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Recent experiments and theoretical studies strongly indicate that water exhibits a liquid-liquid phase transition (LLPT) in the supercooled domain. An open question is how the LLPT of water can affect the properties of aqueous solutions. Here, we study the structural and thermodynamic properties of supercooled glycerol-water microdroplets at dilute conditions ($\chi_g=3.2~\%$ glycerol mole fraction). The combination of rapid evaporative cooling with ultrafast X-ray scattering allows us to outrun crystallization and gain access to the deeply supercooled regime down to $T=229.3$ K. We find that the density fluctuations of the glycerol-water solution or, equivalently, its isothermal compressibility, $\kappa_T$, increases upon cooling. This is confirmed by molecular dynamics simulations, which indicate that the presence of glycerol shifts the temperature of maximum $\kappa_T$ from $T=230$ K in pure water down to $T=223$ K in the solution. Our findings elucidate the interplay between the complex behavior of water, including its LLPT, and the properties of aqueous solutions at low temperatures, which can have practical consequences in cryogenic biological applications and cryopreservation techniques.

Vibrational polaritons are formed by strong coupling of molecular vibrations and photon modes in an optical cavity. Experiments have demonstrated that vibrational strong coupling can change molecular properties and even affect chemical reactivity. However, the interactions in a molecular ensemble are complex, and the exact mechanisms that lead to modifications are not fully understood yet. We simulate two-dimensional infrared spectra of molecular vibrational polaritons based on the double quantum coherence technique to gain further insight into the complex many-body structure of these hybrid light-matter states. Double quantum coherence uniquely resolves the excitation of hybrid light-matter polaritons and allows to directly probe the anharmonicities of the resulting states. By combining the cavity Born-Oppenheimer Hartree-Fock ansatz with a full quantum dynamics simulation of the corresponding eigenstates, we go beyond simplified model systems. This allows us to study the influence of self-polarization and the response of the electronic structure to the cavity interaction on the spectral features even beyond the single-molecule case.

As pioneering experiments have shown, strong vibrational coupling between molecular vibrations and light modes in an optical cavity can significantly alter molecular properties and even affect chemical reactivity. However, the current theoretical description is limited and far from complete. To explore the origin of this exciting observation, we investigate how the molecular structure changes under strong light-matter coupling using an ab-initio method based on the cavity Born-Oppenheimer Hartree-Fock ansatz. By optimizing H$_2$O and H$_2$O$_2$ resonantly coupled to cavity modes, we study the importance of reorientation and geometric relaxation. In addition, we show that the inclusion of one or two cavity modes can change the observed results. On the basis of our findings, we derive a simple concept to estimate the effect of the cavity interaction on the molecular geometry using the molecular polarizability and the dipole moments.

Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH$^+$ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.

Recent experiments have revealed the profound effect of strong light-matter interactions in optical cavities on the electronic ground state of molecular systems. This phenomenon, known as vibrational strong coupling (VSC), can modify reaction rates and induce the formation of molecular vibrational polaritons, hybrid states involving both photon modes and vibrational modes of molecules. We present an ab-initio methodology, based on the cavity Born-Oppenheimer Hartree-Fock ansatz, which is specifically powerful for ensembles of molecules, to calculate vibro-polaritonic IR spectra. This method allows a comprehensive analysis of these hybrid states. Our semi-classical approach, validated against full quantum simulations, reproduces key features of the vibro-polaritonic spectra. The underlying analytic gradients also pave the way for optimizing cavity-coupled molecular systems and performing semi-classical dynamics simulations

Experimental studies indicate that optical cavities can affect chemical reactions, through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models, that take into account inter-molecular interactions to describe ensembles, are therefore essential to understand the mechanisms governing polaritonic chemistry. We present an ab-initio Hartree-Fock ansatz in the framework of the cavity Born-Oppenheimer approximation and study molecules strongly interacting with an optical cavity. This ansatz provides a non-perturbative, self-consistent description of strongly coupled molecular ensembles taking into account the cavity-mediated dipole self-energy contributions. To demonstrate the capability of the cavity Born-Oppenheimer Hartree-Fock ansatz, we study the collective effects in ensembles of strongly coupled diatomic hydrogen fluoride molecules. Our results highlight the importance of the cavity-mediated inter-molecular dipole-dipole interactions, which lead to energetic changes of individual molecules in the coupled ensemble.

We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full non-relativistic Pauli-Fierz problem of an ensemble of strongly-coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles). Thus collective vibrational strong coupling can alter individual molecules strongly for localized "hotspots" within the ensemble. Moreover, the discovered cavity-induced polarization pattern possesses a zero net polarization, which resembles a continuous form of a spin glass (or better polarization glass). Our findings suggest that the thorough understanding of polaritonic chemistry, requires a self-consistent treatment of dressed electronic structure, which can give rise to numerous, so far overlooked, physical mechanisms.

Collective coupling of an ensemble of particles to a light field is commonly described by the Tavis--Cummings model. This model includes numerous eigenstates which are optically decoupled from the optically bright polariton states. To access these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in molecular Tavis--Cummings model. The system is modelled with a Lindblad equation that includes pure dephasing, as they would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of the pure dephasing, as well as the number of particles, has a significant influence on the dark state population.

Linear off-resonant X-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explore different combination schemes for the probe pulse, as well as the impact of parameters of the pulse trains on the signals. Furthermore, we show how Raman selection rules and symmetry consideration affect the spectroscopic signal, and we discuss the importance of vibrational contributions to the overall signal. We use two different model systems, representing molecules of different symmetry, and quantum dynamics simulations to study the difference in the spectra. The results suggest that such pulse trains are well suited to capture the key features associated with the electronic coherence.

The installation of quantum chemistry software packages is commonly done manually and can be a time-consuming and complicated process. An update of the underlying Linux system requires a reinstallation in many cases and can quietly break software installed on the system. In this paper, we present an approach that allows for an easy installation of quantum chemistry software packages, which is also independent of operating system updates. The use of the Nix package manager allows building software in a reproducible manner, which allows for a reconstruction of the software for later reproduction of scientific results. The build recipes that are provided can be readily used by anyone to avoid complex installation procedures.

Many recent experimental ultrafast spectroscopy studies have hinted at non-adiabatic dynamics indicating the existence of conical intersections, but their direct observation remains a challenge. The rapid change of the energy gap between the electronic states complicated their observation by requiring bandwidths of several electron volts. In this manuscript, we propose to use the combined information of different X-ray pump-probe techniques to identify the conical intersection. We theoretically study the conical intersection in pyrrole using transient X-ray absorption, time-resolved X-ray spontaneous emission, and linear off-resonant Raman spectroscopy to gather evidence of the curve crossing.

Optical cavities, e.g. as used in organic polariton experiments, often employ low finesse mirrors or plasmonic structures. The photon lifetime in these setups is comparable to the timescale of the nuclear dynamics governing the photochemistry. This highlights the need for including the effect of dissipation in the molecular simulations. In this study, we perform wave packet dynamics with the Lindblad master equation, to study the effect of a finite photon lifetime on the dissociation of the MgH$^+$ molecule model system. Photon lifetimes of several different orders of magnitude are considered to encompass an ample range of effects inherent to lossy cavities.

Coherent control experiments in molecules are often done with shaped laser fields. The electric field is described classically and control over the time evolution of the system is achieved by shaping the laser pulses in the time or frequency domain. Moving on from a classical to a quantum description of the light field allows to engineer the quantum state of light to steer chemical processes. The quantum field description of the photon mode allows to manipulate the light-matter interaction directly in phase-space. In this paper we will demonstrate the basic principle of coherent control with quantum light on the avoided crossing in lithium fluoride. Using a quantum description of light together with the nonadiabatic couplings and vibronic degrees of freedoms opens up new perspective on quantum control. We show the deviations from control with purely classical light field and how back-action of the light field becomes important in a few photon regime.

Nonadiabatic effects appear due to avoided crossings or conical intersections that are either intrinsic properties in field-free space or induced by a classical laser field in a molecule. It was demonstrated that avoided crossings in diatomics can also be created in an optical cavity. Here, the quantized radiation field mixes the nuclear and electronic degrees of freedom creating hybrid field-matter states called polaritons. In the present theoretical study we go further and create conical intersections in diatomics by means of a radiation field in the framework of cavity quantum electrodynamics (QED). By treating all degrees of freedom, that is the rotational, vibrational, electronic and photonic degrees of freedom on an equal footing we can control the nonadiabatic quantum light-induced dynamics by means of conical intersections. First, the pronounced difference between the the quantum light-induced avoided crossing and the conical intersection with respect to the nonadiabatic dynamics of the molecule is demonstrated. Second, we discuss the similarities and differences between the classical and the quantum field description of the light for the studied scenario.

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/acceptor substituted stilbene.

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 of the transition charge densities (off-diagonal elements of the charge-density operator). Simulations are presented for the nonadiabatic harpooning process in the excited states of sodium fluoride.

This submission is a comment on an article that had previously appeared in Phys. Rev. Lett., Comment: Phys. Rev. Lett. (in press)

Recently developed circularly polarized X-ray light sources can probe ultrafast chiral electronic and nuclear dynamics through spatially localized resonant core transitions. We present simulations of time-resolved circular dichroism (TRCD) signals given by the difference of left and right circularly polarized X-ray probe transmission following an excitation by a circularly polarized optical pump with variable time delay. Application is made to formamide which is achiral in the ground state and assumes two chiral geometries upon optical excitation to the first valence excited state. Probes resonant with various K-edges (C, N and O) provide different local windows onto the parity breaking geometry change thus revealing enantiomer asymmetry.

Free-electron laser hard X-ray light sources can provide high fluence, femtosecond pulses, enabling the time-resolved probing of structural dynamics and elementary relaxation processes in molecules. Traditional X-ray elastic scattering from crystals in the ground state consists of sharp Bragg diffraction peaks that arise from pairs of molecules and reveal the ground state charge density. Scattering of ultrashort X-ray pulses from gases, liquids, and even single molecules is more complex and involves both single- and two- molecule contributions, diffuse (non-Bragg) features, elastic and inelastic components, contributions of electronic coherences in nonstationary states, and interferences between scattering off different states (heterodyne detection). We present a unified description that covers all these processes and discuss their relative magnitudes for gas-phase NaI. Conditions for the observation of holographic (heterodyne) interference, which has been recently discussed [1], are clarified.

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 an 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 and demonstrate how it offers a novel tool to monitor non-adiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can enhance the time resolution and provide direct signatures of electronic coherences, which affect many primary photochemical and biological events.

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior is evaluated for a model function in 2, 3 and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.

Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces 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.

Conical intersections (CoIn) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CoIns 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 CoIn with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond/attosecond X-ray pulse to detect the electronic coherences (rather than populations) that are generated as the system passes through the CoIn.

The problem of antiproton scattering on the molecular Hydrogen is investigated by means of wave packet dynamics. The electronically potential energy surfaces of the antiproton H2 system are presented within this work. Excitation and dissociation probabilities of the molecular Hydrogen for collision energies in the ultra low energy regime below 10 eV are computed.

The efficiency of cavity sideband cooling of trapped molecules is theoretically investigated for the case where the IR transition between two rovibrational states is used as a cycling transition. The molecules are assumed to be trapped either by a radio-frequency or optical trapping potential, depending on whether they are charged or neutral, and confined inside a high-finesse optical resonator which enhances radiative emission into the cavity mode. Using realistic experimental parameters and COS as a representative molecular example, we show that in this setup cooling to the trap ground state is feasible.

We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of non-resonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits., Comment: 4 pages, 3 figures

We present detailed calculations at the basis of our recent proposal for simultaneous cooling the rotational, vibrational and external molecular degrees of freedom. In this method, the molecular rovibronic states are coupled by an intense laser and an optical cavity via coherent Raman processes enhanced by the strong coupling with the cavity modes. For a prototype system, OH, we showed that the translational motion is cooled to few micro Kelvin and the molecule is brought to the internal ground state in about a second. Here, we investigate numerically the dependence of the cooling scheme on the molecular polarizability, selecting NO as a second example. Furthermore, we demonstrate the general applicability of the proposed cooling scheme to initially vibrationally and rotationally hot molecular systems., Comment: 11 pages, 12 figures