Core-Hole Coherent Spectroscopy in Molecules.

We study the ultrafast dynamics initiated by a coherent superposition of core-excited states of nitrous oxide molecule. Using high-level ab initio methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof-of-concept experiment using the harmonic up-conversion scheme available at x-ray free-electron laser facilities to trace the evolution of the created core-excited-state coherence through a time-resolved x-ray photoelectron spectroscopy.

Inverse Optically-Induced Ring Currents in Ring-Shaped Molecules.

Permanent electronic ring currents are supported within manifolds of ΓE degenerate excited electronic states as E± = Ex ± iEy excitations. In [ Phys. Rev. Res. 2021, 3, L042003] we showed the existence of inverse-current manifolds, where the direction of the electronic ring current in each degenerate state E± is opposite to the circular polarization of the generating light fields. This vibronic effect is caused by the exchange of orbital angular momentum between the electrons and the vibrational modes with the required symmetry. Here we consider the case of fixed nuclei and find that ring-shaped molecular systems possess inverse-current manifolds on a purely electronic-structure basis, i.e., without intervention of vibronic coupling. The effect is explained first on a tight-binding model with cyclic symmetry and then considering the ab initio electronic structure of benzene and sym-triazine. A framework for discriminating regular- and inverse-current ΓE manifolds in molecules using quantum chemistry calculations is provided.

Time-Dependent Resonant Inelastic X-ray Scattering of Pyrazine at the Nitrogen K-Edge: A Quantum Dynamics Approach.

We calculate resonant inelastic X-ray scattering spectra of pyrazine at the nitrogen K-edge in the time domain including wavepacket dynamics in both the valence and core-excited state manifolds. Upon resonant excitation, we observe ultrafast non-adiabatic population transfer between core-excited states within the core-hole lifetime, leading to molecular symmetry distortions. Importantly, our time-domain approach inherently contains the ability to manipulate the dynamics of this process by detuning the excitation energy, which effectively shortens the scattering duration. We also explore the impact of pulsed incident X-ray radiation, which provides a foundation for state-of-the-art time-resolved experiments with coherent pulsed light sources.

Compact sum-of-products form of the molecular electronic Hamiltonian based on canonical polyadic decomposition.

We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin-orbitals. The algorithm for obtaining the canonical polyadic form starts from an exact sum-of-products, which is then optimally compactified using an alternating least squares procedure. We discuss the relation of this specific SOP with related forms, namely the Tucker format and the matrix product operator often used in conjunction with matrix product states. We benchmark the method on the electronic dynamics of an excited water molecule, trans-polyenes, and the charge migration in glycine upon inner-valence ionization. The quantum dynamics are performed with the multilayer multiconfiguration time-dependent Hartree method in second quantization representation. Other methods based on tree-tensor Ansätze may profit from this general approach.

Coupling Molecular Systems with Plasmonic Nanocavities: A Quantum Dynamics Approach.

Plasmonic nanoparticles have the capacity to confine electromagnetic fields to the subwavelength regime and provide strong coupling with few or even a single emitter at room temperature. The photophysical properties of the emitters are highly dependent on the relative distance and orientation between them and the nanocavity. Therefore, there is a need for accurate and general light-matter interaction models capable of guiding their design in application-oriented devices. In this work, we present a Hermitian formalism within the framework of quantum dynamics and based on first-principles electronic structure calculations. Our vibronic approach considers the quantum nature of the plasmonic excitations and the dynamics of nonradiative channels to model plasmonic nanocavities and their dipolar coupling to molecular electronic states. Thus, the quantized and dissipative nature of the nanocavity is fully addressed.

Modification of Thermal Chemical Rates in a Cavity via Resonant Effects in the Collective Regime.

The modification of thermal chemical rates in Fabry-Perot cavities, as observed in experiments, still poses theoretical challenges. While we have a better grasp of how the reactivity of isolated molecules and model systems changes under strong coupling, we lack a comprehensive understanding of the combined effects and the specific roles played by activated and spectator molecules during reactive events. In this study, we investigate an ensemble of randomly oriented gas-phase HONO molecules undergoing a cis-trans isomerization reaction on an ab initio potential energy surface. One thermally activated molecule can overcome the reaction barrier, while the other molecules are nonactivated but coupled to the cavity as well. Using the classical reactive flux method, we analyze the transmission coefficient and determine the conditions that lead to accelerated rates within the collective regime. We identify two main mechanistic aspects: First, nonactivated molecules enhance the cavity's ability to dissipate excess energy from the activated molecule postreactive event. Second, the activated molecule couples with the polaritonic resonance created by the nonactivated molecules and the cavity at a shifted resonance frequency with respect to the bare cavity.

Time-Resolved Resonant Auger Scattering Clocks Distortion of a Molecule.

Resonant Auger scattering (RAS) provides information on the core-valence electronic transition and impresses a rich fingerprint of the electronic structure and nuclear configuration at the time-initiating RAS process. Here, we suggest using a femtosecond X-ray pulse to trigger RAS in a distorted molecule, which is generated from the nuclear evolution on a valence excited state pumped by a femtosecond ultraviolet pulse. With the time delay varied, the amount of molecular distortion can be controlled and the RAS measurements imprint both their electronic structures and changing geometries. This strategy is showcased in H2O prepared in an O-H dissociative valence state, where molecular and fragment lines appear in RAS spectra as signatures of ultrafast dissociation. Given the generality of this approach for a broad class of molecules, this work opens a new alternative pump-probe technique for mapping the core and valence dynamics with ultrashort X-ray probe pulses.

Vibrational Energy Redistribution and Polaritonic Fermi Resonances in the Strong Coupling Regime.

Intramolecular vibrational energy redistribution (IVR) plays a significant role in cavity-modified chemical reaction rates. As such, understanding the fundamental mechanisms by which the cavity modifies the IVR pathways is a fundamental step toward engineering the effect of the confined electromagnetic modes on the outcome of chemical processes. Here we consider an ensemble of M two-mode molecules with intramolecular anharmonic couplings interacting with an infrared cavity mode and consider their quantum dynamics and infrared spectra. Polaritonic Fermi resonances involving fundamental and overtone states of the polaritonic subsystem mediate efficient energy transfer pathways between otherwise off-resonant molecular states. These pathways are of collective nature, yet enabled by the intramolecular anharmonic couplings. Hence, through polaritonic Fermi resonances, cavity excitation can efficiently spread toward low-frequency modes while becoming delocalized over several molecules.

Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering.

The multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extension (ML-MCTDH) are powerful algorithms for the efficient computation of nuclear quantum dynamics in high-dimensional systems. By providing time-dependent variational orbitals and an optimal choice of layered effective degrees of freedom, one is able to reduce the computational cost to an amenable number of configurations. However, choices related to selecting properly the mode grouping and tensor tree are strongly system dependent and, thus far, subjectively based on intuition and/or experience. Therefore, herein we detail a new protocol based on multivariate statistics─more specifically, factor analysis and hierarchical clustering─for a reliable and convenient guiding in the optimal design of such complex "system-of-systems" tensor-network decompositions. The advantages of employing the new algorithm and its applicability are tested on water and two floppy protonated water clusters with large amplitude motions.

State-resolved infrared spectrum of the protonated water dimer: revisiting the characteristic proton transfer doublet peak.

The infrared (IR) spectra of protonated water clusters encode precise information on the dynamics and structure of the hydrated proton. However, the strong anharmonic coupling and quantum effects of these elusive species remain puzzling up to the present day. Here, we report unequivocal evidence that the interplay between the proton transfer and the water wagging motions in the protonated water dimer (Zundel ion) giving rise to the characteristic doublet peak is both more complex and more sensitive to subtle energetic changes than previously thought. In particular, hitherto overlooked low-intensity satellite peaks in the experimental spectrum are now unveiled and mechanistically assigned. Our findings rely on the comparison of IR spectra obtained using two highly accurate potential energy surfaces in conjunction with highly accurate state-resolved quantum simulations. We demonstrate that these high-accuracy simulations are important for providing definite assignments of the complex IR signals of fluxional molecules.

The coupling of the hydrated proton to its first solvation shell.

The Zundel ([Formula: see text]) and Eigen ([Formula: see text]) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit. Embedded in the static environment of the parent Eigen cation, this subunit reproduces the positions and broadenings of its main excess-proton bands. In isolation, its spectrum reverts to the well-known Zundel ion. Hence, the dynamics of this subunit polarized by an environment suffice to explain the spectral signatures and anharmonic couplings of the solvated proton in its first solvation shell.

Sum-of-products form of the molecular electronic Hamiltonian and application within the MCTDH method.

We introduce two different approaches to represent the second-quantized electronic Hamiltonian in a sum-of-products form. These procedures aim at mitigating the quartic scaling of the number of terms in the Hamiltonian with respect to the number of spin orbitals and thus enable applications to larger molecular systems. Here, we describe the application of these approaches within the multi-configuration time-dependent Hartree framework. This approach is applied to the calculation of eigenenergies of LiH and electronic ionization spectrum of H2O.

Suppression and Enhancement of Thermal Chemical Rates in a Cavity.

The observed modification of thermal chemical rates in Fabry-Perot cavities remains a poorly understood effect theoretically. Recent breakthroughs explain some of the observations through the Grote-Hynes theory, where the cavity introduces friction with the reaction coordinate, thus reducing the transmission coefficient and the rate. The regime of rate enhancement, the observed sharp resonances at varying cavity frequencies, and the survival of these effects in the collective regime remain mostly unexplained. In this Letter, we consider the cis-trans isomerization of HONO atomistically using an ab initio potential energy surface. We evaluate the transmission coefficient using the reactive flux method and identify the conditions for rate acceleration. In the underdamped, low-friction regime of the reaction coordinate, the cavity coupling enhances the rate with increasing coupling strength until reaching the Kramers turnover point. Sharp resonances in this regime are related to cavity-enabled energy redistribution channels.

A bosonic perspective on the classical mapping of fermionic quantum dynamics.

We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when evolving from the same initial many-body state. The MM classical mapping is exact for non-interacting bosons, and therefore, it yields the exact time-dependent one-body density for non-interacting fermions as well. Starting from this observation, the MM mapping is compared to different mappings specific for fermionic systems, namely, the spin mapping with and without including a Jordan-Wigner transformation and the Li-Miller mapping (LMM). For non-interacting systems, the inclusion of fermionic anti-symmetry through the Jordan-Wigner transform does not lead to any improvement in the performance of the mappings, and instead, it worsens the classical description. For an interacting impurity model and for models of excitonic energy transfer, the MM and LMM mappings perform similarly, and in some cases, the former outperforms the latter when compared to a full quantum description. The classical mappings are able to capture interference effects, both constructive and destructive, that originate from equivalent energy transfer pathways in the models.

Quantum state tomography of molecules by ultrafast diffraction.

Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments capture only the probability density of the nuclear wavepackets to determine the time-dependent molecular structures, while the full quantum state has not been accessed. Here, we introduce a framework for the preparation and ultrafast coherent diffraction from rotational wave packets of molecules, and we establish a new variant of quantum state tomography for ultrafast electron diffraction to characterize the molecular quantum states. The ability to reconstruct the density matrix, which encodes the amplitude and phase of the wavepacket, for molecules of arbitrary degrees of freedom, will enable the reconstruction of a quantum molecular movie from experimental x-ray or electron diffraction data.

Generalized discrete truncated Wigner approximation for nonadiabatic quantum-classical dynamics.

Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the system's complexity increases, and it is thus desirable to have accurate yet affordable methods for their simulation. Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g., the Meyer-Miller-Stock-Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the identity operator and other operators on an equal footing. As numerical benchmarks on two linear vibronic coupling models and Tully's models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independent of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.

Ultrafast imaging of spontaneous symmetry breaking in a photoionized molecular system.

The Jahn-Teller effect is an essential mechanism of spontaneous symmetry breaking in molecular and solid state systems, and has far-reaching consequences in many fields. Up to now, to directly image the onset of Jahn-Teller symmetry breaking remains unreached. Here we employ ultrafast ion-coincidence Coulomb explosion imaging with sub-10 fs resolution and unambiguously image the ultrafast dynamics of Jahn-Teller deformations of [Formula: see text] cation in symmetry space. It is unraveled that the Jahn-Teller deformation from C3v to C2v geometries takes a characteristic time of 20 ± 7 fs for this system. Classical and quantum molecular dynamics simulations agree well with the measurement, and reveal dynamics for the build-up of the C2v structure involving complex revival process of multiple vibrational pathways of the [Formula: see text] cation.

Ultraviolet Pump-Probe Photodissociation Spectroscopy of Electron-Rotation Coupling in Diatomics.

The electronic angular momentum projected onto the diatomic axis couples with the angular momentum of the nuclei, significantly affecting the rotational motion of the system under electronic excitations by intense lasers. In this letter, we propose a pump-probe photodissociation scheme for an accurate determination of electron-rotation coupling effects induced by the strong fields. As a showcase we study the CH+ molecule excited by a short intense ultraviolet pump pulse to the A1Π state, which triggers coupled rovibrational dynamics. The dynamics is observed by measuring the kinetic energy release and angular resolved photofragmentation upon photodissociation induced by the time-delayed probe pulse populating the C1Σ+ state. Simulations of the rovibrational dynamics unravel clear fingerprints of the electron-rotation coupling effects that can be observed experimentally. The proposed pump-probe scheme opens new possibilities for the study of ultrafast dynamics following valence electronic transitions with current laser technology, and possible applications are also discussed.

Ultrafast Transfer and Transient Entrapment of Photoexcited Mg Electron in Mg@C_{60}.

Electron relaxation is studied in endofullerene Mg@C_{60} after an initial localized photoexcitation in Mg by nonadiabatic molecular dynamics simulations. Two approaches to the electronic structure of the excited electronic states are used: (i) an independent particle approximation based on a density-functional theory description of molecular orbitals and (ii) a configuration-interaction description of the many-body effects. Both methods exhibit similar relaxation times, leading to an ultrafast decay and charge transfer from Mg to C_{60} within tens of femtoseconds. Method (i) further elicits a transient trap of the transferred electron that can delay the electron-hole recombination. Results shall motivate experiments to probe these ultrafast processes by two-photon transient absorption or photoelectron spectroscopy in gas phase, in solution, or as thin films.

On the generation of electronic ring currents under vibronic coupling effects.

We study the generation of electronic ring currents in the presence of nonadiabatic coupling using circularly polarized light. For this, we introduce a solvable model consisting of an electron and a nucleus rotating around a common center and subject to their mutual Coulomb interaction. The simplicity of the model brings to the forefront the non-trivial properties of electronic ring currents in the presence of coupling to the nuclear coordinates and enables the characterization of various limiting situations transparently. Employing this model, we show that vibronic coupling effects play a crucial role even when a single E degenerate eigenstate of the system supports the current. The maximum current of a degenerate eigenstate depends on the strength of the nonadiabatic interactions. In the limit of large nuclear to electronic masses, in which the Born-Oppenheimer approximation becomes exact, constant ring currents and time-averaged oscillatory currents necessarily vanish.