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Simultaneous imaging of vibrational, rotational, and electronic wave-packet dynamics in a triatomic molecule

Light-induced molecular dynamics often involve the excitation of several electronic, vibrational, and rotational states. Since the ensuing electronic and nuclear motion determines the pathways and outcomes of photoinduced reactions, our ability to monitor and understand these dynamics is crucial for molecular physics, physical chemistry, and photobiology. However, characterizing this complex motion represents a significant challenge when different degrees of freedom are strongly coupled. In this Letter, we demonstrate how the interplay between vibrational, rotational, and electronic degrees of freedom governs the evolution of molecular wave packets in the low-lying states of strong-field-ionized sulfur dioxide. Using time-resolved Coulomb explosion imaging (CEI) and quantum mechanical wave packet simulations, we directly map the bending vibrations of the molecule, show how the vibrational wave packet is influenced by molecular alignment, and elucidate the consequences of nuclear motion for the coupling between the two lowest electronic states of the cation. Furthermore, our results demonstrate that multicoincident CEI can be an efficient experimental tool for characterizing coupled electronic and nuclear motion in polyatomic molecules.

Atomic & molecular processes in external fields↗

Orbital-resolved calculations of two-center interferences in linear triatomic molecules

In this report we perform ab initio calculations of high-harmonic spectroscopy (HHS) of two-center interference phenomena in oriented carbon-dichalcogen molecules, using time-dependent density functional theory (TDDFT). We show that by resolving the harmonic response into contributions from individual Kohn-Sham orbitals, we can extract target-specific characteristics for both the spectral amplitude and phase. We also discuss that this extraction is predicated on a careful analysis and normalization of the harmonic spectrum. Finally, we present field-free scattering calculations that mimic the recollision step in high-order-harmonic generation and allow the calculation of recombination dipole matrix elements without explicitly calculating the scattering states of a molecule. We show that the orbital-resolved TDDFT HHS results and results based on our field-free scattering calculations are in very good agreement with each other.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Parity-doublet coherence times in optically trapped polyatomic molecules

Polyatomic molecules provide complex internal structures that are ideal for applications in quantum information science, quantum simulation and precision searches for physics beyond the standard model. A key feature of polyatomic molecules is the presence of parity-doublet states. These structures, which generically arise from the rotational and vibrational degrees of freedom afforded by polyatomic molecules, are a powerful feature to pursue diverse quantum science applications. Linear triatomic molecules contain ℓ-type parity-doublet states in the vibrational bending mode, which are predicted to exhibit robust coherence properties. Here we report optically trapped CaOH molecules prepared in ℓ-type parity-doublet states and realize a bare qubit coherence time of $T$$^{*}_{2}$, which is longer than the 0.36 s lifetime of the bending mode. We suppress differential Stark shifts by cancelling ambient electric fields using molecular spectroscopy and characterize parity-dependent trap shifts, which are found to limit the coherence time. Furthermore, the parity-doublet coherence times achieved in this work are a defining milestone for the use of polyatomic molecules in quantum science.

Quantum information↗

Raman Sideband Cooling of Molecules in an Optical Tweezer Array to the 3D Motional Ground State

Ultracold polar molecules are promising for quantum information processing and searches for physics beyond the standard model. Laser cooling to ultracold temperatures is an established technique for trapped diatomic and triatomic molecules. Further cooling of the molecules to near the motional ground state is crucial for reducing various dephasings in quantum and precision applications. In this work, we demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their motional ground state, with average motional occupation quantum numbers of n ¯ x = 0.16 ( 12 ) , n ¯ y = 0.17 ( 17 ) (radial directions), and n ¯ z = 0.22 ( 16 ) (axial direction), and a 3-D motional-ground-state probability of 54 ± 18 % of the molecules that survive the RSC. This process paves the way to increase molecular coherence times in optical tweezers for robust quantum computation and simulation applications. Published by the American Physical Society 2024

Physics↗

Predissociation-based measurements of bond dissociation energies: US 2 , OUS, and USe

The uranium-containing molecules US 2 , OUS, and USe have been investigated using a pulsed laser ablation supersonic beam molecular source with time-of-flight mass spectrometric detection. Spectra have been recorded using the resonant two-photon ionization method over the spectroscopic range from 277 to 238 nm. These species have a myriad of excited electronic states in this spectroscopic region, leading to spectra that are highly congested and appear quasicontinuous. Sharp predissociation thresholds are observed, allowing precise bond dissociation energies to be measured. In the case of the triatomic molecules, it was necessary to use one laser for excitation and a delayed laser for ionization in order to observe a sharp predissociation threshold that allowed a precise bond dissociation energy to be measured. The resulting thermochemical values are D 0 (SU-S) = 4.910 ± 0.003 eV, D 0 (OU-S) = 5.035 ± 0.004 eV, and D 0 (USe) = 4.609 ± 0.009 eV. These results provide the first measurement of D 0 (USe) and reduce the error limits in the previous values of D 0 (SU-S) and D 0 (OU-S) by a factor of more than 70.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Separability of H 2 O molecular potential surfaces in hyperspherical coordinates via adiabatic approximation

An adiabatic scheme for separation of the three-dimensional (3D) nuclear dynamics on the ground electronic Born-Oppenheimer potential energy surface of an H 2 O molecule in hyperspherical coordinates is presented. It is found that the three vibrational modes are weakly coupled and the 3D vibrational wave function can be approximated as a product of three separable functions: one represented by the hyperradius and two by the two hyperangles individually. Additionally, this framework is then used for investigation of the formation and the role of a saddlelike barrier arising in the two hyperspherical angles that is to moderate the OH + H dissociation process. In order to test the validity of the framework, vibrational states with energies up to 19 500 cm -1 are constructed under the assumptions of adiabaticity and separability and compared to full three-dimensional high-precision numerical calculations yielding remarkable correspondence. As a result we present a simple construction scheme for separated molecular vibration states as the first step towards theoretical investigation of laser-driven molecular dynamics of triatomic molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone

Here, several alternative methods for the description of the interaction between rotation and vibration are compared and contrasted using hyperspherical coordinates for a triatomic molecule. These methods differ by the choice of the z -axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, a block-structure of the rotational–vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit. This theory is then employed to compute ro-vibrational spectra of singly substituted ozone; roughly, 600 vibrational states of 16 O 18 O 16 O and 16 O 16 O 18 O isomers combined, with rotational excitations up to J = 5 and both inversion parities (21600 coupled ro-vibrational states in total). Splittings between the states of different parities, so-called K -doublings, are calculated and analyzed. The roles of the asymmetric-top rotor term and the Coriolis coupling term are determined individually, and it is found that they both affect these splittings, but in the opposite directions. Thus, the two effects partially cancel out, and the residual splittings are relatively small. Energies of the ro-vibrational states reported in this work for 16 O 18 O 16 O and 16 O 16 O 18 O are in excellent agreement with literature (available for low-vibrational excitation). New data obtained here for the highly excited vibrational states enable the first systematic study of the Coriolis effect in symmetric and asymmetric isotopomers of ozone.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Second Linear Response Theory and the Analytic Calculation of Excited-State Properties

We present a method based on second linear response time-dependent density func- tional theory (TDDFT) to calculate permanent and transition multipoles of excited states, which are required to compute excited-state absorption/emission spectra, multi- photon optical processes, among others. In previous work, we examined computations based on second linear response theory in which linear response TDDFT was employed twice. In contrast, the present methodology only requires information from a single linear response calculation to compute the excited-state properties. These are eval- uated analytically through various algebraic operations involving electron repulsion integrals and excitation vectors. The present derivation focuses on full many-body wave functions instead of single orbitals, as in our previous approach. Here, we test the proposed method by applying it to several diatomic and triatomic molecules. This shows that the computed excited-state dipoles are consistent with respect to reference equation-of-motion coupled cluster calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational–vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric ( 18 O 16 O 18 O) and asymmetric ( 18 O 18 O 16 O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric ( 16 O 18 O 16 O) and asymmetric ( 16 O 16 O 18 O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

C2QA - Bosonic Qiskit

The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have recently been demonstrated by experiments with bosonic codes that reach the break-even point for quantum error correction [1]–[5] and by efficient Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic molecules [6] that is well beyond the capabilities of current qubit-only hardware. The goal of this Co-design Center for Quantum Advantage (C2QA) project is to develop an instruction set architecture (ISA) for hybrid qubit/bosonic mode systems that contains an inventory of the fundamental operations and measurements that are possible in such hardware. The corresponding abstract machine model (AMM) would also contain a description of the appropriate error models associated with the gates, measurements and time evolution of the hardware. This information has been implemented as an extension of IBM Qiskit. IBM Qiskit is an open-source software development toolkit (SDK) for simulating the quantum state of a quantum circuit and for running the same circuits on prototype hardware within the IBM Quantum Experience. We introduce the Bosonic Qiskit software to enable the simulation of hybrid qubit/bosonic systems using the existing Qiskit software development kit [7]. This implementation can be used for simulating new hybrid systems, verifying proposed physical systems, and modeling systems larger than can currently be constructed. We also cover tutorials and example use cases included within the software to study JaynesCummings models, bosonic Hubbard models, plotting Wigner functions and animations, and calculating maximum likelihood estimations using Wigner functions.

quantum, boson, Qiskit↗

An evaluation for geometries, formation enthalpies, and dissociation energies of diatomic and triatomic (C, H, N, O), NO 3 , and HNO 3 molecules from the PAW DFT method with PBE and optB88-vdW functionals

The structural geometries, formation enthalpies, and dissociation energies of all diatomic and triatomic molecules consisting of the four basic elements C, H, N, and/or O are calculated using the projector augmented wave density functional theory (DFT) method with the Perdew–Burke–Ernzerhof and optB88-vdW exchange-correlation functionals. The calculations are also extended to two larger molecules NO 3 and HNO 3 , which consist of four and five atoms, respectively. In total, 82 molecules or isomers are considered in the calculations. The geometric parameters including 42 bond lengths and 15 bond angles of these molecules calculated using the planewave DFT method are highly satisfactory, relative to the available experimental data. The error analysis is also performed for 49 formation enthalpies and 138 dissociation energies (including 51 atomization energies as well as the corresponding bond dissociation energies). The results are also compared with the previous data from various atomic-orbital-based methods for molecules and from similar or different planewave DFT methods for various solids and other molecules. This provides an informative and instructive evaluation especially for calculating the large-size material systems containing these small molecules as well as for developing the DFT methods further.

74 ATOMIC AND MOLECULAR PHYSICS↗

On the performance of composite schemes in determining equilibrium molecular structures

Determination of equilibrium molecular structures is an essential ingredient in predicting spectroscopic parameters that help in identifying molecular carriers of microwave transitions. Here, in this study, the performance of two different ab initio composite approaches for obtaining equilibrium structures, “energy scheme” and “geometry scheme,” is explored and compared to semi-experimental equilibrium structures. This study is performed for a set of 11 molecules which includes diatomics, linear triatomics, and a few non-linear molecules. The ab initio calculations were performed using three tiers of composite chemical recipes. The current results show that as the overall rigor of calculation is increased, the semi-experimental and the ab initio numbers agree to within 0.0003 Å for all molecules in the test set. The composite approach based on correcting the potential energy surface (energy scheme) and the one based on correcting the geometry directly (geometry scheme) show excellent agreement with each other. This work represents a step toward development of efficient and highly accurate procedures for computing ab initio equilibrium structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pathway toward Optical Cycling and Laser Cooling of Functionalized Arenes

Rapid and repeated photon cycling has enabled precision metrology and the development of quantum information systems using atoms and simple molecules. Extending optical cycling to structurally complex molecules would provide new capabilities in these areas, as well as in ultracold chemistry. Increased molecular complexity, however, makes realizing closed optical transitions more difficult. Building on already established strong optical cycling of diatomic, linear triatomic, and symmetric top molecules, recent work has pointed the way to cycling of larger molecules, including phenoxides. The paradigm for these systems is an optical cycling center bonded to a molecular ligand. Theory has suggested that cycling may be extended to even larger ligands, like naphthalene, pyrene, and coronene. For this paper, we study optical excitation and fluorescent vibrational branching of CaO-[illus. chemical structure], SrO-[illus. chemical structure], and CaO-[illus. chemical structure] and find only weak decay to excited vibrational states, indicating a promising path to full quantum control and laser cooling of large arene-based molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Filming enhanced ionization in an ultrafast triatomic slingshot

Abstract Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e., filmed) by ionizing at an adjustable delay with respect to the start of interatomic motion. Results are distorted, however, by ultrafast motion during the ionizing pulse. We studied this effect in water and filmed the rapid “slingshot” motion that enhances ionization and distorts CEI results. Our investigation uncovered both the geometry and mechanism of the enhancement which may inform CEI experiments in many other polyatomic molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SpectrumSDT: A program for parallel calculation of coupled rotational-vibrational energies and lifetimes of bound states and scattering resonances in triatomic systems

In this work, we present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over the user-defined regions of potential energy surface, which helps to classify these states. In this release of the code, SpectrumSDT is limited to ABA-type molecules with wave functions that do not extend into the regions near Eckart singularities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Breaking covalent bonds in the context of the many-body expansion (MBE). I. The purported “first row anomaly” in XH n (X = C, Si, Ge, Sn; n = 1–4)

We present a new, novel implementation of the Many-Body Expansion (MBE) to account for the breaking of covalent bonds, thus extending the range of applications from its previous popular usage in the breaking of hydrogen bonds in clusters to molecules. A central concept of the new implementation is the in situ atomic electronic state of an atom in a molecule that casts the one-body term as the energy required to promote it to that state from its ground state. The rest of the terms correspond to the individual diatomic, triatomic, etc., fragments. Its application to the atomization energies of the XH n series, X = C, Si, Ge, Sn and n = 1–4, suggests that the (negative, stabilizing) 2-B is by far the largest term in the MBE with the higher order terms oscillating between positive and negative values and decreasing dramatically in size with increasing rank of the expansion. The analysis offers an alternative explanation for the purported “first row anomaly” in the incremental H n–1 X–H bond energies seen when these energies are evaluated with respect to the lowest energy among the states of the XH n molecules. Due to the “flipping” of the ground/first excited state between CH 2 ( 3 B 1 ground state, 1 A 1 first excited state) and XH 2 , X = Si, Ge, Sn ( 1 A 1 ground state, 3 B 1 first excited state), the overall picture does not exhibit a “first row anomaly” when the incremental bond energies are evaluated with respect to the molecular states having the same in situ atomic states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Water Network Shape-Dependence of Local Interactions with the Microhydrated –NO 2 – and –CO 2 – Anionic Head Groups by Cold Ion Vibrational Spectroscopy

We report the structural evolutions of water networks and solvatochromic response of the CH 3 NO 2 – radical anion in the OH and CH stretching regions by analysis of the vibrational spectra displayed by cryogenically cooled CH 3 NO 2 – ·(H 2 O) n=1–6 clusters. The OH stretching bands evolve with a surprisingly large discontinuity at n = 6, which features the emergence of an intense, strongly red-shifted band along with a weaker feature that appears in the region assigned to a free OH fundamental. Very similar behavior is displayed by the perdeuterated carboxylate clusters, RCO 2 – ·(H 2 O) n=5–7 (R = CD 3 CD 2 ), indicating that this behavior is a general feature in the microhydration of the triatomic anionic domain and not associated with CH oscillators. Electronic structure calculations trace this behavior to the formation of a “book” isomer of the water hexamer that adopts a configuration in which one of the water molecules resides in an acceptor–acceptor–donor (AAD) (A = acceptor, D = donor) H-bonding site. Excitation of the bound OH in the AAD site explores the local network topology best suited to stabilize an incipient –XO 2 H–OH–(H 2 O) 2 intracluster proton-transfer reaction. These systems thus provide particularly clear examples where the network shape controls the potential energy landscape that governs water network-mediated, intracluster proton transfer. The CH stretching bands of the CH 3 NO 2 – ·(H 2 O) n=1–6 clusters also exhibit strong solvatochromic shifts, but in this case, they smoothly blue-shift with increasing hydration with no discontinuity at n = 6. Furthermore, this behavior is analyzed in the context of the solute-ion polarizability response and partial charge transfer to the water networks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dissociative electron recombination and rotational cooling of the deuterated triatomic hydrogen ions H 2 ⁡D + and D 2 ⁢H +

We have measured the dissociative recombination (DR) of the deuterated triatomic hydrogen ions H 2 ⁡D + and D 2 ⁢H + as a function of storage time at the Cryogenic Storage Ring (CSR). Both molecular ions were stored for up to 1000 s inside the cryogenic vacuum of the CSR prior to the electron recombination measurements, allowing them to cool to their lowest rotational states. We implement a comprehensive model for all relevant processes to predict the internal state evolution of the ions during storage inside the CSR, employing calculated radiative transition strengths and state-selective rate coefficients for electron collisions. Our DR rate coefficient measurements with deuterated triatomic hydrogen ions in defined quantum states allow for meaningful comparisons with state-of-the-art theoretical calculations, paving the way for a better understanding of the complex DR process for polyatomic molecular ions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗