Strong Anisotropy in Liquid Water upon Librational Excitation Using Terahertz Laser Fields.

Tracking the excitation of water molecules in the homogeneous liquid is challenging due to the ultrafast dissipation of rotational excitation energy through the hydrogen-bonded network. Here we demonstrate strong transient anisotropy of liquid water through librational excitation using single-color pump-probe experiments at 12.3 THz. We deduce a third-order response of χ3 exceeding previously reported values in the optical range by 3 orders of magnitude. Using a theory that replaces the nonlinear response with a material property amenable to molecular dynamics simulation, we show that the rotationally damped motion of water molecules in the librational band is resonantly driven at this frequency, which could explain the enhancement of the anisotropy in the liquid by the external terahertz field. By addition of salt (MgSO4), the hydration water is instead dominated by the local electric field of the ions, resulting in reduction of water molecules that can be dynamically perturbed by THz pulses.

Accurate prediction of chemical shifts for aqueous protein structure on "Real World" data.

Here we report a new machine learning algorithm for protein chemical shift prediction that outperforms existing chemical shift calculators on realistic data that is not heavily curated, nor eliminates test predictions ad hoc. Our UCBShift predictor implements two modules: a transfer prediction module that employs both sequence and structural alignment to select reference candidates for experimental chemical shift replication, and a redesigned machine learning module based on random forest regression which utilizes more, and more carefully curated, feature extracted data. When combined together, this new predictor achieves state-of-the-art accuracy for predicting chemical shifts on a randomly selected dataset without careful curation, with root-mean-square errors of 0.31 ppm for amide hydrogens, 0.19 ppm for Hα, 0.84 ppm for C', 0.81 ppm for Cα, 1.00 ppm for Cß, and 1.81 ppm for N. When similar sequences or structurally related proteins are available, UCBShift shows superior native state selection from misfolded decoy sets compared to SPARTA+ and SHIFTX2, and even without homology we exceed current prediction accuracy of all other popular chemical shift predictors.

Multiresolution 3D-DenseNet for Chemical Shift Prediction in NMR Crystallography.

We have developed a deep learning algorithm for chemical shift prediction for atoms in molecular crystals that utilizes an atom-centered Gaussian density model for the 3D data representation of a molecule. We define multiple channels that describe different spatial resolutions for each atom type that utilizes cropping, pooling, and concatenation to create a multiresolution 3D-DenseNet architecture (MR-3D-DenseNet). Because the training and testing time scale linearly with the number of samples, the MR-3D-DenseNet can exploit data augmentation that takes into account the property of rotational invariance of the chemical shifts, thereby also increasing the size of the training data set by an order of magnitude without additional cost. We obtain very good agreement for 13C, 15N, and 17O chemical shifts when compared to ab initio quantum chemistry methods, with the highest accuracy found for 1H chemical shifts that is comparable to the error between the ab initio results and experimental measurements. Principal component analysis (PCA) is used to both understand these greatly improved predictions for 1H , as well as indicating that chemical shift prediction for 13C, 15N, and 17O, which have far fewer training environments than the 1H atom type, will improve once more unique training samples are made available to exploit the deep network architecture.

Monitoring Ultrafast Spin Crossover Intermediates in an Iron(II) Complex by Broad Band Stimulated X-ray Raman Spectroscopy.

The photoinduced spin crossover dynamics of transition metal complexes is of fundamental scientific importance and is used for sensor device applications and solar energy harvesting. Current X-ray and optical spectroscopy experiments for [FeII(bpy)3], an archetypal earth-abundant metal complex, show conflicting spin dynamics. We have simulated the broad band transient X-ray absorption and hybrid (broad + narrow band) X-ray stimulated Raman signals at the N and Fe K-edges of the key excited state intermediates involved in the spin crossover process of this complex. We find that these signals are much more sensitive to electron and spin populations than transition absorption and may be useful in the design of photovoltaic and artificial photosynthetic systems.

Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction.

Ultrafast time-resolved X-ray scattering, made possible by free-electron laser sources, provides a wealth of information about electronic and nuclear dynamical processes in molecules. The technique provides stroboscopic snapshots of the time-dependent electronic charge density traditionally used in structure determination and reflects the interplay of elastic and inelastic processes, nonadiabatic dynamics, and electronic populations and coherences. The various contributions to ultrafast off-resonant diffraction from populations and coherences of molecules in crystals, in the gas phase, or from single molecules are surveyed for core-resonant and off-resonant diffraction. Single-molecule [Formula: see text] scaling and two-molecule [Formula: see text] scaling contributions, where N is the number of active molecules, are compared. Simulations are presented for the excited-state nonadiabatic dynamics of the electron harpooning at the avoided crossing in NaF. We show how a class of multiple diffraction signals from a single molecule can reveal charge-density fluctuations through multidimensional correlation functions of the charge density.

X-Ray Sum Frequency Diffraction for Direct Imaging of Ultrafast Electron Dynamics.

X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved x-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear x-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation carried out with a visible pump and a broadband x-ray diffraction pulse, yields snapshots of the transition charge densities, which represent the electron density variations upon optical excitation. The technique is illustrated by ab initio simulations of transition charge density imaging for the optically induced electronic dynamics in a donor or acceptor substituted stilbene.

Linear and nonlinear frequency- and time-domain spectroscopy with multiple frequency combs.

Two techniques that employ equally spaced trains of optical pulses to map an optical high frequency into a low frequency modulation of the signal that can be detected in real time are compared. The development of phase-stable optical frequency combs has opened up new avenues to metrology and spectroscopy. The ability to generate a series of frequency spikes with precisely controlled separation permits a fast, highly accurate sampling of the material response. Recently, pairs of frequency combs with slightly different repetition rates have been utilized to down-convert material susceptibilities from the optical to microwave regime where they can be recorded in real time. We show how this one-dimensional dual comb technique can be extended to multiple dimensions by using several combs. We demonstrate how nonlinear susceptibilities can be quickly acquired using this technique. In a second class of techniques, sequences of ultrafast mode locked laser pulses are used to recover pathways of interactions contributing to nonlinear susceptibilities by using a photo-acoustic modulation varying along the sequences. We show that these techniques can be viewed as a time-domain analog of the multiple frequency comb scheme.

Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime.

Crossings of electronic potential energy surfaces in nuclear configuration space, known as conical intersections, determine the rates and outcomes of a large class of photochemical molecular processes. Much theoretical progress has been made in computing strongly coupled electronic and nuclear motions at different levels, but how to incorporate them in different spectroscopic signals and the approximations involved are less established. This will be the focus of the present review. We survey a wide range of time-resolved spectroscopic techniques which span from the infrared to the X-ray regimes and can be used for probing the nonadiabatic dynamics in the vicinity of conical intersections. Transient electronic and vibrational probes and their theoretical signal calculations are classified by their information content. This includes transient vibrational spectroscopic methods (transient infrared and femtosecond off-resonant stimulated Raman), resonant electronic probes (transient absorption and photoelectron spectroscopy), and novel stimulated X-ray Raman techniques. Along with the precise definition of what to calculate for predicting the various signals, we outline a toolbox of protocols for their simulation.

Utilizing Microcavities To Suppress Third-Order Cascades in Fifth-Order Raman Spectra.

Nonlinear optical signals in the condensed phase are often accompanied by sequences of lower-order processes, known as cascades, which share the same phase matching and power dependence on the incoming fields and are thus hard to distinguish. The suppression of cascading in order to reveal the desired nonlinear signal has been a major challenge in multidimensional Raman spectroscopy, that is, the χ(5) signal being masked by cascading signals given by a product of two χ(3) processes. Because cascading originates from the exchange of a virtual photon between molecules, it can be manipulated by performing the experiment in an optical microcavity which modifies the density of radiation field modes. Using a quantum electrodynamical (QED) treatment, we demonstrate that the χ(3) cascading contributions can be greatly suppressed. By optimizing the cavity size and the incoming pulse directions, we show that up to ∼99.5% suppression of the cascading signal is possible.

Monitoring nonadiabatic avoided crossing dynamics in molecules by ultrafast X-ray diffraction.

We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, and inelastic scattering. The former probes the charge density and delivers direct information on the evolving molecular geometry. The latter two contributions are weaker and carry spatial information through the transition charge densities (off-diagonal elements of the charge-density operator). Simulations are presented for the nonadiabatic harpooning process in the excited state of sodium fluoride.

Novel photochemistry of molecular polaritons in optical cavities.

Violations of the Born-Oppenheimer approximation (BOA) and the consequent nonadiabatic dynamics have long been an object of intense study. Recently, such dynamics have been induced via strong coupling of the molecule to a high-amplitude (spatially confined) mode of the electromagnetic field in optical cavities. However, the effects of a cavity on a pre-existing avoided crossing or conical intersection are relatively unexplored. The dynamics of molecules dressed by cavity modes are usually calculated by invoking the rotating wave approximation (RWA), which greatly simplifies the calculation but breaks down when the cavity mode frequency is higher than the relevant material frequencies. We develop a protocol for computing curve crossing dynamics in an optical cavity by exploiting a recently-developed method of solving the quantum Rabi model without invoking the RWA. The method is demonstrated for sodium iodide.

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons.

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences. We demonstrate how streaked photoelectrons offer a novel tool for monitoring nonadiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can provide high time resolution direct signatures of electronic coherences, which affect many primary photochemical and biological events.

Cavity Femtochemistry: Manipulating Nonadiabatic Dynamics at Avoided Crossings.

Molecular potential energy surfaces can be actively manipulated by light. This is usually done by strong classical laser light but was recently demonstrated for the quantum field in an optical cavity. The photonic vacuum state of a localized cavity mode can be strongly mixed with the molecular degrees of freedom to create hybrid field-matter states known as polaritons. We simulate the avoided crossing of sodium iodide in a cavity by incorporating the quantized cavity field into the nuclear wave packet dynamics calculation. The quantized field is represented on a numerical grid in quadrature space, thus avoiding the limitations set by the rotating wave approximation (RWA) when the field is expanded in Fock space. This approach allows the investigation of cavity couplings in the vicinity of naturally occurring avoided crossings and conical intersections, which is too expensive in the fock space expansion when the RWA does not apply. Numerical results show how the branching ratio between the covalent and ionic dissociation channels can be strongly manipulated by the optical cavity.

Non-adiabatic dynamics of molecules in optical cavities.

Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces thereby opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use quantities readily accessible from quantum chemistry codes like the adiabatic potential energy surfaces and dipole moments to carry out wave packet simulations in the dressed basis. The implications for photochemistry are demonstrated for a set of model systems representing typical situations found in molecules.

Nonadiabatic Dynamics May Be Probed through Electronic Coherence in Time-Resolved Photoelectron Spectroscopy.

We present a hierarchy of Fermi golden rules (FGRs) that incorporate strongly coupled electronic/nuclear dynamics in time-resolved photoelectron spectroscopy (TRPES) signals at different levels of theory. Expansion in the joint electronic and nuclear eigenbasis yields the numerically most challenging exact FGR (eFGR). The quasistatic Fermi Golden Rule (qsFGR) neglects nuclear motion during the photoionization process but takes into account electronic coherences as well as populations initially present in the pumped matter as well as those generated internally by coupling between electronic surfaces. The standard semiclassical Fermi Golden Rule (scFGR) neglects the electronic coherences and the nuclear kinetic energy during the ionizing pulse altogether, yielding the classical Condon approximation. The coherence contributions depend on the phase-profile of the ionizing field, allowing coherent control of TRPES signals. The photoelectron spectrum from model systems is simulated using these three levels of theory. The eFGR and the qsFGR show temporal oscillations originating from the electronic or vibrational coherences generated as the nuclear wave packet traverses a conical intersection. These oscillations, which are missed by the scFGR, directly reveal the time-evolving splitting between electronic states of the neutral molecule in the curve-crossing regime.

Nonlinear Spectroscopy of Core and Valence Excitations Using Short X-Ray Pulses: Simulation Challenges.

Measuring the nonlinear response of electrons and nuclei to attosecond broadband X-ray radiation has become possible by newly developed free electron lasers and high harmonic generation light sources. The design and interpretation of these novel experiments poses considerable computational challenges. In this chapter we survey the basic description of nonlinear X-ray spectroscopy signals and the electronic structure protocols which may be used for their simulation.

Study of double core hole excitations in molecules by X-ray double-quantum-coherence signals: a multi-configuration simulation.

The multi-configurational self-consistent field method is employed to simulate the two-dimensional all-X-ray double-quantum-coherence (XDQC) spectroscopy, a four-wave mixing signal that provides direct signatures of double core hole (DCH) states. The valence electronic structure is probed by capturing the correlation between the single (SCH) and double core hole states. The state-averaged restricted-active-space self-consistent field (SA-RASSCF) approach is used which can treat the valence, SCH, and DCH states at the same theoretical level, and applies to all types of DCHs (located on one or two atoms, K-edge or L-edge), with both accuracy and efficiency. Orbital relaxation introduced by the core hole(s) and the static electron correlation is properly accounted for. The XDQC process can take place via different intermediate DCH state channels by tuning the pulse frequencies. We simulate the XDQC signals for the three isomers of aminophenol at 8 pulse frequency configurations, covering all DCH pathways involving the N1s and O1s core hole (N1sN1s, O1sO1s and N1sO1s), which reveal different patterns of valence excitations.

Catching Conical Intersections in the Act: Monitoring Transient Electronic Coherences by Attosecond Stimulated X-Ray Raman Signals.

Conical intersections (CIs) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CIs have not been directly observed yet and the experimental evidence is being inferred from fast reaction rates and some vibrational signatures. We show that short x-ray (rather than optical) pulses can directly detect the passage through a CI with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond or attosecond x-ray pulse to detect the electronic coherences (rather than populations) that are generated as the system passes through the CI.

Probing electronic and vibrational dynamics in molecules by time-resolved photoelectron, Auger-electron, and X-ray photon scattering spectroscopy.

We present a unified description for time-resolved electron and photon scattering spectroscopies from molecules prepared in nonstationary states. Signals are expressed in terms of superoperator Green's functions and a systematic procedure for treating various degrees of freedom consistently at different levels of theory is developed. The standard Fermi Golden Rule expressions for photoelectron spectra, which are limited to broad, slowly-varying signals, are obtained as a limiting case of our more general theory that applies to broader parameter regimes.