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Superatomic molecular orbitals (SAMOs) have symmetries (angular quantum numbers) similar to those of atoms and thus it is possible to realize Rydberg state excitations (RSEs) in superatomic molecules. In this letter, the feasibility of superatomic Rydberg state excitation (SRSE) is explored using gold superatoms based on first-principles calculations. The results show that the SRSE exists in both the high and low excited states of the gold superatoms and their SAMOs make a major contribution to electronic transitions. The radial distribution function (RDF) of electronic density shows that the main distribution of electrons in the lowest unoccupied molecular orbitals and other unoccupied superatomic molecular orbitals is extremely far from the geometric center and thus they can be unambiguously identified as Rydberg orbitals. We found that due to two-dimensional ductility of planar superatoms’ transition orbitals, superatoms have the superiority in RSE regulation. Our findings provide a new source of superatom-based RSE and will contribute to the regulation and efficient preparation of Rydberg states.

We investigate the long-range, two-body interactions between rubidium and potassium atoms in highly excited ($n=70$) Rydberg states. After establishing properly symmetrized asymptotic basis states, we diagonalize an interaction Hamiltonian consisting of the standard Coulombic potential expansion and atomic fine structure to calculate electronic potential energy curves. We find that when both atoms are excited to either the $70s$ state or the $70p$ state, both the $\Omega=0+$ symmetry interactions and the $\Omega=0-$ symmetry interactions demonstrate a deep potential well capable of supporting many bound levels; the size of the corresponding dimer states are on the order of 2.25 $\mu$m. We estabish $n$-scaling relations for the equilibrium separation $R_e$ and the dissociation energy $D_e$ and find these relations to be consistent with similar calculations involving the homonuclear interactions between rubidium and cesium. We discuss the specific effects of $\ell$-mixing and the exact composition of the calculated potential well \textit{via} the expansion coefficients of the asymptotic basis states. Finally, we apply a Landau-Zener treatment to show that the dimer states are stable with respect to predissociation., Comment: 8 pages, 4 figures, 4 tables

An analysis is performed of data on the trans → cis-photoisomerization of azobenzene (trans-AB) in light of the Rydberg 3s orbital (R3s) of the azo-group induces the formation of electronically (e-) polarized tautomers (Z+) in addition to its electrically neutral tautomer (Z). The Z+ tautomers have a chromogenic center in the form of a phenylaminyl type cation (PhAT) with a Vis excitation band at λm = 445–450 nm. It is found that the isomerization of trans-AB under the action of Vis light and UV radiation proceeds through the photoexcited polarized e-tautomer Z+*, which undergoes adiabatic changes in its e-configurations under the influence of the R3s-orbital. The Z+* state (with one PhAT cation) then transitions to the Z++* state (with two PhAT cations), which participates in competitive transformations: isomerization in cis-AB and a return to Z+*, which relaxes in Z+. It is shown that a rotational isomerization pathway can form when there are no steric obstacles blocking rotation around the N–N bond. When there are such obstacles, isomerization proceeds through adiabatic displacement of the ph-rings in intermediate Z++*, first into its rectilinear conformation, and then toward one another through the stage of intermediate e-polarized excited state cis-AB*, which has a three-electron bond in addition to the σ-bond of the azo-group between adjacent sp2 orbitals.

Photodissociation dynamics of the jet-cooled vinoxy radical (CH2CHO) via the B2A″ state was studied in the near-ultraviolet (near-UV) region of 308-328 nm using high-n Rydberg H atom time-of-flight (HRTOF) and resonance-enhanced multiphoton ionization (REMPI) techniques. The vinoxy radical beam was produced by 193 nm photolysis of ethyl vinyl ether followed by supersonic expansion. The H + CH2CO product channel was observed directly in the H atom TOF spectra. The H atom photofragment yield (PFY) spectra were obtained by integrating the H atom TOF spectra and measuring the H atom REMPI signals, and showed several vibronic bands of the B2A″ state. The translational energy distributions of the H + CH2CO products, P(ET)'s, were obtained at several vibronic transitions. The P(ET) distributions were broad, peaking at a low energy of ∼3500 cm-1. The product translational energy release was moderate; the average translational energy release in the maximum available energy, ⟨fT⟩, was in the range of 0.24-0.27. The product angular distributions in this wavelength region were slightly anisotropic, with the β parameter in the range of 0.10-0.24. The near-UV photodissociation mechanism of the H + CH2CO product channel of the vinoxy radical is consistent with unimolecular dissociation on the electronic ground state (X2A″) following internal conversion from the B2A″ state to the A2A' state and then to the X2A″ state (although unimolecular dissociation from the first excited A2A' may also contribute).

Exciton polaron is a hypothetical many-body quasiparticle that involves an exciton dressed with a polarized electron-hole cloud in the Fermi sea. It has been evoked to explain the excitonic spectra of charged monolayer transition metal dichalcogenides, but the studies were limited to the ground state. Here we measure the reflection and photoluminescence of monolayer MoSe2 and WSe2 gating devices encapsulated by boron nitride. We observe gate-tunable exciton polarons associated with the 1 s–3 s exciton Rydberg states. The ground and excited exciton polarons exhibit comparable energy redshift (15~30 meV) from their respective bare excitons. The robust excited states contradict the trion picture because the trions are expected to dissociate in the excited states. When the Fermi sea expands, we observe increasingly severe suppression and steep energy shift from low to high exciton-polaron Rydberg states. Their gate-dependent energy shifts go beyond the trion description but match our exciton-polaron theory. Our experiment and theory demonstrate the exciton-polaron nature of both the ground and excited excitonic states in charged monolayer MoSe2 and WSe2. An exciton polaron is a quasiparticle composed of an exciton dressed with an electron-hole cloud, and this concept has been used to explain the ground excitonic states in charged monolayer transition metal dichalcogenides. Here the authors present experimental and theoretical evidence of exciton-polaron Rydberg states in monolayer MoSe2 and WSe2.

Condensation of hydrogen Rydberg atoms (highly electronically excited) into the lowest energy state of condensed hydrogen i.e. the ultra-dense hydrogen phase, H(0), has gained increased attention not only from the fundamental aspects but also from the applied point of view. The physical properties of ultra-dense hydrogen H(0) were recently reviewed (Physica Scripta 2019 https://doi.org/10.1088/1402-4896/ab1276 ), summarizing the results reported in 50 publications during the last ten years. The main application of H(0) so far is as the fuel and working medium in nuclear particle generators and nuclear fusion reactors which are under commercial development. The first fusion process showing sustained operation above break-even was published in 2015 (AIP Advances) and used ultra-dense deuterium D(0) as fuel. The first generator giving a high-intensity muon flux intended for muon-catalyzed fusion reactors was patented in 2017, using H(0) as the working medium. Here, we first focus on the different nuclear processes using hydrogen isotopes for energy generation, and then on the detailed processes of formation of H(0). The production of H(0) employs heterogeneous catalysts which are active in hydrogen transfer reactions. Iron oxide-based, alkali promoted catalysts function well, but also platinum group metals and carbon surfaces are active in this process. The clusters of highly excited Rydberg hydrogen atoms H(l) are formed upon interaction with alkali Rydberg matter. The final conversion step from ordinary hydrogen Rydberg matter H(l) to H(0) is spontaneous and does not require a solid surface. It is concluded that the exact choice of catalyst is not very important. It is also concluded that the crucial feature of the catalyst is to provide excited alkali atoms at a sufficiently high surface density and in this way enabling formation and desorption of H(0) clusters. Finally, the relation to industrial catalytic processes which use H(0) formation catalysts is described and some important consequences like the muon and neutron radiation from H(0) are discussed.

We have used 308 nm photolysis of acetaldehyde to measure a photoionization spectrum of the formyl (HCO) radical between 8 and 11.5 eV using an 11 meV FWHM photoionization energy resolution. We have confirmed that the formyl radical is the carrier of the spectrum by generating an identical spectrum of the HCO product in the Cl + H2CO reaction. The spectrum of HCO and its deuterated isotopologue (DCO) have several resolved autoionizing resonances above the Franck-Condon envelope, which we assign to autoionization after initial excitation into neutral 3sσ and 3p Rydberg states converging to the first triplet excited state of HCO+(a 3A'). The quantum defects for these states are δ3sσ = 1.06 ± 0.02 and δ3p = 0.821 ± 0.019. We report absolute photoionization cross-section measurements of σHCOPI(9.907 eV) = 4.5 ± 0.9 Mb, σHCOPI(10.007 eV) = 4.8 ± 1.0 Mb, σHCOPI(10.107 eV) = 6.0 ± 1.2 Mb, σHCOPI(10.107 eV) = 5.7 ± 1.2 Mb, and σHCOPI(10.304 eV) = 10.6 ± 2.2 Mb relative to the photoionization cross section of the methyl radical. The absolute cross-section measurements are a factor of ∼1.5 larger than those determined in past studies, although the presence of strong autoionizing features supports a dependence on photoionization energy resolution. We propose that the semiempirical model of Xu and Pratt for estimation of free radical photoionization cross sections is more accurate when applied with a reference species containing the same atoms as the free radical rather than isoelectronic species with different atoms.

We have theoretically investigated the modulation structures of the excited-state population of an argon atom exposed to a linearly polarized 800-nm laser pulse in the tunneling region. The numerical result identifies a nearly opposite phase modulation structure between the low-lying n = 4–7 states and over all higher $$n>7$$ states. This phase-dependent alternating population phenomenon is found to be related to the periodic channel-closing effect that results from ac-Stark-shifted multiphoton resonances. Moreover, the angular momentum states attributed to different parities have a similar alternating effect, which confirms a multiphoton process in the tunneling region. We introduce a mechanism of two-photon $$\Lambda $$ -type Raman transitions involving Rydberg and continuum states with a simultaneous redistribution of states to account successfully for this observed out-of-phase angular momentum state population.

In this paper, we proposed a model based on Rydberg atoms for controlling the optical bistability (OB) and optical multistability (OM) in a ring cavity. The atoms interact with an elliptical polarized probe light and a strong coupling light in the presence of external magnetic field. We realized that the threshold of OB can be controlled by elliptical polarized parameter when the first excited states of the atoms interact with Rydberg state. Also, we found that by adjusting the elliptical parameter of probe light, the switching from OB to OM is possible when we consider the strong coupling between Rydberg level and first excited state of the atomic system. We find that when the probe light becomes linearly the OB and OM disappear due to Rydberg electromagnetically induced transparency. However, by adjusting the polarized parameter of the probe light the threshold of OB can be controlled due to Rydberg electromagnetically absorption. Our proposed model can be used as an all-optical device for switching between OB and OM with potential applications in optical communication.

We have observed the ultrafast conformational dynamics of electronically excited N-methyl piperidine (NMP) using time-resolved Rydberg fingerprint spectroscopy. Optical excitation at various wavelengths ranging from 212 nm to 229 nm leads to the 3s or 3p Rydberg states and induces coherent oscillatory motions with periods of about 700 fs. These coherent motions survive the internal conversion from 3p to 3s but then dephase on a time scale of a few oscillations. Intramolecular vibrational energy redistribution on a picosecond time scale leads to an equilibrium between two conformeric structures that are separated in binding energy by 0.09 eV. Model calculations using the DFT-SIC method are in excellent agreement with the experiments and identify the conformers as the chair and twist structures of NMP. The analysis of the equilibrium parameters at long time delays as a function of excitation wavelength allows for the extraction of thermodynamic parameters for the conformeric transformation. We derive an enthalpy of the chair to the twist reaction in the 3s excited state of 62 meV with an entropy of 19.70 Jmol-1K-1. An activation energy of 276 meV is also obtained with a kinetic model.

A cold Rydberg gas, with its atoms prepared initially all in the excited state |n0> , with n0 »1, contains an excessive amount of energy, and presumably is to relax by the Penning-type molecular auto-ionization (MAI), in which a portion of excess energy of one atom is given to another near-by atom and ionizing it. Its complementary process, the resonant energy transfer (RET), is discussed, in which the excess energy of one atom is used on another to form a hyper-excited atomic state |na> with na»n0. This process is always present, provided certain resonance energy conditions are satisfied. In this report, the n0 and density dependences of the RET rates are studied in detail, employing a simple model: 1) at low densities, the RET is mediated by the dipole-dipole coupling Vdd and its rates are generally much smaller than that of MAI, especially for small n0. But 2) as the density increases, our model shows that the rates become of comparable magnitude or even larger than the MAI rates. The Vdd is no longer adequate. We, then construct a semi-empirical potential to describe the RET process. 3) At high densities, we show that the atomic orbital of |na> overlaps with that of neighboring atoms, and the electron-electron potential becomes prominent, resulting in much higher rates.

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.

Multiple Rydberg series converging to the O2+c4Σ-u state, accessed by 20-25 eV extreme ultraviolet (XUV) light, serve as important model systems for the competition between nuclear dissociation and electronic autoionization. The dynamics of the lowest member of these series, the 3sσg state around 21 eV, has been challenging to study owing to its ultra-short lifetime (

We report a comprehensive study on the electronic excited states of tetrafluoro-1,4-benzoquinone, through high-resolution vacuum ultraviolet photoabsorption spectroscopy and time-dependent density functional theory calculations performed within the nuclear ensemble approach. Absolute cross section values were experimentally determined in the 3.8-10.8 eV energy range. The present experimental results represent the highest resolution data yet reported for this molecule and reveal previously unresolved spectral structures. The interpretation of the results was made in close comparison with the available data forpara-benzoquinone [Joneset al.,J. Chem. Phys., 2017,146, 184303]. While the dominant absorption features for both molecules arise from analogous π* ← π transitions, some remarkable differences have been identified. The perfluoro effect manifests in different ways: shifts in band positions and cross sections, appearance of features associated with excitations to σ CF* orbitals, and spectrum broadening by quenching of either vibrational or Rydberg progressions. The level of agreement between experiment and theory is very satisfactory, yet that required the inclusion of nuclear quantum effects in the calculations. We have also discussed the role of temperature on the absorption spectrum, as well as the involvement of core-excited resonances in promoting dissociative electron attachment reactions in the 3-5 eV range.

The state-resolved photodissociation of the CO(1Σ+) + S(1S0) photoproduct channel, formed by vacuum ultraviolet photoexcitation of OCS to a progression of the symmetric stretching vibration (ν1′) in the E and F states, has been investigated by using the time-sliced velocity map ion imaging technique. The total kinetic energy release spectra and the vibrational state specific anisotropy parameters (β) were obtained based on the raw images of S(1S0) photoproducts detected in the wavelength ranges of 134.40–140.98 nm, respectively. Except for vibrational band origins, the CO(1Σ+) photoproducts are found to have more significant populations at highly vibrationally excited states as the symmetric stretching vibrational excitation of the E and F states increases. Furthermore, the vibrational-state specific β values for the CO(1Σ+) + S(1S0) channel via the E and F states both show a sudden change from negative to positive in the vicinity of moderately vibronic levels of the E and F states. This anomalous phenomenon suggests that multiple excited states with different symmetries are involved in the photoexcitation process at relatively short photolysis wavelengths due to the strong vibronic couplings existing in the higher vibronic levels of the E and F states, and the formation of CO(1Σ+) + S(1S0) photoproducts may proceed by different nonadiabatic interactions from the prepared excited states to the lower dissociative state 1Σ+, with strong dependence of the initially symmetric stretching excitation in the Rydberg-type transitions.

The excited-state decay dynamics of 2-ethylpyrrole following UV excitation in the wavelength range of 254.8-218.0 nm is investigated in detail using the femtosecond time-resolved photoelectron imaging method. The time-resolved photoelectron spectra and photoelectron angular distributions at all pump wavelengths are carefully analysed and the following picture is derived: at the longest pump wavelengths (254.8, 248.3 and 246.1 nm), 2-ethylpyrrole is excited to the S1(1πσ*) state having a lifetime of about 50 fs. At 248.3, 246.1 and 237.4 nm, another excited state of Rydberg character is excited. The lifetime of this state is ∼570 fs at 237.4 nm and becomes slightly longer at other two pump wavelengths. At the shortest pump wavelengths (230.8 and 218.0 nm), 2-ethylpyrrole is excited to a state which is tentatively assigned to the 11ππ* state, having a lifetime of 75 ± 15 and 48 ± 10 fs for the longer and shorter pump wavelengths, respectively. Internal conversion to the S1(1πσ*) state might be one of the decay mechanisms of the 11ππ* state.

The energy dependence of the rates of the reactions between He+ and ammonia (NY3, Y = {H,D}), forming NY2+, Y and He as well as NY+, Y2 and He, and the corresponding product branching ratios have been measured at low collision energies Ecoll between 0 and kB·40 K using a recently developed merged-beam technique [Allmendinger et al., ChemPhysChem, 2016, 17, 3596]. To avoid heating of the ions by stray electric fields, the reactions are observed within the large orbit of a highly excited Rydberg electron. A beam of He Rydberg atoms was merged with a supersonic beam of ammonia using a curved surface-electrode Rydberg–Stark deflector, which is also used for adjusting the final velocity of the He Rydberg atoms, and thus the collision energy. A collision-energy resolution of about 200 mK was reached at the lowest Ecoll values. The reaction rate coefficients exhibit a sharp increase at collision energies below ∼kB·5 K and pronounced deviations from Langevin-capture behaviour. The experimental results are interpreted in terms of an adiabatic capture model describing the rotational-state-dependent orientation of the ammonia molecules by the electric field of the He+ atom. The model faithfully describes the experimental observations and enables the identification of three classes of |JKMp〉 rotational states of the ammonia molecules showing different low-energy capture behaviour: (A) high-field-seeking states with |KM| ≥ 1 correlating to the lower component of the umbrella-motion tunnelling doublet at low fields. These states undergo a negative linear Stark shift, which leads to strongly enhanced rate coefficients; (B) high-field-seeking states subject to a quadratic Stark shift at low fields and which exhibit only weak rate enhancements; and (C) low-field-seeking states with |KM| ≥ 1. These states exhibit a positive Stark shift at low fields, which completely suppresses the reactions at low collision energies. Marked differences in the low-energy reactivity of NH3 and ND3—the rate enhancements in ND3 are more pronounced than in NH3—are quantitatively explained by the model. They result from the reduced magnitudes of the tunnelling splitting and rotational intervals in ND3 and the different occupations of the rotational levels in the supersonic beam caused by the different nuclear-spin statistical weights. Thermal capture rate constants are derived from the model for the temperature range between 0 and 10 K relevant for astrochemistry. Comparison of the calculated thermal capture rate coefficients with the absolute reaction rates measured above 27 K by Marquette et al. (Chem. Phys. Lett., 1985, 122, 431) suggests that only 40% of the close collisions are reactive.

The vacuum ultraviolet photodissociation of OCS via the F 31Π Rydberg states was investigated in the range of 134–140 nm by means of the time-sliced velocity map ion imaging technique. The images of S(1D2) products from the CO(X1Σ+)+S(1D2) dissociation channel were acquired at five photolysis wavelengths, corresponding to a series of symmetric stretching vibrational excitations in OCS(F 31Π, υ1=0–4). The total translational energy distributions, vibrational populations and angular distributions of CO(X1Σ+, υ) coproducts were derived. The analysis of experimental results suggests that the excited OCS molecules dissociate to CO(X1Σ+) and S(1D2) products via non-adiabatic couplings between the upper F 31Π states and the lower-lying states both in the C∞υ and Cs symmetry. Furthermore, strong wavelength dependent behavior has been observed: the greatly distinct vibrational populations and angular distributions of CO(X1Σ+, υ) products from the lower (υ1=0–2) and higher (υ1=3, 4) vibrational states of the excited OCS(F 31Π, υ1) demonstrate that very different mechanisms are involved in the dissociation processes. This study provides evidence for the possible contribution of vibronic coupling and the crucial role of vibronic coupling on the vacuum ultraviolet photodissociation dynamics.

We present an overview of experimental and theoretical investigations exploring the dynamical evolution of Rydberg-to-valence character in the electronically excited states of small polyatomic mole...

A strong Coulomb interaction could lead to a strongly bound exciton with high-order excited states, similar to the Rydberg atom. The interaction of giant Rydberg excitons can be engineered for a correlated ordered exciton array with a Rydberg blockade, which is promising for realizing quantum simulation. Monolayer transition metal dichalcogenides, with their greatly enhanced Coulomb interaction, are an ideal platform to host the Rydberg excitons in two dimensions. Here, we employ helicity-resolved magneto-photocurrent spectroscopy to identify Rydberg exciton states up to 11s in monolayer WSe2. Notably, the radius of the Rydberg exciton at 11s can be as large as 214 nm, orders of magnitude larger than the 1s exciton. The giant valley-polarized Rydberg exciton not only provides an exciting platform to study the strong exciton-exciton interaction and nonlinear exciton response but also allows the investigation of the different interplay between the Coulomb interaction and Landau quantization, tunable from a low- to high-magnetic-field limit.

The reaction of chlorine atom Cl(2P) (Cl(2P3/2) and Cl∗(2P1/2)) with D2 was investigated at collision energy from 4.5 kcal/mol to 6.5 kcal/mol with a high-resolution crossed molecular beam apparatus using the technique of D-atom Rydberg tagging detection. The contribution from the spin-orbit excited reaction Cl∗(2P1/2)+D2, which is prohibited by Born-Oppenheimer (BO) approximation, was observed. Collision-energy dependence of differential cross sections (DCSs) near the backward scattering direction was measured. The BO-forbidden reaction Cl∗+D2 was found to be dominant at lower collision energy. As collision energy increases, reactivity of BO-allowed reaction Cl+D2 increases much faster than that of BO-forbidden reaction and becomes dominant at higher collision energy. Our experiment indicates that the additional energy of spin-orbit excitation in Cl∗ facilitates BO-forbidden reaction to pass through the barrier at lower collision energy, while BO approximation is still valid at collision energy near and above the reaction barrier. This tendency of reactivity of Cl/Cl∗+D2 is similar to the isotopic reaction of Cl/Cl∗+H2.

Quantum beats in fluorescence decay from Zeeman-split magnetic sublevels have been measured for helium Rydberg states excited by synchrotron radiation. The Zeeman quantum beats observed in this prototypical case were fitted with an equation from a theoretical formulation. It is proposed that Zeeman quantum beat measurement can be a useful way to simply evaluate the polarization characteristics of extreme ultraviolet light.

We report on the results of studying the radio emission of the Rydberg states of atoms and molecules in the Earth’s upper atmosphere at ionospheric altitudes when the ionosphere is modified by high-power HF radio waves radiated by the Sura heating facility. Radio emission from the upper atmosphere, caused by the emission of highly excited Rydberg atoms and molecules with the principal quantum number n = 163–169 and n = 225 (decimeter wavelength range) and two spectral features that coincide with the frequencies of transitions between Rydberg states m = 169 → n = 168 with the transition frequency νn = 1375.35 MHz and m = 166 → n = 165 with νn = 1451.5 MHz were detected. Characteristic altitudes of the Rydberg radiation generation region were 150–250 km. The radio emission intensity corresponds to 10–45 K, which is comparable with the intensity of the radio emission generated during solar flares.

We investigated the $1S\text{\ensuremath{-}}2P$ transitions of the indirect excitons in diamond around 70 meV in the high-frequency terahertz region via time-resolved Lyman spectroscopy. We discovered significant splitting of the $2P$ levels and attributed it to the rotational-symmetry-breaking effect owing to the cubic crystal environment. The maximum energy separation of 14.9 meV reached 18% of the excitonic Rydberg constant---83.5 \ifmmode\pm\else\textpm\fi{} 2.9 meV---which deviated from the binding energy of the $1S$ ground state: 93.3 \ifmmode\pm\else\textpm\fi{} 2.0 meV. In addition to the anisotropy of the valence bands, we found the impact of the rotational symmetry breaking of the conduction band valleys, which leads to a significant deviation from the case with direct excitons. Detailed knowledge of the ground and excited states of long-lifetime excitons provides an unprecedented opportunity to develop the study of quantum many-body physics and quantum chaos.

We investigate the atomic recombination of stopped muons in dense plasmas of potential μ-catalysis concern. It is shown that in addition to the usual two-body radiative μ-ion recombination R2 highlighting low excited states and moderate plasma temperature T, a novel three-body process R3 involving ion–ion correlations could deliver a contribution several order of magnitudes above R2, steadily increasing with atomic excitation and T. It thus appears possible to explore the feasibility of μ catalysis in less dense Z or MTF plasmas but with longer lifetimes than laser-produced inertial confinement relevance ones.

The authors developed a highly sensitive method based on a quantum-control double-resonance-spectroscopy scheme to study electronically excited states of molecular ions that do not dissociate. The method is used to study the $3d\phantom{\rule{0}{0ex}}\ensuremath{\delta}$ Rydberg state of MgAr${}^{+}$, and the results contribute to the first extensive characterization of the Rydberg states of a molecular cation.

Negative ions do not possess Rydberg states but can have Rydberg-like nonvalence excited states near the electron detachment threshold, including dipole-bound states (DBSs) and quadrupole-bound states (QBSs). While DBSs have been studied extensively, quadrupole-bound excited states have been more rarely observed. 4-cyanophenoxide (4CP−) was the first anion observed to possess a quadrupole-bound exited state 20 cm−1 below its detachment threshold. Here, we report the observation of a DBS in the isoelectronic 4-ethynylphenoxide anion (4EP−), providing a rare opportunity to compare the behaviors of a dipole-bound and a quadrupole-bound excited state in a pair of very similar anions. Photodetachment spectroscopy (PDS) of cryogenically cooled 4EP− reveals a DBS 76 cm−1 below its detachment threshold. Photoelectron spectroscopy (PES) at 266 nm shows that the electronic structure of 4EP− and 4CP− is nearly identical. The observed vibrational features in both the PDS and PES, as well as autodetachment from the nonvalence excited states, are also found to be similar for both anions. However, resonant two-photon detachment (R2PD) from the bound vibrational ground state is observed to be very different for the DBS in 4EP− and the QBS in 4CP−. The R2PD spectra reveal that decays take place from both the DBS and QBS to the respective anion ground electronic states within the 5 ns detachment laser pulse due to internal conversion followed by intramolecular vibrational redistribution and relaxation, but the decay mechanisms appear to be very different. In the R2PD spectrum of 4EP−, we observe strong threshold electron signals, which are due to detachment, by the second photon, of highly rotationally excited anions resulted from the decay of the DBS. On the other hand, in the R2PD spectrum of 4CP−, we observe well-resolved vibrational peaks due to the three lowest-frequency vibrational modes of 4CP−, which are populated from the decay of the QBS. The different behaviors of the R2PD spectra suggest unexpected differences between the relaxation mechanisms of the dipole-bound and quadrupole-bound excited states.

We study effects of a magnetic field on the classical bound motion of a highly excited (Rydberg) electron around a polar molecule, the latter being treated as the point-like electric dipole. We consider the magnetic field B to be parallel or antiparallel to the electric dipole, so that the system has the axial symmetry. (The $${B} = 0$$ case was studied analytically in one of our previous papers.) We obtain analytical results for the arbitrary strength of the magnetic field. We show that the presence of the magnetic field opens up new ranges of the bound oscillatory-precessional motion of the Rydberg electron, the oscillations being in the meridional direction ( $$\theta $$ -direction) and the precession being along parallels of latitude ( $$\varphi $$ -direction). In particular, it turns out that in one of the new ranges of the motion, the period of the $$\theta $$ -oscillations has the non-monotonic dependence on primary parameter of the system. This is a counterintuitive result.

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.

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting Square Gradient Minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant $\Delta$SCF and spin-purified Restricted Open-Shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the Maximum Overlap Method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that $\Delta$SCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

The response of a molecule to photoexcitation is governed by the coupling of its electronic states. However, if the energetic spacing between the electronically excited states at the Franck-Condon window becomes sufficiently small, it is infeasible to selectively excite and monitor individual states with conventional time-resolved spectroscopy, preventing insight into the energy transfer and relaxation dynamics of the molecule. Here, we demonstrate how the combination of time-resolved spectroscopy and extensive surface hopping dynamics simulations with a global fit approach on individually excited ensembles overcomes this limitation and resolves the dynamics in the n3p Rydberg states in acetone. Photoelectron transients of the three closely spaced states n3px, n3py, and n3pz are used to validate the theoretical results, which in turn allow retrieving a comprehensive kinetic model describing the mutual interactions of these states for the first time.

Photodissociation dynamics of H2O and D2O via the state by one-photon excitation have been investigated using the H/D atom Rydberg tagging time-of-flight technique. The TOF spectra of the H/D-atom product in both parallel and perpendicular polarizations have been measured. Product translational energy distributions and angular distributions have been derived from TOF spectra. By simulating these distributions, quantum state distributions of the OH/OD product as well as the state-resolved angular anisotropy parameters were determined. The most important pathway of H2O/D2O dissociation via the state leads to highly rotationally excited OH/OD(X, v = 0) products, while vibrationally excited OH/OD products with v ≥ 1 comprise only one third of the total OH/OD(X) population. The branching ratios of OH(A)/OH(X) and OD(A)/OD(X) have also been determined, 1.0/3.0 for H2O at 122.12 nm and 1.0/2.2 for D2O at 121.95 nm, which are reasonably consistent with the values predicted by the previous theory.

Mass resolved REMPI spectra, as well as CH3+and I+ ion and photoelectron images, were recorded for two-photon resonant excitations of CH3I via s, p and d Rydberg states (CH3I**) in the excitation region of 55 700 to 70 000 cm−1. Photoelectron (PE) and ion kinetic energy release spectra (KERs) were derived from the images. The data revealed that after the two-photon resonant excitation, an additional photon is absorbed to form one or more superexcited state(s) (CH3I#), followed by branching into three pathways. The major one is the dissociation of CH3I# to form excited Rydberg states of iodine atoms (I**) along with CH3(X), a phenomenon not commonly observed in methyl halides. The second (minor) pathway involves autoionization of CH3I# towards CH3I+(X), which absorbs another photon to form CH3+ along with I/I* and the third one (minor) is CH3I# dissociation towards the ion pair, CH3+ + I−, prior to I− electron ejection. Furthermore, one-photon non-resonant dissociation of CH3I to form CH3(X) and I/I* prior to three-photon ionization of the fragments is also detected.

The doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2 - 9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.

The vacuum ultraviolet (VUV) absorption spectra of cyclic ethers consist primarily of Rydberg ← n transitions. By studying three cyclic ethers of varying ring size (tetrahydropyran, tetrahydrofuran and trimethylene oxide, n = 6-4), we investigated the influence of ring size on the VUV excited-state dynamics of the 3d Rydberg manifold using time-resolved photoelectron spectroscopy (TRPES), time-resolved mass spectroscopy (TRMS) and ab initio electronic structure calculations. Whereas neither the electronic characters nor the term energies of the excited-states are substantially modified when the ring-size is reduced from n = 6 to 5 to 4, the excited-state lifetimes concomitantly decrease five-fold. TRPES and TRMS allow us to attribute the observed dynamics to a Rydberg cascade from the initially excited d-Rydberg manifold via the p-Rydberg manifold to the s-Rydberg state. Cuts through potential energy surfaces along the C-O bond reveal that a nσ* state crossing brings the s-Rydberg state along a path to the ring-opened ground state. The observed difference in excited-state lifetimes is attributed to an increasing slope along the repulsive C-O bond coordinate as ring size decreases.

The main chemical reactions that lead to formation of the nonequilibrium two-temperature plasma and highly excited Rydberg complexes are considered. A special attention is given to l-mixing reaction responsible for the formation of quantum resonance properties for radio wave propagation medium. A detailed analysis of the influence of Rydberg states to the behavior of GPS signals in D and E layers of the ionosphere is presented. It is shown that the transition frequencies between the excited states of orbitally degenerate Rydberg complex are resonant with respect to the carrier frequencies of GPS. That is why these states are the main cause of the GPS signal distortion. The mechanism of GPS signal delay in D and E layers is also discussed.

The available experimental data provided by ultrafast dynamics studies of pyrrole and its derivatives in excited states of mixed Rydberg/valence 3s/πσ* character are strongly affected by the interaction with the laser pulses. Understanding these data has constituted an endeavor for several groups during the past few years. Here we apply a simple theoretical model that, including the interaction with the laser pulses, allows one to clarify some aspects of the discrepancies between measurements monitoring different experimental observables. New experimental data on pyrrole, 2,4-dimethylpyrrole, and 2,5-dimethylpyrrole are also provided to check the validity of the model and to gain more insight into the excited state dynamics of pyrrole systems.

In this paper, coherent Rydberg excitation of a single four-level atom in tightly confining trap so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT) by considering Laguerre Gaussi...

The potential for spectroscopy in a multilayer cell with rarefied gas medium is theoretically investigated where said cell can be used as a compact analog of a large number of plane-parallel beams of atoms (or molecules) in an optically excited quantum level. In particular, this situation occurs for metastable and highly excited long-lived Rydberg states of atoms and molecules. Velocity selection of atoms (molecules) excited to said quantum level by broadband optical pumping was found to be efficient because of their characteristic transit and collisional relaxation in said cell. Sub-Doppler resonances at the optical transition frequencies from a given level were narrow as a result of the selection when the monochromatic probe light beam was absorbed.

Photodissociation dynamics of DNCO + hν → D + NCO at photolysis wavelengths between 200 and 235 nm have been studied using the D-atom Rydberg tagging time-of-flight technique. Product translational energy distributions and angular distributions have been determined. Nearly statistical distribution of the product translational energy with nearly isotropic angular distribution was observed at 210–235 nm, which may come from the predissociation pathway of internal conversion from S1 to S0 state followed by decomposition on S0 surface. At shorter photolysis wavelengths, in addition to the statistical distribution, another feature with anisotropic angular distribution appears at high translational energy region, which can be attributed to direct dissociation on S1 surface. Compared with HNCO, the direct dissociation pathway for DNCO photodissociation opens at higher excitation energy. According to our assignment of the NCO internal energy distribution, dominantly bending and a little stretching excited NCO was produced via both dissociation pathways.

Double-hybrid density functionals are currently the most accurate density functionals for ground-state properties and electronic excitations. Nevertheless, the lack of a long-range correction scheme makes them unreliable when it comes to long-range excitations. For this reason, we propose the first two time-dependent double-hybrid functionals with correct asymptotic long-range behavior named ωB2PLYP and ωB2GPPLYP. Herein, we demonstrate their excellent performance and show that they are the most accurate and robust time-dependent density functional theory methods for electronic excitation energies. They provide a balanced description of local-valence, Rydberg, and charge-transfer states. They are also able to tackle the difficult first two transitions in polycyclic aromatic hydrocarbons and show very promising results in a preliminary study on transition-metal compounds, exemplified for titanium dioxide clusters. This work shows that double hybrids can be systematically improved also for excitation energies, and further work in this field is warranted.

The coherence and dephasing of vibrational motions of molecules constitute an integral part of chemical dynamics, influence material properties and underpin schemes to control chemical reactions. Considerable progress has been made in understanding vibrational coherence through spectroscopic measurements, but precise, direct measurement of the structure of a vibrating excited-state polyatomic organic molecule has remained unworkable. Here, we measure the time-evolving molecular structure of optically excited N-methylmorpholine through scattering with ultrashort X-ray pulses. The scattering signals are corrected for the differences in electron density in the excited electronic state of the molecule in comparison to the ground state. The experiment maps the evolution of the molecular geometry with femtosecond resolution, showing coherent motion that survives electronic relaxation and seems to persist for longer than previously seen using other methods.

Large-scale four-component relativistic calculations have been carried out for excited states of the tris-(allyl)-iridium complex, Ir(C3H5)3, using the relativistic polarization propagator method. The main focus was on providing insight into the lowest excited states of the three different structural forms of the complex, C3, C3h, and C1, including prediction of the excitation spectra and elucidation of spin-orbit coupling (SOC) effects for these forms. To unravel SOC effects, results of spin-orbit (SO) calculations were contrasted to results of spin-free (SF) calculations. Both the SO and SF calculations predict the lowest excited states of all three forms are of Rydberg type. We identified several Rydberg series, characterized by different hole configurations, that constitute the low-energy parts of the SO and SF excitation spectra. The SO spectra, however, differ notably from the corresponding SF spectra, pointing out to the influence of SOC. The most pronounced differences are observed for the SO and SF spectra of the C3h form. Our analysis indicates that SOC in this form causes strong alterations of the frontier occupied orbitals, participating in the excitations. As a result, excited states belonging to the first two Rydberg series are characterized by different electronic structure (hole configurations) in the SO and SF cases. Besides the orbital alteration effect, two other SOC effects, zero-field splitting and singlet-triplet mixing were identified in the SO spectra of all three forms. These effects result in new lines in the SO spectra and notable redistribution of the spectral intensity.

The photodissociation dynamics of jet-cooled thiomethoxy radical (CH3S) via the B2A2 ← X2E transition was studied in the ultraviolet region of 216-225 nm using the high-n Rydberg H-atom time-of-flight (HRTOF) technique. The H-atom product channel was directly observed from the H-atom TOF spectra (using both dimethyl disulfide and dimethyl sulfide precursors). The H-atom photofragment yield spectrum showed a broad feature in the region of 216-225 nm and three B2A2 vibronic peaks at 217.7, 220.3, and 221.5 nm. Several H-atom dissociation pathways were identified. The excited-state CH3S had a repulsive, prompt dissociation pathway to the ground-state H2CS(X1A1) + H products, with the product translational energy peaking near the maximum available energy, a predominant C-S stretch vibrational excitation in H2CS(X1A1), and an anisotropic angular distribution. The main pathway was the H2CS(X1A1) + H product channel via the unimolecular dissociation of internally hot CH3S radical in the ground electronic state after internal conversion from the electronic excited state, with a modest translational energy release (peaking at a low translational energy of ∼11 kcal/mol and extending near the maximum available energy) and a nearly isotropic angular distribution. The H + H2CS(A1A2) and H + H2CS(a3A2) product channels were also observed but were minor channels. The C-H bond dissociation energy of CH3S to the H + H2CS(X1A1) products was determined to be 48.8 ± 0.7 kcal/mol.

We present herein the first comprehensive study of the one‐ and two‐photon absorption of Fe(CO)5 utilising a hierarchy of linear‐ and quadratic‐response coupled cluster (LR‐ and QR‐CC) methodologies to provide an in‐depth characterisation, as well as potential energy curves for axial and equatorial bond dissociations, highlighting the state crossings leading from the bright 1A2′′ state through to the dissociative 1E′ state. We have characterised a range of metal‐to‐ligand charge transfer (MLCT) and ligand field (LF) states that are in agreement with both previous studies and experiment, including the identification of a series of E′ states that present Rydberg character in the 5.9–7.2 eV region. Due to the rapid excited state dissociation of Fe(CO)5 through the low lying 1E′ and 2E′′ ligand‐field states, we have also included an LR‐CCSD analysis of the major dissociative product, Fe(CO)4. Analysis of the C2v geometry of Fe(CO)4 reveals four accessible ligand field states at 1.085, 1.684, 1.958, and 2.504 eV respectively, reinforcing the highly unstable nature of Fe(CO)4 along with a strong MLCT band between 4.300 and 5.573 eV. This band overlaps with one in the spectra of Fe(CO)5 suggesting that full fragmentation could proceed by two paths: two‐photon excitation leading to dissociation, or through sequential one‐photon absorption events, the first causing dissociation to and the second initiating further fragmentation of the complex.

Analytical expressions for spontaneous and induced by blackbody radiation energy shifts and widths of atomic circular states are derived. The features of asymptotic behavior of the total width and energy shifts for highly excited Rydberg circular states in the blackbody radiation field are described. Approximate equations are proposed for simple evaluations of energy characteristics and an absence of temperature-independent spontaneous contribution to the total energy width in a range of high temperatures and principal quantum numbers is demonstrated.

The ultrafast dissociation dynamics of NO $_2$ molecules was investigated by femtosecond laser pump-probe mass spectra and ion images. The results show that the kinetic energy release of NO $^+$ ions has two components, 0.05 eV and 0.25 eV, and the possible dissociation channels have been assigned. The channel resolved transient measurement of NO $^+$ provides a method to disentangle the contribution of ultrafast dissociation pathways, and the transient curves of NO $^+$ ions at different kinetic energy release are fitted by a biexponential function. The fast component with a decay time of 0.25 ps is generated from the evolution of Rydberg states. The slow component is generated from two competitive channels, one of the channel is absorbing one 400 nm photon to the excited state $A^2$ B $_2$ , which has a decay time of 30.0 ps, and the other slow channel is absorbing three 400 nm photons to valence type Rydberg states which have a decay time less than 7.2 ps. The channel and time resolved experiment present the potential of sorting out the complex ultrafast dissociation dynamics of molecules.

Excited-state energy levels for quartet states 1s22l2l′nl″ (n=2–7; l=s, p; l′=s, p; l″=s, p, d, f) pertaining to 4Le,o (m) (L=S, P, D; m=1–5) Rydberg series in Si9+ ion are studied, using multi-configuration Rayleigh-Ritz variation method. Corrections for the relativistic effects, mass polarization effect, and quantum electrodynamics (QED) effect are taken into account to obtain the accurate relativistic energies. Transition probabilities, line strengths, oscillator strengths, and wavelengths of electric-dipole transitions between these quartet states are systematically calculated and compared with available reference data. These calculated data could be used for the identification of spectral lines arising from the coronal atmospheres and experimental study in future work.

A spectrum of field-ionized triplet Rydberg states of gerade symmetry H2 has been measured, excited from the υ″ = 0, N″ = 1-3 rovibrational levels of the metastable c3Πu-2pπ state in a 6 keV fast molecular beam. The field-ionized spectrum is kinetic energy labeled in order to separate it from the well-studied υ+ ≥ 1 autoionization spectrum. The spectrum consists of both ns and nd Rydberg series with n between 10 and 28 converging to the υ+ = 0, N+ = 1-3 levels of the X+ 2Σg+ ground state of H2+. Transitions with changes in vibration and/or rotation are also identified. The spectral positions of 59 transitions in the field ionization spectrum are identified and assigned quantum numbers using the predictions of multichannel quantum-defect theory (MQDT). The transition energies and subsequent effective quantum defects are compared between the experiment and theory. Most of the observed transitions, within the experimental uncertainty of 0.2 cm-1, agree with the energies predicted by MQDT.

At intermediate to high densities, electron (de-)excitation collisions are the dominant process for populating or depopulating high Rydberg states. In particular, the accurate knowledge of the energy changing ($n$-changing) collisional rates is determinant for predicting the radio recombination spectra of gaseous nebula. The different datasets present in the literature come either from impact parameter calculations or semi-empirical fits and the rate coefficients agree within a factor of two. We show in this paper that these uncertainties cause errors lower than 5% in the emission of radio recombination lines (RRL) of most ionized plasmas of typical nebulae. However, in special circumstances where the transitions between Rydberg levels are amplified by maser effects, the errors can increase up to 20%. We present simulations of the optical depth and H$n\alpha$ line emission of Active Galactic Nuclei (AGN) Broad Line Regions (BLRs) and the Orion Nebula Blister to showcase our findings., Comment: 16 pages (accepted by MNRAS, replaced)