Perturbation-facilitated Optical-optical Double Resonance Research Articles

Observation of the O u−( 3P 1) ion-pair state of Cl 2 by perturbation-facilitated optical-optical double resonance

Perturbation-facilitated optical-optical double resonance spectroscopy was used to study the O u −( 3P 1) ion-pair state of Cl 2 correlating to Cl −( 1S) + Cl +( 3P 1). The O u −( 3P 1) state was combined with the X 1 Σ g + ground state in a (1 + 2) photoexcitation sequence through A 3 Π(1 u) ∼ B′ 3 Π(O u −) mixed intermediate levels. The spectra were analyzed by including the heterogeneous interaction with a new 1 u( 3P 1) state, and the Dunham coefficients were derived for the O u −( 3P 1) state.

The 2 3Πg and 3 3Πg states of 7Li2: Optical–optical double resonance spectroscopy and ab initio calculations

The (2p+2p) 2 3Πg and (2s+3p) 3 3Πg states of 7Li2 have been studied both experimentally and theoretically. Vibrational levels v=0–41 of the 2 3Πg state and v=6–10 of the 3 3Πg state have been observed by perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy. Our ab initio calculations show that the 2 3Πg state, although dissociating into 2p+2p atomic limit, is a Rydberg state and strongly mixed with the (2s+3p) 3 3Πg and (2s+3d) 4 3Πg Rydberg states. Our theoretical calculations show good agreement with our experimental results.

The doubly excited 1 3Σ−g state of 7Li2

This paper reports the first experimental observation of the doubly excited valence (2p+2p)3Σ−g state of 7Li2. We used cw perturbation-facilitated optical–optical double resonance (PFOODR) fluorescence excitation and resolved fluorescence spectroscopic techniques. All the observed levels have been detected through perturbations by the 2 3Πg state. The deperturbed primary molecular constants of this 1 3Σ−g state are Te=34 045.354(43) cm−1, ωe=216.820(37) cm−1, Be=0.673 69(47) cm−1, Re=2.670 81(94) Å, and De=4279.306(43) cm−1. The equilibrium internuclear distance of the 1 3Σ−g state is smaller than that of the X 1Σ+g ground state.

Spectroscopic Study of the Na 2 2 3Σ +g State by cw Perturbation-Facilitated Optical-Optical Double-Resonance Spectroscopy

The Na 2(3 sσ g )(4 sσ g ) 2 3Σ + g state of Na 2 has been observed and studied by cw perturbation-facilitated optical-optical double-resonance (PFOODR) spectroscopy for the first time. A single-mode dye laser and a Ti-sapphire laser served as the pump and the probe lasers, respectively. A total of 543 PFOODR excitation signals have been assigned to the 2 3Σ + g ← b 3Π 1u transitions. Absolute vibrational numbering was determined by counting nodes in the 2 3Σ + g → a 3Σ + u bound-free spectra. Spectroscopic constants and the corresponding RKR potential energy curve are presented in this vsork. The values of T e, R e, and D e, are found to be 25 551.237(49) cm −1, 3.53463(35) Å, and 6211.5(1) cm −1 respectively.

Rotational energy transfer in the Na2 b 3Πu state: Propensity rules for transitions between hyperfine components

The changes in the hyperfine quantum number (F′) that accompany collision-induced ΔJ, ΔΩ, and Δ(e/f-parity) transitions in the Na2 b 3Πu-state have been studied by sub-Doppler, cw, perturbation-facilitated optical–optical double resonance (PFOODR) spectroscopy. The Na2 is contained in a heat pipe oven at ∼1 Torr and the primary collision partner is Na(3s 2S). The PUMP laser selectively excites a single b 3Π0u v′=12, J′=43e, s or 44e, a rotational level, the parent level. All F′ hyperfine components of the parent J′ level are directly populated by the PUMP laser, but with different velocity projections relative to the laser propagation direction. Thus each parent hf component is labeled by its longitudinal velocity. As the PROBE laser is scanned through various 2 3ΠΩg v=2, J←b 3ΠΩ′u v′=12, J′ transitions, sub-Doppler hyperfine structure can be resolved on each parent and daughter rotational line in the PFOODR fluorescence excitation spectrum. The collisional propensity rule ΔF=ΔJ is obeyed for (s, a permutation symmetry conserving) ΔJ′=0, ΔΩ′=0, +1, and +2 and ΔJ′=±1, ±2, ΔΩ′=0 collision-induced transitions. No systematic exploration of the parent-J′, Ω′ dependence of the ΔF propensity was undertaken; in particular, the present study was restricted to the high-J limit where the Na2/Na collisions are not sudden relative to the rotational (half) period and where J≫I. The ΔF=ΔJ hyperfine propensity rule observed for high-J levels of the Na2 b 3Πu state is consistent with previous theoretical predictions of a ΔF=0 propensity for collision-induced ΔJ=0 transitions between Λ-doublet components of the OH X 2Π state and a ΔF=ΔJ propensity for collision-induced transitions between CaBr X 2Σ+ rotational levels.

Perturbation-facilitated all-optical triple resonance spectroscopy of the Na2 b 3Πu state

The Na2 b 3Πu state has been studied by the continuous wave (cw) all-optical triple resonance (AOTR) technique. The AOTR technique used here corresponds to a perturbation-facilitated optical–optical double resonance (PFOODR) excitation through A 1Σu+∼b 3Πu mixed intermediate levels from the ground state to the 2 3Πg state and stimulated emission pumping (SEP) of the 2 3Πg→b 3Πu transition. This sub-Doppler high-resolution PFOODR-SEP technique has allowed us to reach many b 3Πu levels (Ω=0, 1, 2, perturbed and unperturbed, including low v below the A 1Σu+ potential minimum and higher vibrational levels up to v=57). Based on these new high resolution data and previous results from high resolution spectroscopy, we have determined a new set of deperturbed molecular constants from the b 3Πu state up to v=57, the corresponding RKR potential energy curve and the A 1Σu+∼b 3Πu spin–orbit interaction constants. This represents an example of a powerful and general technique for observing a ‘‘dark’’ (e.g., triplet) perturbing state when only the ‘‘bright’’ (e.g., singlet) perturbed state is well known from single photon spectroscopy.

Observations of the 3(3 d) 3Σ g+ state of Na 2

The 3(3 d) 3Σ g + state of the Na 2 molecule has been observed for the first time by perturbation-facilitated optical-optical double-resonance (PFOODR) excitation spectroscopy through A 1Σ u + ∼ b 3Π u mixed intermediate levels. The rotational structure and the fine-hyperfine splittings of the 3 3Σ g + ← b 3Π u transitions are similar to the 4 3Σ g + ← b 3Π u transitions of Na 2. Absolute vibrational numbering of the 3 3Σ g + state was determined by comparing the experimental excitation intensities with the calculated Franck-Condon factors. Molecular constants and the RKR potential curve are also reported. A comparison of the molecular constants of all eight observed states dissociating to the same 3 s + 3 d asymptote with ab initio theory shows remarkably good agreement.

Hyperfine splitting of the 1 3Δg Rydberg state of 7Li2

The hyperfine structure of the 1 3Δg Rydberg state of Na2 has been studied by sub-Doppler CW perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy via A 1Σu+∼b 3Πu mixed intermediate levels.

The Na 2 2 3Δ g state: CW perturbation-facilitated optical-optical double resonance spectroscopy

The Na 2 ( σ g 3 s)(4 dδ g ) 2 3Δ g state has been studied by CW sub-Doppler perturbation-facilitated optical-optical double resonance (PFOODR) spectroscopy. Twenty-three vibrational levels have been observed with resolved fine-hyperfine structure. The fine-hyperfine coupling scheme of the 2 3Δ g state is exactly the same as the Na 2 ( σ g 3 s)(3 dδ g ) 1 3Δ g : case b βs coupling with Fermi contact constant b = 221.7 MHz. Absolute vibrational numbering of the 2 3Δ g state has been determined from the PFOODR fluorescence to the b 3Π u state. The Dunham coefficients were then derived and the corresponding RKR potential curve was determined.

Hyperfine structure of the Na 2 1 3Δ g state

The hyperfine structure in the Na 2 1 3Δ g state is partially resolved by perturbation facilitated optical-optical double resonance (PFOODR) spectroscopy via A 1Σ u + ∼ b 3Π u mixed intermediate levels. The hyperfine splitting and intensity patterns are shown to be consistent with the Hund's case b βS limit, which implies that J-destroying hyperfine matrix elements are large relative to all fine structure splittings. The fine and hyperfine splitting in the 1 3Δ g state is dominated by the Fermi contact coupling constant associated with the σ g 3 s valence orbital. The fitted coupling constant, b = 210 ± 8 MHz, agrees well with a simple prediction, 221 MHz, based on the atomic Na 3 2 S Fermi contact constant. We suggest that all nlλ 3Λ triplet Rydberg states of Na 2 and Li 2, built on the X 2Σ g + ion-core ground state, will exhibit case b βS limiting behavior with fine and hyperfine structure dominated by an n,l,λ-independent Fermi contact coupling constant.

Absolute vibrational numbering and molecular constants of the Na 2 2 3Π g state

The perturbation facilitated optical-optical double resonance (PFOODR) technique has been used to characterize 20 additional vibrational levels ( v = v ∗ − 67 through v ∗ − 63 and v = v ∗ − 58 through v ∗ − 43 ) of the 2 3Π g state. These levels lie below the 3 3Π g v = 0 level and are therefore free of the effects of 2 3Π g ∼ 3 3Π g perturbations that affect most of the 36 previously reported vibrational levels of the 2 3Π g state ( v = v ∗ − 27 through v ∗ + 19 ). An absolute vibrational numbering, v ∗ = 67 , has been inferred from a comparison of intensity patterns in observed and calculated 2 3 Π g v = v ∗ − 67 through v ∗ − 63 , v = v ∗ − 58 and v ∗ − 56 → a 3 Σ u + PFOODR resolved fluorescence spectra. The (effective) 2 3Π 0 g molecular constants, from the perturbation-free and weakly perturbed 2 3Π 0 g levels, are (1σ uncertainties) T e = 28 789.49(6) cm −1, ω e = 94.35(1) cm −1, ω e x e = 0.3760(7) cm −1, ω e y e = 1.91(2) × 10 −3 cm −1, ω e z e = −1.34(2) × 10 −5 cm −1, B e = 0.07316(23) cm −1, α e = 2.20(7) × 10 −4 cm −1, and R e = 4.477(6) A ̊ . From a preliminary fit (neglecting 3Π ∼ 1Σ + perturbations) of the observed (and weakly perturbed) 2 3Π g v = 2, Ω = 0, 1, and 2 rotational levels to a 3Π model, values were obtained for the spin-orbit constant, A = 4.04(10) cm −1, and the true rather than effective rotational constant, B( 3 Π) = B( 3 Π 0) + 0.00185(15) cm −1 . The true B e and R e values for the 2 3Π g state are, respectively, 0.07501(30) cm −1 and 4.422(9) Å.

The hyperfine structure of the Na243Σ+gstate

The fine and hyperfine structure in the Na2 4 3Σ+ g state is partially resolved by Perturbation Facilitated Optical Optical Double Resonance (PFOODR) spectroscopy via A 1Σ+ u ∼ b 3Π u mixed intermediate levels. The hyperfine splitting and intensity patterns are shown to be consistent with the Hund's case b βS limit, when the 4 3Σ+ g state is free of perturbations by nearby vibrational levels of the case a β 2 3Π g and 3 3Π g states. Perturbed levels of 4 3Σ+ g show case b βJ hyperfine structure. The crucial difference between cases b βJ and b βS is the absence, in b βS , of fine structure intervals EN, J - E N, J ± 1 large relative to ΔN = 0, ΔJ = ± 1 J-destroying matrix elements of the hyperfine hamiltonian. It appears that case b βS coupling will be the rule rather than the exception for triplet Rydberg states of Na2, Li2, and H2 built on the ion-core X 2Σ+ g electronic ground state. The fine and hyperfine structure will be dominated by an nlγ-invariant and N-independent Fermi Contact contribution from the singly occupied σ g ns valence molecular orbital. For Na2 4 3Σ+ g , the bI. S coupling constant is b = 214 ± 50 MHz, in satisfactory agreement with semi-empirical values of 221 or 150 MHz naively derived from the free Na atom 3 2 S F = 2 - F = 1 interval.

HIGH RESOLUTION SPECTROSCOPIC STUDIES OF SMALL MOLECULES

The spectra of small molecules in the gas phase are often extremely complicated. Much of this complexity is gratuitous, and can be made to disappear when a suitable double resonance scheme is employed. Sometimes it is necessary to devise devious schemes for circumventing obstacles (selection rules, Franck-Condon factors, potential energy barriers) to important types of molecular structural information (e.g. dissociation energies) or classes of molecular energy levels (e.g. triplets, localized vibrational excitations suited for bond specific photochemistry). The traditional spectroscopic concepts and well-trodden path from spectrum to potential energy surface via molecular constants is ill suited for characterizing the large amplitude displacements of atoms from their equilibrium positions which occur in simple unimolecular dynamical processes. Cross-correlation of double resonance spectra may provide a direct view of specifiable intramolecular processes. Four spectroscopic examples will be discussed : (i) Stimulated Emission Pumping (SEP) spectroscopy of formaldehyde, an example of a well-behaved molecule in the small amplitude limit, for which a complete set of harmonic vibrational frequencies (ω1) and anharmonicities (xij) is determined ; (ii) Perturbation Facilitated Optical-Optical Double Resonance (PFOODR) spectroscopy of Li2, illustrating access to triplet states and the phenomenon of ; (iii) determination of an upper bound to the HCC-H dissociation energy of acetylene by Zeeman Anti-Crossing (ZAC) spectroscopy, a cooperative predissociation scheme similar to the accidental predissociation in Li2 whereby, despite potential energy barriers, one can ensure that the onset of dissociation will be detected not far above the thermochemical limit ; (iv) detection and characterization of a vinylidene vibrational level through the effect of acetylen-vinylidene isomerization on the cross-correlation of acetylene SEP spectra, illustrating a new, direct way of sampling intramolecular dynamics at such high internal energies that vibrational spectra are intrinsically unassignable.

CW Optical-Optical Double Resonance studies of the 2 3Π g, 3 3Π g, 4 3Π g+, and 1 3Δ g Rydberg states of Na 2

The 2 3Π g , 3 3Π g , 4 3Σ g +, and 1 3Δ g states of the Na 2 molecule are observed by sub-Doppler Perturbation Facilitated Optical-Optical Double Resonance (PFOODR) spectroscopy. Absolute vibrational assignments and molecular constants are obtained for two of these states (3 3Π g , v = 0–25 observed, and 4 3Σ g +, v = 3–5, 13, 14 observed). Tentative vibrational assignments and provisional molecular constants are obtained for the 2 3Π g ( v = 43–89 observed) and 1 3Δ g ( v = 31–35, 40, 46–51 observed) states. Spin-orbit, spin-spin, and hyperfine splittings are observed. The direct 3Λ g + → a 3Σ u , 2 3Π g ∼ 3 3Π g perturbation-induced, and collision-induced contributions of these four 3Λ g states to the ubiquitous Na-vapor violet and ultraviolet emission bands are discussed.