Absolute Vibrational Numbering Research Articles

Absolute numbering of asymptotic vibrational levels of diatomic molecules from cold-physics experiments

We present a simple method for determination of absolute vibrational numbering of isolated near dissociation levels in diatomic molecules, usually observed in cold physics experiments. The method is based on the isotope shift and works even when energies of only two levels from one isotopologue and one level from another isotopologue have been measured. It is demonstrated on data from recently reported precise measurements of binding energies of levels lying close to the dissociation limits in ultracold Yb2, CsYb, RbSr and RbYb molecules. Its predictions agree with these of much more elaborate multi-isotope potential curve fitting. PACS numbers: 31.50.Bc, 33.20.Kf, 33.20.Vq, 33.50.Dq

Absolute vibrational numbering from isotope shifts in fragmentary spectroscopic data

We discuss application of the isotope effect to establish the absolute vibrational numbering in electronic states of diatomic molecules. This is illustrated by examples of states with potential energy curves of both regular and irregular shape, with one or two potential minima. The minimum number of spectroscopic data (either term values or spectral line positions) necessary to provide a unique numbering is considered. We show that at favourable conditions just four term energies (or spectral lines) in one isotopologue and one term energy in the other suffice.

Dissociation Energy and Electronic and Vibrational Spectroscopy of Co+(H2O) and Its Isotopomers

The electronic spectra of Co(+)(H(2)O), Co(+)(HOD), and Co(+)(D(2)O) have been measured from 13,500 to 18,400 cm(-1) using photodissociation spectroscopy. Transitions to four excited electronic states with vibrational and partially resolved rotational structure are observed. Each electronic transition has an extended progression in the metal-ligand stretch, v(3), and the absolute vibrational quantum numbering is assigned by comparing isotopic shifts between Co(+)(H(2)(16)O) and Co(+)(H(2)(18)O). For the low-lying excited electronic states, the first observed transition is to v(3)' = 1. This allows the Co(+)-(H(2)O) binding energy to be determined as D(0)(0 K)(Co(+)-H(2)O) = 13730 ± 90 cm(-1) (164.2 ± 1.1 kJ/mol). The photodissociation spectrum shows a well-resolved K(a) band structure due to rotation about the Co-O axis. This permits determination of the spin rotation constants ε(aa)" = -6 cm(-1) and ε(aa)' = 4 cm(-1). However, the K(a) rotational structure depends on v(3)'. These perturbations in the spectrum make the rotational constants unreliable. From the nuclear spin statistics of the rotational structure, the ground state is assigned as (3)B(1). The electronic transitions observed are from the Co(+)(H(2)O) ground state, which correlates to the cobalt ion's (3)F, 3d(8) ground state, to excited states which correlate to the (3)F, 3d(7)4s and (3)P, 3d(8) excited states of Co(+). These excited states of Co(+) interact less strongly with water than the ground state. As a result, the excited states are less tightly bound and have longer metal-ligand bonds. Calculations at the CCSD(T)/aug-cc-pVTZ level also predict that binding to Co(+) increases the H-O-H angle in water from 104.1° to 106.8°, as the metal removes electron density from the oxygen lone pairs. The O-H stretching frequencies of the ground electronic state of Co(+)(H(2)O) and Co(+)(HOD) have been measured by combining IR excitation with visible photodissociation in a double resonance experiment. In Co(+)(H(2)O) the O-H symmetric stretch is ν(1)" = 3609.7 ± 1 cm(-1). The antisymmetric stretch is ν(5)" = 3679.5 ± 2 cm(-1). These values are 47 and 76 cm(-1), respectively, lower than those in bare H(2)O. In Co(+)(HOD) the O-H stretch is observed at 3650 cm(-1), a red shift of 57 cm(-1) relative to bare HOD.

Observation and assignment of the [formula omitted] state of [formula omitted

The 21∏g state of Rb2 has been observed using the infrared infrared double resonance method. The low part of the potential curve of the state is characterized for the first time. The absolute vibrational numbers are determined with isotope effect. The molecular constants of this state are obtained from a Dunham fit and the potential curve of the state is constructed using the Rydberg–Klein–Rees method.

Photodissociation Studies of the Electronic and Vibrational Spectroscopy of Ni+(H2O)

The electronic spectrum of Ni⁺(H₂O) has been measured from 16200 to 18000 cm⁻¹ using photofragment spectroscopy. Transitions to two excited electronic states are observed; they are sufficiently long-lived that the spectrum is vibrationally and partially rotationally resolved. An extended progression in the metal-ligand stretch is observed, and the absolute vibrational quantum numbering is assigned by comparing isotopic shifts between ⁵⁸Ni⁺(H₂O) and ⁶⁰Ni⁺(H₂O). Time-dependent density functional calculations aid in assigning the spectrum. Two electronic transitions are observed, from the ²A₁ ground state (which correlates to the ²D, 3d⁹ ground state of Ni⁺) to the 3²A₁ and 2²A₂ excited states. These states are nearly degenerate and correlate to the ²F, 3d⁸4s excited state of Ni⁺. Both transitions are quite weak, but surprisingly, the transition to the ²A₂ state is stronger, although it is symmetry-forbidden. The 3d⁸4s states of Ni⁺ interact less strongly with water than does the ground state; therefore, the excited states observed are less tightly bound and have a longer metal-ligand bond than the ground state. Calculations at the CCSD(T)/aug-cc-pVTZ level predict that binding to Ni⁺ increases the H-O-H angle in water from 104.2 to 107.5° as the metal removes electron density from the oxygen lone pairs. The photodissociation spectrum shows well-resolved rotational structure due to rotation about the Ni-O axis. This permits determination of the spin rotation constants ε(αα)'' = -12 cm⁻¹ and ε(αα)' = -3 cm⁻¹ and the excited state rotational constant A' = 14.5 cm⁻¹. This implies a H-O-H angle of 104 ± 1° in the 2²A₂ excited state. The O-H stretching frequencies of the ground state of Ni⁺(H₂O) were measured by combining IR excitation with visible photodissociation in a double resonance experiment. The O-H symmetric stretch is ν₁'' = 3616.5 cm⁻¹; the antisymmetric stretch is ν₅'' = 3688 cm⁻¹. These values are 40 and 68 cm⁻¹ lower, respectively, than those in bare H₂O.

Spectroscopic characterization and potential energy functions of the six low-lying electronic states of ArKr+

Pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectra of ArKr have been recorded in the wavenumber range 108,000–118,000 cm−1 using a 1 + 1′ two-photon resonant excitation scheme from the ground X 0+ state of ArKr via selected intermediate states located just below the Ar(1S0) + Kr([5p[1/2]0) dissociation limit. The positions of ionic vibrational levels with quantum numbers from 1 to 30, from 0 to 8 and from 0 to 6 were determined for the X(1/2), A1(3/2) and A2(1/2) states, respectively. The assignment of absolute vibrational quantum numbers of the ionic states was derived from the isotopic shifts of the spectral lines. Combining these data with literature data on the B(1/2) → X(1/2), C1(3/2) → A1(3/2) and C2(1/2) → A2(1/2) band systems of ArKr+ enabled the derivation of potential energy functions for the lowest six electronic states of ArKr+ using a global potential model that includes the effects of the spin-orbit, charge-exchange and long-range interactions.

Spectroscopic study of the 61Πu state in Li2

The 61Πu ← X1 band system in the Li2 molecule is investigated by the polarisation labelling spectroscopy technique. The excited state is characterised by a set of Dunham coefficients describing f parity levels υ = 0–11, J = 2–47 in the 7Li2 isotopologue and the absolute vibrational numbering is determined by observation of the isotopic effect. The state is identified as 61Πu(2s + 4d) by comparison with theoretical calculations. The main equilibrium constants are Te = 36863.25(5) cm−1 (with respect to the minimum of the electronic ground state), ωe = 253.567(36) cm−1, Re = 3.1639(2) Å.

The 5 1Π u electronic state of the lithium dimer

Polarisation labelling spectroscopy has been used to study the previously unobserved 5 1Π u state of the Li 2 molecule. Molecular constants are derived from a Dunham expansion and the Rydberg-Klein-Rees (RKR) potential curve is constructed. Absolute vibrational numbering of the 5 1Π u state is determined by observation of the isotope effect. The values of T e, ω e and B e are 36390.97(2), 232.03(3) and 0.46832(4) cm −1, respectively.

The 4 3Σ+ state of NaK: Potential energy curve and hyperfine structure

High-resolution spectra, including hyperfine structure, have been observed for numerous vibrational-rotational levels (v,N) of the 4 3Σ+ Rydberg state of the NaK molecule. The data have been used to construct a Rydberg–Klein–Rees potential curve, and this molecular potential has been further refined using the inverse perturbation approximation method. Bound-free emission from the 4 3Σ+ electronic state to the repulsive a(1) 3Σ+ state has also been measured and used to determine both the absolute vibrational numbering and the transition dipole moment function M(R). The experimentally derived potential curve and M(R) are compared with recent theoretical calculations of Magnier et al.; the agreement is very good. Each of the levels (v,N) is typically split into three sets of sublevels by the Fermi contact interaction bI⋅S. Further splitting (of order 0.004 cm−1) has been attributed to the spin-rotation interaction γN⋅S. The patterns observed exhibit a clear transition from Hund’s case bβS for small N toward Hund’s case bβJ for large N. The data can be fitted very well using a theoretical model based on setting up and diagonalizing a 12×12 Hamiltonian matrix with two adjustable parameters (b and γ). The values of b that fit the data best are ∼(0.99±0.04)×10−2 cm−1, with a weak dependence on v. The best fit values of γ are in the range 1–6×10−4 cm−1 and depend strongly on v. The values of γ appear to exhibit anomalous structure for (v,N) levels perturbed by nearby levels of the 3 3Π state.

Observation of the K2 4 3Δ g state by cw perturbation-facilitated optical–optical double resonance spectroscopy

This paper reports for the first time both, an experimental observation and theoretical calculations of the K 2 4 3Δ g state. For the experiment we used cw perturbation-facilitated optical–optical double resonance (PFOODR) spectroscopy. A single mode Ti-sapphire laser and a dye laser served as the pump and probe lasers, respectively. A total of 55 PFOODR signals have been assigned to the 4 3Δ g ← b 3Π u transitions. Absolute vibrational numbering was determined by using quantum defect analysis combined with comparing observed intensities with calculated Franck–Condon factors (FCF). For the former we used known parameters from the 2 3Δ g state since the 2 3Δ g and the 4 3Δ g states belong to the same Rydberg series. We report here our experimental and calculated spectroscopic constants, the corresponding RKR potential energy curve, the Franck–Condon table for the 4 3Δ g ↔ b 3 Π u system, as well as a comparison with the theoretical potential energy curve. The T e value is found to be 28408.938(52) cm −1.

Spectroscopic Study of the C 1Σ+ State of 6LiH and 7LiD

The C 1Σ+ excited electronic state of 6LiH and 7LiD isotopomers has been studied by a pulsed optical−optical double resonance fluorescence depletion spectroscopic technique, in which a band-resolved laser-induced fluorescence detection scheme was used. Forty-two 6LiH vibrational (v = 2−43) levels and fifty-five 7LiD vibrational (v = 4−58) levels have been separately observed. The absolute vibrational numbering of the 7LiD C 1Σ+ state is identified via a comparison between observed term values and those calculated with a hybrid potential energy curve reported previously for the 7LiH C 1Σ+ state. Among the highest observed vibrational levels, the highest observed rovibrational levels are respectively the (43,5) level for 6LiH and the (58,8) level for 7LiD, compared to the level (43,8) reported previously for the 7LiH case. The spectral term values for the vibrational levels lying above v = 33 for 6LiH, and those above v = 44 for 7LiD, occur in an irregular order. The v = 34, J = 0 level of 6LiH and the v = 45, J = 0 level of 7LiD lie mainly in the inner, small well. The term values for the observed rovibrational levels, for 2 ≤ v ≤ 32, 0 ≤ J ≤ 11 of 6LiH and for 4 ≤ v ≤ 44, 0 ≤ J ≤ 13 of 7LiD, in the outer ionic well are described by a set of Dunham-type coefficients. Together with previous observed term values of 7LiH, a combined isotopomer Dunham-type analysis has been performed, and five hydrogen and three lithium mass-dependent Born−Oppenheimer breakdown correction terms for the C 1Σ+ state are determined.

The 43Πg State of Na2: Vibrational Numbering and Hyperfine Structure

The Na2 43Πg state has been studied by continuous-wave (cw) perturbation-facilitated optical–optical double resonance (PFOODR) fluorescence excitation and resolved fluorescence spectroscopy. The absolute vibrational numbering was determined by resolved fluorescence to the a3Σ+u state. The OODR excitation lines of the 43Πg (Kv, N) ← b3Πu (Kvb′, J′) ∼ A1Σ+u (KvA′, J′) ← X1Σ+g (Kv", J") transitions show hyperfine splittings, and the hyperfine coupling scheme of the upper 43Πg levels is case bβS. Although this 43Πg state dissociates to the 3p + 3p atomic limit, it is a Rydberg state at a small internuclear distance, and the hyperfine splitting is caused mainly by the Fermi contact interaction of the ςg3s valence electron with the nuclei. The Fermi contact constant was determined to be bF = 218.3 ± 3.9 MHz.

New Vibrational Numbering and Potential Energy Curve for the 33ΠgElectronic State of the Li2Molecule

An experimental study of the 33Πgelectronic state of7Li2, using the Perturbation–Facilitated Optical–Optical Double Resonance (PFOODR) technique, was recently reported [A. Yiannopoulouet al., J. Chem. Phys.103, 5898, (1995)]. However, due to the very small number of known7Li2A1Σ+u∼b3Πuwindow levels, only 13 ro-vibrational levels (spanning a range of vibrational levels designated υx− 1 to υx+ 3 in that reference) could be observed. Dunham coefficients, based on the assignment υx= 7, were found to fit the observed term values and give a qualitative fit to the intensities of the first six lines of the 33Πg(υ = υx,N= 11) →b3Πuemission spectrum. However, due to the limited number of levels used in the fit, both the absolute vibrational numbering and the 33ΠgRKR potential curve obtained from the Dunham coefficients, must be considered to be uncertain. In the present work, we show that the previously reported 33ΠgRKR curve is unable to reproduce the experimental intensity distribution in the7Li233Πg(υx= 7,N= 11) →a3Σ+uemission continuum. We report new experimental data for the7Li233Πg(υx+ 1,N= 11) →a3Σ+ubound-free continuum and discrete 33Πg(υx± 1,N= 11) →b3Πuspectra obtained using the PFOODR experimental technique. We demonstrate that the correct vibrational numbering and an improved RKR potential curve can be obtained by analyzing the experimental term values in combination with all observed bound-free and discrete spectra. Finally, term values for four6Li233Πgro-vibrational levels were obtained using PFOODR spectroscopy. The measured isotope shifts confirm the absolute vibrational numbering obtained from the present analysis.

Spectroscopic study of the C 1Σ+ state of 7LiH

Forty-two vibrational (v=2–43) levels of the 7LiH C 1Σ+ excited electronic state have been observed by a pulsed optical–optical double resonance fluorescence depletion spectroscopic technique. The absolute vibrational numbering of the C 1Σ+ state is identified with the measurements of the isotopic shifts between 7LiH and 6LiH among several rotation-vibration bands of the C 1Σ+−A 1Σ+ electronic system, and it is further demonstrated by the consistency between observed spectral intensities and calculated ones. The highest observed quasi bound rotational level for the v=43 level is J=8. The spectral term values for those vibrational levels lying above v=33 occur in an irregular order. The level of v=34 lies mainly in the inner, tiny well. The term values for the observed rovibrational levels (2⩽v⩽32, 0⩽J⩽11) in the outer ionic well are described by a set of Dunham-type coefficients, with which a Rydberg–Klein–Rees (RKR) potential energy curve is constructed. This RKR potential is combined with an ab initio potential to construct an effective hybrid potential. The calculated electronic transition moment function for the C-A transition is also given.

Experimental Study of the NaK 31Π State

We report the results of an optical–optical double resonance experiment to determine the NaK 31Π state potential energy curve. In the first step, a narrow band cw dye laser (PUMP) is tuned to line center of a particular 2(A)1Σ+(v′,J′) ← 1(X)1Σ+(v",J") transition, and its frequency is then fixed. A second narrowband tunable cw Ti:Sapphirelaser (PROBE) is then scanned, while 31Π → 1(X)1Σ+violet fluorescence is monitored. The Doppler-free signals accurately map the 31Π(v,J) ro-vibrational energy levels. These energy levels are then fit to a Dunham expansion to provide a set of molecular constants. The Dunham constants, in turn, are used to construct an RKR potential curve. Resolved 31Π(v,J) → 1(X)1Σ+(v",J") fluorescence scans are also recorded with both PUMP and PROBE laser frequencies fixed. Comparison between observed and calculated Franck–Condon factors is used to determine the absolute vibrational numbering of the 31Π state levels and to determine the variation of the 31Π → 1(X)1Σ+transitiondipole moment with internuclear separation. The recent theoretical calculation of the NaK 31Π state potential reported by Magnier and Millié (1996,Phys. Rev. A54, 204) is in excellent agreement with the present experimental RKR curve.

Threshold photoelectron spectroscopy of HCl and DCl

We have measured the threshold photoelectron spectra of HCl and DCl with varying resolution (3–40 meV) using tunable synchrotron radiation and employing the penetrating-field electron-spectroscopic technique over a wide photon energy range (up to 34 eV) that includes the inner-valence ionization region in the molecules. The observed spectra display features produced by both direct ionization and autoionization processes. Autoionization is found to play a particularly important role in the outer-valence ionization region of these molecules. For example, in the formation of the v +=0 band of the X ( 2 Π 3/2) subsystem, in the populating of high vibrational levels of the X ( 2 Π i) system in the Franck–Condon gap region between the X ( 2 Π i) and A ( 2 Σ +) states, and in the predissociated levels of the A ( 2 Σ +) state. The production of extended vibrational structure in the X ( 2 Π i) system is attributed to resonance autoionization of 4sσ, 5sσ and 6sσ 1 Σ + Rydberg states. These and other threshold photoelectron results suggest a propensity for threshold electron production from sσ Rydberg states. Photoionization of HCl and DCl in the inner-valence ionization region between 25 and 30 eV yields nine vibrationally resolved band systems that include the `main line' 3sσ −1 band system and four sets of pairs of vibrationally very similar satellite ion systems. Absolute vibrational numbering in these systems was greatly facilitated by having the isotopomer threshold photoelectron spectra.

Threshold photoelectron spectroscopy of HBr and DBr

The threshold photoelectron spectra of HBr and DBr have been recorded with varying resolution (3–20 meV) over a wide photon energy range (11.5–31.5 eV) using synchrotron radiation and a penetrating-field electron spectrometer, encompassing both the outer- and inner-valence ionization regions. Extensive vibrational structure has been observed in the X( 2 Π i ) band systems for both isotopomers in the Franck–Condon gap region, between the X( 2 Π i ) and A( 2 Σ + ) states, that is attributed to the resonance autoionization of 5sσ, 6sσ and 7sσ 1 Σ + Rydberg states. Resonance autoionization is also found to play a role in the vibrational bands within the A( 2 Σ + ) system that is associated with both non-predissociated and predissociated vibrational levels of the A( 2 Σ + ) state. This is evident by the observed increased broadening of these vibrational bands in comparison to those formed in conventional photoelectron spectroscopy obtained at a similar resolution. Photoionization of HBr and DBr in the inner-valence ionization region between 23 and 29 eV shows four sets of pairs of very similar, vibrationally resolved band systems that are identified as being due to satellite ion states and a single, vibrationally resolved, band system assigned to the `main-line' 4sσ −1 ionization. Absolute vibrational numbering in these systems was greatly facilitated by having the isotopomer threshold photoelectron spectra. Evidence for the direct excitation of repulsive ion states in the 17.5–23.0 eV range has been found.

Observation of the 5 1Πu, 6 1Σu+, and 7 1Σu+ states of Na2 through a Franck–Condon window by all-optical triple resonance spectroscopy

We have observed the 5 1Πu, 6 1Σu+, and 7 1Σu+ states of Na2 by using all-optical triple resonance excitation and an ultrasensitive shielded cylindrical space-charge-limited ionization detector (presumably detecting Na3+ produced by Na2*+Na associative ionization). Although the absolute vibrational numbering is uncertain, the rotational constants are obtained. The Franck–Condon window concept is presented with calculated Franck–Condon factors based on the theoretical 5 1Πu, 6 1Σu+, and 7 1Σu+ potential energy curves of Magnier.

The 21ΠgState of39K2Studied by cw Sub-Doppler Optical–Optical Double Resonance Spectroscopy

The 21Πgstate of39K2, which dissociates to the 4s+ 3dasymptote, has been observed for the first time via the intermediate levels of theA1Σ+u(v = 1–12) state using high-resolution cw optical–optical double resonance excitation spectroscopy. Absolute vibrational numbering has been assigned. A set of molecular constants has been fitted by using the observed term values. The Rydberg–Klein–Rees potential curve is calculated with the fitted molecular constants. The dissociation energy of this state has been determined to be 2318.09 ± 0.13 cm−1.

Photofragmentation spectrum of the Sr+Ar complex

The photofragmentation spectrum of the weakly bound Sr+Ar is measured over the 418–448 nm wavelength region. Two vibrational progressions are observed and are attributed to transitions from the X2 Σ1/2 electronic ground state to vibrational levels of the excited A 2Π1/2 and A 2Π3/2 states. Isotope-resolved measurements of several of the observed transitions are performed to obtain the absolute vibrational numbering. From these, the spectroscopic constants of the involved states are deduced. We obtain ωe′=120.8 cm−1, ωeχe′=1.67 cm−1, and D0′=2303±232 cm−1 for the A 2Π1/2 state and ωe′=122 cm−1, ωeχe′=1.6 cm−1, and D0′=2575±256 cm−1 for the A 2Π3/2 state. For the ground X 2Σ1/2 state the observed hot bands yield ΔG1/2″=48 cm−1. Furthermore a value of 803±244 cm−1 is estimated for D0″. Finally the potential constants are compared with pseudopotential calculations from literature and the trends of binding energies for group II cation–argon complexes are discussed.