Fundamental vibration of molecular hydrogen

Hydrogen Tag Shifts as Vibrational Reporters for Positional Isomers of Formylphenides: Surprising Mobility of the Carbanion Center upon Collisional Decarboxylation of the Parent Benzoates

Infrared photodissociation of weakly bound "mass tags" is widely used to determine the structures of ions by analyzing their vibrational spectra. Molecular hydrogen is a common choice for tagging in cryogenic radio-frequency ion traps. Although the H2 molecules can introduce distortions in the target species, we demonstrate an advantage of H2 tagging in the analysis of positional isomers adopted by the molecular anions derived from decarboxylation of formylbenzoates. Attachment of H2 to the carbanion centers of three such isomers yields distinct shifts in the H2 stretch, which can be used to determine the distribution of isomers in an unknown sample. Electronic structure calculations indicate that the position-dependent shifts are due to different reactivities of the carbanion sites with respect to an intracluster proton-transfer reaction with the H2 molecule. We exploit this spectroscopic method to quantify the surprisingly facile migrations of the anionic center that have been previously reported for phenide rearrangements.

Precision spectroscopy of molecular hydrogen

Precision measurements on the hydrogen molecule are of fundamental importance in understanding molecular theory. Comparison of accurate experimental data and theoretical results are used to test the quantum electrodynamics theory and determine physical constants used in the calculation. We review recent advances and perspectives in the precision spectroscopy of molecular hydrogen, representing state-of-the-art molecular spectroscopy methods and cutting-edge high-precision calculations.

Lamb Dip of a Quadrupole Transition in H_{2}

The saturated absorption spectrum of the hyperfineless S(0) quadrupole line in the (2-0) band of H_{2} is measured at λ=1189  nm, using the NICE-OHMS technique under cryogenic conditions (72 K). It is the first time that a Lamb dip of a molecular quadrupole transition has been recorded. At low (150-200 W) saturation powers a single narrow Lamb dip is observed, ruling out an underlying recoil doublet of 140 kHz. Studies of Doppler-detuned resonances show that the redshifted recoil component can be made visible for low pressures and powers, and prove that the narrow Lamb dip must be interpreted as the blue recoil component. A transition frequency of 252 016 361 164 (8) kHz is extracted, which is off by -2.6 (1.6) MHz from molecular quantum electrodynamical calculations therewith providing a challenge to theory.

Probing the binding and activation of small molecules by gas-phase transition metal clusters via IR spectroscopy

Isolated transition metal clusters have been established as useful models for extended metal surfaces or deposited metal particles, to improve the understanding of their surface chemistry and of catalytic reactions. For this objective, an important milestone has been the development of experimental methods for the size-specific structural characterization of clusters and cluster complexes in the gas phase. This review focusses on the characterization of molecular ligands, their binding and activation by small transition metal clusters, using cluster-size specific infrared action spectroscopy. A comprehensive overview and a critical discussion of the experimental data available to date is provided, reaching from the initial results obtained using line-tuneable CO₂ lasers to present-day studies applying infrared free electron lasers as well as other intense and broadly tuneable IR laser sources.

Structures and Chemical Rearrangements of Benzoate Derivatives Following Gas Phase Decarboxylation

Decarboxylation of carboxylate ions in the gas phase provides a useful window into the chemistry displayed by these reactive carbanion intermediates. Here, we explore the species generated by decarboxylation of two benzoate derivatives: 2-formylbenzoate (2FBA) and 2-benzoylbenzoate (2BBA). The nascent product anions are transferred to a cryogenic ion trap where they are cooled to ∼15 K and analyzed by their pattern of vibrational bands obtained with IR photodissociation spectroscopy of weakly bound H₂ molecules. The structures of the quenched species are then determined by comparison of these spectra with those predicted by electronic structure calculations for local minima on the potential energy surface. The 2-phenide carbanion generated by decarboxylation of 2FBA occurs in two isomeric forms that differ in the orientation of the formyl group, both of which yield a very large (∼110 cm^-1) redshift in the stretching frequency of the H₂ molecule attached to the anionic carbon center. Although calculated to be a local minimum, the analogous 2-phenide species could not be isolated upon decarboxylation of 2BBA. Rather, the anionic product adopts a ring-closed structure, indicating efficient nucleophilic attack on the pendant phenyl group by the nascent phenide. The barrier for ring closing is evaluated with electronic structure calculations.

The (2-0) R(0) and R(1) transition frequencies of HD determined to a 10-10 relative accuracy by Doppler spectroscopy at 80 K

The Doppler broadened R(0) and R(1) lines of the (2-0) vibrational band of HD have been measured at liquid nitrogen temperature and at pressures of 2 Pa, with a comb referenced continuous-wave cavity ring-down spectrometer set-up. Transition frequencies of 214905335185 kHz and 217105181898 kHz were derived from 33 and 83 recordings, with corresponding root mean squared deviation of 53 and 33 kHz for the R(0) and R(1) transition, respectively. This is the first sub-MHz frequency determination of the R(0) transition frequency and represents a three order of magnitude accuracy improvement compared to literature. The R(1) transition frequency is in very good agreement with previous determinations in saturation regime reported with similar accuracy. To achieve such accuracy, the transition frequency of the (101)-(000) 2₁₁-3₁₂ line of H₂¹⁶O interfering with the R(0) line had to be precisely determined and is reported with a standard error of 100 Hz at 214904329826.49(10) kHz (relative uncertainty of 5 × 10^-13). These measurement sets provide stringent reference values for validating future advances in the theoretical description of the hydrogen (and water) molecule.

Dehydrochlorination of PCDDs on SWCN-Supported Ni10 and Ni13 Clusters, a DFT Study

Polychlorinated dibenzo-p-dioxins (PCDDs) are known to be a group of compounds of high toxicity for animals and, particularly, for humans. Given that the most common method to destroy these compounds is by high-temperature combustion, finding other routes to render them less toxic is of paramount importance. Taking advantage of the physisorption properties of nanotubes, we studied the reactions of atomic hydrogen on physisorbed PCDDs using DFT; likewise, we investigated the reaction of molecular hydrogen on PCDDs aided by Ni10 and Ni13 clusters adsorbed on single-wall carbon nanotubes. Because dihydrogen is an easily accessible reactant, we found these reactions to be quite relevant as dehydrohalogenation methods to address PCDD toxicity.

From vibrational spectroscopy and quantum tunnelling to periodic band structures – a self-supervised, all-purpose neural network approach to general quantum problems

A general, feedforward neural network strategy for the treatment of a broad range of quantum problems including rotational and vibrational spectroscopy, tunnelling and band structure calculations is presented in this study.

Shape Resonances in H_{2} as Photolysis Reaction Intermediates

Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30 MHz (1.4 mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.

Advances, challenges and perspectives of quantum chemical approaches in molecular spectroscopy of the condensed phase

The purpose of this review is to demonstrate advances, challenges and perspectives of quantum chemical approaches in molecular spectroscopy of the condensed phase. Molecular spectroscopy, particularly vibrational spectroscopy and electronic spectroscopy, has been used extensively for a wide range of areas of chemical sciences and materials science as well as nano- and biosciences because it provides valuable information about structure, functions, and reactions of molecules. In the meantime, quantum chemical approaches play crucial roles in the spectral analysis. They also yield important knowledge about molecular and electronic structures as well as electronic transitions. The combination of spectroscopic approaches and quantum chemical calculations is a powerful tool for science, in general. Thus, our article, which treats various spectroscopy and quantum chemical approaches, should have strong implications in the wider scientific community. This review covers a wide area of molecular spectroscopy from far-ultraviolet (FUV, 120-200 nm) to far-infrared (FIR, 400-10 cm-1)/terahertz and Raman spectroscopy. As quantum chemical approaches, we introduce several anharmonic approaches such as vibrational self-consistent field (VSCF) and the combination of periodic harmonic calculations with anharmonic corrections based on finite models, grid-based techniques like the Numerov approach, the Cartesian coordinate tensor transfer (CCT) method, Symmetry-Adapted Cluster Configuration-Interaction (SAC-CI), and the ZINDO (Semi-empirical calculations at Zerner's Intermediate Neglect of Differential Overlap). One can use anharmonic approaches and grid-based approaches for both infrared (IR) and near-infrared (NIR) spectroscopy, while CCT methods are employed for Raman, Raman optical activity (ROA), FIR/terahertz and low-frequency Raman spectroscopy. Therefore, this review overviews cross relations between molecular spectroscopy and quantum chemical approaches, and provides various kinds of close-reality advanced spectral simulation for condensed phases.

Chemical Reduction of NiII Cyclam and Characterization of Isolated NiI Cyclam with Cryogenic Vibrational Spectroscopy and Inert-Gas-Mediated High-Resolution Mass Spectrometry

Ni^II cyclam (cyclam = 1,4,8,11-tetraazacyclotetradecane) is an efficient catalyst for the selective reduction of CO₂ to CO. A crucial elementary step in the proposed catalytic cycle is the coordination of CO₂ to a Ni^I cyclam intermediate. Isolation and spectroscopic characterization of this labile Ni^I species without solvent has proven to be challenging, however, and only partial IR spectra have previously been reported using multiple photon fragmentation of ions generated by gas-phase electron transfer to the Ni^II cyclam dication at 300 K. Here, we report a chemical reduction method that efficiently prepares Ni^I cyclam in solution. This enables the Ni^I complex to be transferred into a cryogenic photofragmentation mass spectrometer using inert-gas-mediated electrospray ionization. The vibrational spectra of the 30 K ion using both H₂ and N₂ messenger tagging over the range 800-4000 cm^-1 were then measured. The resulting spectra were analyzed with the aid of electronic structure calculations, which show strong method dependence in predicted band positions and small molecule activation. The conformational changes of the cyclam ligand induced by binding of the open shell Ni^I cation were compared with those caused by the spherical, closed-shell Li^I cation, which has a similar ionic radius. We also report the vibrational spectrum of a Ni^I cyclam complex with a strongly bound O₂ ligand. The cyclam ligand supporting this species exhibits a large conformational change compared to the complexes with weakly bound N₂ and H₂, which is likely due to significant charge transfer from Ni to the coordinated O₂.

An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter

Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.

Molecular Hydrogen as a Lewis Base in Hydrogen Bonds and Other Interactions

The second-order Møller–Plesset perturbation theory calculations with the aug-cc-pVTZ basis set were performed for complexes of molecular hydrogen. These complexes are connected by various types of interactions, the hydrogen bonds and halogen bonds are most often represented in the sample of species analysed; most interactions can be classified as σ-hole and π-hole bonds. Different theoretical approaches were applied to describe these interactions: Quantum Theory of ‘Atoms in Molecules’, Natural Bond Orbital method, or the decomposition of the energy of interaction. The energetic, geometrical, and topological parameters are analysed and spectroscopic properties are discussed. The stretching frequency of the H-H bond of molecular hydrogen involved in intermolecular interactions is considered as a parameter expressing the strength of interaction.

Precision measurement of the fundamental vibrational frequencies of tritium-bearing hydrogen molecules: T2, DT, HT

High-resolution coherent Raman spectroscopic measurements of all three tritium-containing molecular hydrogen isotopologues T2, DT and HT were performed to determine the ground electronic state fundamental Q-branch (v = 0 → 1, ΔJ = 0) transition frequencies at accuracies of 0.0005 cm-1. An over hundred-fold improvement in accuracy over previous experiments allows the comparison with the latest ab initio calculations in the framework of non-adiabatic perturbation theory including nonrelativisitic, relativisitic and QED contributions. Excellent agreement is found between experiment and theory, thus providing a verification of the validity of the NAPT-framework for these tritiated species. While the transition frequencies were corrected for ac-Stark shifts, the contributions of non-resonant background as well as quantum interference effects between resonant features in the nonlinear spectroscopy were quantitatively investigated, also leading to corrections to the transition frequencies. Methods of saturated CARS with the observation of Lamb dips, as well as the use of continuous-wave radiation for the Stokes frequency were explored, that might pave the way for future higher-accuracy CARS measurements.

Vibration overtone hyperpolarizability measured for H2

The second hyperpolarizability (γ) of the H₂ molecule was measured by gas-phase electric field induced second harmonic generation at the frequencies of the one-photon resonance for the 3-0 Q(J) overtone transitions (v, J = 0, J → 3, J for J = 0, 1, 2, and 3). The magnitude of the resonant contribution to γ was measured with 2% accuracy using the previously determined non-resonant γ for calibration. Pressure broadening and frequency shift for the transitions were also measured. A theoretical expression for the resonant vibrational γ contribution in terms of transition polarizabilities is compared to the observations. The measured γ resonance strength is 4%-14% larger than the results obtained from this theoretical expression evaluated using ab initio transition polarizabilities.

Ultrahigh finesse cavity-enhanced spectroscopy for accurate tests of quantum electrodynamics for molecules

We report the most accurate, to the best of our knowledge, measurement of the position of the weak quadrupole S(2) 2-0 line in $ {{\rm D}_2} $D₂. The spectra were collected with a frequency-stabilized cavity ringdown spectrometer (FS-CRDS) with an ultrahigh finesse optical cavity ($ {\cal F} = 637 000 $F=637000) and operating in the frequency-agile, rapid scanning spectroscopy (FARS) mode. Despite working in the Doppler-limited regime, we reached 40 kHz of statistical uncertainty and 161 kHz of absolute accuracy, achieving the highest accuracy for homonuclear isotopologues of molecular hydrogen. The accuracy of our measurement corresponds to the fifth significant digit of the leading term in quantum electrodynamics (QED) correction. We observe $ 2.3\sigma $2.3σ discrepancy with the recent theoretical value.

Fundamental vibration frequency and rotational structure of the first excited vibrational level of the molecular helium ion ( He 2 + )

The term values of the rotational levels of the first excited vibrational state of the electronic ground state of He 2 + with a rotational quantum number N ⁺ ≤ 13 have been determined with an accuracy of 1.2 × 10^-3 cm^-1 (∼35 MHz) by multichannel-quantum-defect-theory-assisted Rydberg spectroscopy of metastable He₂. Comparison of the experimental term values with the most accurate ab initio results for He 2 + available in the literature [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] reveals inconsistencies between the theoretical and experimental results that increase with increasing rotational quantum numbers. The fundamental vibrational wavenumber of He 2 + was determined to be 1628.3832(12) cm^-1 by fitting effective molecular constants to the obtained term values.

Unmasking Rare, Large-Amplitude Motions in D2-Tagged I-·(H2O)2 Isotopomers with Two-Color, Infrared-Infrared Vibrational Predissociation Spectroscopy

We describe a two-color, isotopomer-selective infrared-infrared population-labeling method that can monitor very slow spectral diffusion of OH oscillators in H-bonded networks and apply it to the I^-·(HDO)·(D₂O) and I^-·(H₂O)·(D₂O) systems, which are cryogenically cooled and D₂-tagged at an ion trap temperature of 15 K. These measurements reveal very large (>400 cm^-1), spontaneous spectral shifts despite the fact that the predissociation spectra in the OH stretching region of both isotopologues are sharp and readily assigned to four fundamentals of largely decoupled OH oscillators held in a cyclic H-bonded network. This spectral diffusion is not observed in the untagged isotopologues of the dihydrate clusters that are generated under the same source conditions but does become apparent at about 75 K. These results are discussed in the context of the large-amplitude "jump" mechanism for H-bond relaxation dynamics advanced by Laage and Hynes in an experimental scenario where rare events can be captured by following the migration of OH groups among the four available positions in the quasi-rigid equilibrium structure.

QED effects on individual atomic orbital energies

Several issues, concerning QED corrections, that are important in precise atomic calculations are presented. The leading QED corrections, self-energy and vacuum polarization, to the orbital energy for selected atoms with 30 ≤ Z ≤ 118 have been calculated. The sum of QED and Breit contributions to the orbital energy is analyzed. It has been found that for ns subshells the Breit and QED contributions are of comparative size, but for np and nd subshells the Breit contribution takes a major part of the QED+Breit sum. It has also, been found that the Breit to leading QED contributions ratio for ns subshells is almost independent of Z. The Z-dependence of QED and Breit+QED contributions per subshell is shown. The fitting coefficients may be used to estimate QED effects on inner molecular orbitals. We present results of our calculations for QED contributions to orbital energy of valence ns-subshell for group 1 and 11 atoms and discuss about the reliability of these numbers by comparing them with experimental first ionization potential data.

Relativistic and QED Effects in the Fundamental Vibration of T_{2}

The hydrogen molecule has become a test ground for quantum electrodynamical calculations in molecules. Expanding beyond studies on stable hydrogenic species to the heavier radioactive tritium-bearing molecules, we report on a measurement of the fundamental T_{2} vibrational splitting (v=0→1) for J=0-5 rotational levels. Precision frequency metrology is performed with high-resolution coherent anti-Stokes Raman spectroscopy at an experimental uncertainty of 10-12 MHz, where sub-Doppler saturation features are exploited for the strongest transition. The achieved accuracy corresponds to a 50-fold improvement over a previous measurement, and it allows for the extraction of relativistic and QED contributions to T_{2} transition energies.

Sub-Doppler Frequency Metrology in HD for Tests of Fundamental Physics

Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at λ=1.38  μm were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1)=217105181895(20)  kHz; R(2)=219042856621(28)  kHz; R(3)=220704304951(28)  kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.

Deep-Ultraviolet Frequency Metrology of H_{2} for Tests of Molecular Quantum Theory

Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.

Disentangling the Complex Vibrational Spectrum of the Protonated Water Trimer, H+(H2O)3, with Two-Color IR-IR Photodissociation of the Bare Ion and Anharmonic VSCF/VCI Theory

Vibrational spectroscopy of the protonated water trimer provides a stringent constraint on the details of the potential energy surface (PES) and vibrational dynamics governing excess proton motion far from equilibrium. Here we report the linear spectrum of the cold, bare H⁺(H₂O)₃ ion using a two-color, IR-IR photofragmentation technique and follow the evolution of the bands with increasing ion trap temperature. The key low-energy features are insensitive to both D₂ tagging and internal energy. The D₂-tagged D⁺(D₂O)₃ spectrum is reported for the first time, and the isotope dependence of the band pattern is surprisingly complex. These spectra are reproduced by large-scale vibrational configuration interaction calculations based on a new full-dimensional PES, which treat the anharmonic effects arising from large amplitude motion. The results indicate such extensive mode mixing in both isotopologues that one should be cautious about assigning even the strongest features to particular motions, especially for the absorptions that occur close to the intramolecular bending mode of the water molecule.

Assessing the predictability of anharmonic vibrational modes at the example of hydroxyl groups – ad hoc construction of localised modes and the influence of structural solute–solvent motifs

The performance of the grid-based Numerov approach for the prediction of vibrational modes has been systematically assessed for analytically solvable model systems and hydroxyl-groups of different molecules.

Complete α^{6} m Corrections to the Ground State of H_{2}

We perform the calculation of all relativistic and quantum electrodynamic corrections of the order of α^{6} m to the ground electronic state of a hydrogen molecule and present improved results for the dissociation and the fundamental transition energies. These results open the window for the high-precision spectroscopy of H_{2} and related low-energy tests of fundamental interactions.

Precision measurements and test of molecular theory in highly excited vibrational states of H2 (v = 11)

Accurate E F 1 Σ g + - X 1 Σ g + transition energies in molecular hydrogen were determined for transitions originating from levels with highly excited vibrational quantum number, v = 11, in the ground electronic state. Doppler-free two-photon spectroscopy was applied on vibrationally excited H 2 ∗ , produced via the photodissociation of H2S, yielding transition frequencies with accuracies of 45 MHz or 0.0015 cm-1. An important improvement is the enhanced detection efficiency by resonant excitation to autoionizing 7 p π electronic Rydberg states, resulting in narrow transitions due to reduced ac-Stark effects. Using known EF level energies, the level energies of X(v = 11, J = 1, 3-5) states are derived with accuracies of typically 0.002 cm-1. These experimental values are in excellent agreement with and are more accurate than the results obtained from the most advanced ab initio molecular theory calculations including relativistic and QED contributions.

Precision measurement of the rotational energy-level structure of the three-electron molecule He2. J Chem Phys 2016;145:204301. [PMID: 27908106 DOI: 10.1063/1.4967256]

The term values of all rotational levels of the ⁴He₂⁺ X^{+  2}Σ_u⁺ (ν⁺=0) ground vibronic state with rotational quantum number N⁺ ≤ 19 have been determined with an accuracy of 8 × 10^-4 cm^-1 (∼25 MHz) by multichannel-quantum-defect-theory-assisted Rydberg spectroscopy of metastable He₂^∗. Comparison of these term values with term values recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309 (2012)] reveals discrepancies that rapidly increase with increasing rotational quantum number and reach values of 0.07 cm^-1 (∼2.1 GHz) at N⁺ = 19.

Infrared Photodissociation Spectroscopy of C4 N- , C6 N- and C8 N. Chemphyschem 2016;17:3783-3789. [PMID: 27378244 DOI: 10.1002/cphc.201600598]

The gas-phase vibrational spectroscopy of cold C_2n N^- (n=2-4) anions is investigated in the CC and CN multiple bond stretching region (1700-2250 cm^-1 ) by means of infrared photodissociation (IRPD) spectroscopy in a cryogenically cooled ion trap of the corresponding messenger-tagged complexes. The IRPD spectra are assigned to N-terminated linear structures with triplet ground states (³ Σ^- ) based on a comparison with harmonic vibrational frequencies and intensities from density functional theory computations. In contrast to the polyacetylenic C_2n+1 N^- anions, the linear C-C chains investigated here exhibit cumulenic character, which is most pronounced in C₄ N^- and decreases with chain length. Additional intense transitions are observed for C₆ N^- above 3000 cm^-1 and are attributed to overtone and combination bands involving the CC stretching modes, based on anharmonic computations. The influence of a D₂ tag on the vibrational features of C_2n N^- anions is shown to be small.

High-Precision Ramsey-Comb Spectroscopy at Deep Ultraviolet Wavelengths

High-precision spectroscopy in systems such as molecular hydrogen and helium ions is very interesting in view of tests of quantum electrodynamics and the proton radius puzzle. However, the required deep ultraviolet and shorter wavelengths pose serious experimental challenges. Here we show Ramsey-comb spectroscopy in the deep ultraviolet for the first time, thereby demonstrating its enabling capabilities for precision spectroscopy at short wavelengths. We excite ^{84}Kr in an atomic beam on the two-photon 4p^{6}→4p^{5}5p[1/2]_{0} transition at 212.55 nm. It is shown that the ac-Stark shift is effectively eliminated, and combined with a counterpropagating excitation geometry to suppress Doppler effects, a transition frequency of 2 820 833 101 679(103) kHz is found. The uncertainty of our measurement is 34 times smaller than the best previous measurement, and only limited by the 27 ns lifetime of the excited state.

Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.

Pushing the limit for the grid-based treatment of Schrödinger's equation: a sparse Numerov approach for one, two and three dimensional quantum problems

The general Numerov method employed to numerically solve ordinary differential equations of second order was adapted with a special focus on matrix sparsity and applications in higher dimensions.

Communication: Test of quantum chemistry in vibrationally hot hydrogen molecules

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The v = 12, J = 0 - 3 rovibrational levels of H2 (X(1)Σg (+)), lying only 2000 cm(-1) below the first dissociation limit, were populated by photodissociation of H2S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on v = 12 level energies with the best ab initio calculations shows a good agreement, where the present experimental accuracy of 3.5 × 10(-3) cm(-1) is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.

A DFT-D study of hydrogen adsorption on functionalized graphene

In this paper, we use density functional theory with dispersion correction functional (DFT-D) as implemented in the Vienna ab initio simulation package in order to investigate hydrogen adsorption on graphane (GH) and fluorographene (GF).

Limits on a gravitational field dependence of the proton-electron mass ratio from H2 in white dwarf stars

Spectra of molecular hydrogen (H2) are employed to search for a possible proton-to-electron mass ratio (μ) dependence on gravity. The Lyman transitions of H2, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions (T∼13 000  K) of their photospheres. We derive sensitivity coefficients Ki which define how the individual H2 transitions shift due to μ dependence. The spectrum of white dwarf star GD133 yields a Δμ/μ constraint of (-2.7±4.7stat±0.2syst)×10(-5) for a local environment of a gravitational potential ϕ∼10(4) ϕEarth, while that of G29-38 yields Δμ/μ=(-5.8±3.8stat±0.3syst)×10(-5) for a potential of 2×10(4) ϕEarth.