Accurate ground state potential of Cu2 up to the dissociation limit by perturbation assisted double-resonant four-wave mixing

Perturbation facilitated double-resonant four-wave mixing is applied to access high-lying vibrational levels of the X ¹Σ_g ⁺ (0_g ⁺) ground state of Cu₂. Rotationally resolved transitions up to v^″ = 102 are measured. The highest observed level is at 98% of the dissociation energy. The range and accuracy of previous measurements are significantly extended. By applying the near dissociation equation developed by Le Roy [R. J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186, 197 (2017)], a dissociation energy of D_e = 16 270(7) hc cm^-1 is determined, and an accurate potential energy function for the X ¹Σ_g ⁺ (0_g ⁺) ground state is obtained. Molecular constants are determined from the measured transitions and by solving the radial Schrödinger equation using this function and are compared with results from earlier measurements. In addition, benchmark multi-reference configuration interaction computations are performed using the Douglas-Kroll-Hess Hamiltonian and the appropriate basis of augmented valence quadruple ζ type. Coupled-cluster single, double, and perturbative triple calculations were performed for comparison.

Spectroscopic disentanglement of the quantum states of highly excited Cu2

Transition metals, characterised by their partially filled d orbitals, provide the basis for many of the most relevant processes in chemistry, biology, and physics. Embedded as single atoms or in small clusters, they give rise to exceptional optical, chemical, and magnetic properties. So far, it has proven impossible to disentangle the complex network of excited quantum states, which greatly hinders prediction and control of material properties. Here, we apply two-colour resonant four-wave mixing to quantitatively resolve the quantum states of the neutral copper dimer. This allows us to unwind the individual spectral lines by isotopic composition and rotational quantum number and reveals a rich network of bright and perturbing dark states. While this work presents a road map for the experimental study of the bonding between and with transition metal atoms, it also provides experimental reference data for prospective quantum chemical approaches on handling systems with a high density of states.

Transition metals are at the basis of key processes in chemistry and biology but their complex electronic structures make understanding of their properties a challenge. Here the authors resolve individual spectral lines of Cu₂ in the deep UV region by two-colour resonant four-wave mixing.

Identification of a new low energy 1u state in dicopper with resonant four-wave mixing

The low energy electronic structure of the copper dimer has been re-investigated using non-linear four-wave mixing spectroscopy and high level ab initio calculations. In addition to the measurement of the previously reported A, B, and C electronic states, a new state denoted A' is identified with T₀ = 20 100.4090(16) cm^-1 (⁶³Cu₂). Rotational analysis of the A'-X (0,0) and (1,0) transitions leads to the assignment of A' 1_u. Ab initio calculations present the first theoretical description of the low energy states of the copper dimer in Hund's case (c) and confirm the experimental assignment. The discovery of this new low energy excited state emphasizes that spin-orbit coupling is significant in states with d-hole electronic configurations and resolves a decades-long mystery in the initial assignment of the A state.

Rovibrational Characterization of High-Lying Electronic States of Cu2 by Double-Resonant Nonlinear Spectroscopy

The available knowledge of the electronically excited states of the copper dimer is limited. This is common for transition metals, as the high density of states hinders both experimental assignment and computation. In this work, two-color resonant four-wave mixing spectroscopy was applied to neutral Cu₂ in the gas phase. The method yielded accurate positions of individual rovibrational lines in the I-X and J-X electronic systems. This revealed the term symbols for the I and J states as ¹Π_u (1_u) and ¹Σ_u⁺ (0_u⁺), respectively. For the ⁶³Cu₂ isotopologue, accurate molecular constants were obtained. The characterization of the J state finally allowed decisive determination of its electron configuration. The J state is obtained from the ground state by promotion of a 3dπ_g electron into the weakly bonding 4pπ_u molecular orbital. From the data analysis, lifetimes of the I state (between 10 ps and 5 ns) and J state (66 ns) were inferred.

Perturbation facilitated two-color four-wave-mixing spectroscopy of C3

Perturbation-facilitated two-color resonant four-wave-mixing spectroscopy is realized to access the (dark) triplet manifold of the C3 molecule from the singlet X̃(1)Σg (+) ground state. The inherent nonlinear signal dependence and coherence of the technique result in a favorable detection of the excited triplet states of interest. The observation of a newly found (3)Δu electronic state is achieved by a two-step excitation via "gate-way" levels (i.e., singlet-triplet mixed levels). Additionally, by fixing the probe laser on a transition exhibiting mainly triplet-triplet character and scanning the pump laser, we demonstrate an effective spin-filtering in a four-wave mixing measurement where only transitions to the perturber (3)Σu(-) state appear exclusively in an otherwise congested spectral range of the Comet band. Ab initio calculations of excited triplet states complement our analysis with the electronic assignment of the observed resonances.

Shedding light on a dark state: the energetically lowest quintet state of C2

In this work we present a deperturbation study of the d (3)Π(g), v=6 state of C(2) by double-resonant four-wave mixing spectroscopy. Accurate line positions of perturbed transitions are unambiguously assigned by intermediate level labeling. In addition, extra lines are accessible by taking advantage of the sensitivity and high dynamic range of the technique. These weak spectral features originate from nearby-lying dark states that gain transition strength through the perturbation process. The deperturbation analysis of the complex spectral region in the (6,5) and (6,4) bands of the Swan system (d(3)Π(g)-a (3)Π(u)) unveils the presence of the energetically lowest high-spin state of C(2) in the vicinity of the d (3)Π(g), v=6 state. The term energy curves of the three spin components of the d state cross the five terms of the 1 (5)Π(g) state at rotational quantum numbers N ≤ 11. The spectral complexity for transitions to the v = 6 level of d (3)Π(g) state is further enhanced by an additional perturbation at N = 19 and 21 owing to the b (3)Σ(g)(-), v=19 state. The spectroscopic characterization of both dark states is accessible by the measurement of 122 "window" levels. A global fit of the positions to a conventional Hamiltonian for a linear diatomic molecule yields accurate molecular constants for the quintet and triplet perturber states for the first time. In addition, parameters for the spin-orbit and L-uncoupling interaction between the electronic levels are determined. The detailed deperturbation study unravels major issues of the so-called high-pressure bands of C(2). The anomalous nonthermal emission initially observed by Fowler in 1910 [Mon. Not. R. Astron. Soc. 70, 484 (1910)] and later observed in numerous experimental environments are rationalized by taking into account "gateway" states, i.e., rotational levels of the d (3)Π(g), v=6 state that exhibit significant (5)Π(g) character through which all population flows from one electronic state to the other.

Picosecond investigation of the collisional deactivation of OH A 2Sigma+(v' = 1, N' = 4, 12) in an atmospheric-pressure flame

The collisional deactivation of the laser excited states A 2Sigma+(v' = 1, N' = 4, 12) of OH in a flame is studied by measurement of spectrally resolved fluorescence decays in the picosecond time domain. Quenching and depolarization rates, as well as vibrational energy-transfer (VET) and rotational energy-transfer (RET) rates are determined. An empirical model describes the temporal evolution of the quenching and VET rates that emerge from the rotational-state relaxation. Fitting this model to the measured 1-0 and 0-0 fluorescence decays yields the quenching and VET rates of the initially excited rotational state along with those that correspond to a rotationally equilibrated vibronic-state population. VET from the higher rotational state (N' = 12) shows a tendency for resonant transitions to energetic close-lying levels. RET is investigated by analysis of the temporal evolution of the 1-1 emission band. The observed RET is well described by the energy-corrected sudden-approximation theory in conjunction with a power-gap law.

Phase-conjugate resonant holographic interferometry applied to NH concentration measurements in a two-dimensional diffusion flame

Resonant holographic interferometry is a diagnostic technique based on the dispersion of light having a frequency close to that of an electronic transition of a molecule. We propose a novel single-laser, two-color setup for the recording of resonant holograms and apply it to two-dimensional (2D) species concentration measurements in a combustion environment. The generation of the second color is achieved by optical phase conjugation from stimulated Brillouin scattering in a cell. The frequency shift of ~8.5 GHz introduced by the phase conjugation matches approximately the linewidth of many molecular transitions at typical flame temperatures and can be implemented to produce holograms of good contrast and diffraction efficiency. Phase-conjugate resonant holographic interferometry is demonstrated in a 2D NH(3) -O(2) flame, yielding interferograms containing information on the NH radical concentration distribution in the flame. Experimental results are quantified by application of a numerical computation of the complex refractive index.