative configuration spaces(CS) in this seam: (i) one away from the equilibrium geometry hosting JT‐CI between two excited states 22A′ and 32A′ and (ii) another CS near the equilibrium geometry hosting JT‐CI between excited states 22A′ and 32A′ as well as a closely spaced JT‐CI between excited states 32A′ and 42A′. Suitable diabatizations have been performed for a range of CS covering these two CI, which help in understanding several dissociation channels of HeH2+ involving the above mentioned excited states, leading to an increase in the yield of dissociation products (He, H, H+). Distribution of Mulliken partial charges, as obtained from Mulliken population analysis have been analyzed for justifying the existence of HeH2+, the possibility of different dissociation products of HeH2+ in different dissociation channels as well as the justification of the CI‐induced charge transfer in excited states.

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.

Non-adiabatic coupling as a frictional force in (He, H, H)+ dynamics and the formation of HeH2 +

It is shown that the Born–Oppenheimer–Huang non-adiabatic coupling terms (NACTs) in a molecular Hamiltonian can be considered as equivalent to a friction force in classical mechanics and consequently responsible for the formation of triatomic species like HeH. The classical equation of motion is solved accordingly for a test case of a helium atom approaching an H molecule at its potential minimum along the collinear axis and lines parallel to it and also for the C geometry. It is shown that the singular NACTs between the first two excited states slow down the motion of the three quasi-ions (He, H, H) while approaching each other and result in substantial loss of kinetic energy in the collision process. These results have profound implications for the formation of di- and triatomic species in the early universe, during the chemical synthesis epoch following the nucleosynthesis that followed the Big Bang.

Time-Derivative Couplings for Self-Consistent Electronically Nonadiabatic Dynamics.

Electronically nonadiabatic dynamics methods based on a self-consistent potential, such as semiclassical Ehrenfest and coherent switching with decay of mixing, have a number of advantages but are computationally slower than approximations based on an unaveraged potential because they require evaluation of all components of the nonadiabatic coupling vector. Here we introduce a new approximation to the self-consistent potential that does not have this computational drawback. The new approximation uses time-derivative couplings evaluated by overlap integrals of electronic wave functions to approximate the nonadiabatic coupling terms in the equations of motion. We present a numerical test of the method for ethylene that shows there is little loss of accuracy in the ensemble-averaged results. This new approximation to the self-consistent potential makes direct dynamics calculations with self-consistent potentials more efficient for complex systems and makes them practically affordable for some cases where the cost was previously too high.

Comparison of Spin-Flip TDDFT-Based Conical Intersection Approaches with XMS-CASPT2.

Determining conical intersection geometries is of key importance to understanding the photochemical reactivity of molecules. While many small- to medium-sized molecules can be treated accurately using multireference approaches, larger molecules require a less computationally demanding approach. In this work, minimum energy crossing point conical intersection geometries for a series of molecules have been studied using spin-flip TDDFT (SF-TDDFT), within the Tamm-Dancoff Approximation, both with and without explicit calculation of nonadiabatic coupling terms, and compared with both XMS-CASPT2 and CASSCF calculated geometries. The less computationally demanding algorithms, which do not require explicit calculation of the nonadiabatic coupling terms, generally fare well with the XMS-CASPT2 reference structures, while the relative energetics are only reasonably replicated with the MECP structure as calculated with the BHHLYP functional and full nonadiabatic coupling terms. We also demonstrate that, occasionally, CASSCF structures deviate quantitatively from the XMS-CASPT2 structures, showing the importance of including dynamical correlation.

On the aspect of plane of appearance of Jahn‐Teller and Renner‐Teller intersections in tetra‐atomic system—A case study with HCNO+

AbstractA search for configuration space with well‐defined topological (Berry) phases corresponding to Jahn‐Teller (JT) conical intersection (CI) and Renner‐Teller (RT) parabolic intersection (PI) in the linear tetra‐atomic molecular system on introduction of bending demonstrates the interesting aspect that these potential intersections may appear in the molecular plane as well as out of the molecular plane. While understanding this aspect is important for following the class of phenomena led by potential intersections, till date, studies on molecular systems, including pairs such as (C2H2+, HCNH) and (N2H2+, HBNH+), have not been able to clarify the issue. The present article includes calculation of nonadiabatic coupling terms involving four low‐lying states of slightly bent HCNO+, a motivated choice of tetra‐atomic with all four different atoms, to study this aspect associated with JT‐CI and RT‐PI in a slightly bent linear system. The plane of appearance of these effects has been advocated to be related to the electronic configuration of the concerned states of the molecular system.