The Ring-Closing Reaction of Cyclopentadiene Probed with Ultrafast X-ray Scattering.

The dynamics of cyclopentadiene (CP) following optical excitation at 243 nm was investigated by time-resolved pump-probe X-ray scattering using 16.2 keV X-rays at the Linac Coherent Light Source (LCLS). We present the first ultrafast structural evidence that the reaction leads directly to the formation of bicyclo[2.1.0]pentene (BP), a strained molecule with three- and four-membered rings. The bicyclic compound decays via a thermal backreaction to the vibrationally hot CP with a time constant of 21 ± 3 ps. A minor channel leads to ring-opened structures on a subpicosecond time scale.

The contribution of Compton ionization to ultrafast x-ray scattering.

We investigate the role of Compton ionization in ultrafast non-resonant x-ray scattering using a molecular model system, which includes the ionization continuum via an orthonormalized plane wave ansatz. Elastic and inelastic components of the scattering signal, as well as coherent-mixed scattering that arises from electron dynamics, are calculated. By virtue of a near-quantitative distinction between scattering related to electronic transitions into bound and continuum states, we demonstrate how Compton ionization contributes to the coherent-mixed component. Analogous to inelastic scattering, the contribution to the coherent-mixed signal is significant and particularly manifests at intermediate and high-momentum transfers. Strikingly, for molecules with inversion symmetry, the exclusion of bound or continuum transitions may lead to the prediction of spurious coherent-mixed signals. We conclude that qualitative and quantitative accuracies of predicted scattering signals on detectors without energy resolution require that elements of the two-electron density operator are used. This approach inherently accounts for all accessible electronic transitions, including ionization.

Efficient Computation of Two-Electron Reduced Density Matrices via Selected Configuration Interaction.

We create an approach to efficiently calculate two-electron reduced density matrices (2-RDMs) using selected configuration interaction wavefunctions. This is demonstrated using the specific example of Monte Carlo configuration interaction (MCCI). The computation of the 2-RDMs is accelerated by using ideas from fast implementations of full configuration interaction (FCI) and recent advances in implementing the Slater-Condon rules using hardware bitwise operations. This method enables a comparison of MCCI and truncated CI 2-RDMs with FCI values for a range of molecules, which includes stretched bonds and excited states. The accuracy in energies, wavefunctions, and 2-RDMs is seen to exhibit a similar behavior. We find that MCCI can reach sufficient accuracy of the 2-RDM using significantly fewer configurations than truncated CI, particularly for systems with strong multireference character.

Towards high-resolution X-ray scattering as a probe of electron correlation.

X-ray scattering cross sections are calculated using a range of increasingly correlated methods: Hartree-Fock (HF), complete active space self-consistent field (CASSCF), Monte Carlo configuration interaction (MCCI), and full configuration interaction (FCI). Even for the seemingly straightforward case of ground state Ne, the accuracy of the total scattering is significantly better with a more correlated wavefunction. Scanning the bond distance in ground state CO shows that the total scattering signal tracks the multireference character. We examine the convergence of the elastic, inelastic, and total scattering of O3. Overall, the inelastic and total components are found to be the most sensitive to the strength of correlation. Our results suggest that highly accurate measurement of X-ray scattering could provide a sensitive probe of pair-wise correlation between electrons.

Observation of the molecular response to light upon photoexcitation.

When a molecule interacts with light, its electrons can absorb energy from the electromagnetic field by rapidly rearranging their positions. This constitutes the first step of photochemical and photophysical processes that include primary events in human vision and photosynthesis. Here, we report the direct measurement of the initial redistribution of electron density when the molecule 1,3-cyclohexadiene (CHD) is optically excited. Our experiments exploit the intense, ultrashort hard x-ray pulses of the Linac Coherent Light Source (LCLS) to map the change in electron density using ultrafast x-ray scattering. The nature of the excited electronic state is identified with excellent spatial resolution and in good agreement with theoretical predictions. The excited state electron density distributions are thus amenable to direct experimental observation.

The Second-Order-Polarization-Propagator-Approximation (SOPPA) in a four-component spinor basis.

A theoretical framework for understanding molecular structures is crucial for the development of new technologies such as catalysts or solar cells. Apart from electronic excitation energies, however, only spectroscopic properties of molecules consisting of lighter elements can be computationally described at a high level of theory today since heavy elements require a relativistic framework, and thus far, most methods have only been derived in a non-relativistic framework. Important new technologies such as those mentioned above require molecules that contain heavier elements, and hence, there is a great need for the development of relativistic computational methods at a higher level of accuracy. Here, the Second-Order-Polarization-Propagator-Approximation (SOPPA), which has proven to be very successful in the non-relativistic case, is adapted to a relativistic framework. The equations for SOPPA are presented in their most general form, i.e., in a non-canonical spin-orbital basis, which can be reduced to the canonical case, and the expressions needed for a relativistic four-component SOPPA are obtained. The equations are one-index transformed, giving more compact expressions that correspond to those already available for the four-component RPA. The equations are ready for implementation in a four-component quantum chemistry program, which will allow both linear response properties and excitation energies to be calculated relativistically at the SOPPA level.

Excited Electronic States in Total Isotropic Scattering from Molecules.

Ultrafast X-ray scattering experiments are routinely analyzed in terms of the isotropic scattering component. Here, we present an analytical method for calculating total isotropic scattering for ground and excited electronic states directly from ab initio two-electron densities. The method is generalized to calculate the isotropic elastic, inelastic, and coherent mixed scattering. The presented computational results focus on the potential for differentiating between electronic states and the decomposition of the total scattering in terms of elastic and inelastic scattering. For the specific example of the umbrella motion in the first excited state of ammonia, we show that the redistribution of electron density along this coordinate leaves a comparably constant fingerprint in the total scattering that is similar in magnitude to the effect of changes in molecular geometry.

Theory of ultrafast x-ray scattering by molecules in the gas phase.

We recast existing theory of ultrafast time-resolved x-ray scattering by molecules in the gas phase into a unified and coherent framework based on first-order time-dependent perturbation theory and quantum electrodynamics. The effect of the detection window is analyzed in detail and the contributions to the total scattering signal are discussed. This includes the coherent mixed component caused by interference between scattering amplitudes from different electronic states. A new, detailed, and fully converged simulation of ultrafast total x-ray scattering by excited H2 molecules illustrates the theory and demonstrates that the inelastic component can contribute strongly to the total difference scattering signal, i.e., on the same order of magnitude as the elastic component.

Single-Molecule Detection of a Fluorescent Nucleobase Analogue via Multiphoton Excitation.

The ability to routinely detect fluorescent nucleobase analogues at the single-molecule level would create a wealth of opportunities to study nucleic acids. We report the multiphoton-induced fluorescence and single-molecule detection of a dimethylamine-substituted extended-6-aza-uridine (DMAthaU). We show that DMAthaU can exist in a highly fluorescent form, emitting strongly in the visible region (470-560 nm). Using pulse-shaped broadband Ti:sapphire laser excitation, DMAthaU undergoes two-photon (2P) absorption at low excitation powers, switching to three-photon (3P) absorption at high incident intensity. The assignment of a 3P process is supported by cubic response calculations. Under both 2P and 3P excitation, the single-molecule brightness was over an order of magnitude higher than reported previously for any fluorescent base analogue, which facilitated the first single-molecule detection of an emissive nucleoside with multiphoton excitation.

Electronic Coherence in Ultrafast X-Ray Scattering from Molecular Wave Packets.

Simulations of nonresonant ultrafast x-ray scattering from a molecular wave packet in H_{2} are used to examine and classify the components that contribute to the total scattering signal. The elastic component, which can be used to determine the structural dynamics of the molecule, is also found to carry a strong signature of an adiabatic electron transfer that occurs in the simulated molecule. The inelastic component, frequently assumed to be constant, is found to change with the geometry of the molecule. Finally, a coherent mixed component due to interferences between different inelastic transitions is identified and shown to provide a direct probe of transient electronic coherences.

How To Excite Nuclear Wavepackets into Electronically Degenerate States in Spin-Vibronic Quantum Dynamics Simulations.

The excited-state dynamics of two functional Fe-carbene complexes, [Fe(bmip)2]2+ (bmip = 2,6-bis(3-methyl-imidazole-1-ylidene)-pyridine) and [Fe(btbip)2]2+ (btbip = 2,6-bis(3- tert-butyl-imidazole-1-ylidene)pyridine), are studied using the spin-vibronic model. In contrast to the usual projection of the ground state nuclear wave function onto an excited state surface, the dynamics are initiated by an explicit interaction term between the external time-dependent electric field (laser pulse) and the transition dipole moment of the molecule. The results show that the spin-vibronic model, as constructed directly from electronic structure calculations, exhibits erroneous, polarization-dependent relaxation dynamics stemming from artificial interference of coupled relaxation pathways. This is due to the lack of rotational invariance in the description of excitation into degenerate states. We introduce and discuss a correction using the spherical basis and complex transition dipole moments. This modification in the interaction Hamiltonian leads to rotationally invariant excitation and produces polarization-independent population dynamics.

Time-resolved X-ray scattering by electronic wave packets: analytic solutions to the hydrogen atom.

Modern pulsed X-ray sources permit time-dependent measurements of dynamical changes in atoms and molecules via non-resonant scattering. The planning, analysis, and interpretation of such experiments, however, require a firm and elaborated theoretical framework. This paper provides a detailed description of time-resolved X-ray scattering by non-stationary electronic wave packets in atomic systems. A consistent application of the Waller-Hartree approximation is discussed and different contributions to the total differential scattering signal are identified and interpreted. Moreover, it is demonstrated how the scattering signal of wave packets in the hydrogen atom can be expressed analytically. This permits simulations without numerical integration and establishes a benchmark for both efficiency and accuracy. Based on that, scattering patterns of an exemplary wave packet in the hydrogen atom are computed for different points in time. In doing so, distinct features of time-resolved X-ray scattering by non-stationary electronic wave packets are illustrated and accentuated in greater detail than it has been done before.

Azadioxatriangulenium and Diazaoxatriangulenium: Quantum Yields and Fundamental Photophysical Properties.

Over the last decade, we have investigated and exploited the photophysical properties of triangulenium dyes. Azadioxatriangulenium (ADOTA) and diazaoxatriangulenium (DAOTA), in particular, have features that make them useful in various fluorescence-based technologies (e.g., bioimaging). Through our work with ADOTA and DAOTA, we became aware that the reported fluorescence quantum yields (ϕfl) for these dyes are lower than their actual values. We thus set out to further investigate the fundamental structure-property relationships in these unique conjugated cationic systems. The nonradiative processes in the systems were explored using transient absorption spectroscopy and time-resolved emission spectroscopy in combination with computational chemistry. The influence of molecular oxygen on the fluorescence properties was explored, and the singlet oxygen sensitization efficiencies of ADOTA and DAOTA were determined. We conclude that, for these dyes, the amount of nonradiative deactivation of the first excited singlet state (S1) of the azaoxa-triangulenium fluorophores is low, that the rate of such deactivation is slower than what is observed in common cationic dyes, that there are no observable radiative transitions occurring from the first excited triplet state (T1) of these dyes, and that the efficiency of sensitized singlet oxygen production is low (Ï•Δ ≤ 10%). These photophysical results provide a solid base upon which technological applications of these fluorescent dyes can be built.