Large Internuclear Separations Research Articles

Potential energy surfaces and dynamic properties via ab initio composite and density functional approaches.

Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction-based ab initio or density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self-consistent field Theory (VSCF) and post-VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode-coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode-mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI-PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post-VSCF methods to generate more accurate representations of computed infrared spectra.

Spectroscopic study of the F[formula omitted] outer well state in H2, HD and D2

Two-photon UV-photolysis of hydrogen sulfide molecules is applied to produce hydrogen molecules in highly excited vibrational levels in the X1Σg+ electronic ground state, up to the dissociation energy and into the quasibound region. Photolysis precursors H2S, HDS and D2S are used to produce vibrationally hot H2, HD and D2. The wave function density at large internuclear separation is excited via two-photon transitions in the F1Σg+ - X1Σg+ system to probe ro-vibrational levels in the first F1Σg+ outer well state of gerade symmetry. Combining with accurate knowledge of the X1Σg+ (v,J) levels from advanced ab initio calculations, energies of rovibrational levels in the F1Σg+ state are determined. For the H2 isotopologue a three-laser scheme is employed yielding level energies at accuracies of 4×10−3 cm−1 for F(v=0,J) up to J=21 and for some low J values of F(v=1). A two-laser scheme was applied to determine level energies in H2 for F(v=0−4) levels as well as for various F levels in HD and D2, also up to large rotational quantum numbers. The latter measurements in the two-laser scheme are performed at lower resolution and the accuracy is strongly limited to 0.5 cm−1 by ac-Stark effects. For H2 a new quasibound resonance X1Σg+ (v=6, J=23) is detected through the Q(23) and O(23) transitions in the F0-X6 band. Also a quasi-bound resonance in D2 is assigned, for the first time in this species: X1Σg+ (v=17 , J=15). The experimental results on F(v,J) level energies are compared with previously reported theoretical results from multi-channel quantum-defect calculations as well as with results from newly performed non-adiabatic quantum calculations.

Resolving rotationally excited states of ultralong-range Rydberg molecules

We report experimental observations of the rotational structure in photoassociative spectroscopy of ultralong-range Rydberg molecules (ULRRMs) in an ultracold gas of $^{86}\mathrm{Sr}$. ULRRM spectroscopy probes scattering wave functions at much larger internuclear separations than photoassociative spectroscopy of low-lying electronic states. At such separations photon recoil momentum can lead to the transfer of significant angular momentum to the Rydberg molecule, evidence of which is provided through the distribution of excited rotational states. The visibility of the rotational structure is enhanced because, for collisions between ground-state $^{86}\mathrm{Sr}$ atoms, the large, near-resonant s-wave scattering length approaches the size of the ULRRM. Similar enhancement is not seen for $^{84}\mathrm{Sr}$, which has a much smaller scattering length. Results are interpreted with the aid of a theory that accounts for the recoil momentum associated with photoexcitation and the large $s$-wave scattering length in the entrance channel. While the observed rotational splittings and the qualitative trends in the relative intensities of the spectral features are well described by theory, the effects of recoil momentum are more prominent in the measured data than in the theory.

Precision measurement of quasi-bound resonances in H2 and the H + H scattering length

Quasi-bound resonances of are produced via two-photon photolysis of S molecules as reactive intermediates or transition states and detected before decay of the parent molecule into three separate atoms. As was previously reported [K. F. Lai et al., Phys. Rev. Lett. 127, 183001 (2021)] four centrifugally bound quantum resonances with lifetimes of multiple μs, lying energetically above the dissociation limit of the electronic ground state of , were observed as , , , and , while also the short-lived ( ns) quasi-bound resonance was probed. The present paper gives a detailed account on the identification of the quasi-bound or shape resonances, based on laser detection via - two-photon transitions, and their strongly enhanced Franck-Condon factors due to the shifting of the wave function density to large internuclear separation. In addition, the assignment of the rotational quantum number is verified by subsequent multi-step laser excitation into autoionisation continuum resonances. Existing frameworks of full-fledged ab initio computations for the bound region in , including Born-Oppenheimer, adiabatic, non-adiabatic, relativistic and quantum-electrodynamic contributions, are extended into the energetic range above the dissociation energy. These comprehensive calculations are compared to the accurate measurements of energies of quasi-bound resonances, finding excellent agreement. They show that the quasi-bound states are in particular sensitive to non-adiabatic contributions to the potential energy. From the potential energy curve and the correction terms, now tested at high accuracy over a wide range of energies and internuclear separations, the s-wave scattering length for singlet H+H scattering is determined at . It is for the first time that such an accurate value for a scattering length is determined based on fully ab initio methods including effects of adiabatic, non-adiabatic, relativistic and QED with contributions up to .

Pulse Energy and Pulse Duration Effects in the Ionization and Fragmentation of Iodomethane by Ultraintense Hard X Rays

The interaction of intense femtosecond x-ray pulses with molecules sensitively depends on the interplay between multiple photoabsorptions, Auger decay, charge rearrangement, and nuclear motion. Here, we report on a combined experimental and theoretical study of the ionization and fragmentation of iodomethane (CH_{3}I) by ultraintense (∼10^{19} W/cm^{2}) x-ray pulses at 8.3keV, demonstrating how these dynamics depend on the x-ray pulse energy and duration. We show that the timing of multiple ionization steps leading to a particular reaction product and, thus, the product's final kinetic energy, is determined by the pulse duration rather than the pulse energy or intensity. While the overall degree of ionization is mainly defined by the pulse energy, our measurement reveals that the yield of the fragments with the highest charge states is enhanced for short pulse durations, in contrast to earlier observations for atoms and small molecules in the soft x-ray domain. We attribute this effect to a decreased charge transfer efficiency at larger internuclear separations, which are reached during longer pulses.

Photolysis Production and Spectroscopic Investigation of the Highest Vibrational States in H2 (X1Σg+ v = 13, 14).

Rovibrational quantum states in the X1Σg+ electronic ground state of H2 are prepared in the v = 13 vibrational level up to its highest bound rotational level J = 7, and in the highest bound vibrational level v = 14 (for J = 1) by two-photon photolysis of H2S. These states are laser-excited in a subsequent two-photon scheme into F1Σg+ outer well states, where the assignment of the highest (v,J) states is derived from a comparison of experimentally known levels in F1Σg+, combined with ab initio calculations of X1Σg+ levels. The assignments are further verified by excitation of F1Σg+ population into autoionizing continuum resonances, which are compared with multichannel quantum defect calculations. Precision spectroscopic measurements of the F-X intervals form a test for the ab initio calculations of ground state levels at high vibrational quantum numbers and large internuclear separations, for which agreement is found.

An ultracold heavy Rydberg system formed from ultra-long-range molecules bound in a stairwell potential

We propose a scheme to realize a heavy Rydberg system (HRS), a bound pair of oppositely charged ions, from a gas of ultracold atoms. The intermediate step to achieve large internuclear separations is the creation of a unique class of ultra-long-range Rydberg molecules bound in a stairwell potential energy curve. Here, a ground-state atom is bound to a Rydberg atom in an oscillatory potential emerging due to attractive singlet p-wave electron scattering. The utility of our approach originates in the large electronic dipole transition element between the Rydberg and the ionic molecule, while the nuclear configuration of the ultracold gas is preserved. The Rabi coupling between the Rydberg molecule and the heavy Rydberg system is typically in the MHz range and the permanent electric dipole moments of the HRS can be as large as one kilo-Debye. We identify specific transitions which place the creation of the heavy Rydberg system within immediate reach of experimental realization.

Excitation of H2 at large internuclear separation: outer well states and continuum resonances

Bound and free quantum resonances of molecular hydrogen exhibiting wave-function density at large internuclear separation, 4–5 a.u., are excited via multi-step laser spectroscopy. Highly excited vibrational levels of H are prepared via two-photon UV-photolysis of HS. Subsequent two-photon Doppler-free precision measurements are performed connecting levels with outer-well levels. Detection and spectroscopic labelling of the quantum states is assisted by further laser excitation into the auto-ionisation continuum employing a third UV-laser. Level energies of high rotational states () in the outer-well state are accurately determined. The three-laser study demonstrates a method for probing resonances in the H ionisation continuum with wave-function density at large internuclear separation 4–5 a.u., large angular momenta J, and energy range 131,100–133,000 cm−1, a hitherto unexplored territory.

Electronic and vibrational spectroscopy of the low-lying states of potassium mono-sulphide KS, and comparison in the series of MS (M = Li, Na, K, Rb, Cs)

ABSTRACTPotential energy curves (PECs) of the lowest electronic states of the potassium mono-sulphide KS have been determined with highly correlated ab initio calculations, using internally contracted multi reference interaction configuration methods including Davidson correction (MRCI + Q) with and without considering spin-orbit effects. For the three low-lying bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. An analysis of the properties of the three bound states, X2Π, 12Σ+ and 22Π, illustrates the common characteristics of the whole series of compounds in the MS family (M = Li, Na, K, Rb, Cs). Indeed, the shapes of the PECs of these bound states are strongly affected by the interactions between the two ionic states, 2Σ+ and 2Π, correlating at large internuclear separations (RMS) to the first ionic dissociation limit [M+ + S−] and the electronic states correlating to the three/four lowest dissociation limits. The spectroscopy of these low-lying electronic states and the lifetime of their vibrational levels are thus affected by the spin-orbit interactions which are mainly related to the S atom and consequently common to all alkali-metal mono-sulphides.

Exact partition potential for model systems of interacting electrons in 1-D

We find the numerically exact partition potential for 1-D systems of interacting electrons designed to model diatomic molecules. At integer fragment occupations, the kinetic contribution to the partition potential develops sharp features in the internuclear region that nearly cancel corresponding features of exchange-correlation. They occur at locations that coincide with those of well-known features of the underlying molecular Kohn-Sham potential. For non-integer fragment occupations, we demonstrate that the fragment Kohn-Sham gaps determine the kinetic part of the partition potential. Our results highlight the importance of non-additive noninteracting kinetic and exchange-correlation energy approximations in density-embedding methods at large internuclear separations and the importance of non-additive noninteracting kinetic energy approximations at all separations.

Asymptotic Solution of A Multichannel Scattering Problem with A Nonadiabatic Coupling

We consider a multichannel scattering problem in an adiabatic representation. We assume that the nonadiabatic coupling matrix has a nontrivial value at large internuclear separations, and we construct asymptotic solutions at large internuclear distances. We show that these solutions up to the first order of the perturbation theory are identical to the asymptotic solutions of the reprojection approach, which was previously proposed as a means for solving the electron translation problem in the context of the Born–Oppenheimer method.

Electronic and Vibrational Spectroscopy of CsS

Using multi configurational ab initio methodologies, we compute the potential energy curves (PECs) of the lowest electronic states of the diatomic CsS. These computations are performed using internally contracted multireference interaction configuration including Davidson correction (MRCI+Q) with and without considering spin-orbit effects. The shapes of the PECs are governed by the interactions between the two ionic states, 2Σ+ and 2Π, correlating at large internuclear separations ( RCsS) to the first ionic dissociation limit and the other electronic states correlating to the three lowest neutral dissociation limits. Computations show the importance of considering a large amount of electron correlation for the accurate description of the PECs and spectroscopy of this molecular system. As expected, these PECs are also strongly affected by the spin-orbit interaction. For the bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, and vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. Moreover, we show that the 22Π state presents a "bowl" potential with a rather flat region extending to large RCsS distances. After being promoted to this state, wavepackets should undergo strong oscillations, similar to those observed by Zewail and co-workers for the NaI molecule. These should provide information on the shape of the PEC for the 22Π state and also on the couplings between this and the neighboring states.

Theoretical study of ultrafast x-ray photoelectron diffraction from molecules undergoing photodissociation.

We present a new theoretical work for the ultrafast x-ray photoelectron diffraction (UXPD) method to track photodissociation of molecules over the long range in femtosecond time scale. Our theory combines the accurate multicenter description of XPD at short to medium distances and the multiple-scattering XPD approach at larger internuclear separations. Then, the theoretical framework is applied to a demonstration of the UXPD profiles from halogen diatomics undergoing photodissociation. The computational results indicate that such a combination of the two theoretical approaches sufficiently works to seamlessly track the conformational evolution during photodissociation. The present study provides information on dissociation kinetics of neutral diatomic molecules available with the UXPD method and is a step towards an approach applied to general photoelimination processes.

Optical imaging with a high-resolution microendoscope to identify sinonasal pathology

ObjectivesHigh-resolution microendoscopy (HRME) is an optical imaging modality that allows real time imaging of epithelial tissue and structural changes within. We hypothesize that HRME, using proflavine, a contrast agent that preferentially stains cell nuclei and allows detection of cellular morphologic changes, can distinguish sinonasal pathology from uninvolved mucosa, potentially enabling real-time surgical margin differentiation. Study designEx vivo imaging of histopathologically confirmed samples of sinonasal pathology and uninvolved, normal sinus epithelium. SettingSingle tertiary-level institution. Subjects and methodsFive inverted papillomas, one oncocytic papilloma, two uninvolved sinus epithelia specimens, and three inflammatory polyps were imaged ex vivo with HRME after surface staining with proflavine. Following imaging, the specimens were submitted for hematoxylin and eosin staining to allow histopathological correlation. ResultsResults show that sinonasal pathology and normal sinus epithelia have distinct HRME imaging characteristics. Schneiderian papilloma specimens show increased nuclear-to-cytoplasmic ratio, nuclear crowding, and small internuclear separation, whereas normal sinus epithelia specimens show small, bright nuclei with dark cytoplasm and relatively large internuclear separation. Inflammatory polyps, however, have varying imaging characteristics, that resemble both Schneiderian papilloma and normal sinus epithelia. ConclusionsThis study demonstrates the feasibility of HRME imaging to discriminate sinonasal pathology from normal sinus epithelia. While the system performed well in the absence of inflammation, discrimination of inflamed tissue was inconsistent, creating a significant limitation for this application. Novel imaging systems such as HRME with alternative contrast agents may assist with real-time surgical margin differentiation, enabling complete surgical resection of inverted papilloma and reducing recurrence rates.

Quasirelativistic potential energy curves and transition dipole moments of NaRb

We report on extensive calculations of quasi-relativistic potential energy curves and, for the first time, transition dipole moments including spin-orbit and scalar-relativistic effects of the NaRb molecule. The calculated curves of the 0+, 0-, 1, 2 and 3 molecular states correlate for large internuclear separation with the fourteen lowest atomic energies up to the Na(3s2S1/2) + Rb(7s2S1/2) atomic limit. Several new features of the potential energy curves have been found.

Theoretical Cross Sections of the Inelastic Fine Structure Transition M(2P1/2) + Ng ↔ M(2P3/2) + Ng for M = K, Rb, and Cs and Ng = He, Ne, and Ar.

Scattering matrix elements of the inelastic fine structure transition M(2P1/2) + Ng ↔ M(2P3/2) + Ng are computed using the channel packet method (CPM) for alkali-metal atoms M = K, Rb, and Cs, as they collide with noble-gas atoms Ng = He, Ne, and Ar. The calculations are performed within the block Born-Oppenheimer approximation where excited state VA2Π1/2(R), VA2Π3/2(R), and VB2Σ1/2(R) adiabatic potential energy surfaces are used together with a Hund's case (c) basis to construct a 6 × 6 diabatic representation of the electronic Hamiltonian. Matrix elements of the angular kinetic energy of the nuclei incorporate Coriolis coupling and, together with the diabatic representation of the electronic Hamiltonian, yield a 6 × 6 effective potential energy matrix. This matrix is diagonal in the asymptotic limit of large internuclear separation with eigenvalues that correlate to the 2Pj alkali atomic energy levels. Scattering matrix elements are computed using the CPM by preparing reactant and product wave packets on the effective potential energy surfaces that correspond to the excited 2Pj alkali states of interest. The reactant wave packet is then propagated forward in time using the split operator method together with a unitary transformation between the adiabatic and diabatic representations. The Fourier transformation of the correlation function between the evolving reactant wave packet and stationary product wave packet yields state-to-state scattering matrix elements as a function of energy for a particular choice of total angular momentum J. Calculations are performed for energies that range from 0.0 to 0.01 hartree and values of J that start with a minimum of J = 0.5 for all M + Ng pairs up to a maximum that ranges from J = 450.5 for KAr to J = 100.5 for CsAr. A sum over J together with an average over energy is used to compute thermally averaged cross sections for a temperature range of T = 0-400 K.

Higher lying resonances in low-energy electron scattering with carbon monoxide*

R-matrix calculations on electron collisions with CO are reported whose aim is to identify any higher-lying resonances above the well-reported and lowest $^2\Pi$ resonance at about 1.6~eV. Extensive tests with respect to basis sets, target models and scattering models are performed. The final results are reported for the larger cc-pVTZ basis set using a 50 state close-coupling (CC) calculation. The Breit-Wigner eigenphase sum and the time-delay methods are used to detect and fit any resonances. Both these methods find a very narrow $^2\Sigma^+$ symmetry Feshbach-type resonance very close to the target excitation threshold of the b $^3\Sigma^+$ state which lies at 12.9 eV in the calculations. This resonance is seen in the CC calculation using cc-pVTZ basis set while a CC calculation using the cc-pVDZ basis set does not produce this feature. The electronic structure of CO$^-$ is analysed in the asymptotic region, 45 molecular states are found to correlate with states dissociating to an anion and an atom. Electronic structure calculations are used to study the behaviour of these states at large internuclear separation. Quantitative results for the total, elastic and electronic excitation cross sections are also presented. The significance of these results for models of the observed dissociative electron attachment of CO in the 10 eV region is discussed.

Long-range interactions between Rydberg atoms

We present an overview over theoretical models to describe adiabatic potential-energy curves, experimental excitation spectra, and electronic and nuclear dynamics in interacting Rydberg-atom pairs at large internuclear separations. The potential-energy curves and molecular wavefunctions are determined from the multipole expansion of the static Coulomb interaction which is evaluated numerically in a product basis of atomic orbitals. The convergence of this approach both in the truncation of the multipole expansion as well as in the size of the product basis is discussed, and the comparison of simulated excitation spectra is established as a useful criterium to test the convergence of the calculation. We finally discuss the dynamics of electronic and nuclear motions of pairs of Rydberg atoms, focusing on the stability of ultralong range Rydberg molecules with respect to autoionization.

Short-range photoassociation from the inner wall of the lowest triplet potential of 85Rb2

Ultracold photoassociation is typically performed at large internuclear separations, where the scattering wavefunction amplitude is large and Franck–Condon overlap is maximized. Recently, work by this group and others on alkali-metal diatomics has shown that photoassociation can efficiently form molecules at short internuclear distance in both homonuclear and heteronuclear dimers. We propose that this short-range photoassociation is due to excitation near the wavefunction amplitude maximum at the inner wall of the lowest triplet potential. We show that Franck–Condon factors (FCFs) from the highest-energy bound state can almost precisely reproduce FCFs from a low-energy scattering state, and that both calculations match experimental data from the near-zero positive-energy scattering state with reasonable accuracy. We also show that the corresponding photoassociation from the inner wall of the ground-state singlet potential at much shorter internuclear distance is weaker and undetectable under our current experimental conditions. We predict from FCFs that the strongest of these weaker short-range photoassociation transitions are one order of magnitude below our current sensitivity.

Two color pumping of the Rb D2 line laser (780 nm) through the photoassociation of Rb-Ar or Rb-Xe thermal pairs: Realization of a quantum efficiency above one

A two color process for optical pumping of the Rb D2 line laser (λ = 780 nm) in Rb vapor-rare gas mixtures is demonstrated to yield an overall quantum efficiency > 1. Combining photoexcitation of the Rb D2 line blue satellite in Rb-Xe or Rb-Ar mixtures with free ← free optical pumping of the A2Π12←X2Σ12+ transition at large internuclear separation (R > 5 Å) also increases the laser efficiency and pump absorption coefficient, relative to the single color, B ← X pumped system, by a factor of 1.7 and more than an order of magnitude, respectively. Simultaneous photopumping of Rb-Xe thermal collision pairs at 760 nm (D2 satellite) and 794.3 nm results in a 780 nm (D2 line) laser with a quantum efficiency of 1.008 which corresponds to the removal of ∼102 cm–1 (12.6 meV) of thermal energy per emitted photon.