Few-femtosecond electronic and structural rearrangements of CH4+ driven by the Jahn-Teller effect.

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 in 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 CH4+ from the initial Td geometry to a nominal C2v relaxed structure range from 1.85 fs over 10 ± 2 fs to 20 ± 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 Q2 scissoring and Q1 symmetric stretching modes, which dephase in 41 ± 10 fs and 13 ± 3 fs, respectively. Significant structural relaxation is found to take place only along the e-symmetry Q2 mode. These results demonstrate that CH4+ created by ionization of CH4 is best thought of as a highly fluxional species that possesses a long-time-averaged vibrational distribution centered around a D2d structure. The methods demonstrated in our work provide guidelines for the understanding of Jahn-Teller driven non-adiabatic dynamics in other more complex systems.

Ultrafast Molecular Frame Quantum Tomography.

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 nonadiabatic wave packet 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 nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. 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.

Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach.

The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs. To reliably extend machine learning protocols to excited state PESs, the occurrence of seams of conical intersections between adiabatic electronic states must be correctly accounted for. This introduces a serious problem, for at such points, the adiabatic potentials are not differentiable to any order, complicating the application of standard machine learning methods. We show that this issue may be overcome by instead learning the coordinate-dependent coefficients of the characteristic polynomial of a simple decomposition of the potential matrix. We demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.

Time-Resolved X-ray Photoelectron Spectroscopy: Ultrafast Dynamics in CS2 Probed at the S 2p Edge.

Recent developments in X-ray free-electron lasers have enabled a novel site-selective probe of coupled nuclear and electronic dynamics in photoexcited molecules, time-resolved X-ray photoelectron spectroscopy (TRXPS). We present results from a joint experimental and theoretical TRXPS study of the well-characterized ultraviolet photodissociation of CS2, a prototypical system for understanding non-adiabatic dynamics. These results demonstrate that the sulfur 2p binding energy is sensitive to changes in the nuclear structure following photoexcitation, which ultimately leads to dissociation into CS and S photoproducts. We are able to assign the main X-ray spectroscopic features to the CS and S products via comparison to a first-principles determination of the TRXPS based on ab initio multiple-spawning simulations. Our results demonstrate the use of TRXPS as a local probe of complex ultrafast photodissociation dynamics involving multimodal vibrational coupling, nonradiative transitions between electronic states, and multiple final product channels.

A perturbative approximation to DFT/MRCI: DFT/MRCI(2).

We introduce a perturbative approximation to the combined density functional theory and multireference configuration interaction (DFT/MRCI) approach. The method, termed DFT/MRCI(2), results from the application of quasi-degenerate perturbation theory (QDPT) and the Epstein-Nesbet partitioning to the DFT/MRCI Hamiltonian matrix. The application of QDPT obviates the need to diagonalize the large DFT/MRCI Hamiltonian; electronic energies are instead obtained as the eigenvalues of a small effective Hamiltonian, affording an orders of magnitude savings in the computational cost. Most importantly, the DFT/MRCI(2) approximation is found to be of excellent accuracy, furnishing excitation energies with a root mean squared deviation from the canonical DFT/MRCI values of less than 0.03 eV for an extensive test set of organic molecules.

Time-resolved photoelectron spectroscopy: the continuing evolution of a mature technique.

Time-resolved photoelectron spectroscopy (TRPES) has become one of the most widespread techniques for probing nonadiabatic dynamics in the excited electronic states of molecules. Furthermore, the complementary development of ab initio approaches for the simulation of TRPES signals has enabled the interpretation of these transient spectra in terms of underlying coupled electronic-nuclear dynamics. In this perspective, we discuss the current state-of-the-art approaches, including efforts to push femtosecond pulses into vacuum ultraviolet and soft X-ray regimes as well as the utilization of novel polarizations to use time-resolved optical activity as a probe of nonadiabatic dynamics. We close this perspective with a forward-looking prospectus on the new areas of application for this technique.

A Comparison of Partial Atomic Charges for Electronically Excited States.

Partial atomic charges are a useful and intuitive concept for understanding molecular properties and chemical reaction mechanisms, showing how changes in molecular geometry can affect the flow of electronic charge within a molecule. However, the use of partial atomic charges remains relatively uncommon in the characterization of excited-state electronic structure. Here, we show how well-established partial atomic charge methods perform for interatomic, intermolecular, and interbond electron transfer in electronically excited states. Our results demonstrate the utility of real-space partial atomic charges for interpreting the electronic structures that arise in excited-state processes. Furthermore, we show how this analysis can be used to demonstrate that analogous electronic structures arise near photochemically relevant conical intersection regions for several conjugated polyenes. On the basis of our analysis, we find that charges computed using the iterative Hirshfeld approach provide results which are consistent with chemical intuition and are transferable between homologous molecular systems.

Electronic relaxation and dissociation dynamics in formaldehyde: pump wavelength dependence.

The effect of the incident UV pump wavelength on the subsequent excited state dynamics, electronic relaxation, and ultimate dissociation of formaldehyde is studied using first principles simulation and Coulomb explosion imaging (CEI) experiments. Transitions in a vibronic progression in the à ← X̃ absorption band are systematically prepared using a tunable UV source which generates pulses centered at 304, 314, 329, and 337 nm. We find, both via ab initio simulation and experimental results, that the rate of excited state decay and subsequent dissociation displays a prominent dependence on which vibronic transition in the absorption band is prepared by the pump. Our simulations predict that nonadiabatic transition rates and dissociation yields will increase by a factor of >100 as the pump wavelength is decreased from 337 to 304 nm. The experimental results and theoretical simulations are in broad agreement and both indicate that the dissociation rate plateaus rapidly after ≈2 ps following an ultrafast sub-ps rise.

Resolving competing conical intersection pathways: time-resolved X-ray absorption spectroscopy of trans-1,3-butadiene.

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.

Removing the Deadwood from DFT/MRCI Wave Functions: The p-DFT/MRCI Method.

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.

Vacuum Ultraviolet Excited State Dynamics of the Smallest Ketone: Acetone.

We combined tunable vacuum-ultraviolet time-resolved photoelectron spectroscopy (VUV-TRPES) with high-level quantum dynamics simulations to disentangle multistate Rydberg-valence dynamics in acetone. A femtosecond 8.09 eV pump pulse was tuned to the sharp origin of the A1(n3dyz) band. The ensuing dynamics were tracked with a femtosecond 6.18 eV probe pulse, permitting TRPES of multiple excited Rydberg and valence states. Quantum dynamics simulations reveal coherent multistate Rydberg-valence dynamics, precluding simple kinetic modeling of the TRPES spectrum. Unambiguous assignment of all involved Rydberg states was enabled via the simulation of their photoelectron spectra. The A1(ππ*) state, although strongly participating, is likely undetectable with probe photon energies ≤8 eV and a key intermediate, the A2(nπ*) state, is detected here for the first time. Our dynamics modeling rationalizes the temporal behavior of all photoelectron transients, allowing us to propose a mechanism for VUV-excited dynamics in acetone which confers a key role to the A2(nπ*) state.

Unmasking the cis-Stilbene Phantom State via Vacuum Ultraviolet Time-Resolved Photoelectron Spectroscopy and Ab Initio Multiple Spawning.

We present the first vacuum ultraviolet time-resolved photoelectron spectroscopy (VUV-TRPES) study of photoisomerization dynamics in the paradigmatic molecule cis-stilbene. A key reaction intermediate in its dynamics, known as the phantom state, has often been invoked but never directly detected in the gas phase. We report direct spectral signatures of the phantom state in isolated cis-stilbene, observed and characterized through a combination of VUV-TRPES and ab initio multiple spawning (AIMS) nonadiabatic dynamics simulations of the channel-resolved observable. The high VUV probe photon energy tracks the complete excited-state dynamics via multiple photoionization channels, from initial excitation to its return to the "hot" ground state. The TRPES was compared with AIMS simulations of the dynamics from initial excitation, to the phantom-state intermediate (an S1 minimum), through to the ultimate electronic decay to the ground state. This combination revealed the unique spectral signatures and time-dependent dynamics of the phantom-state intermediate, permitting us to report here its direct observation.

A quantum molecular movie: polyad predissociation dynamics in the VUV excited 3pσ2Σu state of NO2.

The optical formation of coherent superposition states, a wavepacket, can allow the study of zeroth-order states, the evolution of which exhibit structural and electronic changes as a function of time: this leads to the notion of a molecular movie. Intramolecular vibrational energy redistribution, due to anharmonic coupling between modes, is the molecular movie considered here. There is no guarantee, however, that the formed superposition will behave semi-classically (e.g. Gaussian wavepacket dynamics) or even as an intuitively useful zeroth-order state. Here we present time-resolved photoelectron spectroscopy (TRPES) studies of an electronically excited triatomic molecule wherein the vibrational dynamics must be treated quantum mechanically and the simple picture of population flow between coupled normal modes fails. Specifically, we report on vibronic wavepacket dynamics in the zeroth-order 3pσ2Σu Rydberg state of NO2. This wavepacket exemplifies two general features of excited state dynamics in polyatomic molecules: anharmonic multimodal vibrational coupling (forming polyads); nonadiabatic coupling between nuclear and electronic coordinates, leading to predissociation. The latter suggests that the polyad vibrational states in the zeroth-order 3p Rydberg manifold are quasi-bound and best understood to be scattering resonances. We observed a rapid dephasing of an initially prepared 'bright' valence state into the relatively long-lived 3p Rydberg state whose multimodal vibrational dynamics and decay we monitor as a function of time. Our quantum simulations, based on an effective spectroscopic Hamiltonian, describe the essential features of the multimodal Fermi resonance-driven vibrational dynamics in the 3p state. We also present evidence of polyad-specificity in the state-dependent predissociation rates, leading to free atomic and molecular fragments. We emphasize that a quantum molecular movie is required to visualize wavepacket dynamics in the 3pσ2Σu Rydberg state of NO2.

Sub-7-femtosecond conical-intersection dynamics probed at the carbon K-edge.

Conical intersections allow electronically excited molecules to return to their electronic ground state. Here, we observe the fastest electronic relaxation dynamics measured to date by extending attosecond transient-absorption spectroscopy (ATAS) to the carbon K-edge. We selectively launch wave packets in the two lowest electronic states (D0 and D1) of C2H4 + The electronic D1 → D0 relaxation takes place with a short time constant of 6.8 ± 0.2 femtoseconds. The electronic-state switching is directly visualized in ATAS owing to a spectral separation of the D1 and D0 bands caused by electron correlation. Multidimensional structural dynamics of the molecule are simultaneously observed. Our results demonstrate the capability to resolve the fastest electronic and structural dynamics in the broad class of organic molecules. They show that electronic relaxation in the prototypical organic chromophore can take place within less than a single vibrational period.

Directing excited state dynamics via chemical substitution: A systematic study of π-donors and π-acceptors at a carbon-carbon double bond.

Functional group substituents are a ubiquitous tool in ground-state organic chemistry often employed to fine-tune chemical properties and obtain desired chemical reaction outcomes. Their effect on photoexcited electronic states, however, remains poorly understood. To help build an intuition for these effects, we have studied ethylene, substituted with electron acceptor (cyano) and/or electron donor (methoxy) substituents, both theoretically and experimentally: using ab initio quantum molecular dynamics and time-resolved photoelectron spectroscopy. Our results show the consistent trend that photo-induced ethylenic dynamics is primarily localized to the carbon with the greater electron density. For doubly substituted ethylenes, the trend is additive when both substituents are located on opposite carbons, whereas the methoxy group (in concert with steric effects) dominates when both substituents are located on a single carbon atom. These results point to the development of rules for structure-dynamics correlations; in this case, a novel mechanistic ultrafast photochemistry for conjugated carbon chains employing long-established chemical concepts.

Capturing roaming molecular fragments in real time.

Since the discovery of roaming as an alternative molecular dissociation pathway in formaldehyde (H2CO), it has been indirectly observed in numerous molecules. The phenomenon describes a frustrated dissociation with fragments roaming at relatively large interatomic distances rather than following conventional transition-state dissociation; incipient radicals from the parent molecule self-react to form molecular products. Roaming has been identified spectroscopically through static product channel-resolved measurements, but not in real-time observations of the roaming fragment itself. Using time-resolved Coulomb explosion imaging (CEI), we directly imaged individual "roamers" on ultrafast time scales in the prototypical formaldehyde dissociation reaction. Using high-level first-principles simulations of all critical experimental steps, distinctive roaming signatures were identified. These were rendered observable by extracting rare stochastic events out of an overwhelming background using the highly sensitive CEI method.

Mechanistic Insight into Bis(amino) Copper Formate Thermochemistry for Conductive Molecular Ink Design.

Increasing attention has been given to amine-copper formate complexes for their use as low-cost printable conductive inks. The structure of amine ligands coordinated to copper centers has been reported to dictate the properties of copper molecular inks, such as stability and printability, thereby influencing the copper reduction pathway during the thermolysis. Yet, the underlying mechanism by which formate is oxidized when complexed with amine ligands is still not fully understood. Here, we propose a mechanistic pathway of copper formate dehydrogenation and decarboxylation and examine the critical role that amine ligands play in their thermal decomposition by employing first-principles electronic structure computations and experimental analyses of thermolysis reactions. Based on the computational characterization of the relevant reaction pathways for a number of primary and secondary amines as well as pyridine ligand complexes, we are the first to show that the hydrogen bonds formed between the amine ligand and formate are the key factors governing the activation energy, providing a design principle for the synthesis of organic ligands that can tune the height of the reaction barriers of the dehydrogenation and decarboxylation reactions. The calculations, confirmed by NMR studies, show that the reduction of Cu(II) to Cu(I) occurs in concert with the release of H2 via the dimerization of Cu(II) hydride. This result suggests that the monomeric elimination of H2 is not favorable for the Cu(II) to Cu(I) reduction and thus identifies dimeric amino copper formate as an important intermediate for copper reduction whose thermodynamic stabilities are also dictated by the nature of the amine ligands.

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.

Substituent effects on nonadiabatic excited state dynamics: Inertial, steric, and electronic effects in methylated butadienes.

The photochemical dynamics of double-bond-containing hydrocarbons is exemplified by the smallest alkenes, ethylene and butadiene. Chemical substituents can alter both decay timescales and photoproducts through a combination of inertial effects due to substituent mass, steric effects due to substituent size, and electronic (or potential) effects due to perturbative changes to the electronic potential energy surface. Here, we demonstrate the interplay of different substituent effects on 1,3-butadiene and its methylated derivatives using a combination of ab initio simulation of nonadiabatic dynamics and time-resolved photoelectron spectroscopy. The purely inertial effects of methyl substitution are simulated through the use of mass 15 "heavy-hydrogen" atoms. As expected from both inertial and electronic influences, the excited-state dynamics is dominated by pyramidalization at the unsubstituted carbon sites. Although the electronic effects of methyl group substitution are weak, they alter both decay timescales and branching ratios by influencing the initial path taken by the excited wavepacket following photoexcitation.

Electron transfer in photoexcited pyrrole dimers.

Following on from previous experimental and theoretical work [Neville et al., Nat. Commun. 7, 11357 (2016)], we report the results of a combined electronic structure theory and quantum dynamics study of the excited state dynamics of the pyrrole dimer following excitation to its first two excited states. Employing an exciton-based analysis of the Ã(π3s/σ*) and B̃(π3s/3p/σ*) states, we identify an excited-state electron transfer pathway involving the coupling of the Ã(π3s/σ*) and B̃(π3s/3p/σ*) states and driven by N-H dissociation in the B̃(π3s/3p/σ*) state. This electron transfer mechanism is found to be mediated by vibronic coupling of the B̃ state, which has a mixed π3s/3p Rydberg character at the Franck-Condon point, to a high-lying charge transfer state of the πσ* character by the N-H stretch coordinate. Motivated by these results, quantum dynamics simulations of the excited-state dynamics of the pyrrole dimer are performed using the multiconfigurational time-dependent Hartree method and a newly developed model Hamiltonian. It is predicted that the newly identified electron transfer pathway will be open following excitation to both the Ã(π3s/σ*) and B̃(π3s/3p/σ*) states and may be the dominant relaxation pathway in the latter case.