An ensemble of excited molecules collectively emits multiple-frequency real and virtual photons.

The interplay of molecules gives rise to collective phenomena absent in a single molecule. Many examples of collective phenomena have been reported as their knowledge is essential for understanding the behavior of matter. Here, we consider molecules sufficiently separated from each other to not form chemical bonds. If these molecules are excited, e.g., by a weak laser, can they concertedly relax by emitting a single high-energy photon possessing the total energy of all the relaxing molecules? We show that this concerted emission process is indeed possible. We estimate its probability and analyze its dependence on molecular properties, intermolecular distances, and relative orientations of the molecules. A numerical example on two pyridine molecules is given. The concerted emission found is a fundamental process expected to be operative in gas phase and clusters. Its true relevance lies in its intimate relationship to concerted emission of virtual photons and thus to collective energy transfer ionizing neighboring systems. The estimated rates and examples discussed of this collective intermolecular Coulombic decay shed much light on recent puzzling experiments.

Coupling polyatomic molecules to lossy nanocavities: Lindblad vs Schrödinger description.

The use of cavities to impact molecular structure and dynamics has become popular. As cavities, in particular plasmonic nanocavities, are lossy and the lifetime of their modes can be very short, their lossy nature must be incorporated into the calculations. The Lindblad master equation is commonly considered an appropriate tool to describe this lossy nature. This approach requires the dynamics of the density operator and is thus substantially more costly than approaches employing the Schrödinger equation for the quantum wave function when several or many nuclear degrees of freedom are involved. In this work, we compare numerically the Lindblad and Schrödinger descriptions discussed in the literature for a molecular example where the cavity is pumped by a laser. The laser and cavity properties are varied over a range of parameters. It is found that the Schrödinger description adequately describes the dynamics of the polaritons and emission signal as long as the laser intensity is moderate and the pump time is not much longer than the lifetime of the cavity mode. Otherwise, it is demonstrated that the Schrödinger description gradually fails. We also show that the failure of the Schrödinger description can often be remedied by renormalizing the wave function at every step of time propagation. The results are discussed and analyzed.

Interatomic and Intermolecular Coulombic Decay.

Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.

Cooperative molecular structure in polaritonic and dark states.

An ensemble of identical, intrinsically non-interacting molecules exposed to quantum light is discussed. Their interaction with the quantum light induces interactions between the molecules. The resulting hybrid light-matter states exhibit a complex structure even if only a single vibrational coordinate per molecule is considered. Since all molecules are identical, it is appealing to start from the uniform situation where all molecules possess the same value of this vibrational coordinate. Then, polaritons and dark states follow like in atoms but are functions of this coordinate, and this vibrational degree of freedom makes the physics different from that of atoms. However, despite all molecules being identical, each molecule does have its own vibrational coordinate. It is thus a vital issue to understand the meaning of the uniform situation and how to depart from it and enable one to realistically investigate the ensemble. A rigorous and physically relevant meaning of the polariton energy curves in the uniform situation has been found. It is proven that any point on a polariton energy curve is a (local) minimum or maximum for departing from the uniform situation. It is shown how to explicitly compute the energetic impact of departing from the uniform situation using solely properties of a single free molecule in the absence of the quantum light. The structure of the dark states and their behavior upon departing from the uniform situation are analyzed as well. Useful techniques not used in this topical domain are introduced, and general results on, for example, minimum energy path and symmetry breaking and restoration are obtained. It is shown how to transfer the findings to include several or even many nuclear degrees of freedom per molecule and thus to address the problem of quantum light interacting with many complex molecules. It is demonstrated that the interplay of several vibrational degrees of freedom in a single molecule of the ensemble is expected to lead to additional and, in part, qualitatively different physics. General consequences are discussed.

Caged-electron states and split-electron states in the endohedral alkali C60.

The low-lying electronic states of neutral X@C60 (X = Li, Na, K, Rb) have been computed and analyzed by employing state-of-the-art high level many-electron methods. Apart from the common charge-separated states, well known to be present in endohedral fullerenes, one non-charge-separated state has been found in each of the investigated systems. In Li@C60 and Na@C60, the non-charge-separated state is a caged-electron state already discussed before for Li@C60. This indicates that the application of this low-lying state of Li@C60 discussed before is also applicable for Na@C60. In K@C60 and Rb@C60, the electronic radial distribution analysis shows that this hitherto unknown non-charge-separated state possesses a different nature from that of a caged-electron state.

Signatures of light-induced nonadiabaticity in the field-dressed vibronic spectrum of formaldehyde.

Nonadiabatic coupling is absent between the electronic ground X and first excited (singlet) A states of formaldehyde. As laser fields can induce conical intersections between these two electronic states, formaldehyde is particularly suitable for investigating light-induced nonadiabaticity in a polyatomic molecule. The present work reports on the spectrum induced by light-the so-called field-dressed spectrum-probed by a weak laser pulse. A full-dimensional ab initio approach in the framework of Floquet-state representation is applied. The low-energy spectrum, which without the dressing field would correspond to an infrared vibrational spectrum in the X-state, and the high-energy spectrum, which without the dressing field would correspond to the X → A spectrum, are computed and analyzed. The spectra are shown to be highly sensitive to the frequency of the dressing light allowing one to isolate different nonadiabatic phenomena.

Endocircular Li Carbon Rings.

By employing accurate state-of-the-art many-electron quantum-chemistry methods, we establish that monocyclic carbon rings can accommodate Li guest atoms. The low-lying electronic states of these endocircular systems are analyzed and found to include both charge-separated states where the guest Li atom appears as a cation and the ring as an anion and encircled-electron states where Li and the ring are neutral. The electron binding energies of the encircled-electron states increase drastically at their highly symmetric equilibrium geometries with increasing size of the ring, and in Li@C24 , this state becomes the ground state. Li is very weakly bound vertical to the rings in the low-lying encircled-electron states, hinting to van-der-Waals binding. Applcations are mentioned.

Site- and energy-selective slow-electron production through intermolecular Coulombic decay.

Irradiation of matter with light tends to electronically excite atoms and molecules, with subsequent relaxation processes determining where the photon energy is ultimately deposited and electrons and ions produced. In weakly bound systems, intermolecular Coulombic decay (ICD) enables very efficient relaxation of electronic excitation through transfer of the excess energy to neighbouring atoms or molecules that then lose an electron and become ionized. Here we propose that the emission site and energy of the electrons released during this process can be controlled by coupling the ICD to a resonant core excitation. We illustrate this concept with ab initio many-body calculations on the argon-krypton model system, where resonant photoabsorption produces an initial or 'parent' excitation of the argon atom, which then triggers a resonant-Auger-ICD cascade that ends with the emission of a slow electron from the krypton atom. Our calculations show that the energy of the emitted electrons depends sensitively on the initial excited state of the argon atom. The incident energy can thus be adjusted both to produce the initial excitation in a chosen atom and to realize an excitation that will result in the emission of ICD electrons with desired energies. These properties of the decay cascade might have consequences for fundamental and applied radiation biology and could be of interest in the development of new spectroscopic techniques.

Bound states and symmetry breaking of the ring C20 - anion.

Determining the geometry of carbon rings is an ongoing challenge. Based on our calculations at a state-of-the-art level, we found that the C20 - ring possesses five bound electronic states, including a superatomic state, which is the first superatomic state found for a ring. The nature of these electronic states is discussed. Our calculation reveals a symmetry breaking of the C20 - ring anion ground electronic structure occurring upon attaching an electron to the neutral ring. The discussion of the possible symmetry breaking mechanisms indicates that the shrinking and distortion of the ring upon electron attachment, leading to the symmetry breaking, is a result of the interplay between the symmetry breaking and the totally symmetric modes. The discussion enriches the palette of possible symmetry breaking phenomena in carbon clusters.

Quantum light-induced nonadiabatic phenomena in the absorption spectrum of formaldehyde: Full- and reduced-dimensionality studies.

The coupling of a molecule to a cavity can induce conical intersections of the arising polaritonic potential energy surfaces. Such intersections give rise to the strongest possible nonadiabatic effects. By choosing an example that does not possess nonadiabatic effects in the absence of the cavity, we can study, for the first time, the emergence of these effects in a polyatomic molecule due to its coupling with the cavity taking into account all vibrational degrees of freedom. The results are compared with those of reduced-dimensionality models, and the shortcomings and merits of the latter are analyzed.

Ab initio complex potential energy curves of the He*(1s2p1P)-Li dimer.

LiHe is an intriguing open-shell dimer. It is an extremely weakly bound system, and its vibrational bound-state radius extends far into the classically forbidden regions. Exciting helium into 1s2p leads to a 2Σ and a 2Π state, in which lithium is in its ground state. These states are located above the ionization threshold of the Li atom, which makes them metastable, i.e., resonance states. Under these conditions, energy transfer between the atoms over large distances is feasible within the framework of interatomic Coulombic decay (ICD). These states are investigated theoretically; herein, we present and analyze the complex potential energy curves of the 2Σ and 2Π states, where their imaginary parts describe the decay rate of these resonance states. We employ the resonance via Padé approach to calculate these potentials. Thereby, we use the equation-of-motion coupled-cluster method to compute stabilization graphs as input data for the analytical dilation (via Padé) into the complex energy plane. The procedure is suitable for studying Feshbach resonances and ICD states such as the LiHe 2Σ and 2Π states. The resulting ab initio complex potential energy curves will be used in future work to describe the dynamics of the process HeLi + hν → He*Li → HeLi+ + eICD, which is amenable to experiment.

Electron transfer mediated decay in HeLi2 cluster: Potential energy surfaces and decay widths.

Electron transfer mediated decay (ETMD) is a process responsible for double ionization of dopants in He droplets. It is initiated by producing He+ in the droplet, which is neutralized by ETMD, and has been shown to strongly enhance the dopant's double ionization cross section. The efficiency of ETMD, the spectra of emitted secondary electrons, and the character of the ionic products depend on the nuclear dynamics during the decay. To date, there has been no theoretical investigation of multimode dynamics which accompanies ETMD, which could help to understand such dynamics in a He droplet. In this article, we consider the He-Li2 cluster where an ab initio examination of multimode dynamics during the electronic decay is feasible. Moreover, this cluster can serve as a minimal model for Li2 adsorbed on the droplet's surface-a system where ETMD can be observed experimentally. In He droplets, Li2 can be formed in both the ground X1Σg + and the first excited a3Σu + states. In this article, we present ab initio potential energy surfaces of the electronic states of the He-Li2 cluster involved in ETMD, as well as the respective decay widths. We show that the structure of these surfaces and expected nuclear dynamics strongly depend on the electronic state of Li2. Thus, the overall decay rate and the appearance of the observable electron spectra will be dictated by the electronic structure of the dopant.

Charge separated states of endohedral fullerene Li@C20.

We report on high-level coupled-cluster calculations of electronic states of the neutral endohedral fullerene Li@C20. All computed states of neutral Li@C20 are found to be the charge separated states of the Li+@C20 - type. Using the state-of-the-art EA-EOM-CCSD method, we found that neutral Li@C20 (D3d) possesses several valence and superatomic charge separated states with considerable electron binding energies, the strongest bound state of Li+@C20 - being the 12Eu state (6.73 eV). The valence charge separated states correspond to two sets of states of C20 -. The states 12Eu, 12A2u, 22Eu, and 22A2u correspond to the respective bound states of C20 -, and the states 22A2g, 12Eg, 12A1g, and 42Eu correspond to the unbound states of C20 -. There are eight superatomic states with electron binding energy higher than 1.0 eV, being much stronger bound than the single weakly bound superatomic state of the parent fullerene anion. The analysis of the radial density distribution of the excess electron on the carbon cage indicates the important role of the inner part of the superatomic states in forming the charge separated states.

Tracing charge transfer in argon dimers by XUV-pump IR-probe experiments at FLASH.

Charge transfer (CT) at avoided crossings of excited ionized states of argon dimers is observed using a two-color pump-probe experiment at the free-electron laser in Hamburg (FLASH). The process is initiated by the absorption of three 27-eV-photons from the pump pulse, which leads to the population of Ar2+*-Ar states. Due to nonadiabatic coupling between these one-site doubly ionized states and two-site doubly ionized states of the type Ar+*-Ar+, CT can take place leading to the population of the latter states. The onset of this process is probed by a delayed infrared (800 nm) laser pulse. The latter ionizes the dimers populating repulsive Ar2+ -Ar+ states, which then undergo a Coulomb explosion. From the delay-dependent yields of the obtained Ar2+ and Ar+ ions, the lifetime of the charge-transfer process is extracted. The obtained experimental value of (531 ± 136) fs agrees well with the theoretical value computed from Landau-Zener probabilities.

Electron spectroscopic study of nanoplasma formation triggered by intense soft x-ray pulses.

Using electron spectroscopy, we investigated the nanoplasma formation process generated in xenon clusters by intense soft x-ray free electron laser (FEL) pulses. We found clear FEL intensity dependence of electron spectra. Multistep ionization and subsequent ionization frustration features are evident for the low FEL-intensity region, and the thermal electron emission emerges at the high FEL intensity. The present FEL intensity dependence of the electron spectra is well addressed by the frustration parameter introduced by Arbeiter and Fennel [New J. Phys. 13, 053022 (2011)].

Ultrafast Intermolecular Energy Transfer from Vibrations to Electronic Motion.

It is discussed how vibrationally excited molecules in their electronic ground state can transfer their vibrational energy to the electronic motion of neighbors and ionize them. Based on explicit examples of vibrationally excited molecules and anionic neighbors, it is demonstrated that the transfer can be extremely efficient at intermolecular distances much beyond distances at which the molecule and its neighbor can form a bond.

Bound electronic states of the smallest fullerene C20- anion.

We report on high-level coupled-cluster calculations for the anion states of the smallest fullerene C20. Using the state-of-the-art EA-EOM-CCSD method we revealed that the C20- anion has five bound electronic states at the C20 neutral ground-state D3d equilibrium configuration. These are two pairs of 2Eu and 2A2u states and one 2A1g state. The binding energies vary from 2.05 eV for the most bound 2Eu state to <1 meV for the 2A1g state. An analysis in terms of radial and angular density distribution of the excess electron revealed that the two 2Eu/2A2u pairs are valence-like states while 2A1g corresponds to a super-atomic-like (SAMO) state. The valence states of the first 2Eu/2A2u pair were found to be of p-type whereas those of the second pair are of hybrid sp-type. We have also applied a simple model to understand the binding of the excess electron in C20-. The model confirms the existence of only one SAMO state of the s-type for C20-. At the same time, it overestimates the number of the bound valence states of C20-.

Communication: Substantial impact of the orientation of transition dipole moments on the dynamics of diatomics in laser fields.

The formation of light-induced conical intersections (LICIs) between electronic states of diatomic molecules has been thoroughly investigated over the past decade. In the case of running laser waves, the rotational, vibrational, and electronic motions couple via the LICI giving rise to strong nonadiabatic phenomena. In contrast to natural conical intersections (CIs) which are given by nature and hard to manipulate, the characteristics of LICIs are easily modified by the parameters of the laser field. The internuclear position of the created LICI is determined by the laser energy, while the angular position is given by the orientation of the transition dipole moment (TDM) with respect to the molecular axis. In the present communication, using MgH+ as a showcase example, we exploit the strong impact of the orientation of the TDMs exerted on the light-induced nonadiabatic dynamics. Comparing the photodissociations induced by parallel or perpendicular transitions, a clear signature of the created LICIs is revealed in the angular distribution of the photofragments.

Damaging Intermolecular Energy and Proton Transfer Processes in Alpha-Particle-Irradiated Hydrogen-Bonded Systems.

Although the biological hazard of alpha-particle radiation is well-recognized, the molecular mechanisms of biodamage are still far from being understood. Irreparable lesions in biomolecules may not only have mechanical origin but also appear due to various electronic and nuclear relaxation processes of ionized states produced by an alpha-particle impact. Two such processes were identified in the present study by considering an acetylene dimer, a biologically relevant system possessing an intermolecular hydrogen bond. The first process is the already well-established intermolecular Coulombic decay of inner-valence-ionized states. The other is a novel relaxation mechanism of dicationic states involving intermolecular proton transfer. Both processes are very fast and trigger Coulomb explosion of the dimer due to creation of charge-separated states. These processes are general and predicted to occur also in alpha-particle-irradiated nucleobase pairs in DNA molecules.

Intrinsic and light-induced nonadiabatic phenomena in the NaI molecule.

Nonadiabatic effects play a very important role in controlling chemical dynamical processes. They are strongly related to avoided crossings (AC) or conical intersections (CIs) which can either be present naturally or induced by classical laser light in a molecular system. The latter are named as "light-induced avoided crossings" (LIACs) and "light-induced conical intersections" (LICIs). By performing one or two dimensional quantum dynamical calculations LIAC and LICI situations can easily be created even in diatomic molecules. Applying such calculations for the NaI molecule, which is a strongly coupled diatomic in field free case, significant differences between the impact of the LIAC and LICI on the ground state population dynamics were observed. Moreover, obtained results undoubtedly demonstrate that the effect of the LIAC and LICI on the dynamics strongly depends on the intensity and the frequency of the applied laser field as well as the permanent dipole moments of the molecule.