Zero-point Level Research Articles

Electronic Spectrum of α-Hydrofulvenyl Radical (C6H7), and a Simple and Accurate Recipe for Predicting Adiabatic Ionization Energies of Resonance-Stabilized Hydrocarbon Radicals.

Using a combination of resonant two-photon two-color ionization (R2C2PI) and laser-induced fluorescence/dispersed fluorescence spectroscopy, we have examined the 2A″ ← 2A″ transition of the resonance-stabilized α-hydrofulvenyl radical, produced from methylcyclopentadiene dimer in a jet-cooled discharge. Like the related 1,4-pentadienyl and cyclohexadienyl radicals, the α-hydrofulvenyl Ã-state lifetime is orders of magnitude shorter than the predicted f-value implies, indicative of rapid nonradiative decay. The transition is fully allowed by symmetry but considerably weakened by transition moment interference. Intensity borrowing among a' modes brings about static (i.e., Condon) and vibronic (i.e., Herzberg-Teller) moments of similar size, the result being a spectrum substantially less origin-dominated than is usually observed for extensively delocalized radicals. Twenty -state modes and twelve -state modes are identified with high confidence and assignments for several others are suggested. In addition, from a series of two-color appearance potential scans with the -state zero-point level serving as an intermediate, we obtain a field-free adiabatic ionization energy (AIE) of 7.012(1) eV. For a set of 21 resonance-stabilized radicals bearing 5 to 11 carbon atoms, it emerges that the field-free AIE obtained by R2C2PI methods under jet-cooled conditions lies very close to the average of B3LYP/6-311G++(d,p) (with harmonic zero-point energy) and CBS-QB3 0 K calculations, with a mean absolute deviation of only 0.010(7) eV (approximately 1 kJ/mol). On average, this represents a nearly 10-fold improvement in accuracy over CBS-QB3 predictions for the same set of radicals.

Probing Dipole-Bound States Using Photodetachment Spectroscopy and Resonant Photoelectron Imaging of Cryogenically Cooled Anions.

Molecular anions with polar neutral cores can support highly diffuse dipole-bound states below their detachment thresholds due to the long-range charge-dipole interaction. Such nonvalence states constitute a special class of excited electronic states for anions and were observed in early photodetachment experiments to measure the electron affinities of organic radicals. Recent experimental advances, in particular, the ability to create cold anions using a cryogenically cooled Paul trap, have allowed the investigation of dipole-bound excited states at a new level. For the first time, the zero-point level of dipole-bound excited states can be observed via resonant two-photon detachment, and resonant photoelectron spectroscopy can be performed via the above-threshold vibrational levels (Feshbach resonances) of the dipole-bound states. This Perspective describes recent progress in the investigation of dipole-bound states in the authors' lab using an electrospray photoelectron spectroscopy apparatus equipped with a cryogenically cooled Paul trap and high-resolution photoelectron imaging.

Subtle hydrogen bond preference and dual Franck-Condon activity - the interesting pairing of 2-naphthol with anisole.

The hydrogen-bonded complexes between 2-naphthol (or β-naphthol) and anisole are explored by detecting their IR absorption in the OH stretching range as well as their UV absorption by means of laser-induced fluorescence and resonance-enhanced two-photon UV ionisation. For the more stable cis and the metastable trans conformations of the OH group in 2-naphthol, hydrogen bonding to the oxygen atom of anisole is consistently detected in different supersonic jet expansions. Alternative hydrogen bonding to the aromatic ring of anisole remains elusive, although the majority of state-of-the-art hybrid DFT functionals with London dispersion correction and - less surprisingly - MP2 wavefunction theory predict it to be slightly more stable at zero-point level, unless three-body dispersion correction is added to the B3LYP-D3(BJ) approach. This changes at the CCSD(T) level, which forecasts an energy advantage of 1-3 kJ mol-1 for the classical hydrogen bond arrangement even after including (DFT) zero-point energy contributions. The UV and IR spectra of the cis complex exhibit clear evidence for intensity redistribution of the primary OH stretch oscillator to combination states with the same low-frequency intermolecular bending mode by Franck-Condon-type vertical excitation mechanisms. This rare case of dual (vibronic and vibrational) Franck-Condon activity of a low-frequency mode invites future studies of homologues where aromatic ring docking of the OH group may be further stabilised, e.g. through anisole ring methylation.

Dipole-Bound State, Photodetachment Spectroscopy, and Resonant Photoelectron Imaging of Cryogenically-Cooled 2-Cyanopyrrolide.

Valence-bound anions with polar neutral cores can have diffuse dipole-bound excited states just below the electron detachment threshold. Because of the similarity in geometry and vibrational frequencies between the dipole-bound states (DBSs) and the corresponding neutrals, DBSs have been exploited as intermediate states to conduct resonant photoelectron spectroscopy (PES), resulting in highly non-Franck-Condon photoelectron spectra via vibrational autodetachment and providing much richer vibrational information than conventional PES. Here, we report a photodetachment and high-resolution photoelectron imaging study of the 2-cyanopyrrolide anion, cooled in a cryogenic ion trap. The electron affinity of the 2-cyanopyrrolyl radical is measured to be 3.0981 ± 0.0006 eV (24 988 ± 5 cm-1). A DBS is observed for 2-cyanopyrrolide at 240 cm-1 below its detachment threshold using photodetachment spectroscopy. Twenty-three above-threshold vibrational resonances (Feshbach resonances) of the DBS are observed. Resonant PES is conducted at each Feshbach resonance, yielding a wealth of vibrational information about the 2-cyanopyrrolyl radical. Resonant two-photon PES confirms the s-like dipole-bound orbital and reveals a relatively long lifetime of the bound zero-point level of the DBS. Fundamental frequencies for 19 vibrational modes (out of a total of 24) are obtained for the cyanopyrrolyl radical, including six out-of-plane modes. The current work provides important spectroscopic information about 2-cyanopyrrolyl, which should be valuable for the study of this radical in combustion or astronomical environments.

Barely fluorescent molecules. I. Twin-discharge jet laser-induced fluorescence spectroscopy of HSnCl and DSnCl.

The divalent tin transient molecules HSnCl and DSnCl have been detected for the first time by laser-induced fluorescence (LIF) spectroscopy. HSnCl/DSnCl were produced in a twin-discharge jet using separate precursor streams of SnH4/SnD4 and the discharge products from HCl/DCl, both diluted in high pressure argon. The Ã1A″-X̃1A' spectrum of HSnCl consists of a single vibronic 00 0 band with a very short fluorescence lifetime (∼30ns). In contrast, the LIF spectrum of DSnCl exhibits three bands (00 0,20 1,and20 2), whose fluorescence lifetimes decrease from 393ns (00) to less than 10ns (22). Single vibronic level emission spectra have been recorded, providing information on all three vibrational modes in the ground state. Previous detailed ab initio studies indicate that these molecules dissociate into SnCl + H on the excited state potential surface and this is the cause of the short fluorescence lifetimes and breaking off of the fluorescence. It is fortunate that the HSnCl excited state zero-point level is still fluorescent or it would not be detectable by LIF spectroscopy.

Innovative mass spectrometer for high-resolution ion spectroscopy.

Conventional ion spectroscopy is inapplicable for ions produced in low concentrations or with low spectral resolutions. Hence, we constructed a high-resolution vacuum ultraviolet mass-analyzed threshold ionization (HR VUV-MATI) spectrometer composed of a four-wave frequency mixing cell capable of generating long-lasting and intense VUV laser pulses of ∼1 × 1010 photons/pulse at wavelengths of 123.6-160.0nm, a space-focused linear time-of-flight photoionization chamber with a new ion-source assembly, and a compact molecular beam chamber with a temperature-controlled pulsed nozzle for ion spectroscopy. The ion-source assembly and pulsing schemes enabled an ∼15-μs-delayed but extremely weak pulsed-field-ionization of the molecules in the zero-kinetic-energy (ZEKE) states and first-order space focusing of the generated MATI ions. These ZEKE states were effectively generated by a minute electric jitter from the high-lying Rydberg states, which were initially prepared via VUV photoexcitation. The spectral and mass resolutions (∼5cm-1 and 2400, respectively) and the signal strength were simultaneously enhanced using this spectrometer. Moreover, it could be used to measure the fine vibrational spectrum from the zero-pointlevel of the cation and the exact adiabatic ionization energy of the neutral molecule. Additionally, it could be used to measure the appearance energies of the photoproducts and elucidate the vibrational structures of the cationic isotopomers, utilizing other pulsing schemes. Furthermore, this spectrometer could be used to analyze the congested vibrational spectrum of a cation with multiple conformations. Thus, the HR VUV-MATI spectrometer-a potential alternative to photoelectron spectrometers-can be used to analyze the conformational structure-dependent reactivities.

Probing Hydrogen-Bonding Interactions within Phenol-Benzimidazole Proton-Coupled Electron Transfer Model Complexes with Cryogenic Ion Vibrational Spectroscopy.

Hydrogen-bonding interactions within a series of phenol-benzimidazole model proton-coupled electron transfer (PCET) dyad complexes are characterized using cryogenic ion vibrational spectroscopy. A highly red-shifted and surprisingly broad (>1000 cm-1) transition is observed in one of the models and assigned to the phenolic OH stretch strongly H-bonded to the N(3) benzimidazole atom. The breadth is attributed to a combination of anharmonic Fermi-resonance coupling between the OH stretch and background doorway states involving OH bending modes and strong coupling of the OH stretch frequency to structural deformations along the proton-transfer coordinate accessible at the vibrational zero-point level. The other models show unexpected protonation of the benzimidazole group upon electrospray ionization instead of at more basic remote amine/amide groups. This leads to the formation of HO-+HN(3) H-bond motifs that are much weaker than the OH-N(3) H-bond arrangement. H-bonding between the N(1)H+ benzimidazole group and the carbonyl on the tyrosine backbone is the stronger and preferred interaction in these complexes. The results show that conjugation effects, secondary H-bond interactions, and H-bond soft modes strongly influence the OH-N(3) interaction and highlight the importance of the direct monitoring of proton stretch transitions in characterizing the proton-transfer reaction coordinate in PCET systems.

S1-State Decay Dynamics of Benzenediols (Catechol, Resorcinol, and Hydroquinone) and Their 1:1 Water Clusters.

The S1-state decaying rates of the three different benzenediols, catechol, resorcinol, and hydroquinone, and their 1:1 water clusters have been state-specifically measured using the picosecond time-resolved parent ion transients obtained by the pump (excitation) and probe (ionization) scheme. The S1 lifetime of catechol is found to be short, giving τ ∼ 5.9 ps at the zero-point level. This is ascribed to the H-atom detachment from the free OH moiety of the molecule. Consistent with a previous report (J. Phys. Chem. Lett. 2013, 4, 3819-3823), the S1 lifetime gets lengthened with low-frequency vibrational mode excitations, giving τ ∼ 9.0 ps for the 116 cm-1 band. The S1 lifetimes at the additional vibronic modes of catechol are newly measured, showing the nonnegligible mode-dependent fluctuations of the tunneling rate. When catechol is complexed with water, the S1 lifetime is enormously increased to τ ∼ 1.80 ns at the zero-point level while it shows an unusual dip at the intermolecular stretching mode excitation (τ ∼ 1.03 ns at 146 cm-1). Otherwise, it is shortened monotonically with increasing the internal energy, giving τ ∼ 0.67 ns for the 856 cm-1 band. Two different asymmetric or symmetric conformers of resorcinol give the respective S1 lifetimes of 4.5 or 6.3 ns at their zero-point levels according to the estimation from our transients taken within the temporal window of 0-2.7 ns. When resorcinol is 1:1 complexed with H2O, the S1 decaying rate is slightly accelerated for both conformers. The S1 lifetimes of trans and cis forms of hydroquinone are measured to be more or less same, giving τ ∼ 2.8 ns at the zero-point level. When H2O is complexed with hydroquinone, the S1 decaying process is facilitated for both conformers, slightly more efficiently for the cis conformer.

Dissipative Stabilization of Squeezing Beyond 3 dB in a Microwave Mode

While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intra-resonator state is limited to 3 dB of squeezing. Here, we implement a reservoir engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intra-resonator state. The raw measurement provides a lower bound on the squeezing at about $6.7 \pm 0.2$ dB below the zero-point level. Further, we show how to correct for resonator evolution during the Wigner tomography and obtain a squeezing as high as $8.2 \pm 0.8$ dB. Moreover, this level of squeezing is achieved with a purity of $-0.4 \pm 0.4$ dB.

Spectroscopy and electronic structure of the low-energy states of ThN

The electronic spectrum of ThN over the range 19,600–21,200 cm−1 is remarkably congested, showing at least twenty vibronic bands originating from the ground state zero-point level. Rotationally resolved spectra for eleven of these bands have been examined to probe the underlying reasons for the dense manifold of states. Dispersed fluorescence spectra and fluorescence decay lifetimes were measured to provide addition insights. The experimental measurements were complemented by electronic structure calculations for the low-energy doublet and quartet states. The ab initio calculations yielded a density of excited states that was consistent with the congested spectrum. These states were derived from the formal configurations Th3+(6d)N3−, Th2+(7s2)N2−(2p5) and Th2+(7s6d)N2−(2p5). The calculations indicated that the rotational and vibrational constants would be characteristic of the electronic configurations. This prediction was not borne out by the experimental data, suggesting that the full range of inter-configurational state interactions were not captured by the computational model.

Quantum motion of a squeezed mechanical oscillator attained via an optomechanical experiment

We experimentally investigate a mechanical squeezed state realized in a parametrically-modulated membrane resonator embedded in an optical cavity. We demonstrate that a quantum characteristic of the squeezed dynamics can be revealed and quantified even in a moderately warm oscillator, through the analysis of motional sidebands. We provide a theoretical framework for quantitatively interpreting the observations and present an extended comparison with the experiment. A notable result is that the spectral shape of each motional sideband provides a clear signature of a quantum mechanical squeezed state without the necessity of absolute calibrations, in particular in the regime where residual fluctuations in the squeezed quadrature are reduced below the zero-point level.

Experimental Observation of the Autler-Townes Splitting in Polyatomic Molecules.

Autler-Townes (AT) splitting has been experimentally observed in the optical transition between the zero-point levels of S1 and S0 for supersonically cooled 2-methoxythiophenol, 2-fluorothiophenol, and 2-chlorothiophenol. This is the first experimental observation of the light-dressed quantum states of polyatomic molecules (N > 3) in the electronic transition. In the resonance-enhanced ionization process involving the optically coupled states, if Rabi cycling is ensured within the nanosecond laser pulse, AT splitting is clearly observed for the open system for which the excited-state lifetime is shorter than hundreds of picoseconds. Semiclassical optical Bloch equations and a dressed-atom approach based on the three-level atomic model describe the experiment quite well, giving deep insights into the light-matter interaction in polyatomic molecular systems.

Real-Time Tunneling Dynamics through Adiabatic Potential Energy Surfaces Shaped by a Conical Intersection.

Dynamic shaping of the adiabatic tunneling barrier in the S-H bond extension coordinate of several ortho-substituted thiophenols has been found to be mediated by low-frequency out-of-plane vibrational modes, which are parallel to the coupling vector of the branching plane comprising the conical intersection. The S-H predissociation tunneling rate (k) measured when exciting to the S1 zero-point level of 2-methoxythiophenol (44 ps)-1 increases abruptly, to k ≈ (22 ps)-1, at the energy corresponding to excitation of the 152 cm-1 out-of-plane vibrational mode and then falls back to k ≈ (40 ps)-1 when the in-plane mode is excited at 282 cm-1. Similar resonance-like peaks in plots of S1 tunneling rate versus internal energy are observed when exciting the corresponding low-frequency out-of-plane modes in the S1 states of 2-fluorothiophenol and 2-chlorothiophenol. This experiment provides clear-cut evidence for dynamical "shaping" of the lower-lying adiabatic potential energy surfaces by the higher-lying conical intersection seam, which dictates the multidimensional tunneling dynamics.

Zero Point Level Effects on Structure, Energy and Spectra of Molecules & Materials

Zero Point Level Effects on Structure, Energy and Spectra of Molecules & Materials

Laser Spectroscopy and Lifetime Measurements of the S1 State of Tetracyanoquinodimethane (TCNQ) in a Cold Gas-Phase Free-Jet.

The S1 electronic state of 7,7,8,8-Tetracyanoquinodimethane (TCNQ) has been investigated by laser induced fluorescence (LIF), dispersed fluorescence (DF) spectroscopy, and lifetime measurements under jet-cooled conditions in the gas-phase. The LIF spectrum showed a weak origin band at 412.13 nm (24262 cm-1 ) with prominent progression and combination bands involving vibrations of 327, 1098, and 2430 cm-1 . In addition, very strong bands appeared at ∼363.6 nm (3300 cm-1 above the origin). Both the LIF and DF spectra indicate considerable geometric change in the S1 state. The fluorescence lifetime of S1 at zero-point level was obtained to be 220 ns. This lifetime is 40 times longer than the radiative lifetime estimated from the S1 -S0 oscillator strength. Furthermore, the lifetimes of the vibronic bands exhibited drastic energy dependence, indicating a strong mixing with the triplet (T1 ) or intramolecular charge-transfer (CT) state. This study is thought to disclose intrinsic nature of TCNQ, which has been well known as a component of organic semiconductors and a versatile p-type dopant.

Correction to "Nonadiabatic Eigenfunctions Can Have Amplitude, Signed Conical Nodes, or Signed Higher Order Nodes at a Conical Intersection with Circular Symmetry".

Numerically exact nonadiabatic eigenfunctions are computed for a two-dimensional conical intersection with circular symmetry, for which a pseudorotation quantum number is conserved and all eigenstates are doubly degenerate. In the calculations reported here, the conical intersection is submerged, with energy below the zero point level. The complete real-valued vibrational-electronic eigenfunctions are visualized using Hunter’s exact factorization for the total vibrational amplitude factor and color for the electronic factor. The zero-point levels have nonzero amplitude at the conical intersection. Nodes in the degenerate nonadiabatic eigenfunctions are classified as accidental if they can be moved or removed by a change in degenerate basis and as essential if they cannot. An integer electronic index defines the order of the nodes for nonadiabatic eigenfunctions by simple closed counterclockwise line integrals. Higher eigenstates can have accidental conical nodes around the conical intersection and essenti...

Gaia Data Release 2

Context. The European Space Agency’s Gaia satellite was launched into orbit around L2 in December 2013. This ambitious mission has strict requirements on residual systematic errors resulting from instrumental corrections in order to meet a design goal of sub-10 microarcsecond astrometry. During the design and build phase of the science instruments, various critical calibrations were studied in detail to ensure that this goal could be met in orbit. In particular, it was determined that the video-chain offsets on the analogue side of the analogue-to-digital conversion electronics exhibited instabilities that could not be mitigated fully by modifications to the flight hardware. Aims. We provide a detailed description of the behaviour of the electronic offset levels on short (<1 ms) timescales, identifying various systematic effects that are known collectively as “offset non-uniformities”. The effects manifest themselves as transient perturbations on the gross zero-point electronic offset level that is routinely monitored as part of the overall calibration process. Methods. Using in-orbit special calibration sequences along with simple parametric models, we show how the effects can be calibrated, and how these calibrations are applied to the science data. While the calibration part of the process is relatively straightforward, the application of the calibrations during science data processing requires a detailed on-ground reconstruction of the readout timing of each charge-coupled device (CCD) sample on each device in order to predict correctly the highly time-dependent nature of the corrections. Results. We demonstrate the effectiveness of our offset non-uniformity models in mitigating the effects in Gaia data. Conclusions. We demonstrate for all CCDs and operating instrument/modes on board Gaia that the video-chain noise-limited performance is recovered in the vast majority of science samples.

Nonadiabatic Eigenfunctions Can Have Amplitude, Signed Conical Nodes, or Signed Higher Order Nodes at a Conical Intersection with Circular Symmetry.

Numerically exact nonadiabatic eigenfunctions are computed for a two-dimensional conical intersection with circular symmetry, for which a pseudorotation quantum number is conserved and all eigenstates are doubly degenerate. In the calculations reported here, the conical intersection is submerged, with energy below the zero point level. The complete real-valued vibrational-electronic eigenfunctions are visualized using Hunter's exact factorization for the total vibrational amplitude factor and color for the electronic factor. The zero-point levels have nonzero amplitude at the conical intersection. Nodes in the degenerate nonadiabatic eigenfunctions are classified as accidental if they can be moved or removed by a change in degenerate basis and as essential if they cannot. An integer electronic index defines the order of the nodes for nonadiabatic eigenfunctions by simple closed counterclockwise line integrals. Higher eigenstates can have accidental conical nodes around the conical intersection and essential nodes of varying circular orders at the conical intersection. The signs of the essential nodes are all opposite the sign of the conical intersection and the signed node orders obey sum rules. Even for submerged conical intersections, the appearance of the exact eigenstates motivates use of signed, half-odd-integral, pseudorotation quantum numbers j. Essential nodes of absolute order (|j| - 1/2) are located on the conical intersection for |j| greater than or equal to 3/2. The eigenfunctions around essential first order nodes are right circular cones with their vertex at the conical intersection.

Hidden role of intermolecular proton transfer in the anomalously diffuse vibrational spectrum of a trapped hydronium ion

We report the vibrational spectra of the hydronium and methyl-ammonium ions captured in the C3v binding pocket of the 18-crown-6 ether ionophore. Although the NH stretching bands of the CH3NH3+ ion are consistent with harmonic expectations, the OH stretching bands of H3O+ are surprisingly broad, appearing as a diffuse background absorption with little intensity modulation over 800 cm-1 with an onset ∼400 cm-1 below the harmonic prediction. This structure persists even when only a single OH group is present in the HD2O+ isotopologue, while the OD stretching region displays a regular progression involving a soft mode at about 85 cm-1 These results are rationalized in a vibrationally adiabatic (VA) model in which the motion of the H3O+ ion in the crown pocket is strongly coupled with its OH stretches. In this picture, H3O+ resides in the center of the crown in the vibrational zero-point level, while the minima in the VA potentials associated with the excited OH vibrational states are shifted away from the symmetrical configuration displayed by the ground state. Infrared excitation between these strongly H/D isotope-dependent VA potentials then accounts for most of the broadening in the OH stretching manifold. Specifically, low-frequency motions involving concerted motions of the crown scaffold and the H3O+ ion are driven by a Franck-Condon-like mechanism. In essence, vibrational spectroscopy of these systems can be viewed from the perspective of photochemical interconversion between transient, isomeric forms of the complexes corresponding to the initial stage of intermolecular proton transfer.

Spectroscopic and theoretical studies of ThCl and ThCl.

The electronic structures of ThCl and ThCl+ have been examined using laser induced fluorescence and two-photon ionization techniques. Rotationally resolved spectra, combined with the predictions from relativistic electronic structure calculations, show that the ground state of the neutral molecule is Th+(7s26d)Cl-, X2Δ3/2. Dispersed fluorescence spectra for ThCl revealed the ground state vibrational levels v = 0-10 and low energy electronic states that also originate from the atomic ion 7s26d configuration. Pulsed field ionization-zero kinetic energy photoelectron spectroscopy established an ionization energy (IE) for ThCl of 51 344(5) cm-1, and the ThCl+ vibrational term energies of the v = 1-3 levels. The zero-point level of the first electronically excited state was found at 949(2) cm-1. Comparisons with high-level theoretical results indicate that the ground and excited states are Th2+(7s6d)Cl- X3Δ1 and Th2+(7s2)Cl- Σ+1, respectively. Relativistic coupled cluster composite thermochemistry calculations yielded an IE within 1.2 kcal/mol of experiment and a bond dissociation energy (118.3 kcal/mol) in perfect agreement with previous experiments.