The spectrum of molecular hydrogen can be measured in the laboratory to very high precision using advanced laser and molecular beam techniques, as well as frequency-comb based calibration [1,2]. The quantum level structure of this smallest neutral molecule can now be calculated to very high precision, based on a very accurate (10⁻¹⁵ precision) Born-Oppenheimer potential [3] and including subtle non-adiabatic, relativistic and quantum electrodynamic effects [4]. Comparison between theory and experiment yields a test of QED, and in fact of the Standard Model of Physics, since the weak, strong and gravitational forces have a negligible effect. Even fifth forces beyond the Standard Model can be searched for [5]. Astronomical observation of molecular hydrogen spectra, using the largest telescopes on Earth and in space, may reveal possible variations of fundamental constants on a cosmological time scale [6]. A study has been performed at a 'look-back' time of 12.5 billion years [7]. In addition the possible dependence of a fundamental constant on a gravitational field has been investigated from observation of molecular hydrogen in the photospheres of white dwarfs [8]. The latter involves a test of the Einsteins equivalence principle. [1] E.J. Salumbides et al., Phys. Rev. Lett. 107, 143005 (2011). [2] G. Dickenson et al., Phys. Rev. Lett. 110, 193601 (2013). [3] K. Pachucki, Phys. Rev. A82, 032509 (2010). [4] J. Komasa et al., J. Chem. Theory Comp. 7, 3105 (2011). [5] E.J. Salumbides et al., Phys. Rev. D87, 112008 (2013). [6] F. van Weerdenburg et al., Phys. Rev. Lett. 106, 180802 (2011). [7] J. Badonaite et al., Phys. Rev. Lett. 114, 071301 (2015). [8] J. Bagdonaite et al., Phys. Rev. Lett. 113, 123002 (2014).

The ground electronic energy levels of H₂ have been used as a benchmark system for the most precise comparisons between ab initio calculations and experimental investigations. Recent examples include the determinations of the ionization energy [1], fundamental vibrational energy splitting [2], and rotational energy progression extending to J=16 [3]. In general, the experimental and theoretical values are in excellent agreement with each other. The energy calculations, however, reduce in accuracy with the increase in rotational and vibrational excitation, limited by the accuracy of non-Born Oppenheimer corrections, as well as the higher-order QED effects. While on the experimental side, it remains difficult to sufficiently populate these excited levels in the ground electronic state. We present here our high-resolution spectroscopic study on the X ¹Σ⁺_g electronic ground state levels with very high vibrational quanta (ν = 10,11,12). Vibrationally-excited H₂ are produced from the photodissociation of H₂S [4], and subsequently probed by a narrowband pulsed dye laser system. The experimental results are consistent with and more accurate than the best theoretical values [5]. These vibrationally-excited level energies are also of interest to studies that extract constraints on the possible new interactions that extend beyond the Standard Model [6]. [1] J. Liu et al., J. Chem. Phys. 130, 174306 (2009). [2] G. Dickenson et al., Phys. Rev. Lett. 110, 193601 (2013). [3] E.J. Salumbides et al., Phys. Rev. Lett. 107, 143005 (2011). [4] J. Steadman and T. Baer, J. Chem. Phys. 91, 6113 (1989). [5] J. Komasa et al., J. Chem. Theory Comp. 7, 3105 (2011). [6] E.J. Salumbides et al., Phys. Rev. D 87, 112008 (2013).

Modern string theories, which seek to produce a consistent description of physics beyond the Standard Model that also includes the gravitational interaction, appear to be most consistent if a large number of dimensions are postulated. For example the mysterious M-theory, which generalizes all consistent versions of superstring theories, require 11 dimensions. We demonstrate that investigations of quantum level energies in simple molecular systems provide a testing ground to constrain the size of compactified extra dimensions, for example those proposed in the ADD [1] and RS scenarios [2]. This is made possible by the recent progress in precision metrology with ultrastable lasers on energy levels in neutral molecular hydrogen (H₂, HD and D₂) [3] and the molecular hydrogen ions (H₂⁺, HD⁺ and D₂⁺) [4]. Comparisons between experiment and quantum electrodynamics calculations for these molecular systems can be interpreted in terms of probing large extra dimensions, under which conditions gravity will become much stronger. Molecules are a probe of space-time geometry at typical distances where chemical bonds are effective, i.e. at length scales of an Å. [1] N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. B 429, 263 (1998) [2] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999). [3] G. Dickenson et al., Phys. Rev. Lett. 110, 193601 (2013). [4] J. C. J. Koelemeij et al., Phys. Rev. Lett. 98, 173002 (2007).

The low temperatures and pressures of the interstellar medium provide an ideal environment for gas phase ion-neutral reactions that play an essential role in the chemistry of the universe. High-precision laboratory spectra of molecular ions are necessary to facilitate new astronomical discoveries and provide a deeper understanding of interstellar chemistry, but forming ions in measurable quantities in the laboratory has proved challenging. Even when cryogenically cooled, the high temperatures and pressures of typical discharge cells lead to diluted and congested spectra from which extracting chemical information is difficult. Here we overcome this challenge by coupling an electric discharge to a continuous supersonic expansion source to form ions cooled to low temperatures. The ion production abilities of the source have been demonstrated previously as ion densities on the order of 10¹⁰-10¹² cm⁻³ have been observed for H₃⁺.^a With a smaller rotational constant and the expectation that it will be formed with comparable densities, HN₂⁺ is used as a reliable measure of the cooling abilities of the source. Ions are probed through the use of a widely tunable mid-infrared (3-5 μm) spectrometer based on light formed by difference frequency generation and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS).^b To improve the sensitivity of the instrument the discharge is electrically modulated and the signal is fed into a lock-in amplifier before being recorded by a custom data acquisition program. Rovibrational transitions of H₃⁺ and HN₂⁺ have been recorded, giving rotational temperatures of 80-120 K and 35-40 K, respectively. With verification that the source is producing rotationally cold ions, we move toward the study of primary ions of more astronomical significance, including H₂CO⁺. ^aK. N. Crabtree, C. A. Kaufman, and B. J. McCall, Rev. Sci. Instrum. 81, 086103 (2010). ^bM. W. Porambo, B. M. Siller, J. M. Pearson, and B. J. McCall, Opt. Lett. 37, 4422 (2012)

The trihydrogen cation, H₃⁺, represents one of the most important and fundamental molecular systems. Having only two electrons and three nuclei, H₃⁺ is the simplest polyatomic system and is a key testing ground for the development of new techniques for calculating potential energy surfaces and predicting molecular spectra. Corrections that go beyond the Born-Oppenheimer approximation, including adiabatic, non-adiabatic, relativistic, and quantum electrodynamic corrections are becoming more feasible to calculateO. Polyansky, et al., Phil. Trans. R. Soc. A (2012), 370, 5014.M. Pavanello, et al., J. Chem. Phys. (2012), 136, 184303.L. Diniz, et al., Phys. Rev. A (2013), 88, 032506.L. Lodi, et al., Phys. Rev. A (2014), 89, 032505.. As a result, experimental measurements performed on the H₃⁺ ion serve as important benchmarks which are used to test the predictive power of new computational methods. By measuring many infrared transitions with precision at the sub-MHz level it is possible to construct a list of the most highly precise experimental rovibrational energy levels for this molecule. Until recently, only a select handful of infrared transitions of this molecule have been measured with high precision ( ∼  1 MHz)J. Hodges, et al., J. Chem. Phys (2013), 139, 164201. Using the technique of Noise Immune Cavity Enhanced Optical Heterodyne Velocity Modulation Spectroscopy, we are aiming to produce the largest high-precision spectroscopic dataset for this molecule to date. Presented here are the current results from our survey along with a discussion of the combination differences analysis used to extract the experimentally determined rovibrational energy levels. O. Polyansky, et al., Phil. Trans. R. Soc. A (2012), 370, 5014.

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L. Diniz, et al., Phys. Rev. A (2013), 88, 032506.

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J. Hodges, et al., J. Chem. Phys (2013), 139, 164201..

The molecular ion OH⁺ is of significant importance to interstellar chemistry. OH⁺ is a key intermediate in the formation of water, and the ratios of OH⁺ to H₂O⁺ and H₃O⁺ have been used to calculate the cosmic ray ionization rates in diffuse molecular clouds.F. Wyrowski et al., Astron. Astrophys., (2010),26,5.E. González-Alfonso et al., Astron. Astrophys., (2013), 550, A25.N. Indriolo et al., Astrophys. J., (2015), 800, 40.o improve on previous spectroscopic work, the sensitive technique Noise Immune Cavity Enhanced Optical Heterodyne Velocity Modulation Spectroscopy (NICE-OHVMS) has been used to record rovibrational transitions of OH⁺. Previously this approach has been used to investigate HCO⁺, H₃⁺, CH₅⁺, and HeH⁺.J.N. Hodges et al., Chem. Phys., (2013), 139, 164201.A.J. Perry et al., J. Chem. Phys., (2014), 141, 101101. Using an optical frequency comb for precise frequency calibration, the OH⁺ line centers have been determined with  ∼ MHz uncertainties. Here the most precise and accurate list of rovibrational transitions of OH⁺ is presented. These values can then be used to empirically determine rotational transitions through combination difference analysis. F. Wyrowski et al., Astron. Astrophys., (2010),26,5.

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N. Indriolo et al., Astrophys. J., (2015), 800, 40.T J.N. Hodges et al., Chem. Phys., (2013), 139, 164201.

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Collision-induced rotational energy transfer among rotational levels of ground state CN (X ²Σ⁺, v = 0) radicals has been probed by saturation recovery experiments, using high-resolution, polarized transient FM spectroscopy to probe the recovery of population and the decay of alignment following ns pulsed laser depletion of selected CN rotational levels. Despite the lack of Doppler selection in the pulsed depletion and the thermal distribution of collision velocities, the recovery kinetics are found to depend on the probed Doppler shift of the depleted signal. The observed Doppler-shift-dependent recovery rates are a measure of the velocity dependence of the inelastic cross sections, combined with the moderating effects of velocity-changing elastic collisions. New experiments are underway, in which the pulsed saturation is performed with sub-Doppler velocity selection. The time evolution of the spectral hole bleached in the initially thermal CN absorption spectrum can characterize speed-dependent inelastic collisions along with competing elastic velocity-changing collisions, all as a function of the initially bleached velocity group and rotational state. The initial time evolution of the depletion recovery spectrum can be compared to a stochastic model, using differential cross sections for elastic scattering as well as speed-dependent total inelastic cross sections, derived from ab initio scattering calculations. Progress to date will be reported. Acknowledgments: Work at Brookhaven National Laboratory was carried out under Contract No. DE-AC02-98CH10886 and DE-SC0012704 with the U.S. Department of Energy and supported by its Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences.

All available spectroscopic data for all stable isotopologues of HeH⁺ are analyzed with a direct-potential-fit (DPF) procedure that uses least-squares fits to experimental data in order to optimize the parameters defining an analytic potential. Since the coefficient of the leading (1/r⁴) inverse-power term is C₄ = α^He/2, when treated as a free parameter in the fit, it provides an independent empirical estimate of the polarizability of the He atom. The fact that the present model for the long-range behaviour includes accurate theoretical C₆, C₇ and C₈ coefficients (which are held fixed in the fits) should make it possible to obtain a good estimate of this quantity. The Boltzmann constant k_B, a fundamental constant that can define temperature, is directly related to the dipole polarizability α of a gas by the expression   k_B = \fracα3ϵ₀(\fracϵ_r+2ϵ_r−1)\fracpT , in which ϵ₀ is the permitivity of free space, and ϵ_r is the relative dielectric permitivity at pressure p and temperature T. If k_B can be determined with greater precision, it can be used to define temperature based on a fundamental constant, rather than based on the rather arbitrary triple point of water, which is only known to 5 digits of precision. α for He is known theoretically to 8 digits of precision, but an empirical value lags behind. This work, examines the question of how precisely α^He can be determined from a DPF to spectroscopic HeH⁺ data, where the limiting long-range tail of the analytic potential has the correct form implied by Rydberg theory: α^He/2r⁴. Although the highest observed vibrational level is bound by over 1000 cm⁻¹, our current fits determine an empirical C₄ = α^He/2 with an uncertainty of only 0.6%. It has been shown that with more precise spectroscopic data near the dissociation, α^He can be determined with high enough precision to determine a more precise k_B and hence redefine temperature more accuratelyDattani N S. & Puchalski M. (2015) Physical Review Letters (in press)

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Dattani N S. & Puchalski M. (2015) Physical Review Letters (in press).

At last year's ISMS meeting, Zaleski et al. reported new broadband MW spectroscopy measurements of pure rotational transitions in the v=0−6 levels of the ²Π_1/2 ground electronic state of PbI. D.P. Zaleski, H. Köckert, S.L. Stephens, N. Walker, L.-M. Dickens, and C. Evans, paper RE08 at the 69^th International Symposium on Molecular Spectroscopy, University of Illinois (2014). The analysis presented at that time was a conventional v-level by v-level `band-constant' analysis performed using the PGopher program. PGopher - a Program for Simulating Rotational Structure, C. M. Western, University of Bristol, http://pgopher.chm.bris.ac.ukThat level-by-level PGopher analysis yielded values of B<sub>v</sub>, D<sub>v</sub> and five spin-splitting parameters for each vibrational level of each isotopologue. Ignoring the spin-splitting information, the B<sub>v</sub> and D<sub>v</sub> values were used to generate a set of synthetic pure R(0) transitions for each level that were taken to represent the "mechanical" information about the molecule contained in these spectra. A standard direct-potential-fit (DPF) analysis DPotFit 2.0: A Computer Program for fitting Diatomic Molecule Spectra to Potential Energy Functions, R.J. Le Roy, J. Seto and Y. Huang, University of Waterloo Chemical Physics Research Report CP-667 (2013); see http://leroy.uwaterloo.ca/programs/.as then used to fit these data to an "Expanded Morse Oscillator" (EMO) potential function form. The well-depth parameter D<sub>e</sub> was fixed at the literature value, while values of the equilibrium distance r<sub>e</sub> and three EMO exponent-coefficient expansion `potential shape' parameters are determined from the fits. The best fits to the data yield potentials whose fundamental vibrational spacings are in excellent agreement with experiment K. Ziebarth, R. Breidohr, O. Shestakov and E.H. Fink, Chem. Phys. Lett. 190, 271 (1992).ogether with reliable predictions for the first five overtone energies.

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 D.P. Zaleski, H. Köckert, S.L. Stephens, N. Walker, L.-M. Dickens, and C. Evans, paper RE08 at the 69^th International Symposium on Molecular Spectroscopy, University of Illinois (2014).   PGopher - a Program for Simulating Rotational Structure, C. M. Western, University of Bristol, http://pgopher.chm.bris.ac.uk   DPotFit 2.0: A Computer Program for fitting Diatomic Molecule Spectra to Potential Energy Functions, R.J. Le Roy, J. Seto and Y. Huang, University of Waterloo Chemical Physics Research Report CP-667 (2013); see http://leroy.uwaterloo.ca/programs/.w  K. Ziebarth, R. Breidohr, O. Shestakov and E.H. Fink, Chem. Phys. Lett. 190, 271 (1992).t

Despite only having 6e⁻, the most sophisticated Li₂(b,1³Π_u) calculationMusial & Kucharski (2014) J. Chem. Theor. Comp. 10, 1200.as an r_e that disagrees with the empirical value by over 1500% of the latter's uncertainty, and energy spacings that disagree with those of the empirical potential by up to over 1.5cm⁻¹. The discrepancy here is far more than for the ground state of the 5e⁻ system BeH, for which the best ab initio calculation gives an r_e which disagrees with the empirical value by less than 200% of the latter's uncertaintyDattani N. S. (2015) J. Mol. Spec. http://dx.doi.org/10.1016/j.jms.2014.09.005 In addition to this discrepancy, other reasons motivating the construction of an analytic empirical potential for Li₂(b,1³Π_u) include (1) the fact that it is the most deeply bound Li₂ state, (2) it is the only Li₂ state out of the lowest five, for which no analytic empirical potential has yet been built, (3) the state it mixes with, the A(1¹Σ_u)-state, is one of the most thoroughly characterized molecular states, but has a small gap of missing data in part of the region where it mixes with the b-state, and (4) it is one of the states accessible by new ultra-high precision techniques based on photoassociationSemczuk M., Li X., Gunton W., Haw M., Dattani N. S., Witz J., Mills A., Jones D. J., Madison K. W. (2013) Phys. Rev. A 87, 052505 ^,Gunton W., Semczuk M., Dattani N. S., Madison K. W. (2013) Phys. Rev. A 88, 062510 Finally (5) there is currently a discrepancy between the most sophisticated 3e^-

Trapped molecular ions provide new systems for precision spectroscopy and tests of fundamental physics. For example, measurements of the permanent electric dipole moment of the electron (eEDM) test time-reversal symmetryThe ACME Collaboration, et al., Science 343, 269 (2014) Currently, we are using Ramsey spectroscopy between spin states of the metastable ³∆₁ state in trapped HfF⁺ for a measurement of the eEDMH. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, E. A. Cornell, Science 342, 1220 (2013).^, A. E. Leanhardt, J. L. Bohn, H. Loh, M. C. Grau, P. Maletinski, E. R. Meyer, L. C. Sinclair, R. P. Stutz, E. A. Cornell, J. Mol. Spec. 270, 1 (2011)..

An experimental search for the permanent electric dipole moment of the electron (eEDM) is currently being performed using the metastable ³∆₁ state in trapped HfF^{+ (}H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, E. A. Cornell, Science 342, 1220 (2013).^). The use of ThF^+ could significantly increase the sensitivity due to the larger effective electric field and longer ^3_1 state lifetime. Previous work by the Heaven group has identified several low−lying ThF^+ electronic statesB. J. Barker, I. O. Antonov, M. C. Heaven, K. A. Peterson, J. Chem. Phys. 136, 104305 (2012). however, the ground state could not be conclusively assigned. In addition, transitions to intermediate electronic states have not been identified, but they are necessary for state detection, manipulation, and readout in an eEDM experiment. To date we have acquired 3700 cm⁻¹of densely−sampled ThF^+ spectra in the 695 – 1020 nm region with frequency combL. C. Sinclair, K. C. Cossel, T. Coffey, J. Ye, E. A. Cornell, PRL 107, 093002 (2011).nd cw−laser velocity modulation spectroscopyK.C. Cossel et. al., Chem. Phys. Lett. 546, 1 (2012). With high resolution, we have accurately fit more than 20 ThF^+ vibronic transitions, including electronic states spaced by the known X−a energy separation^b. We will report on the ThF^+ B. J. Barker, I. O. Antonov, M. C. Heaven, K. A. Peterson, J. Chem. Phys. 136, 104305 (2012).;L. C. Sinclair, K. C. Cossel, T. Coffey, J. Ye, E. A. Cornell, PRL 107, 093002 (2011).aK.C. Cossel et. al., Chem. Phys. Lett. 546, 1 (2012)..

The 13.81(8)s half-life of the halo nucleonic atom ¹¹Be is orders of magnitude longer than those for any other halo nucleonic atom known, and makes Be-based diatomics the most promising candidates for the formation of the first halo nucleonic molecules. However, the 4e⁻ species LiH and BeH⁺ are some of the first molecules for which the highest accuracy ab initio methods are not accessible, so empirical potential energy functions will be important for making predictions and for benchmarking how ab initio calculations break down at this transition from 3e⁻ to 4e⁻. BeH⁺ is also very light, and has one of the most extensive data sets involving a tritium isotopologue, making it a very useful benchmark for studying Born-Oppenheimer breakdown. We therefore seek to determine an empirical analytic potential energy function for BeH⁺ that has as much precision as possible. To this end, all available spectroscopic data for all stable isotopologues of BeH⁺ are analyzed in a standard direct-potential-fit procedure that uses least-squares fits to optimize the parameters defining an analytic potential. The "Morse/Long-range" (MLR) model used for the potential energy function incorporates the inverse-power long-range tail required by theory, and the calculation of the leading long-range coefficients C₄, C₆, C₇, and C₈ include non-adiabatic terms, and up to 4th order QED corrections. As a by-product, we have calculated some fundamental properties of 1e⁻ systems with unprecedented precision, such as the dipole, quadrupole, octupole, non-adiabatic, and mixed higher order polarizabilities of hydrogen, deuterium, and tritium. We provide good first estimates for the transition energies for the halo nucleonic species ¹¹BeH⁺ and ¹⁴BeH⁺.