Adiabatic Ground State Research Articles

Hydrogen-iodine scattering. II. Rovibronic analysis and collisional dynamics.

Our recently published [Weike et al., J. Chem. Phys. 159, 244119 (2023)] spin-orbit coupled diabatic potential energy model for HI is used in a thorough analysis of bound and quasi-bound states as well as elastic and inelastic processes in H + I collisions. The potential energy model, designed explicitly for studying scattering, accurately describes the various couplings in the system, which lead to complex dynamics. Ro-vibronic bound and quasi-bound states related to the adiabatic electronic ground state and an excited electronic state are analyzed. Calculations using the full 104 × 104 diabatic matrix model or a single adiabatic state are compared in order to investigate approximations in the latter. Elastic and inelastic scattering cross sections as well as thermal rates between the ground and first excited fine structure levels of iodine are computed for collision energies up to 12 500 cm-1. Resonances related to the quasi-bound states are analyzed in terms of their energy, width, lifetime, and decay probabilities. The effect of different resonances on the thermal rates is discussed. Resonances between 30 000 and 40 000 cm-1 are also studied for selected values of the total angular momentum, in particular their decay probabilities into different final states of iodine and hence their potential effect on branching ratios in photodissociation of HI.

Adiabatic ground-state preparation of fermionic many-body systems from a two-body perspective

Adiabatic ground-state preparation of fermionic many-body systems from a two-body perspective

Ab-initio simulations of coherent phonon-induced pumping of carriers in zirconium pentatelluride

Laser-driven coherent phonons can act as modulated strain fields and modify the adiabatic ground state topology of quantum materials. Here we use time-dependent first-principles and effective model calculations to simulate the effect of the coherent phonon induced by strong terahertz electric field on electronic carriers in the topological insulator ZrTe5. We show that a coherent A1g Raman mode modulation can effectively pump carriers across the band gap, even though the phonon energy is about an order of magnitude smaller than the equilibrium band gap. We reveal the microscopic mechanism of this effect which occurs via Landau–Zener-Stückelberg tunneling of Bloch electrons in a narrow region in the Brillouin zone center where the transient energy gap closes when the system switches from strong to weak topological insulator. The quantum dynamics simulation results are in excellent agreement with recent pump-probe experiments in ZrTe5 at low temperature.

Resonance theory and quantum dynamics simulations of vibrational polariton chemistry.

We present numerically exact quantum dynamics simulations using the hierarchical equation of motion approach to investigate the resonance enhancement of chemical reactions due to the vibrational strong coupling (VSC) in polariton chemistry. The results reveal that the cavity mode acts like a "rate-promoting vibrational mode" that enhances the ground state chemical reaction rate constant when the cavity mode frequency matches the vibrational transition frequency. The exact simulation predicts that the VSC-modified rate constant will change quadratically as the light-matter coupling strength increases. When changing the cavity lifetime from the lossy limit to the lossless limit, the numerically exact results predict that there will be a turnover of the rate constant. Based on the numerical observations, we present an analytic rate theory to explain the observed sharp resonance peak of the rate profile when tuning the cavity frequency to match the quantum transition frequency of the vibrational ground state to excited states. This rate theory further explains the origin of the broadening of the rate profile. The analytic rate theory agrees with the numerical results under the golden rule limit and the short cavity lifetime limit. To the best of our knowledge, this is the first analytic theory that is able to explain the sharp resonance behavior of the VSC-modified rate profile when coupling an adiabatic ground state chemical reaction to the cavity. We envision that both the numerical analysis and the analytic theory will offer invaluable theoretical insights into the fundamental mechanism of the VSC-induced rate constant modifications in polariton chemistry.

Adiabatic Ground States in Non-smooth Spacetimes

Ground states are a well-known class of Hadamard states in smooth spacetimes. In this paper, we show that the ground state of the Klein–Gordon field in a non-smooth ultrastatic spacetime is an adiabatic state. The order of the state depends linearly on the regularity of the metric. We obtain the result by combining a propagation of singularities result for non-smooth pseudodifferential operators, properties of the causal propagator, and eigenvalue asymptotics for elliptic operators of low regularity.

Electronic frustration, Berry’s phase interference and slow dynamics in some tight-binding systems coupled to harmonic baths

Conical intersections in two-state systems require a coordinate-dependent coupling. This paper identifies and investigates conical intersections in cyclic tight-binding system-bath Hamiltonians with an odd number of sites and a constant site-to-site coupling. In the absence of bath degrees of freedom, such tight-binding systems with a positive coupling parameter exhibit electronic frustration and a doubly-degenerate ground state. When these systems interact with a harmonic bath, the degeneracy becomes a conical intersection between the adiabatic ground and first excited states. Under weak system-bath coupling, overlapping wavefunctions associated with different sites give rise to distinct pathways with interfering geometric phases, which lead to considerably slower transfer dynamics. The effect is most pronounced in the presence of low-temperature dissipative baths characterized by a continuous spectral density. It is found that the transfer dynamics and equilibration time of a cyclic dissipative three-site system with a positive coupling exceeds that of a similar three-site system with a negative coupling, as well as that of cyclic four-site systems, by an order of magnitude.

Ultrafast Dynamics of Photochemical Nitrile Imine Formation.

The chemical reactivity of nitrile imines is of great utility in organic synthesis with applications rapidly expanding into the materials and life sciences. Yet, our understanding of the electronic and molecular structures of nitrile imines remains incomplete and the elementary mechanism of their photoinduced generation is entirely unknown. Here, femtosecond infrared spectroscopy after 266 nm‐excitation of 2,5‐diphenyltetrazole has been carried out to temporally resolve the formation and structural relaxation dynamics of the nascent diphenylnitrile imine in liquid solution under ambient conditions. The infrared‐spectroscopic evolution is interpreted by an initial sequence of intersystem crossings within 250 fs followed by the cleavage of N2 with formation of a structurally relaxed nitrile imine on the adiabatic ground‐state singlet surface within a few tens of picoseconds. The infrared spectrum supports the notion of a “floppy” nitrile imine molecule whose equilibrium character ranges from fully propargylic to fully allenic in the room temperature liquid solution.

Minimal Active Space for Diradicals Using Multistate Density Functional Theory.

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.

Quantum Fluctuations in Vacuum Energy: Cosmic Inflation as a Dynamical Phase Transition

A variety of models of inflation in the early Universe have been proposed and applied to describe successfully the origin of all possible structures in the Universe. On the other hand, inflation theory is still phenomenological and needs systematic physical foundations, including the relation to dark matter and dark energy. The essence of cosmic inflation would be a dynamical phase transition and the spontaneous symmetry breaking process, which are common in ordinary physics in the laboratory. At the beginning of the phase transition, the system is often in an adiabatic ground state and produces a squeezed state. This is widely interpreted as the generation of classical structures; however, it is not. The common notion of decoherence is not sufficient to describe the inflationary phase transition: a particular trajectory must be singled out in the dynamics. When an interaction turns on, dissipation or the energy flow/cascade is possible, and the c-number random field appears. The separation of these classical statistical fluctuations from the deterministic time evolution is indicated by the secular divergence or the infrared divergence of the system. We describe this phase transition based on the closed-time-path method and derive a quantum Langevin equation with classical noise, which sources the development of a coherent state. Introducing the effective action method to describe the evolution of the coherent state, we describe the order parameter that characterizes the phase transition and the associated spontaneous symmetry breaking. Since this phase transition process is common in physics, we discuss further applications of this formalism in other physical systems.

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions.

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study [S. J. Quiton et al., J. Chem. Phys. 153, 054122 (2020)], exploits the low-rank character of the polynomial expansion of potential energy to recover vibrational frequencies (square roots of eigenvalues of nuclear Hessians) constituting the reaction path using a small sample of its entities. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the sole exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

Theoretical Investigations on the Hydroxyl-Initialized Oxidation of Hexafluoro-2-butyne in the Presence of Oxygen.

Hexafluoro-2-butyne (C4F6) is a potential eco-friendly alternative gas in plasma, refrigerants, and electrical insulation applications. Mechanisms for the reactions of C4F6 with OH/O2 have been revealed in detail using various theoretical methods including ROCBS-Q, RCCSD(T), multireference RS2C, and extrapolations to the complete basis-set limit with Aug-cc-pVnZ (n = T, Q, 5) basis sets. Rate coefficients and product branching ratios were predicted for a wide range of temperatures and pressures using the solution of master equations. The vibrationally adiabatic ground-state barrier for the initial C4F6 + OH association was best estimated to be 1.53-2.26 kcal/mol. Energetically preferable decomposition paths for the conformation-dependent C4F6OH adducts include six-center HF elimination, four-center proton migration, and C-C bond cleavage, but the collisional deactivation is dominant under ambient conditions. The subsequent oxidation of C4F6OH by O2 bifurcates in two orientations and proceeds without any well-defined barrier followed by the successive isomerization/elimination steps, forming perfluorobiacetyl to regenerate OH radicals or trifluoroacetic acid with trifluoroacetyl radicals. The OH-recycling path accounts for a branching ratio of 70% under ambient conditions. Theoretical rate coefficients are in good agreement with the available experimental results. The effect of fluorination on the reactivity of alkynes toward OH/O2 is discussed.

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.

State preparation and measurement in a quantum simulation of the O(3) sigma model

Recently, Singh and Chandrasekharan showed that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. In a paper by the NuQS collaboration, the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from and measure a dynamical quantity of interest, the O(3) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. We then present and analyze a quantum algorithm based on non-unitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.

Ultrafast critical ground state preparation via bang–bang protocols

The fast and faithful preparation of the ground state of quantum systems is a challenging but crucial task for several applications in the realm of quantum-based technologies. Decoherence limits the maximum time-window allowed to an experiment to faithfully achieve such desired states. This is of particular significance in systems featuring a quantum phase transition, where the vanishing energy gap challenges an adiabatic ground state preparation. We show that a bang–bang protocol, consisting of a time evolution under two different values of an externally tunable parameter, allows for a high-fidelity ground state preparation in evolution times no longer than those required by the application of standard optimal control techniques, such as the chopped-random basis quantum optimization. In addition, owing to their reduced number of variables, such bang–bang protocols are very well suited to optimization tasks, reducing the high computational cost of other optimal control protocols. We benchmark the performance of such approach through two paradigmatic models, namely the Landau–Zener and the Lipkin–Meshkov–Glick model. Remarkably, we find that the critical ground state of the latter model, i.e. its ground state at the critical point, can be prepared with a high fidelity in a total evolution time that scales slower than the inverse of the vanishing energy gap.

Theoretical kinetics of hydrogen abstraction and hydroperoxyl addition reactions of 3-hexene by hydroperoxyl radicals

The reaction kinetics of alkenes + hydroperoxyl (HȮ2) system is of importance to low/intermediate temperature chemistry of alkanes. This work is a follow up of our previous study on 3-hexene + ȮH [1],. The rate coefficients were determined using the canonical variational transition-state theory. Results revealed that the asymmetric geometry of the HȮ2 radical generated numerous reaction sub-channels. The rate coefficients, with a conservative uncertainty (factor of 5), were obtained to develop the detailed chemical mechanism of 3-hexene. Additionally, potential energy surface, minimum reaction path, adiabatic ground-state energy, and activation free Gibbs energy change (ΔG) calculations were also performed.

Adiabatic ground state preparation in an expanding lattice

We implement and characterize a numerical algorithm inspired by the $s$-source framework [Phys. Rev.~B 93, 045127 (2016)] for building a quantum many-body ground state wavefunction on a lattice of size $2L$ by applying adiabatic evolution to the corresponding ground state at size $L$, along with $L$ interleaved ancillae. The procedure can in principle be iterated to repeatedly double the size of the system. We implement the algorithm for several one dimensional spin model Hamiltonians, and find that the construction works particularly well when the gap is large and, interestingly, at scale invariant critical points. We explain this feature as a natural consequence of the lattice expansion procedure. This behavior holds for both the integrable transverse-field Ising model and non-integrable variations. We also develop an analytic perturbative understanding of the errors deep in either phase of the transverse field Ising model, and suggest how the circuit could be modified to parametrically reduce errors. In addition to sharpening our perspective on entanglement renormalization in 1D, the algorithm could also potentially be used to build states experimentally, enabling the realization of certain long-range correlated states with low depth quantum circuits.

Three-dimensional potential energy surfaces of ArNO (X̃ 2Π).

Until now, the potential energy surfaces (PESs) of the ArNO complex found in the literature were two-dimensional, with the NO interatomic distance being fixed. In this work, we present the first accurate three-dimensional ground state X̃ 2Π PESs (both A' and A″) of ArNO computed at the CCSD(T)/CBS level of theory. The equilibrium geometries and the well depths (De) are compared to several other electronic structure methods. We found that using the multireference method, MRCI-F12 makes the surfaces much shallower (by 25%) and the depth of the surfaces does not agree with experimental data. The explicitly correlated coupled-cluster method underestimates the well depth as well. Analytic representations for both A' and A″ surfaces were fit to 4380 ab initio points to within 2.71 cm-1. A three-dimensional Numerov propagator method in Delves coordinates is used to compute the bound state spectrum up to Jtot = 6.5. The recommended dissociation energies are D0 = 97.2 cm-1 for the adiabatic ground state and De = 133.7 (128.1) cm-1 for A' (A″).

Calculation of vibrationally resolved absorption and fluorescence spectra of the rylenes.

A generating function method was used to simulate the vibrationally resolved absorption and emission spectra of perylene, terrylene and quaterrylene. This method operates on the basis of adiabatic excitation energies and electronic ground and excited state vibrational frequencies. These parameters were calculated using density functional theory with the PBE0 functional for perylene and terrylene and with the BH-LYP functional for quaterrylene. The vertical excitation energies of the lower excited states were calculated using functionals with differing amounts of Hartree-Fock exchange. The optimal functional for each molecule was chosen by comparing these energies to literature excitation energies. Using this technique the calculated absorption spectra and the calculated emission spectrum of perylene were found to be in excellent agreement with the literature experimental spectra after introducing a shift and a scaling factor. The most prominent bands of the absorption spectra were assigned to their respective vibronic transitions.

Non-adiabatic quantum dynamics of the ultracold Li+LiNa→ Li2+Na chemical reaction

SynopsisWe report non-adiabatic dynamics of the Li+LiNa→Li2+Na chemical reaction at cold and ultracold temperatures employing accurate ab initio electronic potential energy surfaces in a quantum dynamics formulation employing a diabatic representation. Results are compared against those from a single adiabatic ground state potential energy surface and a universal model based on the long-range interaction potential. We discuss signatures of non-universal behavior in the total rate coefficients as well as strong non-adiabatic effects in the state-to-state rotationally resolved rate coefficients.

Fully coupled (J > 0) time-dependent wave-packet calculations using hyperspherical coordinates for the H + O2 reaction on the CHIPR potential energy surface.

Quantum dynamics of the H + O2→ O + OH reaction has been extensively studied on the adiabatic ground state of CHIPR [A. J. C. Varandas, J. Chem. Phys., 2013, 138, 134117] potential energy surfaces by employing a coupled 3D time-dependent wavepacket approach in hyperspherical coordinates. Calculations have been performed for all non-zero J values for various initial rotational states of the diatom [O2(v = 0, j = 1-5)]. State-to-state and total integral cross sections are calculated using fully converged reaction probabilities, where initial state selected and Boltzmann averaged thermal rate constants are also subsequently calculated. Moreover, a comparison of various reaction attributes obtained by using the fully close coupled approach with the ones obtained from the J-shifting approximation and extrapolation scheme is presented along with other theoretical results and experimental observations.