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Charge transfer is a fundamental phenomenon in biology and chemistry, and involves the movement of charge through a system driven by nuclear dynamics. Because of the involvement of nuclear motion, it is generally assumed that charge transfer will occur on a time-scale of some few tens-to-hundreds of femtoseconds. Using the example of ethylene excited to its $1s\pi^{*}$ manifold, we demonstrate that ultrafast, few-femtosecond core-level charge transfer may occur following core-excitation, driven by the formation of electronic coherences by non-adiabatic dynamics. Here, transfer of core-electron density from one side of the molecule to the other is driven by a breakdown of the Born-Oppenheimer approximation, and results in core-hole localisation occuring within 5 fs, followed by core-hole delocalisation, all within the Auger decay window. These results serve to demonstrate that ultra-fast core-level charge transfer driven by nuclear dynamics may occur on the same timescale as purely electronic, i.e., charge migration, dynamics following core-excitation.

Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography: the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data. Here, we explore the application of MaxEnt-based QST on photoexcited ammonia, necessitating the operator form of observables specific to the performed measurements. We present two methodologies for constructing these operators: one leveraging Molecular Angular Distribution Moments (MADMs) which accurately capture the orientation-dependent vibronic dynamics of molecules; and another utilizing Angular Momentum Coherence Operators to construct measurement operators for the full rovibronic density matrix in the symmetric top basis. A key revelation of our study is the direct link between Lagrange multipliers in the MaxEnt formalism and the unique set of MADMs. Furthermore, we achieve a groundbreaking milestone by constructing, for the first time, the entanglement entropy of the electronic subsystem: a metric that was previously inaccessible. The entropy vividly reveals and quantifies the effects of coupling between the excited electron and nuclear degrees of freedom. Consequently, our findings open new avenues for research in ultrafast molecular spectroscopy within the broader domain of quantum information science., Comment: 18 pages, 4 figures

The Jahn-Teller effect (JTE) is central to the understanding of the physical and chemical properties of a broad variety of molecules and materials. Whereas the manifestations of the JTE on stationary properties of matter are relatively well studied, the study of JTE-induced dynamics is still in its infancy, largely owing to its ultrafast and non-adiabatic nature. For example, the time scales reported for the distortion of CH$_4^+$ from the initial $T_{\rm d}$ geometry to a nominal $C_{\rm 2v}$ relaxed structure range from 1.85~fs over 10$\pm$2~fs to 20$\pm$7~fs. Here, by combining element-specific attosecond transient-absorption spectroscopy and quantum-dynamics simulations, we show that the initial electronic relaxation occurs within 5~fs and that the subsequent nuclear dynamics are dominated by the $Q_2$ scissoring and $Q_1$ symmetric stretching modes, which dephase in 41$\pm$10~fs and 13$\pm$3~fs, respectively. Significant structural relaxation is found to take place only along the e-symmetry $Q_2$ mode. These results demonstrate that CH$_4^+$ created by ionization of CH$_4$ is best thought of as a highly fluxional species that possesses a long-time-averaged vibrational distribution centered around a $D_{\rm 2d}$ structure. The methods demonstrated in our work provide guidelines for the understanding of Jahn-Teller driven non-adiabatic dynamics in other, more complex systems., Comment: 28 pages, 10 figures

We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically non-adiabatic wavepacket in ammonia (NH$_3$). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH$_3$, we observe that electronic coherences are induced by nuclear dynamics which non-adiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is non-adiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer time scales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

In most cases the ultrafast dynamics of resonantly excited molecules are considered, and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here we provide a formalism in terms of a lab frame density matrix which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences which are potentially experimentally accessible are rejected by the orientation-averaged reduced vibronic density matrix. Instead, Molecular Angular Distribution Moments (MADMs) are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography, and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.

We introduce a perturbative approximation to the combined density functional theory and multireference configuration interaction (DFT/MRCI) method. The method, termed DFT/MRCI(2), results from the application of quasi-degenerate perturbation theory and the Epstein-Nesbet partitioning of the DFT/MRCI Hamiltonian matrix. This results in the replacement of the diagonalization of the large DFT/MRCI Hamiltonian with that of a small effective Hamiltonian, and affords orders of magnitude savings in terms of computational cost. Moreover, the DFT/MRCI(2) approximation is found to be of excellent accuracy, furnishing excitation energies with a root mean squared deviation from the DFT/MRCI values of less than 0.03 eV for an extensive test set of organic molecules.

Time-resolved X-ray absorption spectroscopy is emerging as a uniquely powerful tool to probe coupled electronic-nuclear dynamics in photo-excited molecules. Theoretical studies to date have established that time-resolved X-ray absorption spectroscopy is an atom-specific probe of excited-state wave packet passage through a seam of conical intersections (CIs). However, in many molecular systems, there are competing dynamical pathways involving CIs of different electronic and nuclear character. Discerning these pathways remains an important challenge. Here, we demonstrate that time-resolved X-ray absorption spectroscopy (TRXAS) has the potential to resolve competing channels in excited-state non-adiabatic dynamics. Using the example of 1,3-butadiene, we show how TRXAS discerns the different electronic structures associated with passage through multiple conical intersections. Trans 1,3-butadiene exhibits a branching between polarized and radicaloid pathways associated with ethylenic "twisted-pyramidalized" and excited-state cis-trans isomerization dynamics, respectively. The differing electronic structures along these pathways give rise to different XAS signals, indicating the possibility of resolving them. Furthermore, this indicates that XAS, and other core-level spectroscopic techniques, offer the appealing prospect of directly probing the effects of selective chemical substitution and its ability to affect chemical control over excited-state molecular dynamics.

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein-Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the accuracy of the original DFT/MRCI method.

The direct observation of non-adiabatic dynamics at conical intersections is a long-standing goal of molecular physics. Novel time-resolved spectroscopies have been proposed which are sensitive to electronic coherences induced by the passage of an excited state wavepacket through a region of conical intersection. Here we demonstrate that inclusion of the geometric phase effect, and its manifestations, is essential for the correct description of the transient electronic coherences that may or may not develop. For electronic states of different symmetry, electronic coherences are suppressed by the geometric phase. Conversely, for states of the same symmetry, appreciable electronic coherences are possible, but their magnitude depends on both the topography of and direction of approach to the conical intersection. These general results have consequences for all studies of electronic coherences at conical intersections., Comment: 7 pages, 3 figures

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 diabatisation strategies are not applicable. We demonstrate, however, that diabatic wavefunctions and potentials can be calculated at the DFT/MRCI level of theory using a propagative variant of the block diagonalisation diabatisation method (P-BDD). The proposed procedure is validated {\it 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.

Ongoing developments in ultrafast X-ray sources offer powerful new means of probing the com- plex non-adiabatically coupled structural and electronic dynamics of photoexcited molecules. These non-Born-Oppenheimer effects are governed by general electronic degeneracies termed conical in- tersections which play a key role, analogous to that of a transition state, in the electronic-nuclear dynamics of excited molecules. Using high level ab initio quantum dynamics simulations, we studied time-resolved X-ray absorption and photoelectron spectroscopy (TRXAS and TRXPS, respectively) of the prototypical unsaturated organic chromophore, ethylene, following excitation to its S2 state. The TRXAS in particular is highly sensitive to all aspects of the ensuing dynamics. These X-ray spectroscopies provide a clear signature of the wavepacket dynamics near conical intersections, related to charge localization effects driven by the nuclear dynamics. Given the ubiquity of charge localization in excited state dynamics, we believe that ultrafast X-ray spectroscopies offer a unique and powerful route to the direct observation of dynamics around conical intersections., Comment: 5 pages, 4 figures