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

Electronic structure of Li1,2,3 +,0,- and nature of the bonding in Li2,3 +,0,

The current study of the small lithium molecules Li2 +,0,- and Li3 +,0,- focuses on the nature of the bonding in these molecules as well as their structures and energetics (bond energies, ionization energies, and electron affinities). Valence CASSCF (2s,2p) calculations incorporate nondynamical electron correlation in the calculations, while the corresponding multireference configuration interaction and coupled cluster calculations incorporate dynamical electron correlation. Treatment of nondynamical correlation is critical for properly describing the Li2,3 +,0,- molecules as well as the Li- anion with dynamical correlation, in general, only fine-tuning the predictions. All lithium molecules and ions are bound, with the Li3 + and Li2 + ions being the most strongly bound, followed by Li3 - , Li2 , Li2 - and Li3 . The minimum energy structures of Li3 +,0,- are, respectively, an equilateral triangle, an isosceles triangle, and a linear structure. The results of SCGVB calculations are analyzed to obtain insights into the nature of the bonding in these molecules. An important finding of this work is that interstitial orbitals, a concept first put forward by McAdon and Goddard in 1985, play an essential role in the bonding of all lithium molecules considered here except for Li2 . The interstitial orbitals found in the Li3 +,0 molecules likely give rise to the non-nuclear attractors/maxima observed in these molecules.

An accurate potential model for the a3Σu+ state of the lithium dimer

An accurate Tang-Toennies (TT) model potential is introduced to describe the interatomic potential of the lithium dimer in the a³Σ_u⁺ state. With only one well-known parameter, the ionization energy, the new model potential compares favorably with the experimentally fitted Morse/Long-range (MLR) potential of Dattani and Le Roy [J. Mol. Spectrosc., 2011, 268, 199] and is in excellent agreement with the state-of-the-art ab initio potential of Lesiuk et al. [Phys. Rev. A, 2020, 102, 062806]. With the known dispersion coefficients and the ionization energy, the new potential requires only two experimental parameters, namely the depth of the potential well D_e and its location R_e. The new potential can be extended to the region of zero separation by the united atom limit.

Quantum control of the spin-orbit interaction using the Autler-Townes effect

We have demonstrated quantum control of the spin-orbit interaction based on the Autler-Townes (ac-Stark) effect in a molecular system using a cw optical field. We show that the enhancement of the spin-orbit interaction between a pair of weakly interacting singlet-triplet rovibrational levels, G (1)Π(g)(v=12,J=21,f)-1 (3)Σ(g)(-)(v=1,N=21,f), separated by 750 MHz in the lithium dimer, depends on the Rabi frequency (laser power) of the control laser. The increase in the spin-orbit interaction due to the control field is observed as a change in the spin character of the individual components of the perturbed pair.

Nonadiabatic coupling in the 3 3Pi and 4 3Pi states of NaK

The excited 3 (3)Pi and 4 (3)Pi electronic states of the NaK molecule exhibit an avoided crossing, leading to the anomalous behavior of many features of the rovibrational energy levels belonging to each state. A joint experimental and theoretical investigation of these states has been carried out. Experimental measurements of the vibrational, rotational, and hyperfine structure of numerous levels of the 3 (3)Pi state were recently obtained using the Doppler-free, perturbation-facilitated optical-optical double resonance technique. Additional measurements for the 4 (3)Pi state as well as bound-free emission spectra from selected 3 (3)Pi, 4 (3)Pi, and mixed 3 (3)Pi to approximately 4 (3)Pi rovibrational levels are reported here. A model is also presented for calculating the mixed rovibrational level energies of the coupled 3 (3)Pi-4 (3)Pi system, starting from a 2x2 diabatic electronic Hamiltonian. The 3 (3)Pi and 4 (3)Pi potential curves and the coupling between them are simultaneously adjusted to fit the observed rovibrational levels of both states. The energy levels of the potential curves determined by the fit are in excellent agreement with experiment. The nonadiabatic coupling is sufficiently strong to cause an overall shift of 2-3 cm(-1) for many rovibrational levels as well as somewhat larger shifts for certain pairs of 3 (3)Pi to approximately 4 (3)Pi levels that would otherwise be very close together.

Ab initio study of low-lying triplet states of the lithium dimer

Observation of Bose-Einstein condensation in Li27 initiated the interest in the scattering length of two ground state lithium atoms when they approach each other as a radical pair triplet aSigmau+3 state. But some properties of this state are still unknown. In present work, a number of low-lying triplet states of lithium molecule are calculated by multi-configuration self-consistent field (MCSCF) and response techniques with account of spin-orbit coupling, spin-spin coupling and some other magnetic perturbations. The singlet-triplet transition probabilities to the ground state are also presented. Most results are connected with the weakly bound lowest triplet a3Sigmau+ state, whose radiative lifetime and spin-splitting are unknown so far in spite of its great importance in Bose-Einstein condensation. Calculations indicate that this state has a very small spin-splitting, lambdass=-0.01 cm-1, which is negligible in comparison with the line-width in experimental Fourier transform spectra published so far. Similar splitting is obtained for the upper state of the 1(3)Sigmag+--a3Sigmau+ transition. This is in agreement with experimental rovibronic analysis of the 1(3)Sigmag+--a3Sigmau+ band system in which the triplet structure was not resolved. The radiative lifetime of the a3Sigmau+ state is predicted to exceed 10 h.

The NaK 1 1,3delta states: theoretical and experimental studies of fine and hyperfine structure of rovibrational levels near the dissociation limit

Earlier high-resolution spectroscopic studies of the fine and hyperfine structure of rovibrational levels of the 1 3delta state of NaK have been extended to include high lying rovibrational levels with v < or = 59, of which the highest levels lie within approximately 4 cm(-1) of the dissociation limit. A potential curve is determined using the inverted perturbation approximation method that reproduces these levels to an accuracy of approximately 0.026 cm(-1). For the largest values of v, the outer turning points occur near R approximately 12.7 angstroms, which is sufficiently large to permit the estimation of the C6 coefficient for this state. The fine and hyperfine structure of the 1 3delta rovibrational levels has been fit using the matrix diagonalization method that has been applied to other states of NaK, leading to values of the spin-orbit coupling constant A(v) and the Fermi contact constant b(F). New values determined for v < or = 33 are consistent with values determined by a simpler method and reported earlier. The measured fine and hyperfine structure for v in the range 44 < or = v < or = 49 exhibits anomalous behavior whose origin is believed to be the mixing between the 1 3delta and 1 1delta states. The matrix diagonalization method has been extended to treat this interaction, and the results provide an accurate representation of the complicated patterns that arise. The analysis leads to accurate values for A(v) and b(F) for all values of v < or = 49. For higher v (50 < or = v < or = 59), several rovibrational levels have been assigned, but the pattern of fine and hyperfine structure is difficult to interpret. Some of the observed features may arise from effects not included in the current model.

Experimental study of the NaK 3 3Pi double minimum state

We have used the Doppler-free, perturbation-facilitated optical-optical double-resonance technique to investigate the vibrational, rotational, and hyperfine structure of the 3 (3)Pi double minimum state of NaK. Since this electronic state arises from an avoided crossing with the nearby 4 (3)Pi state, we observe striking patterns in the data that provide a sensitive probe of the electronic wave function in the various regions of the double well potential. A single-mode cw dye laser excites 2(A) (1)Sigma(+)(v(A),J) approximately 1(b) (3)Pi(Omega=0)(v(b),J) mixed singlet-triplet "window" levels from thermally populated rovibrational ground state levels, 1(X) (1)Sigma(+)(v(X),J+/-1). Further excitation by a single-mode cw Ti:sapphire laser selects various 3 (3)Pi(0)(v(Pi),J(Pi)) rovibrational levels, which are detected by observing direct 3 (3)Pi(0)-->1(a) (3)Sigma(+) fluorescence in the green spectral region. Using the inverse perturbation approximation method, we have determined a 3 (3)Pi(0) potential curve that reproduces the measured energies to approximately 0.24 cm(-1). In addition, the hyperfine and spin-orbit constants, b(F) and A(v), have been determined for each region of the potential curve.

Enhanced Access to the Dark Triplet States of (7)Li(2) through New Singlet-Triplet A(1)Sigma(+)(u) approximately b(3)Pi(u) Perturbation Window Levels: Perturbation-Facilitated Optical-Optical Double Resonance Study of the 2(3)Sigma(+)(g) State

Two new pairs of singlet-triplet A(1)Sigma(+)(u) approximately b(3)Pi(u) mixed levels of (7)Li(2) have been observed and used here as "window" levels in cw perturbation-facilitated optical-optical double-resonance (PFOODR) experiments. Previously, only one b(3)Pi(u) vibrational level, v = 19, was known to mix with the singlet A(1)Sigma(+)(u) v = 13 level, resulting in three perturbed A approximately b pairs [L. Li, T. An, T.-J. Whang, A. M. Lyyra, W. C. Stwalley, R. W. Field, and R. A. Bernheim, J. Chem. Phys. 96, 3342 (1992)]. The scarcity of window levels and the resulting difficulty in accessing the dark triplet states of Li(2) is caused by the weak spin-orbit interaction of Li(2). The two new mixed b(3)Pi(u) v = 15 and 22 levels reported here enhance access to the dark triplet state manifold through expansion of the Franck-Condon overlap factor range. Furthermore, the earlier range of accessible rotational levels, N = 5, 7, and 10, is now expanded to include N = 8 and N = 16, thereby allowing for more reliable determination of the excited triplet states rotational structure. To demonstrate the importance of the new A(1)Sigma(+)(u) approximately b(3)Pi(u) mixed levels, we have studied the 2(3)Sigma(+)(g) state by cw PFOODR fluorescence excitation spectroscopy. New molecular constants and RKR potential curve have been determined. As previously reported [L. Li, G. Lazarov, and A. M. Lyyra, J. Mol. Spectrosc. 191, 387 (1998)], the 2(3)Sigma(+)(g) state interacts with the repulsive 1(3)Pi(g) state by L-uncoupling and predissociates. We show that some 2(3)Pi(g) levels predissociate accidentally by the 1(3)Pi(g) state via the 2(3)Sigma(+)(g) state through L-uncoupling. Copyright 2001 Academic Press.

The Predissociation of the 1(3)Sigma(-)(g) State of (7)Li(2)

The predissociation of the 1(3)Sigma(-)(g) v >/= 10 levels of (7)Li(2) has been observed by pulsed and continuous-wave perturbation-facilitated optical-optical double-resonance spectroscopy (PFOODR). Our ab initio calculation shows that the inner wall of the 1(3)Sigma(-)(g) potential intersects the 1(3)Pi(g) repulsive potential at internuclear distance R = 2.00 Å. The predissociation is due to a DeltaS = 0, DeltaLambda = +/-1 rotational-electronic interaction with the repulsive 1(3)Pi(g) state. Copyright 2001 Academic Press.

The Perturbation between the G(1)Pi(g) and 2(1)Delta(g) States of (7)Li(2)

We have observed the rotational levels in the v = 2, 3, 5, 6, 7, and 8 vibrational manifolds of the 2(1)Delta(g) state of (7)Li(2) via the A(1)Sigma(+)(u) intermediate levels by DeltaLambda = 2 transitions. This violation of the DeltaLambda = 0, +/-1 selection rule is due to the interaction with the G(1)Pi(g) state. Band-by-band deperturbations of the G(1)Pi(g) approximately 2(1)Delta(g) (v(Pi), v(Delta)) = (11, 2), (12, 3), (15, 5), (16, 6), (18, 7), and (19, 8) bands have been performed. Deperturbed molecular constants and rotational-electronic interaction parameters are reported here. Copyright 2000 Academic Press.

The 2(3)Delta(g) State of (7)Li(2)

Using pulsed perturbation-facilitated optical-optical double resonance (PFOODR) spectroscopy, the 2(3)Delta(g) state of (7)Li(2) (electronic configuration (varsigma(g)2s) (4ddelta(g)), effective principal quantum number n* = 4.101) has been observed and assigned. Molecular constants and a RKR potential energy curve were obtained. The major molecular constants are Copyright 2000 Academic Press.

The 6svarsigma, 6dvarsigma, and 7dvarsigma Rydberg (1)Sigma(+)(g) States and Two Doubly Excited (1)Sigma(+)(g) States of Na(2)

Five highly excited (1)Sigma(+)(g) states of Na(2) were observed for the first time by pulsed optical-optical double resonance (OODR) fluorescence excitation spectroscopy. Three of the five states are assigned to the 6svarsigma (1)Sigma(+)(g), 6dvarsigma (1)Sigma(+)(g), and 7dvarsigma (1)Sigma(+)(g) Rydberg states. The other two states are assigned to doubly excited (1)Sigma(+)(g) states. Copyright 1999 Academic Press.

Rotational Pattern Difference in Resolved Fluorescence Spectra with Different Detection Schemes

The relative intensities of rotational lines in resolved fluorescence spectra are dependent on the detection direction and the choice of the detection scheme when a grating monochromator is used. These differences arise from the spatially anisotropic distribution of the fluorescence, the rotational branch dependence of the fluorescence polarization, and the polarization dependence of the monochromator grating efficiency. Both the anisotropy of the emission and the rotational branch dependence of the fluorescence polarization are enhanced in double-resonance excitation schemes. In the present work, we analyze the relative intensities in the (7)Li(2) 1(3)Sigma(-)(g) --> 1(b)(3)Pi(u) and 1(3)Delta(g) --> 1(b)(3)Pi(u) resolved fluorescence spectra, observed following double-resonance excitation, for three different detection schemes. Copyright 1999 Academic Press.

Precise Molecular Constants for the 6Li2 A1Sigma+u-X1Sigma+g System by Sub-Doppler Polarization Spectroscopy

We report here new and more accurate molecular constants from sub-Doppler polarization spectroscopy of the A1Sigma+u-X1Sigma+g system of 6Li2 using single mode cw dye lasers. These new constants cover the range of vibrational levels from v" = 0-8 in the ground state and v' = 0-24 in the excited state. New molecular constants and RKR potential energy curves for the A1Sigma+u and X1Sigma+g states are given. The Te value for the A1Sigma+u state is 14068.043(34) cm-1. The analysis indicates that there is a noticeable breakdown of the Born-Oppenheimer approximation for the 6Li2 and 7Li2 isotopomers. Copyright 1998 Academic Press.

Strongly bound doubly excited states of Be2

The triplet and singlet potential curves of Be2 generated by single and double excitations from 2σu into 3σg and (or) 1πu are studied with a multireference configuration interaction (MRD-CI) method. Relative to X1Σg+(2σg2 σu2) with Re = 4.72 bohr and ωe = 258 cm−1 (calculated here), these antibonding MO → bonding MO excitations lead to average decreases in bond distance (in bohr) of 0.55 (2σu → 3σg), 0.88 (2σu → 1πu), 0.93 (2σu2 → 3σg1πu), and 1.22 (2σu2 → 1πu2). The increase in vibrational frequencies ranges from 240 to 600 cm−1. The 3σg MO is found to be less bonding than 1πu, confirming predictions made by Bader et al. The experimental states A1Πu and B1Σu+ correspond to doubly excited 11Πu (2σu2 → 3σg1πu) and singly excited 11Σu+(2σu → 3σg), respectively. The 13Σg− and 11Δg states, both 2σu2 → 1πu2, preserve their doubly excited structure up to dissociation. Within the Franck–Condon region, 13Πu changes from bound (2σu2 → 3σg1πu) to repulsive (mixed 2σu → 1πg/2σg → 1πu), thereby creating the unusual situation of a strongly bound potential (short Re, high ωe) with an adiabatic dissociation energy near zero. The singlet counterpart 11Πu, however, behaves regularly as its doubly excited character is maintained up to large R(Be—Be). Key words: ab initio calculations, beryllium dimer, doubly excited states, electronic transitions, potential curves.