Coupling Hamiltonian Research Articles

Nonadiabatic Absorption Spectra and Ultrafast Dynamics of DNA and RNA Photoexcited Nucleobases.

We have recently proposed a protocol for Quantum Dynamics (QD) calculations, which is based on a parameterisation of Linear Vibronic Coupling (LVC) Hamiltonians with Time Dependent (TD) Density Functional Theory (TD-DFT), and exploits the latest developments in multiconfigurational TD-Hartree methods for an effective wave packet propagation. In this contribution we explore the potentialities of this approach to compute nonadiabatic vibronic spectra and ultrafast dynamics, by applying it to the five nucleobases present in DNA and RNA. For all of them we computed the absorption spectra and the dynamics of ultrafast internal conversion (100 fs timescale), fully coupling the first 2–3 bright states and all the close by dark states, for a total of 6–9 states, and including all the normal coordinates. We adopted two different functionals, CAM-B3LYP and PBE0, and tested the effect of the basis set. Computed spectra are in good agreement with the available experimental data, remarkably improving over pure electronic computations, but also with respect to vibronic spectra obtained neglecting inter-state couplings. Our QD simulations indicate an effective population transfer from the lowest energy bright excited states to the close-lying dark excited states for uracil, thymine and adenine. Dynamics from higher-energy states show an ultrafast depopulation toward the more stable ones. The proposed protocol is sufficiently general and automatic to promise to become useful for widespread applications.

Parameterization of a linear vibronic coupling model with multiconfigurational electronic structure methods to study the quantum dynamics of photoexcited pyrene.

With this work, we present a protocol for the parameterization of a Linear Vibronic Coupling (LVC) Hamiltonian for quantum dynamics using highly accurate multiconfigurational electronic structure methods such as RASPT2/RASSCF, combined with a maximum-overlap diabatization technique. Our approach is fully portable and can be applied to many medium-size rigid molecules whose excited state dynamics requires a quantum description. We present our model and discuss the details of the electronic structure calculations needed for the parameterization, analyzing critical situations that could arise in the case of strongly interacting excited states. The protocol was applied to the simulation of the excited state dynamics of the pyrene molecule, starting from either the first or the second bright state (S2 or S5). The LVC model was benchmarked against state-of-the-art quantum mechanical calculations with optimizations and energy scans and turned out to be very accurate. The dynamics simulations, performed including all active normal coordinates with the multilayer multiconfigurational time-dependent Hartree method, show good agreement with the available experimental data, endorsing prediction of the excited state mechanism, especially for S5, whose ultrafast deactivation mechanism was not yet clearly understood.

Low-Cost, Balle-Flygare-Type Cavity Fourier Transform Microwave Spectrometer and Pure Rotational Spectroscopy Laboratory for Teaching Physical Chemistry and Astronomy

Few laboratory exercises exist that introduce undergraduate students to both the concepts and instrumentation used in rotational spectroscopy. Because of this gap in undergraduate laboratory training, a teaching laboratory for the pure rotational spectroscopy of benzonitrile has been developed and reported. Owing to benzonitrile’s recent discovery in space, the molecular spectroscopic technique and target are applicable to both the physical chemistry and astronomy disciplines. Because of the size of the dipole moment and relative safety of the molecule chosen, the laboratory approach allows undergraduates to directly load, tune, measure, and assign spectra using the same quantum chemical approaches and spectroscopic assigning tools available to a researcher in the field. Concepts taught in this laboratory include the rigid and semirigid rotor, as well as low-level nuclear electric quadrupole coupling Hamiltonians. To minimize the budget and allow the students to get hands-on training with the rotational spectroscopy instrumentation, an interactive, low-cost, Balle-Flygare-type, cavity Fourier transform microwave (FTMW) spectrometer of research-grade quality was developed and is reported. Implementation of the laboratory exercise, time of exercise, and student response to the exercise is also reported.

On the role of symmetry in XDW-CASPT2.

Herewith, we propose two new exponents for the recently introduced XDW-CASPT2 method [S. Battaglia and R. Lindh, J. Chem. Theory Comput. 16, 1555-1567 (2020)], which fix one of the largest issues hindering this approach. By using the first-order effective Hamiltonian coupling elements, the weighting scheme implicitly takes into account the symmetry of the states, thereby averaging Fock operators only if the zeroth-order wave functions interact with each other. The use of Hamiltonian couplings also provides a physically sounder approach to quantitate the relative weights; however, it introduces new difficulties when these rapidly die off to zero. The improved XDW-CASPT2 method is critically tested on several systems of photochemical relevance, and it is shown that it succeeds in its original intent of maintaining MS-CASPT2 accuracy for the evaluation of transition energies and at the same time providing smooth potential energy surfaces around near-degenerate points akin to XMS-CASPT2.

Flat-band conditions influenced by spin-orbit interaction in the presence of external magnetic field

We deduct conditions for the Hamiltonian coupling strengths necessary to achieve flat bands in polymers (i.e. a pentagon chain) considering many-body spin-orbit coupling and external magnetic field. We consider itinerant electrons on pentagon chains with first neighbour hoppings, on-site electron potentials and spin-flip first neighbour hoppings representing the Rashba type spin-orbit interaction (SOI). The external magnetic field is also present in the system via the Peierls phase factors. The band structure is obtained by solving the secular equation of the diagonalized one particle part of the Hamiltonian in k-space (momentum-space). The flat band conditions make the bands k-independent, providing a highly a degenerate state, which gives broad possibilities for applications. In our work we have shown how the SOI is able to relax the strict, rigid flat band conditions given by the Hamiltonian coupling strengths. The role of the external magnetic field was also investigated.

An effective methodology to predict infrared spectra of van der Waals complexes: A case of Ar–CO complex

In this work, we developed an effective methodology to predict infrared spectra of van der Waals complexes and successfully applied it to the prototype system of Ar–CO complex. The basic idea is to divide strictly the full-dimensional Hamiltonian of a complex into three parts, named as rigid-rotor-approximation Hamiltonian, monomer Hamiltonian, and intramolecular and intermolecular coupling Hamiltonian, respectively. Following the three parts, intermolecular potential energy surfaces (IPESs) were firstly constructed at the rigid rotor approximation for ground and vibrationally excited states of Ar–CO complex. Then, potential curves were calculated for ground and vibrationally excited states of CO monomer with the intermolecular equilibrium structural parameters fixed. Based on these PESs, the bound state calculations were performed to obtain the rovibrational levels and average structural parameters. Finally, the intermolecular and intramolecular coupling Hamiltonian was calculated using the average structural parameters obtained from the previous steps. Our predicted vibrational shifts and spectroscopic parameters for Ar–CO complex are all in good agreement with available experimental data. The vibrational shift was calculated to be –0.4384 cm–1 for the fundamental and –0.8925 cm–1 for the overtone bands, which reproduce experimental results with the error of 0.16% (–0.4377 cm–1) and 1.68% (–0.8778 cm–1), respectively. In brief, the advantages of this methodology are its higher accuracy for predicting infrared spectra and are less computing resources for constructing IPESs than those of the full-dimensional quantum calculations.

Non-equilibrium steady-states of memoryless quantum collision models

We investigate the steady state properties arising from the open system dynamics described by a memoryless (Markovian) quantum collision model, corresponding to a master equation in the ultra-strong coupling regime. By carefully assessing the work cost of switching on and off the system-environment interaction, we show that only a coupling Hamiltonian in the energy-preserving form drives the system to thermal equilibrium, while any other interaction leads to non-equilibrium steady states that are supported by steady-state currents. These currents provide a neat exemplification of the housekeeping work and heat. Furthermore, we characterize the specific form of system-environment interaction that drives the system to a steady-state exhibiting coherence in the energy eigenbasis, thus, giving rise to families of states that are non-passive.

Density Functional Computations of Vibrational Circular Dichroism Spectra beyond the Born-Oppenheimer Approximation.

Transition-metal complexes provide rich features in vibrational circular dichroism (VCD) spectra, including significant intensity enhancements, and become thus useful in structural and functional studies of molecules. Quite often, however, the vibrational spectral bands are mixed with the electronic ones, and interpretation of such experiments is difficult. In the present study, we elaborate on the theory needed to calculate the VCD intensities beyond the Born-Oppenheimer (BO) approximation. Within a perturbation approach, the coupling between the electronic and vibrational states is estimated using the harmonic approximation and simplified wave functions obtainable from common density functional theory (DFT) computations. Explicit expressions, including Slater determinants and derivatives of molecular orbitals, are given. On a model diamine complex, the implementation is tested and factors affecting spectral intensities and frequencies are investigated. For two larger molecules, the results are in a qualitative agreement with previous experimental data. Typically, the electronic-vibrational interaction Hamiltonian coupling elements are rather small (∼0 to 10 cm-1), which provides negligible contributions to vibrational frequencies and absorption intensities. However, significant changes in VCD spectra are induced due to the large transition magnetic dipole moment associated with the d-d metal transitions. The possibility to model the spectra beyond the BO limit opens the way to further applications of chiral spectroscopy and transition-metal complexes.

Quantum dynamics and geometric phase in E⊗e Jahn-Teller systems with general Cnv symmetry.

E ⊗ e Jahn-Teller (JT) systems are considered the prototype of symmetry-induced conical intersections and of the corresponding geometric phase effect (GPE). For decades, this has been analyzed for the most common case originating from C3v symmetry and these results usually were generalized. In the present work, a thorough analysis of the JT effect, vibronic coupling Hamiltonians, GPE, and the effect on spectroscopic properties is carried out for general Cnv symmetric systems (and explicitly for n = 3-8). It turns out that the C3v case is much less general than often assumed. The GPE due to the vibronic Hamiltonian depends on the leading coupling term of a diabatic representation of the problem, which is a result of the explicit n, α, and β values of a CnvEα ⊗ eβ system. Furthermore, the general existence of n/m (m∈N depending on n, α, and β) equivalent minima on the lower adiabatic sheet of the potential energy surface (PES) leads to tunneling multiplets of n/m states (state components). These sets can be understood as local vibrations of the atoms around their equilibrium positions within each of the local PES wells symmetrized over all equivalent wells. The local vibrations can be classified as tangential or radial vibrations, and the quanta in the tangential mode together with the GPE determine the level ordering within each of the vibronic multiplets. Our theoretical predictions derived analytically are tested and supported by numerical model simulations for all possible Eα ⊗ eβ cases for Cnv symmetric systems with n = 3-8. The present interpretation allows for a full understanding of the complex JT spectra of real systems, at least for low excitation energies. This also opens a spectroscopic way to show the existence or absence of GPEs.

Excited state dynamics initiated by an electromagnetic field within the Variational Multi-Configurational Gaussian (vMCG) method

The Variational Multi-Configurational Gaussian (vMCG) approach offers a framework to perform exact trajectory-based quantum dynamics. Herein we use two model vibronic coupling Hamiltonians of pyrazine to explore, for the first time, the influence of the coupling between the external field and the Gaussian basis functions (GBFs) in vMCG on the dynamics. We show that when the excitation pulse is short compared to the nuclear dynamics, vertical projection without a field and explicit description of the external field converge. For longer pulses, a sizeable change is observed. We demonstrate that comparatively few GBFs are sufficient to provide qualitative agreement to MCTDH dynamics and a quantitative agreement can be achieved using ∼100 GBFs. Longer pulses require more GBFs due to the prolonged coupling between the ground and excited states. Throughout this work the single set formalism offers the fastest convergence.

Quantum state tomography with time-continuous measurements: reconstruction with resource limitations

We propose and analyze quantum state estimation (tomography) using continuous quantum measurements with resource limitations, allowing the global state of many qubits to be constructed from only measuring a few. We give a proof-of-principle investigation demonstrating successful tomographic reconstruction of an arbitrary initial quantum state for three different situations: single qubit, remote qubit, and two interacting qubits. The tomographic reconstruction utilizes only a continuous weak probe of a single qubit observable, a fixed coupling Hamiltonian, together with single-qubit controls. In the single qubit case, a combination of the continuous measurement of an observable and a Rabi oscillation is sufficient to find all three unknown qubit state components. For two interacting qubits, where only one observable of the first qubit is measured, the control Hamiltonian can be implemented to transfer all quantum information to the measured observable, via the qubit-qubit interaction and Rabi oscillation controls applied locally on each qubit. We discuss different sets of controls by analyzing the unitary dynamics and the Fisher information matrix of the estimation in the limit of weak measurement, and simulate tomographic results numerically. As a result, we obtained reconstructed state fidelities in excess of 0.98 with a few thousand measurement runs.

Evolution of interlayer and intralayer magnetism in three atomically thin chromium trihalides

We conduct a comprehensive study of three different magnetic semiconductors, CrI3, CrBr3, and CrCl3, by incorporating both few-layer and bilayer samples in van der Waals tunnel junctions. We find that the interlayer magnetic ordering, exchange gap, magnetic anisotropy, and magnon excitations evolve systematically with changing halogen atom. By fitting to a spin wave theory that accounts for nearest-neighbor exchange interactions, we are able to further determine a simple spin Hamiltonian describing all three systems. These results extend the 2D magnetism platform to Ising, Heisenberg, and XY spin classes in a single material family. Using magneto-optical measurements, we additionally demonstrate that ferromagnetism can be stabilized down to monolayer in more isotropic CrBr3, with transition temperature still close to that of the bulk.

Non-Markov enhancement of maximum power for quantum thermal machines

In this work we study how the non-Markovian character of the dynamics can affect the thermodynamic performance of a quantum thermal engine, by analysing the maximum power output of Carnot and Otto cycles departing from the quasi-static and infinite-time-thermalization regime respectively, introducing techniques for their control optimization in general dynamical models. In our model, non-Markovianity is introduced by allowing some degrees of freedom of the reservoirs to be taken into account explicitly and share correlations with the engine by Hamiltonian coupling. It is found that the non-Markovian effects can fasten the control and improve the power output.

Fast trajectory tracking of the steady state of open quantum systems

We present a control strategy to speed up the steady-state tracking for open quantum systems governed by a time-dependent Markovian master equation. With this fast trajectory tracking strategy, the quantum state strictly follows the instantaneous steady state of open quantum systems and evolves into the target state without any fidelity loss. A compact expression for the counterdiabatic term is derived in terms of a superoperator formalism in Liouville space. To be specific, we utilize a universal method to transform the counterdiabatic superoperator into the ordinary operator form. It can be seen from the operator form that in addition to the coherent control field, an incoherent control is required for the fast trajectory tracking. The control strategy is successfully applied in two examples: One is a two-level quantum system with a time-dependent Hamiltonian coupling to a heat bath, the other is a two-level system following an isothermal process.

Renner-Teller and pseudo-Renner-Teller interactions in the electronic ground and excited states of the dicyanoacetylene radical cation: Assignment of vibronic spectrum and elucidation of nonradiative and radiative decay mechanisms

Vibronic interactions in the first five energetically lowest electronic states (X̃2Πu-Ã2Σg+-B̃2Σu+-C̃2Πg-D̃2Πu) of dicyanoacetylene radical cation (C4N2·+) and their effect on the nuclear dynamics are examined in this article. The spectroscopy of C4N2·+ is a subject of outstanding complexity and addressed by the [see, the recent article, J. Chem. Phys. 139, 184304 (2013)]. The energetic ordering of electronic states and the emission mechanism of the states seem to have ambiguity. Here we have undertaken a detailed theoretical study in an attempt to resolve it. A vibronic coupling Hamiltonian of the five electronic states mentioned above is constructed in a diabatic electronic basis and with the aid of ab initio quantum chemistry calculations. Quantum nuclear dynamics studies are carried out by both time-independent and time-dependent quantum mechanical methods. The vibronic spectrum is calculated and the progressions are identified in terms of vibrational modes and compared with experimental slow photoelectron spectroscopy results. Renner-Teller (RT) coupling within the degenerate electronic states (X̃, C̃ and D̃) and the pseudo-Renner-Teller (PRT) coupling among states are examined in detail to elucidate their impact on the vibronic structure of the state and its decay mechanism to the ground (X̃) electronic state. While the dynamics of the X̃ and D̃ states is somewhat simple, the same of the Ã, B̃ and C̃ states is outstandingly complex due to strong RT and PRT interactions.

Quantum theory of superfluorescence based on two-point correlation functions

Irradiation of a medium by short intense pulses from x-ray / XUV free electron lasers can result in saturated photoionization of inner electronic shells. As a result an inversion of populations between core levels appears. The resulting fluorescent radiation can be amplified during its propagation through the inverted medium and results in intense, quasi transform-limited radiation bursts. While the optical counterpart of this phenomena, known as superfluorescence, was intensively investigated, a generalized treatment is needed in the x-ray / XUV domain, where the dynamics of pumping and evolution due to fast decay processes play a crucial role. To provide a general theoretical approach, we start from the fundamental, quantized minimal coupling Hamiltonian of light-matter interaction and after a series of approximations arrive at a closed system of equations for the two-point correlation function of atomic coherences and the two-time correlation function of the emitted field. The obtained formalism enables us to investigate collective spontaneous emission in various regimes. It is extended consistently to include incoherent processes that are relevant in the x-ray / XUV domain. These processes are introduced into the formalism by corresponding Lindblad superoperators. The connection to other approaches is discussed and numerical examples related to recent experiments are presented.

Charger-mediated energy transfer in exactly solvable models for quantum batteries

We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two level systems and quantum harmonic oscillators. In particular, we study energy transfer processes from a given quantum system, termed charger, to another one, i.e. the proper battery. In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by properly accounting them in the global energy balance of the model.

Vacuum ultraviolet excited state dynamics of the smallest ring, cyclopropane. I. A reinterpretation of the electronic spectrum and the effect of intensity borrowing.

Cyclopropane, the smallest organic ring compound, exhibits complex spectroscopy and excited state dynamics. In Paper I, we reinterpret the vacuum ultraviolet (VUV) electronic absorption spectrum of cyclopropane via ab initio computation. The first two bands in the VUV spectrum are simulated using wavepacket propagations employing the multiconfigurational time-dependent Hartee method and a newly parameterized linear vibronic coupling Hamiltonian. The parameters of the model Hamiltonian are obtained directly from high level multireference configuration interaction calculations. An analysis of the results, with an emphasis on previously neglected vibronic coupling effects, reveals that these vibronic coupling terms must be included in order to account for strong intensity borrowing effects. This treatment dramatically changes the assignment of much of the VUV spectrum, with intensity borrowing by the optically dark (σ3p x /3p y ) and (σ3p x /3p y ) states from the E'(σ3p x /3p y ) state being found to give rise to almost all the spectral intensities below 8 eV. This is in stark contrast to previous studies, which attributed the first two bands to transitions to the E'(σ3p x /3p y ) state. This highlights the limitations of assigning spectral features based solely on calculated electronic excitation energies and oscillator strengths. Furthermore, we address the significant but infrequently discussed difficulties involved in determining the electronic character of a wavepacket produced in the pump step of ultrafast pump-probe experiments for systems exhibiting strong vibronic coupling.

NMR evidence for f -electron excitations in the multipolar ground state of NpO2

An analysis is presented of the $^{237}\mathrm{Np}\ensuremath{-}^{17}\mathrm{O}$ cross-relaxation (CR) process at temperatures below $T=10$ K that was reported [Tokunaga et al., Phys. Rev. B 74, 064421 (2006)] in $^{17}\mathrm{O}$ NMR studies of ${\mathrm{NpO}}_{2}$. The CR evidently results from $^{237}\mathrm{Np}$ spin fluctuations driven by indirect spin-spin interactions analogous to the Suhl-Nakamura [Nakamura, Prog. Theor. Phys. 20, 542 (1958)] effect in conventional magnets. Here, however, there is a body of evidence that the interacting ${\mathrm{Np}}^{4+}$ ions are in a magnetic, rank-5 dotriakontadipolar ground state [Santini et al., Phys. Rev. Lett. 97, 207203 (2006); Magnani et al., Phys. Rev. B 78, 104425 (2008)]. Owing to the observed exponential form of the fluctuation spectrum, it is possible to evaluate explicitly the CR bandwidth in terms of any specified $^{237}\mathrm{Np}\ensuremath{-}^{237}\mathrm{Np}$ (spin-spin) coupling Hamiltonian. We model the latter as an enhanced dipolar coupling. The enhancement is concluded to be compound, with the ``enlarged nuclear moment'' mechanism identified in the paramagnetic state [Tokunaga et al., Phys. Rev. B 74, 064421 (2006)] responsible for a factor $\ensuremath{\sim}22$, while the indirect $^{237}\mathrm{Np}\ensuremath{-}^{237}\mathrm{Np}$ coupling effect is found to be $\ensuremath{\sim}240$ times the amplitude of the classical dipolar interaction. We suggest that these results are consistent with the identification of a magnetic rank 5 multipolar ground state [Magnani et al., Phys. Rev. B 78, 104425 (2008)] for ${\mathrm{NpO}}_{2}$.

Vibronic coupling model to calculate the photoelectron spectrum of phenol

The photoelectron spectrum for the two lowest ionisation bands of phenol has been simulated using quantum dynamic methods. A vibronic coupling Hamiltonian was set up consisting of seven vibrational modes and the first two ionised states. Parameters for the model are obtained by fitting adiabatic surfaces to a series of points calculated using ab initio methods. Such a model allows non-adiabatic couplings between the states to be included. CASSCF calculations used in this work provide reliable quantum chemical information for the model and the calculated photoelectron spectrum shows good agreement to experiment. The vibrational fine structure of both bands are reassessed and different assignments to those previously reported are detailed. The existence of a conical intersection between the ionised states is reported and its role in the dynamics of phenol upon ionisation is examined.