Diabatic Potentials Research Articles

First-Principles Nonadiabatic Dynamics of Molecules at Metal Surfaces withVibrationally Coupled Electron Transfer.

Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving electron transfer has been a long-standing challenge for theory. Here, we tackle this problem by first constructing high-dimensional neural network diabatic potentials including state crossings determined by constrained density functional theory, then applying mixed quantum-classical surface hopping simulations to evolve coupled electron-nuclear motion. Our approach accurately describes the nonadiabatic effects in CO scattering from Au(111) without empirical parameters and yields results agreeing well with experiments under various conditions for this benchmark system. We find that both adiabatic and nonadiabatic energy loss channels have important contributions to the vibrational relaxation of highly vibrationally excited CO(v_{i}=17), whereas relaxation of low vibrationally excited states of CO(v_{i}=2) is weak and dominated by nonadiabatic energy loss. The presented approach paves the way for accurate first-principles simulations of electron transfer mediated nonadiabatic dynamics at metal surfaces.

Diabatic Valence-Hole Concept.

A global diabatization scheme, based on the "valence-hole" concept, has been previously applied to model webs of avoided crossings that exist in four electronic-state symmetry manifolds of C2 (1Πg, 3Πg, 1Σu+, and 3Σu+). Here, this model is extended to the electronically excited states of four more molecules: CN (2Σ+), N2 (3Πu), SiC (3Π), and Si2 (3Πg). Many strangenesses in the spectroscopic observations (e.g., energy level structure, predissociation linewidths, and radiative lifetimes) for all four electronic state systems discussed here are accounted for by this unified model. The key concept of the model is valence-hole electron configurations: 3σ24σ11π45σ2 in CN (2Σ+), 2σg22σu11πu43σg21πg1 in N2 (3Πu), 5σ26σ17σ22π3 in SiC (3Π), and 4σg24σu15σg22πu3 in Si2 (3Πg), all of which have a triply occupied "valence-core" (i.e., 2σg22σu1 or the equivalent). These valence-hole configurations have a nominal bond order of three or higher and correlate with high-energy separated-atom limits with an np ← ns (n = 2, 3) promotion in one of the atomic constituents. On its way to dissociation, the strongly bound diabatic valence-hole state crosses multiple weakly bound or repulsive states, which belong to electron configurations with a completely filled valence-core. These curve crossings between diabatic potentials result in a network of many avoided crossings among multiple electronic states, analogous to the well-studied electronic structure landscape of ionic-covalent crossings in strongly ionic molecules. Considering the unique role of valence-hole states in shaping the global electronic structure, the valence-hole concept should be added to our intuitive framework of chemical bonding.

Counterdiabatic optimized driving in quantum phase sensitive models

State preparation plays a pivotal role in numerous quantum algorithms, including quantum phase estimation. This paper extends and benchmarks counterdiabatic driving protocols across three one-dimensional spin systems characterized by phase transitions: the axial next-nearest neighbor Ising, XXZ, and Haldane–Shastry models. We perform a shallow quantum optimal control over the counterdiabatic protocols by optimizing an energy cost function. Moreover, we provide a code package for computing symbolically various adiabatic gauge potentials. This protocol consistently surpasses standard annealing schedules, often achieving performance improvements of several orders of magnitude. The axial next-nearest neighbor Ising model stands out as a notable example, where fidelities exceeding 0.5 are attainable in most cases. Furthermore, the optimized paths exhibit promising generalization capabilities to higher-dimensional systems, allowing for the extension of parameters from smaller models. Nevertheless, our investigations reveal limitations in the case of the XXZ and Haldane–Shastry models, particularly when transitioning away from the ferromagnetic phase. This suggests that finding optimal diabatic gauge potentials for specific systems remains an important research direction.

Classically forbidden nonadiabatic transitions in multidimensional chemical dynamics.

An accurate method is proposed to deal with such nonadiabatic transitions as those energetically inaccessible, namely, classically forbidden transitions. This is formulated by using the corresponding Zhu-Nakamura formulas and finding the optimal paths in the classically forbidden tunneling regions that maximize the overall transition probabilities. This can be done for both the nonadiabatic tunneling type (so-called normal case in electron transfer) in which two diabatic potentials have opposite signs of slopes and the Landau-Zener type (inverted case) in which two diabatic potentials have the same sign of slopes. The method is numerically demonstrated to be useful for clarifying chemical and biological dynamics.

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.

2500 vibronic eigenstates of the NO3 radical.

The nitrate radical NO3 plays an important role in atmospheric chemistry, yet many aspects of its coupled and anharmonic vibronic structure remain elusive. Here, using an accurate, coupled full-dimensional diabatic potential that includes five electronic states, we revisit the vibronic spectrum associated with the electronic state. Using recently developed tensor network state methods, we are able to compute more than 2500 vibronic states, thereby increasing the number of computed full-dimensional states by a factor of 50, compared to previous work. While we obtain good agreement with experiment for most of the assigned vibronic levels, for several others, we observe striking disagreement. Further, for the antisymmetric bending motion we find remarkably large symmetry-induced level splittings that are larger than the zero-order reference. We discuss non-negligible nonadiabatic effects and show that the Born-Oppenheimer approximation leads to significant errors in the spectrum.

Combined Modelling of Triply Paired Electronic States of HO2 + ion with 3 Symmetry using Coupled Eigen Model.

The multi state triply paired coupled adiabatic electronic states of , symmetries for the title ion have been modelled using the triply paired coupled eigen valued functions with the principal aim of getting a set of well optimized triply paired coupled functions, capable of explaining all the microscopic topograhical features present in the chosen coupled electronic states. The high quality size truncated dynamically correlated points at the limit of complete basis set (CBS) were utilized for this purpose. The proposed model function are presented in an "easy to understand" linear form with respect to the pre-defined variables which are directly dependent on the diabatic potentials and coupling strengths found in the diabatic matrix. Its most important feature (an essential criterion to be selected for modelling the triply degenerate seam pathway) is the ability to predict the existence of an uniquely defined triply degenerate iso-energetic geometry among the chosen coupled states in addition to the prediction of the existence of many doubly degenerate iso-energetic geometries in those states and hence can be adaptable to any general molecular system where such triply or doubly degenerate geometries are believed to occur. The title ion is one among them where many doubly iso-energetic geometries were located but not the triply degenerate one as it is a three atomic system unlike the polyatomic case where the triply degenerate geometry will most likely to be found. To do this work, one requires the knowledge of four asymptotic diatomic curves upon atom+diatom dissociation whose correct correlated spectroscopic states are O2 + , O2 , O2 + , OH+ . The quality and the characteristics of analytical surface of the ion is discussed well in detail.

Nucleon Density Distributions and Diabatic Potential in Heavy Ion Reactions

Nucleon Density Distributions and Diabatic Potential in Heavy Ion Reactions

Modelling ultrafast dynamics at a conical intersection with regularized diabatic states: An approach based on multiplicative neural networks

• Neural network (NN) potentials for quantum dynamics of cis–trans photoisomerization. • Multiplicative NNs adapted to regularized diabatic states at a conical intersection. • NN potentials match a sum-of-products form required by MCTDH wavefunction propagation. • Good agreement found for highly correlated dynamics with up to 13 degrees of freedom. Neural-network (NN) potentials are employed in conjunction with the Multiconfiguration Time-Dependent Hartree (MCTDH) method in order to simulate an ultrafast photoinduced cis–trans type isomerization process induced by a conical intersection. To this end, NN potentials are fitted to a diabatic potential of regularized diabatic states type [Köppel et al., J. Chem. Phys. 115, 2377 (2001)], which entirely relies on adiabatic potential information. Multiplicative NNs are employed which match the sum-of-products form of the multiconfigurational MCTDH wavefunction. Good agreement with the reference dynamics is obtained for simulations of the highly correlated dynamics with up to 13 degrees of freedom. This study contributes to developing NN methodologies suitable for photochemical dynamics at complex excited-state topologies.

Quantum dynamics of intramolecular CCOH torsional motions in 1-Naphthol followed through the OH stretching chromophore

Intramolecular vibrational dynamics of CCOH torsions and OH stretching vibrations in 1-naphthol were followed by Fourier transform infrared (FTIR) spectroscopy and quantum-theoretical computations. The possibility of unintentional trans → cis transformation induced by broad- and narrowband incident IR radiation during the standard IR experiment was considered in detail. Spontaneous transitions from cis to trans rotamer by both classical rotation over the potential barrier as well as by quantum tunneling were analyzed by combining experimental data and theoretical calculations. Torsional correlation times for the cis → trans transitions were calculated by purely classical and quantum mechanical approaches. Both adiabatic and diabatic torsional potentials were considered in this context. At the same time, Anharmonic vibrational frequencies of the OH stretching chromophore were calculated within a one-dimensional approximation for both cis and trans conformers of 1 -naphthol. This was done by carrying out a series of pointwise energy calculations at series of intramolecular geometries corresponding to excitation of the OH stretching local mode, subsequently fitting the data to a fifth-order polynomial function, transforming the bond stretching coordinates to Simons-Parr-Finlan coordinates and finally numerically solving the vibrational Schrödinger equation by variational technique. Excellent agreement between theoretical calculations (carried out at MP2/6-311++G(3df,3pd) and B3LYP/6-311++G(3df,3pd) levels) and experimental data were obtained for the differences in OH stretching frequencies in trans and cis conformers (Δv(trans→cis)ex.= +13cm1, Δv(trans→cis) B3LYP. = +12.6 cm1). Frequency blue shift-induced upon trans → cis conformational change occurs as a consequence of intramolecular vibrational confinement. The OH stretching chromophore is a very sensitive probe for both intra- and intermolecular dynamics of the title system. It is therefore a rather significant indicator of the molecular environment in condensed phase systems.

Coupled-channel meson-meson scattering in the diabatic framework

We apply the diabatic framework, a QCD-based formalism for the unified study of quarkoniumlike systems in terms of heavy quark-antiquark and open-flavor meson-meson components, to the description of coupled-channel meson-meson scattering. For this purpose, we first introduce a numerical scheme to find the solutions of the diabatic Schr\"odinger equation for energies in the continuum, then we derive a general formula for calculating the meson-meson scattering amplitudes from these solutions. We thus obtain a completely nonperturbative procedure for the calculation of open-flavor meson-meson scattering cross sections from the diabatic potential, which is directly connected to lattice QCD calculations. A comprehensive analysis of various elastic cross sections for open-charm and open-bottom meson-meson pairs is performed in a wide range of the center-of-mass energies. The relevant structures are identified, showing a spectrum of quasiconventional and unconventional quarkoniumlike states. In addition to the customary Breit-Wigner peaks, we obtain nontrivial structures such as threshold cusps and minimums. Finally, our results are compared with existing data and with results from our previous bound-state--based analysis, finding full compatibility with both.

N–H photodissociation dynamics of electronically excited aniline: a three dimensional time-dependent quantum wavepacket study

We have simulated the dynamics of 1πσ* state-mediated nonadiabatic N-H bond dissociation in photo-excited aniline (C6H5NH2). A three electronic state diabatic model potential, involving the ground, 1ππ*, and 1πσ* diabatic states, and focussing on the NH2 degrees of freedom alone is constructed using XMS-CASPT2 energies. Using a kinetic energy operator in the polyspherical framework, wavepacket dynamics in three vibrational modes, viz. NH stretch, NH2 out-of-plane wag and torsion, is carried out using the Chebyshev propagation scheme. For optically bright 1ππ* excitation, the wavepacket can access the 1πσ*/1ππ* and 1ππ/1πσ* conical intersections that lie en route to dissociation. For both intersections, NH2 out-of-plane wag and torsional motions are the most dominant coupling coordinates. Carrying out dynamics with initial wavepackets varying in excitation in the three degrees of freedom, we probe their roles in the evolution of the state populations, probability densities, and product branching for the NH dissociation process.

Effects of conical intersections on hyperfine quenching of hydroxyl OH in collision with an ultracold Sr atom

The effect of conical intersections (CIs) on electronic relaxation, transitions from excited states to ground states, is well studied, but their influence on hyperfine quenching in a reactant molecule is not known. Here, we report on ultracold collision dynamics of the hydroxyl free-radical OH with Sr atoms leading to quenching of OH hyperfine states. Our quantum-mechanical calculations of this process reveal that quenching is efficient due to anomalous molecular dynamics in the vicinity of the conical intersection at collinear geometry. We observe wide scattering resonance features in both elastic and inelastic rate coefficients at collision energies below k_{text {B}}times 10 , hbox {mK}. They are identified as either p- or d-wave shape resonances. We also describe the electronic potentials relevant for these non-reactive collisions, their diabatization procedure, as well as the non-adiabatic coupling between the diabatic potentials near the CIs.

Numerical verification of the exact WKB formula for the generalized Landau-Zener-Stueckelberg problem

The WKB analysis for higher order differential equations had not been developed until recent progress of the so-called exact WKB method, so it was difficult to find WKB solutions for multistate nonadiabatic models in general, whereas enormous efforts were made especially for the study of generalized Landau-Zener models. Under such circumstances Aoki-Kawai-Takei provided a closed expression for the $S$ matrix of a time-dependent multistate nonadiabatic system, in which diabatic potential curves are given as polynomial functions of time and they all intersect with each other. Their result is completely explicit, and the model covers much wider classes of systems than multistate nonadiabatic models studied so far. Here we numerically show how their exact WKB formula works as long as crossing points of diabatic potential curves are well separated. The model studied includes the cases where diabatic potential functions are nonlinear, not like generalized Landau-Zener models. We also discuss the situations where virtual turning points and new Stokes curves, new components in the Stokes geometry appearing only for higher order differential equations, come into play. In particular, we examine how the presence of new Stokes curves affects final transition probabilities using a couple of concrete examples.

Propagative block diagonalization diabatization of DFT/MRCI electronic states.

We present a framework for the calculation of diabatic states using the combined density functional theory and multireference configuration interaction (DFT/MRCI) method. Due to restrictions present in the current formulation of the DFT/MRCI method (a lack of analytical derivative couplings and the inability to use non-canonical Kohn-Sham orbitals), most common diabatization strategies are not applicable. We demonstrate, however, that diabatic wavefunctions and potentials can be reliably calculated at the DFT/MRCI level of theory using a propagative variant of the block diagonalization diabatization method (P-BDD). The proposed procedure is validated via the calculation of diabatic potentials for LiH and the simulation of the vibronic spectrum of pyrazine. In both cases, the combination of the DFT/MRCI and P-BDD methods is found to correctly recover the non-adiabatic coupling effects of the problem.

Electron Attachment to DNA Base Pairs: An Interplay of Dipole- and Valence-Bound States.

We have investigated the electron-attached states in Watson-Crick guanine-cytosine and adenine-thymine base pairs using the highly accurate equation-of-motion coupled-cluster (EOM-CC) method and extended basis sets. Both base pairs have two bound anionic states. The dipole-bound state is stable even at the neutral geometry, but the valence-bound state is only adiabatically bound. The initial electron attachment results in the formation of a dipole-bound state that acts as a doorway to the valence-bound anionic state. The adiabatic potential energy surface of ground and first excited states of an anion shows an avoided crossing, indicating mixing of the electronic and nuclear degrees of freedom. We have calculated the coupling strength between the valence- and dipole-bound states by fitting a simple diabatic model potential to a cut through the two adiabatic surfaces of the anions obtained from the EOM-CC calculations. The transfer of the electron from the initial dipole-bound to the final valence-bound state has been found to happen at an ultrafast time scale.

Diabatic neural network potentials for accurate vibronic quantum dynamics-The test case of planar NO3.

A recently developed scheme to produce high-dimensional coupled diabatic potential energy surfaces (PESs) based on artificial neural networks (ANNs) [D. M. G. Williams and W. Eisfeld, J. Chem. Phys. 149, 204106 (2019)] is tested for its viability for quantum dynamics applications. The method, capable of reproducing high-quality ab initio data with excellent accuracy, utilizes simple coupling matrices to produce a basic low-order diabatic potential matrix as an underlying backbone for the model. This crude model is then refined by making its expansion coefficients geometry-dependent by the output neurons of the ANN. This structure, strongly guided by a straightforward physical picture behind nonadiabatic coupling, combines structural simplicity with high accuracy, reproducing ab initio data without introducing unphysical artifacts to the surface, even for systems with complicated electronic structure. The properties of diabatic potentials obtained by this method are tested thoroughly in the present study. Vibrational/vibronic eigenstates are computed on the X̃ and à states of NO3, a notoriously difficult Jahn-Teller system featuring strong nonadiabatic couplings and complex spectra. The method is investigated in terms of how consistently it produces dynamics results for PESs of similar (fitting) quality and how the results depend on the ANN size and ANN topography. A central aspect of this work is to understand the convergence properties of the new method in order to evaluate its predictive power. A previously developed, high-quality model utilizing a purely (high-order) polynomial ansatz is used as a reference to showcase improvements of the overall quality which can be obtained by the new method.

Direct diabatization and analytic representation of coupled potential energy surfaces and couplings for the reactive quenching of the excited 2Σ+ state of OH by molecular hydrogen.

We have employed extended multiconfiguration quasidegenerate perturbation theory, fourfold-way diabatic molecular orbitals, and configurational uniformity to develop a global three-state diabatic representation of the potential energy surfaces and their couplings for the electronically nonadiabatic reaction OH* + H2 → H2O + H, where * denotes electronic excitation to the A 2Σ+ state. To achieve sign consistency of the computed diabatic couplings, we developed a graphics processing unit-accelerated algorithm called the cluster-growing algorithm. Having obtained consistent signs of the diabatic couplings, we fit the diabatic matrix elements (which consist of the diabatic potentials and the diabatic couplings) to analytic representations. Adiabatic potential energy surfaces are generated by diagonalizing the 3 × 3 diabatic potential energy matrix. The comparisons between the fitted and computed diabatic matrix elements and between the originally computed adiabatic potential energy surfaces and those generated from the fits indicate that the current fit is accurate enough for dynamical studies, and it may be used for quantal or semiclassical dynamics calculations.

Vibronically and spin-orbit coupled diabatic potentials for X(2P) + CH4 → HX + CH3 reactions: Neural network potentials for X = Cl.

Vibronically and spin-orbit (SO) coupled diabatic potentials for the Cl(2P) + CH4 → HCl + CH3 reaction are constructed based on a recently developed approach [T. Lenzen and U. Manthe, J. Chem. Phys. 150, 064102 (2019)]. Diabatic potentials and couplings describing the entrance channel of the reaction are obtained based on ab initio data using a diabatization by an ansatz scheme. A detailed investigation of the electronic structure in the entrance channel using multireference configuration interaction (MRCI), coupled cluster [CCSD/CCSD(T)], and SO-MRCI calculations is presented. Neural networks using permutationally invariant polynomials as inputs are employed to represent the elements of the diabatic potential energy matrix. The same set of diabatic states is also used in the transition state region and all four exit channels. Here, the lowest adiabatic potential energy surface (PES) derived from the diabatic model is chosen to reproduce an adiabatic PES recently developed by Li and Guo. The accuracy of the resulting PES is evaluated, and the properties of the newly developed coupled diabatic potentials are analyzed in detail.

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

AbstractIn this work, we examine nonadiabatic population dynamics for 11B1 and 11A2 states of ozone molecule (O3). In O3, two lowest singlet excited states, 1A2 and 1B1, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born‐Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O3, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang‐Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second‐order perturbation theory with a full‐valence complete active space self‐consistent field methods and augmented Dunning's standard correlation‐consistent‐polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O3, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 11B1 and 11A2 excited electronic states for the first 500 fs after photoexcitation.