Random to Chaotic Statistic Transformation in Low-Field Fano-Feshbach Resonances of Cold Thulium Atoms.

Here, we report on the observation of a random to chaotic temperature transformation in the statistics of nearest-neighbor spacings of Fano-Feshbach resonances in the ultracold polarized gas of thulium-169 atoms. We associate this transformation to the appearance of so-called d resonances as well as the shift of other resonances with the temperature. In addition to this statistical change, it has been observed that the characters of s- and d-resonance temperature shifts are quite different: s resonances experience almost no shift or even negative shift with the temperature, while d resonances experience an obvious positive shift. The sign change was attributed to the difference in polarizability of Feshbach molecules and free thulium atoms. In addition, careful analysis of the broad Fano-Feshbach resonances enabled the determination of the sign of thulium's background scattering length. A rethermalization experiment made it possible to estimate a length value of a_{bg}=+144±38 a.u. This indicates that thulium atoms are suitable for achieving Bose-Einstein condensation.

Heat- and light-induced transformations of Yb trapping sites in an Ar matrix.

The low-lying electronic states of Yb isolated in a solid Ar matrix grown at 4.2 K are characterized through absorption and emission spectroscopy. Yb atoms are found to occupy three distinct thermally stable trapping sites labeled "red," "blue," and "violet" according to the relative positions of the absorption features they produce. Classical simulations of the site structure and relative stability broadly reproduced the experimentally observed matrix-induced frequency shifts and thus identified the red, blue, and violet sites as due to respective single substitutional (ss), tetravacancy (Tv), and hexavacancy (Hv) occupation. Prolonged excitation of the (1)S → (1)P transition was found to transfer the Yb population from hv sites into Tv and ss sites. The process showed reversibility in that annealing to 24 K predominantly transferred the Tv population back into Hv sites. Population kinetics were used to deduce the effective rate parameters for the site transformation processes. Experimental observations indicate that the blue and violet sites lie close in energy, whereas the red one is much less stable. Classical simulations identify the blue site as the most stable one.

Electronic spectroscopy of ytterbium in a neon matrix.

The low-lying electronic states of Yb isolated in a solid Ne matrix are characterized through absorption and emission spectroscopy. The absorption spectra of matrix isolated Yb while pumped into its triplet states have been recorded for the first time and the 6s6p (3)P(J) → 5d6s (3)D(1, 2) transition frequencies obtained. Under matrix conditions, the structure of these states is found to be qualitatively the same as in the free atom, but the intersystem crossing rate is observed to be several orders of magnitude greater. A proposed explanation for this is curve crossings between the bound potential energy surface correlated to the 6s6p (1)P(1) state and the potential energy surfaces correlated to the 5d6s (3)D(1, 2) states in isolation. The potentials of the Yb·Ne dimer in its lowest electronic states are computed ab initio and used in a pairwise cluster model to explicitly demonstrate these curve crossings.

Properties of the B+-H2 and B+-D2 complexes: A theoretical and spectroscopic study.

The rotationally resolved infrared spectrum of the B(+)-D(2) ion-neutral complex is recorded in the D-D stretch vibration region (2805-2875 cm(-1)) by detecting B(+) photofragments. Analysis of the spectrum confirms a T-shaped equilibrium geometry for the B(+)-D(2) complex with a vibrationally averaged intermolecular bond length of 2.247 Å, around 0.02 Å shorter than for the previously characterised B(+)-H(2) complex [V. Dryza, B. L. J. Poad, and E. J. Bieske, J. Am. Chem. Soc. 130, 12986 (2008)]. The D-D stretch band centre occurs at 2839.76 ± 0.10 cm(-1), representing a -153.8 cm(-1) shift from the Q(1)(0) transition of the free D(2) molecule. A new three dimensional ab initio potential energy surface for the B(+)+H(2) interaction is calculated using the coupled cluster RCCSD(T) method and is used in variational calculations for the rovibrational energies of B(+)-H(2) and B(+)-D(2). The calculations predict dissociation energies of 1254 cm(-1) for B(+)-H(2) with respect to the B(+)+H(2) (j = 0) limit, and 1313 cm(-1) for B(+)-D(2) with respect to the B(+)+D(2) (j = 0) limit. The theoretical approach reproduces the rotational and centrifugal constants of the B(+)-H(2) and B(+)-D(2) complexes to within 3%, and the magnitude of the contraction of the intermolecular bond accompanying excitation of the H(2) or D(2) sub-unit, but underestimates the H-H and D-D vibrational band shifts by 7%-8%. Combining the theoretical and experimental results allows a new, more accurate estimation for the B(+)-H(2) band origin (3939.64 ± 0.10 cm(-1)).

Ab initio long-range interaction and adiabatic channel capture model for ultracold reactions between the KRb molecules.

The coefficients at the lowest-order electrostatic, induction, and dispersion terms of the anisotropic long-range potential between the two KRb((1)Σ(+)) molecules are evaluated through the static and dynamic molecular properties using the ab initio coupled cluster techniques. Adiabatic channel potentials for the ground-state molecules are obtained and used for the numerical quantum capture probability calculations in the spirit of the statistical adiabatic channel models. Capture rate coefficients for indistinguishable (polarized) and distinguishable (unpolarized) molecules at temperatures below 10 µK agree well with those computed with the simple isotropic dispersion R(-6) potential, but underestimate the measured ones [Ospelkaus et al., Science 327, 853 (2010)] up to a factor of 3. Preliminary assessment of the effects of higher-order long-range terms, retardation of dispersion forces, and magnetic dipole-dipole interaction does not offer any clear perspectives for drastic improvement of the capture approximation for the reactions studied.

Rotationally resolved infrared spectrum of the Na(+)-D2 complex: an experimental and theoretical study.

The infrared spectrum of mass-selected Na(+)-D(2) complexes is recorded in the D-D stretch vibration region (2915-2972 cm(-1)) by detecting Na(+) photofragments resulting from photo-excitation of the complexes. Analysis of the rotationally resolved spectrum confirms a T-shaped equilibrium geometry for the complex and a vibrationally averaged intermolecular bond length of 2.461 Å. The D-D stretch band centre occurs at 2944.04 cm(-1), representing a -49.6 cm(-1) shift from the Q(1)(0) transition of the free D(2) molecule. Variational rovibrational energy level calculations are performed for Na(+)-D(2) utilising an ab initio potential energy surface developed previously for investigating the Na(+)-H(2) complex [B. L. J. Poad et al., J. Chem. Phys. 129, 184306 (2008)]. The theoretical approach predicts a dissociation energy for Na(+)-D(2) of 923 cm(-1) with respect to the Na(+)+ D(2) limit, reproduces the experimental rotational constants to within 1-2%, and gives a simulated spectrum closely matching the experimental infrared spectrum.

He-ThO(1Σ+) interactions at low temperatures: elastic and inelastic collisions, transport properties, and complex formation in cold 4He gas.

We present an ab initio study of cold (4)He + ThO((1)Σ(+)) collisions based on an accurate potential energy surface (PES) evaluated by the coupled cluster method with single, double, and noniterative triple excitations using an extended basis set augmented by bond functions. Variational calculations of rovibrational energy levels show that the (4)He-ThO van der Waals complex has a binding energy of 10.9 cm(-1) in its ground J = 0 rotational state. The calculated energy levels are used to obtain the temperature dependence of the chemical equilibrium constant for the formation of the He-ThO complex. We find that complex formation is thermodynamically favored at temperatures below 1 K and predict the maximum abundance of free ground-state ThO(v = 0, j = 0) molecules between 2 and 3 K. The calculated cross sections for momentum transfer in elastic He + ThO collisions display a rich resonance structure below 5 cm(-1) and decline monotonically above this collision energy. The cross sections for rotational relaxation accompanied by momentum transfer decline abruptly to zero at low collision energies (<0.1 cm(-1)). We find that Stark relaxation in He + ThO collisions can be enhanced by applying an external dc electric field of less than 100 kV∕cm. Finally, we present calculations of thermally averaged diffusion cross sections for ThO in He gas, and find these to be insensitive to small variations of the PES at temperatures above 1 K.

Potential energy surface and rovibrational calculations for the Mg+-H2 and Mg+-D2 complexes.

A three-dimensional potential energy surface is developed to describe the structure and dynamical behavior of the Mg(+)-H(2) and Mg(+)-D(2) complexes. Ab initio points calculated using the RCCSD(T) method and aug-cc-pVQZ basis set (augmented by bond functions) are fitted using a reproducing kernel Hilbert space method [Ho and Rabitz, J. Chem. Phys. 104, 2584 (1996)] to generate an analytical representation of the potential energy surface. The calculations confirm that Mg(+)-H(2) and Mg(+)-D(2) essentially consist of a Mg(+) atomic cation attached, respectively, to a moderately perturbed H(2) or D(2) molecule in a T-shaped configuration with an intermolecular separation of 2.62 Å and a well depth of D(e) = 842 cm(-1). The barrier for internal rotation through the linear configuration is 689 cm(-1). Interaction with the Mg(+) ion is predicted to increase the H(2) molecule's bond-length by 0.008 Å. Variational rovibrational energy level calculations using the new potential energy surface predict a dissociation energy of 614 cm(-1) for Mg(+)-H(2) and 716 cm(-1) for Mg(+)-D(2). The H-H and D-D stretch band centers are predicted to occur at 4059.4 and 2929.2 cm(-1), respectively, overestimating measured values by 3.9 and 2.6 cm(-1). For Mg(+)-H(2) and Mg(+)-D(2), the experimental B and C rotational constants exceed the calculated values by ∼1.3%, suggesting that the calculated potential energy surface slightly overestimates the intermolecular separation. An ab initio dipole moment function is used to simulate the infrared spectra of both complexes.

Dynamics and mechanism of the non-adiabatic transitions from the ungerade I2(D0+u) state induced by collisions with rare gas atoms.

The stepwise three-photon two-color laser excitation scheme is used for selective population of the first-tier ion-pair D0(+)(u) state of molecular iodine. Collection and analysis of the luminescence after the excitation of the v(D) = 6, 8, 13 and 18 vibronic levels of the D state in the pure iodine vapor and the gas-phase mixtures with He, Ar and Xe provide the total and, whenever possible, partial rate constants for the collision-induced non-adiabatic transitions to the other ion-pair states of the first tier. Comparison with the analogous data obtained previously for the non-adiabatic transitions from the E0(+)(g) state reveals the similarity between two cases. For He, the D ↔ E transitions are preferable, whereas for Ar and Xe transitions to the D' and ß states dominate at v(D) = 6, 8 and 13, in accord with the statistical considerations. Efficient population of the δ state at v(D) = 18 in Ar and Xe is the most prominent non-statistical feature observed. The vibrational product state distributions for the D → E transitions are also obtained. In contrast to the previously studied E → D transition, they show significant positive vibronic energy transfer. The measurements for He and Ar are accompanied by the quantum scattering calculations that reproduce well the main qualitative features of the experimental results.

The Na(+)-H(2) cation complex: Rotationally resolved infrared spectrum, potential energy surface, and rovibrational calculations.

The rotationally resolved infrared spectrum of the Na(+)-H(2) cation complex is recorded in the H-H stretch region (4067-4118 cm(-1)) by monitoring the production of Na(+) photofragments. Altogether 42 lines are identified, 40 of which are assigned to K(a)=1-1 transitions (associated with complexes containing ortho-H(2)) and two tentatively assigned to K(a)=0-0 transitions (associated with complexes containing para-H(2)). The K(a)=1-1 subband lines were fitted using a Watson A-reduced Hamiltonian, yielding effective spectroscopic constants. The band origin is estimated as 4094.6 cm(-1), a shift of -66.6 cm(-1) with respect to the Q(1)(0) transition of the free H(2) molecule. The results demonstrate that Na(+)-H(2) has a T-shaped equilibrium configuration with the Na(+) ion attached to a slightly perturbed H(2) molecule but that large-amplitude vibrational motions significantly influence the rotational constants derived from the asymmetric rigid rotor analysis. The vibrationally averaged intermolecular separation in the ground vibrational state is estimated as 2.493 A, increasing slightly (by 0.002 A) when the H(2) subunit is vibrationally excited. A new three-dimensional potential energy surface is developed to describe the Na(+)-H(2) complex. Ab initio points calculated using the CCSD(T) method and aug-cc-pVQZ basis set augmented by bond functions are fitted using a reproducing kernel Hilbert space method [Ho et al., J. Chem. Phys. 104, 2584 (1996)] to give an analytical representation of the potential energy surface. Ensuing variational calculations of the rovibrational energy levels demonstrate that the potential energy surface correctly predicts the frequency of the nu(HH) transition (to within 2.9 cm(-1)) and the dissociation energies [842 cm(-1) for Na(+)-H(2)(para) and 888 cm(-1) for Na(+)-H(2)(ortho)]. The B and C rotational constants are slightly underestimated (by 1.7%), while the vibrationally averaged intermolecular separation is overestimated by 0.02 A.

The Al+ -H(2) cation complex: rotationally resolved infrared spectrum, potential energy surface, and rovibrational calculations.

The infrared spectrum of the Al(+)-H(2) complex is recorded in the H-H stretch region (4075-4110 cm(-1)) by monitoring Al(+) photofragments. The H-H stretch band is centered at 4095.2 cm(-1), a shift of -66.0 cm(-1) from the Q(1)(0) transition of the free H(2) molecule. Altogether, 47 rovibrational transitions belonging to the parallel K(a)=0-0 and 1-1 subbands were identified and fitted using a Watson A-reduced Hamiltonian, yielding effective spectroscopic constants. The results suggest that Al(+)-H(2) has a T-shaped equilibrium configuration with the Al(+) ion attached to a slightly perturbed H(2) molecule, but that large-amplitude intermolecular vibrational motions significantly influence the rotational constants derived from an asymmetric rotor analysis. The vibrationally averaged intermolecular separation in the ground vibrational state is estimated as 3.03 A, decreasing by 0.03 A when the H(2) subunit is vibrationally excited. A three-dimensional potential energy surface for Al(+)-H(2) is calculated ab initio using the coupled cluster CCSD(T) method and employed for variational calculations of the rovibrational energy levels and wave functions. Effective dissociation energies for Al(+)-H(2)(para) and Al(+)-H(2)(ortho) are predicted, respectively, to be 469.4 and 506.4 cm(-1), in good agreement with previous measurements. The calculations reproduce the experimental H-H stretch frequency to within 3.75 cm(-1), and the calculated B and C rotational constants to within approximately 2%. Agreement between experiment and theory supports both the accuracy of the ab initio potential energy surface and the interpretation of the measured spectrum.

On the role of scattering resonances in the F+HD reaction dynamics.

We study scattering resonances in the F+HD-->HF+D reaction using a new method for direct evaluation of the lifetime Q-matrix [Aquilanti et al., J. Chem. Phys. 2005, 123, 054314]. We show that most of the resonances are due to van der Waals states in the entrance and exit reaction channels. The metastable states observed in the product reaction channel are assigned by calculating the energy levels and wave functions of the HF...D van der Waals complex. The behavior of resonance energies, widths, and decay branching ratios as functions of total angular momentum is analyzed. The effect of isotopic substitution on resonance energies and lifetimes is elucidated by comparison with previous results for the F+H2 reaction. It is demonstrated that HF(v'=3) products near threshold are formed by decay of the narrow resonances supported by van der Waals wells in the exit channel. State-to-state differential cross sections in the HF(v'=3) channel exhibit characteristic forward-backward peaks due to the formation of a long-lived metastable complex. The role of the exit-channel resonances in the interpretation of molecular beam experiments is discussed.

Ab initio potential energy surface, infrared spectra, and dynamics of the ion-molecule complexes between Br- and H2, D2, and HD.

A three-dimensional potential energy surface (PES) for the Br(-)-H(2) complex is computed using the ab initio CCSD(T) method and an extended basis set. The PES has two equivalent minima at the linear geometries (equilibrium interfragment distance R(e)=3.34 A and interaction energy D(e)=670 cm(-1)) separated by the barrier at the T-shaped configuration (interfragment distance R(e)=4.03 A and barrier height of 610 cm(-1)). Ab initio points are fitted to a flexible analytical form and used in the variational rovibrational energy level calculations. Simulated infrared spectra of the Br(-)-H(2) and Br(-)-D(2) complexes in the monomer stretching excitation region are in good agreement with the measured ones. Nonstatistical intensity ratios of the complexes of para- and ortho-monomers are qualitatively explained by monomer ligand exchange reactions. Predissociation of the complexes containing vibrationally excited monomers is analyzed and shown to proceed through the near-resonant vibration-to-rotation energy transfer. For complexes involving Br(-) and the HD monomer, two energetically low-lying states are predicted, corresponding predominately to the Br(-)-DH and Br(-)-HD isomeric forms. The results demonstrate the close similarity of the bromide containing complexes to their analogs containing the chloride anion.

Electronic interaction anisotropy between open-shell lanthanide atoms and helium from cold collision experiment.

Based on measurements of the Zeeman relaxation in a cold gas of (3)He [C. I. Hancox, S. C. Doret, M. I. Hummon, L. Luo, and J. M. Doyle, Nature (London) 431, 281 (2004)], we show that the electronic interaction anisotropy between rare-earth atoms with nonzero electronic orbital angular momenta and helium is extremely small. The interaction of the rare-earth atoms with He gives rise to several adiabatic potentials with different electronic symmetries. It is demonstrated that the energy splitting between these potentials does not exceed 0.09 cm(-1) at interatomic distances larger than the turning point for collisions at 0.8 K, including the region of the van der Waals interaction minima.

Interaction potentials of the RG-I anions, neutrals, and cations (RG = He, Ne, Ar).

Interaction potentials of the iodine atom, atomic cation, and anion with light rare-gas atoms from He to Ar are calculated within the unified ab initio approach using the unrestricted coupled-cluster with singles and doubles and perturbative treatment of triples correlation treatment, relativistic small-core pseudopotential, and an extended basis set. Ab initio points are fit to a flexible analytical function. The calculated potentials are compared with available literature data, assessed in the I(-)-and I+-ion mobility calculations and the Ar-I(-)-anion zero electron kinetic-energy spectra simulations, and analyzed using the correlation rules. The results indicate a high precision of the reported potentials.

Collision-induced nonadiabatic transitions in the second-tier ion-pair states of iodine molecule: experimental and theoretical study of the I2(f0g+) collisions with rare gas atoms.

Nonadiabatic transitions induced by collisions with He, Ar, Kr, and Xe atoms in the I(2) molecule excited to the f0(g)(+) second-tier ion-pair state are investigated by means of the optical-optical double resonance spectroscopy. Fluorescence spectra reveal that the transition to the F0(u)(+) state is a dominant nonradiative decay channel for f state in He, Ar, and Kr, whereas the reactive quenching is more efficient for collisions with Xe atom. Total rate constants and vibrational product state distributions for the f-->F electronic energy transfer are determined and analyzed in terms of energy gaps and Franck-Condon factors for the combining vibronic levels at initial vibrational excitations v(f)=8, 10, 14, and 17. Quantum scattering calculations are performed for collisions with He and Ar atoms, implementing a combination of the diatomics-in-molecule and long-range perturbation theories to evaluate diabatic PESs and coupling matrix elements. Calculated rate constants and vibrational product state distributions agree well with the measured ones, especially in case of Ar. Qualitative comparison is made with the previous results for the second-tier f0(g)(+)-->F0(u)(+) transition in collisions with I(2)(X) molecule and the first-tier E0(g)(+)-->D0(u)(+) transition induced by collisions with the rare gas atoms.

The open-shell interaction of He with the B 3Piu(0+) state of Br2: an ab initio study and its comparison with a diatomics-in-molecule perturbation model.

The interaction of He with Br2 in electronically excited B 3Piu state is investigated using spin-unrestricted single and double coupled-cluster approach with noniterative perturbative treatment of triple excitations. Internal electrons of the Br atom are described by effective core pseudopotentials. The validity of this approach is analyzed by comparing the lowest 2Sigma+ and 2Pi electronic states of the HeBr molecule with those obtained in all electron calculations [J. Chem. Phys. 115, 10438 (2001)]. In this context, we examine the performance of different basis sets and saturation with bond functions. The comparison of theoretical blue-shifts with the experiment provides confidence about the present ab initio calculations. In addition, He-Br results of ab initio calculations at the same level are used to obtain approximate He-Br2 (3Piu) interactions in the framework of the diatomics-in-molecule first order perturbation theory (IDIM-PT1) [J. Chem. Phys. 104, 9913 (1996)]. Overall, the IDIM-PT1 model results show a good agreement with the ab initio ones, being the main difference the sensitivity to the elongation of the Br-Br bond.

Isomeric interconversion in the linear Cl(-)-HD anion complex.

The rotationally resolved infrared photodissociation spectrum of Cl(-)-HD is measured in the HD stretch region. Two Sigma-Sigma bands are observed, corresponding to transitions from the ground state [the (nuHD = 0, n = 0) level] and first excited intermolecular bend state [the (nuHD = 0, n = 1) level]. The (nuHD = 0, n = 0) and (nuHD = 0, n = 1) states are predominantly associated with the linear Cl-...DH and Cl-...HD geometries, respectively. The spectrum is complicated by perturbative interactions between levels of the (nuHD = 0, n = 0) and (nuHD = 0, n = 1) rotational manifolds and between levels of the (nuHD = 1, n = 0) and (nuHD = 1, n = 1) rotational manifolds. A global fit to the transition frequencies, taking the lower and upper state perturbations into account, yields zero-order rotational and centrifugal distortion constants and allows us to establish that the (nuHD = 0, n = 1, J" = 0) level lies 13.7 cm(-1) above the (nuHD = 0, n = 0, J" = 0) level. Rovibrational energy level calculations performed using a recent ab initio potential energy surface confirm the picture emerging from the experimental data and provide good agreement with measured molecular parameters. The results emphasize the importance of quantum mechanical interconversion between two isomeric structures of a simple anion complex.