Time-Resolved Line Shapes of Single Quantum Emitters via Machine Learned Photon Correlations.

Solid-state single-photon emitters (SPEs) are quantum light sources that combine atomlike optical properties with solid-state integration and fabrication capabilities. SPEs are hindered by spectral diffusion, where the emitter's surrounding environment induces random energy fluctuations. Timescales of spectral diffusion span nanoseconds to minutes and require probing single emitters to remove ensemble averaging. Photon correlation Fourier spectroscopy (PCFS) can be used to measure time-resolved single emitter line shapes, but is hindered by poor signal-to-noise ratio in the measured correlation functions at early times due to low photon counts. Here, we develop a framework to simulate PCFS correlation functions directly from diffusing spectra that match well with experimental data for single colloidal quantum dots. We use these simulated datasets to train a deep ensemble autoencoder machine learning model that outputs accurate, noiseless, and probabilistic reconstructions of the noisy correlations. Using this model, we obtain reconstructed time-resolved single dot emission line shapes at timescales as low as 10 ns, which are otherwise completely obscured by noise. This enables PCFS to extract optical coherence times on the same timescales as Hong-Ou-Mandel two-photon interference, but with the advantage of providing spectral information in addition to estimates of photon indistinguishability. Our machine learning approach is broadly applicable to different photon correlation spectroscopy techniques and SPE systems, offering an enhanced tool for probing single emitter line shapes on previously inaccessible timescales.

A rotational investigation of the three isomeric forms of cyanoethynylbenzene (HCC-C6H4-CN): benchmarking experiments and calculations using the "Lego brick" approach.

We report the study of three structural isomers of phenylpropiolonitrile (3-phenyl-2-propynenitrile, C6H5-C3N) containing an alkyne function and a cyano group, namely ortho-, meta-, and para-cyanoethynylbenzene (HCC-C6H4-CN). The pure rotational spectra of these species have been recorded at room temperature in the millimeter-wave domain using a chirped-pulse spectrometer (75-110 GHz) and a source-frequency modulation spectrometer (140-220 GHz). Assignments of transitions in the vibrational ground state and several vibrationally excited states were supported by quantum chemical calculations using the so-called "Lego brick" approach [A. Melli, F. Tonolo, V. Barone and C. Puzzarini, J. Phys. Chem. A, 2021, 125, 9904-9916]. From these assignments, accurate spectroscopic (rotational and centrifugal distortion) constants have been derived: for all species and all observed vibrational states, predicted rotational constants show relative accuracy better than 0.1%, and often of the order of 0.01%, compared to the experimental values. The present work hence further validates the use of the "Lego brick" approach for predicting spectroscopic constants with high precision.

A Search for Heterocycles in GOTHAM Observations of TMC-1.

We have conducted an extensive search for nitrogen-, oxygen-, and sulfur-bearing heterocycles toward Taurus Molecular Cloud 1 (TMC-1) using the deep, broadband centimeter-wavelength spectral line survey of the region from the GOTHAM large project on the Green Bank Telescope. Despite their ubiquity in terrestrial chemistry, and the confirmed presence of a number of cyclic and polycyclic hydrocarbon species in the source, we find no evidence for the presence of any heterocyclic species. Here, we report the derived upper limits on the column densities of these molecules obtained by Markov Chain Monte Carlo (MCMC) analysis and compare this approach to traditional single-line upper limit measurements. We further hypothesize why these molecules are absent in our data, how they might form in interstellar space, and the nature of observations that would be needed to secure their detection.

Molecule Identification with Rotational Spectroscopy and Probabilistic Deep Learning.

A proof-of-concept framework for identifying molecules of unknown elemental composition and structure using experimental rotational data and probabilistic deep learning is presented. Using a minimal set of input data determined experimentally, we describe four neural network architectures that yield information to assist in the identification of an unknown molecule. The first architecture translates spectroscopic parameters into Coulomb matrix eigenspectra as a method of recovering chemical and structural information encoded in the rotational spectrum. The eigenspectrum is subsequently used by three deep learning networks to constrain the range of stoichiometries, generate SMILES strings, and predict the most likely functional groups present in the molecule. In each model, we utilize dropout layers as an approximation to Bayesian sampling, which subsequently generates probabilistic predictions from otherwise deterministic models. These models are trained on a modestly sized theoretical dataset comprising ∼83 000 unique organic molecules (between 18 and 180 amu) optimized at the ωB97X-D/6-31+G(d) level of theory, where the theoretical uncertainties of the spectoscopic constants are well-understood and used to further augment training. Since chemical and structural properties depend strongly on molecular composition, we divided the dataset into four groups corresponding to pure hydrocarbons, oxygen-bearing species, nitrogen-bearing species, and both oxygen- and nitrogen-bearing species, training each type of network with one of these categories, thus creating "experts" within each domain of molecules. We demonstrate how these models can then be used for practical inference on four molecules and discuss both the strengths and shortcomings of our approach and the future directions these architectures can take.

Bayesian Analysis of Theoretical Rotational Constants from Low-Cost Electronic Structure Methods.

With an ever-increasing usage of electronic structure programs by the microwave spectroscopy community, there is a growing need to assess the performance of commonly used, low-cost quantum chemical methods, particularly with respect to rotational constants because these quantities are central in guiding experiments. Here, we systematically benchmark the predictive power afforded by several low-level ab initio and density functionals combined with a variety of basis sets that are commonly employed in the rotational spectroscopy literature. The data set in our analysis consists of 6916 optimized geometries of 76 representative species where high-resolution experimental gas-phase rotational constants are available. We adopted a Bayesian approach for analyzing the performance of each method and basis set combination, employing Hamiltonian Monte Carlo sampling to determine the uncertainty in theoretical predictions of rotational constants and dipole moments. Our analysis establishes a hierarchy of accuracy and uncertainty, with commonly used methods in the rotational spectroscopy literature such as B3LYP and MP2 yielding lower accuracy and higher uncertainty than newer-generation functionals such as those from the Minnesota family, and ωB97X-D, which, when paired with a modestly sized 6-31+G(d) basis, provides optimal performance with respect to computational cost. Additionally, we provide statistical scaling factors that can be used to empirically correct for vibration-rotation effects, as a means to further improve the accuracy of rotational constants predicted from these relatively low-cost theoretical methods. As part of this, we demonstrate that the uncertainties can be used in simulations of rotational spectra to cross-correlate with broadband spectra, a methodology that could be used to quickly and efficiently survey experimental spectra for new molecules.

Exhaustive Product Analysis of Three Benzene Discharges by Microwave Spectroscopy.

Using chirped and cavity microwave spectroscopies, automated double resonance, new high-speed fitting and deep learning algorithms, and large databases of computed structures, the discharge products of benzene alone, or in combination with molecular oxygen or nitrogen, have been exhaustively characterized between 6.5 and 26 GHz. In total, more than 3300 spectral features were observed; 89% of these, accounting for 97% of the total intensity, have now been assigned to 152 distinct chemical species and 60 of their variants (i.e., isotopic species and vibrationally excited states). Roughly 50 of the products are entirely new or poorly characterized at high resolution, including many heavier by mass than the precursor benzene. These findings provide direct evidence for a rich architecture of two- and three-dimensional carbon and indicate that benzene growth, particularly the formation of ring-chain molecules, occurs facilely under our experimental conditions. The present analysis also illustrates the utility of microwave spectroscopy as a precision tool for complex mixture analysis, irrespective of whether the rotational spectrum of a product species is known a priori or not. From this large quantity of data, for example, it is possible to determine with confidence the relative abundances of different product masses, but more importantly the relative abundances of different isomers with the same mass. The complementary nature of this type of analysis to traditional mass spectrometry is discussed.

Gas-phase synthetic pathways to benzene and benzonitrile: a combined microwave and thermochemical investigation.

The recent astronomical detection of benzonitrile (C6H5CN) in the cold, starless cloud TMC-1 demonstrates that aromatic chemistry is efficient even in the primordial stages of star and planet formation. C6H5CN may serve as a convenient observational proxy for benzene, which is otherwise challenging to detect in space, provided the chemistry linking these two molecules is tightly constrained. Here we present a high-resolution microwave spectroscopic study in combination with an accurate thermochemical treatment of the formation chemistry of C6H5CN and benzene. We demonstrate that C6H5CN is a highly useful tracer for benzene in the presence of CN radical, either in space or in the laboratory, and by inference, that the reaction C2H + CH2(CH)2CH2 yields benzene, along with its high-energy polar isomer fulvene. In addition, we find that the higher energy isomer, C6H5NC, is formed at <0.1% abundance relative to C6H5CN. By exploiting -CN tagging, formation pathways to produce benzene using a variety of acyclic hydrocarbon precursors are then explored. A robust, self-consistent, and chemically accurate theoretical treatment has also been undertaken for several key reactions. The results are discussed both in the context of aromatic molecule synthesis and astrochemistry.

Generation and structural characterization of Ge carbides GeCn (n = 4, 5, 6) by laser ablation, broadband rotational spectroscopy, and quantum chemistry.

Following the recent discovery of T-shaped GeC2, rotational spectra of three larger Ge carbides, linear GeC4, GeC5, and GeC6 have been observed using chirped pulse and cavity Fourier transform microwave spectroscopy and a laser ablation molecule source, guided by new high-level quantum chemical calculations of their molecular structure. Like their isovalent Si-bearing counterparts, Ge carbides with an even number of carbon atoms beyond GeC2 are predicted to possess 1Σ ground electronic states, while odd-numbered carbon chains are generally 3Σ; all are predicted to be highly polar. For the three new molecules detected in this work, rotational lines of four of the five naturally occurring Ge isotopic variants have been observed between 6 and 22 GHz. Combining these measurements with ab initio force fields, the Ge-C bond lengths have been determined to high precision: the derived values of 1.776 Å for GeC4, 1.818 Å for GeC5, and 1.782 Å for GeC6 indicate a double bond between these two atoms. Somewhat surprisingly, the spectrum of GeC5 very closely resembles that of a 1Σ molecule, implying a spin-spin coupling constant λ in excess of 770 GHz for this radical, a likely consequence of the large spin-orbit constant of atomic Ge (∼1000 cm-1). A systematic comparison between the production of SiCn and GeCn chains by laser ablation has also been undertaken. The present work suggests that other large metal-bearing molecules may be amenable to detection by similar means.

Characterization of the simplest hydroperoxide ester, hydroperoxymethyl formate, a precursor of atmospheric aerosols.

Atmospheric aerosols are large clusters of molecules and particulate matter that profoundly affect the Earth's radiation budget and climate. Gas-phase oxidation of volatile organic compounds is thought to play a key role in nucleation and aerosol growth, but remains poorly understood. One reaction proposed to trigger formation of condensable, low volatility organic compounds is that between Criegee intermediates and carboxylic acids to yield hydroperoxide esters. Here we isolate in high yield the simplest hydroperoxide ester, hydroperoxymethyl formate (HOOCH2OCHO), as a secondary product in the ozonolysis of ethylene, and establish by rotational spectroscopy that this ester adopts a nearly-rigid cyclic structure owing to a strong hydrogen bond between the peroxy hydrogen and carbonyl oxygen. Subsequent detection of this ester in the ozonolysis of propylene and isoprene suggests that terminal alkenes readily undergo specific types of second-order oxidation reactions that have been implicated in the formation of atmospheric aerosols.

Vibrational satellites of C2S, C3S, and C4S: microwave spectral taxonomy as a stepping stone to the millimeter-wave band.

We present a microwave spectral taxonomy study of several hydrocarbon/CS2 discharge mixtures in which more than 60 distinct chemical species, their more abundant isotopic species, and/or their vibrationally excited states were detected using chirped-pulse and cavity Fourier-transform microwave spectroscopies. Taken together, in excess of 85 unique variants were detected, including several new isotopic species and more than 25 new vibrationally excited states of C2S, C3S, and C4S, which have been assigned on the basis of published vibration-rotation interaction constants for C3S, or newly calculated ones for C2S and C4S. On the basis of these precise, low-frequency measurements, several vibrationally exited states of C2S and C3S were subsequently identified in archival millimeter-wave data in the 253-280 GHz frequency range, ultimately providing highly accurate catalogs for astronomical searches. As part of this work, formation pathways of the two smaller carbon-sulfur chains were investigated using 13C isotopic spectroscopy, as was their vibrational excitation. The present study illustrates the utility of microwave spectral taxonomy as a tool for complex mixture analysis, and as a powerful and convenient 'stepping stone' to higher frequency measurements in the millimeter and submillimeter bands.

Zero-point energy conservation in classical trajectory simulations: Application to H2CO.

A new approach for preventing zero-point energy (ZPE) violation in quasi-classical trajectory (QCT) simulations is presented and applied to H2CO "roaming" reactions. Zero-point energy may be problematic in roaming reactions because they occur at or near bond dissociation thresholds and these channels may be incorrectly open or closed depending on if, or how, ZPE has been treated. Here we run QCT simulations on a "ZPE-corrected" potential energy surface defined as the sum of the molecular potential energy surface (PES) and the global harmonic ZPE surface. Five different harmonic ZPE estimates are examined with four, on average, giving values within 4 kJ/mol-chemical accuracy-for H2CO. The local harmonic ZPE, at arbitrary molecular configurations, is subsequently defined in terms of "projected" Cartesian coordinates and a global ZPE "surface" is constructed using Shepard interpolation. This, combined with a second-order modified Shepard interpolated PES, V, allows us to construct a proof-of-concept ZPE-corrected PES for H2CO, V eff, at no additional computational cost to the PES itself. Both V and V eff are used to model product state distributions from the H + HCO → H2 + CO abstraction reaction, which are shown to reproduce the literature roaming product state distributions. Our ZPE-corrected PES allows all trajectories to be analysed, whereas, in previous simulations, a significant proportion was discarded because of ZPE violation. We find ZPE has little effect on product rotational distributions, validating previous QCT simulations. Running trajectories on V, however, shifts the product kinetic energy release to higher energy than on V eff and classical simulations of kinetic energy release should therefore be viewed with caution.

Photodissociation of acetone from 266 to 312 nm: Dynamics of CH3 + CH3CO channels on the S0 and T1 states.

The photodissociation dynamics of acetone (CH3)2CO, cooled in a molecular beam, have been explored over the wavelength range 266-312 nm. Nascent CH3 fragments were detected by resonance-enhanced multiphoton ionization, followed by mass-selected ion imaging. For photolysis at λ = 306 nm, the image shows a sharp ring, which, when converted to a translational energy distribution, reveals a narrow Gaussian peak with a maximum at 90% of the available energy. As the photolysis energy is increased, the distribution slowly broadens and shifts to higher recoil translational energy. The fraction of available energy in translation energy decreases in favour of internal energy of the CH3CO fragment. These observations are consistent with a dynamical model in which the energy of the exit channel barrier on the T1 surface evolves mostly into relative translational energy. Energy in excess of the barrier is partitioned statistically into all degrees of freedom. No evidence was found for any other dynamical pathway producing CH3 fragments, including reaction on S0 or S1, for dissociation between 306 and 266 nm. For λ > 306 nm, a diffuse, slow recoil component to the image appears. The translational energy distribution for this component is fit well by a statistical prior distribution of energy. We attribute this component to dissociation on the S0, ground state surface; to our knowledge, this is the first direct observation of this channel. The appearance of S0 dynamics and the disappearance of the T1 component are consistent with previously inferred barrier height on T1 for the production of CH3CO + CH3. The possible atmospheric implications of our findings are discussed.

Detection and structural characterization of nitrosamide H2NNO: A central intermediate in deNOx processes.

The structure and bonding of H2NNO, the simplest N-nitrosamine, and a key intermediate in deNOx processes, have been precisely characterized using a combination of rotational spectroscopy of its more abundant isotopic species and high-level quantum chemical calculations. Isotopic spectroscopy provides compelling evidence that this species is formed promptly in our discharge expansion via the NH2 + NO reaction and is collisionally cooled prior to subsequent unimolecular rearrangement. H2NNO is found to possess an essentially planar geometry, an NNO angle of 113.67(5)°, and a N-N bond length of 1.342(3) Å; in combination with the derived nitrogen quadrupole coupling constants, its bonding is best described as an admixture of uncharged dipolar (H2N-N=O, single bond) and zwitterion (H2N+=N-O-, double bond) structures. At the CCSD(T) level, and extrapolating to the complete basis set limit, the planar geometry appears to represent the minimum of the potential surface, although the torsional potential of this molecule is extremely flat.

Cation States of Ethane: HEAT Calculations and Vibronic Simulations of the Photoelectron Spectrum of Ethane.

High-accuracy ab initio calculations have been carried out on ethane and its radical cation. With the HEAT-345(Q) scheme, adiabatic ionization potentials of 11.52 and 11.57 eV are determined for the X̃ (2)Eg and à (2)A1g states, respectively, with an uncertainty of ±0.015 eV. Also considered in this report are linear and quadratic vibronic coupling involving both states. With this simple vibronic model, the photoelectron spectrum of ethane was simulated in the 11-15 eV region using linear and full quadratic Jahn-Teller coupling Hamiltonians, and with up to 70 billion direct product basis functions in a high-performance computing environment. Although the linear vibronic coupling model adequately reproduces the spectral envelope, the quadratic vibronic treatment results in much better agreement with the observed spectrum.

Detection of two interstellar polycyclic aromatic hydrocarbons via spectral matched filtering.

Unidentified infrared emission bands are ubiquitous in many astronomical sources. These bands are widely, if not unanimously, attributed to collective emissions from polycyclic aromatic hydrocarbon (PAH) molecules, yet no single species of this class has been identified in space. Using spectral matched filtering of radio data from the Green Bank Telescope, we detected two nitrile-group-functionalized PAHs, 1- and 2-cyanonaphthalene, in the interstellar medium. Both bicyclic ring molecules were observed in the TMC-1 molecular cloud. In this paper, we discuss potential in situ gas-phase PAH formation pathways from smaller organic precursor molecules.

Study of Benzene Fragmentation, Isomerization, and Growth Using Microwave Spectroscopy.

Using a combination of broadband and cavity Fourier transform microwave spectroscopies, and newly developed analysis and assignment tools, the discharge products of benzene have been extensively studied in the 2-18 GHz frequency range. More than 450 spectral features with intensities greater than 6σ of the noise RMS were identified, of which of roughly four-fifths (82%) constituting 90% of the total spectral intensity were assigned to 38 species previously detected in the radio band, and nine entirely new hydrocarbon molecules were identified. The new species include both branched and chain fragments of benzene, high energy C6H6 isomers, and larger molecules such as phenyldiacetylene and isomers of fulvenallene; taken together they account for roughly half of the number of observed transitions and 51% of the spectral line intensity. Transitions from vibrationally excited states of several molecules were also identified in the course of this investigation. A key aspect of the present analysis was implementation of a rapid and efficient workflow to assign spectral features from known molecules and to identify line progressions by pattern recognition techniques.