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DOE OSTI2021

Understanding, quantifying, and controlling the molecular ordering of semiconducting polymers: from novices to experts and amorphous to perfect crystals

Molecular packing and texture of semiconducting polymers are often critical to the performance of devices using these materials. Although frameworks exist to quantify the ordering, interpretations are often just qualitative, resulting in imprecise use of terminology. Here, we reemphasize the significance of quantifying molecular ordering in terms of degree of crystallinity (volume fractions that are ordered) and quality of ordering and their relation to the size scale of an ordered region. We are motivated in part by our own imprecise and inconsistent use of terminology in the past, as well as the need to have a primer or tutorial reference to teach new group members. We strive to develop and use consistent terminology with regards to crystallinity, semicrystallinity, paracrystallinity, and related characteristics. To account for vastly different quality of ordering along different directions, we classify paracrystals into 2D and 3D paracrystals and use paracrystallite to describe the spatial extent of molecular ordering in 1–10 nm. We show that a deeper understanding of molecular ordering can be achieved by combining grazing-incidence wide-angle X-ray scattering and differential scanning calorimetry, even though not all aspects of these measurements are consistent, and some classification appears to be method dependent. We classify a broad range of representative polymers under common processing conditions into five categories based on the quantitative analysis of the paracrystalline disorder parameter (g) and thermal transitions. A small database is presented for 13 representative conjugated and insulating polymers ranging from amorphous to semi-paracrystalline. Lastly, we outline the challenges to rationally design more perfect polymer crystals and propose a new molecular design approach that envisions conceptual molecular grafting that is akin to strained and unstrained hetero-epitaxy in classic (compound) semiconductors thin film growth.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Influence of the molecular weight and size distribution of PSS on mixed ionic-electronic transport in PEDOT:PSS

The commercially available polyelectrolyte complex poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) is ubiquitous in organic and hybrid electronics. As such, it has often been used as a benchmark material for fundamental studies and the development of new electronic devices. Yet, most studies on PEDOT:PSS have focused on its electronic conductivity in dry environments, with less consideration given to its ion transport, coupled ionic-electronic transport, and charge storage properties in aqueous environments. These properties are essential for applications in bioelectronics (sensors, actuators), charge storage devices, and electrochromic displays. Importantly, past studies on mixed ionic-electronic transport in PEDOT:PSS neglected to consider how the molecular structure of PSS affects mixed ionic-electronic transport. Herein, we therefore investigated the effect of the molecular weight and size distribution of PSS on the electronic properties and morphology of PEDOT:PSS both in dry and aqueous environments, and overall performance in organic electrochemical transistors (OECTs). Using reversible addition–fragmentation chain transfer (RAFT) polymerization with two different chain transfer agents, six PSS samples with monomodal, narrow (D = 1.1) and broad (D = 1.7) size distributions and varying molecular weights were synthesized and used as matrices for PEDOT. We found that using higher molecular weight of PSS (Mn = 145 kg mol –1 ) and broad dispersity led to OECTs with the highest transconductance (up to 16 mS) and [μC*] values (~140 F cm –1 V –1 s –1 ) in PEDOT:PSS, despite having a lower volumetric capacitance (C* = 35 ± 4 F cm –3 ). The differences were best explained by studying the microstructure of the films by atomic force microscopy (AFM). We found that heterogeneities in the PEDOT:PSS films (interconnected and large PEDOT- and PSS-rich domains) obtained from high molecular weight and high dispersity PSS led to higher charge mobility (μOECT ~4 cm 2 V –1 s –1 ) and hence transconductance. Furthermore, these studies highlight the importance of considering molecular weight and size distribution in organic mixed ionic-electronic conductor, and could pave the way to designing high performance organic electronics for biological interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Molecular catalyst and co-catalyst systems based on transition metal complexes for the electrochemical oxidation of alcohols

Molecular catalysts allow deeper study of underlying mechanisms relative to heterogeneous systems by offering a discrete active site to monitor. Mechanistic study with knowledge of key intermediates subsequently enables the development of design principles through an understanding of how improved reactivity or selectivity can be achieved through modification of the catalyst structure. The co-catalytic inclusion of redox mediators (RM), which are small molecules that can aid in the transfer of protons and electrons, has been shown to improve product conversion and selectivity in many molecular systems, through intercepting key intermediates to direct reaction pathways. The primary focus for the majority of molecular electrocatalysts has been on optimizing design for reductive reactions, such as the hydrogen evolution reaction (HER), the oxygen reduction reaction (ORR), and the carbon dioxide reduction reaction (CO 2 RR). By comparison, there has been much less focus on key oxidative reactions by molecular species, apart from the oxygen evolution reaction (OER). The focus of this review is to highlight molecular catalyst systems optimized for the electrochemical oxidation of alcohols. The electrochemical alcohol oxidation reaction (AOR) can serve a role in synthesizing value-added chemicals and can serve as the counterpart to the CO 2 RR by releasing electricity from energy-rich molecules. State-of-the-art molecular systems for the AOR are divided between single-site catalysts and co-catalytic systems with redox mediators. The AOR is contextualized as an energy relevant reaction, an overview of the area is provided, foundational improvements in catalyst systems are highlighted, and future development principles for incorporating redox mediators are suggested.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. Here, we recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Experimental validation of a collision-radiation dataset for molecular hydrogen in plasmas

Quantitative spectroscopy of molecular hydrogen has generated substantial demand, leading to the accumulation of diverse elementary process data encompassing radiative transitions, electron-impact transitions, predissociations, and quenching. However, their rates currently available are still sparse, and there are inconsistencies among those proposed by different authors. In this study, we demonstrate an experimental validation of such a molecular dataset by composing a collisional-radiative model (CRM) for molecular hydrogen and comparing experimentally obtained vibronic populations across multiple levels. From the population kinetics of molecular hydrogen, the importance of each elementary process in various parameter space is studied. In low-density plasmas (electron density ne≲1017 m−3) the excitation rates from the ground states and radiative decay rates, both of which have been reported previously, determine the excited state population. The inconsistency in the excitation rates affects the population distribution the most significantly in this parameter space. However, in higher density plasmas (ne≳1018 m−3), the excitation rates from excited states become important, which have never been reported in the literature, and may need to be approximated in some way. In order to validate these molecular datasets and approximated rates, we carried out experimental observations for two different hydrogen plasmas; a low-density radio frequency heated plasma (ne≈1016 m−3) and the Large Helical Device (LHD) divertor plasma (ne≳1018 m−3). The visible emission lines from EF1Σg+, HH¯1Σg+, D1Πu±, GK1Σg+, I1Πg±, J1Δg±, h3Σg+, e3Σu+, d3Πu±,g3Σg+, i3Πg±, and j3Δg± states were observed simultaneously and their population distributions were obtained from their intensities. We compared the observed population distributions with the CRM prediction, in particular the CRM with the rates compiled by Janev et al., Miles et al., and those calculated with the molecular convergent close-coupling (MCCC) method. The MCCC prediction gives the best agreement with the experiment, particularly for the emission from the low-density plasma. However, the population distribution in the LHD divertor shows a worse agreement with the CRM than those from low-density plasma, indicating the necessity of the precise excitation rates from excited states. We also found that the rates for the electron attachment is inconsistent with experimental results. This requires further investigation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Can Third-Body Stabilization of Bimolecular Collision Complexes in Cold Molecular Clouds Happen?

For more than half a century, networks of radiative association, dissociative recombination, and bimolecular reactions have been postulated to drive the low-temperature chemistry of cold molecular clouds. Third-body stabilizations of collision complexes have been assumed to be 'irrelevant' due to short lifetime of such complexes. Here, we conduct crossed molecular beam studies of ground state atomic silicon with diacetylene in combination with electronic structure calculations and microcanonical kinetics models operating under cold molecular cloud conditions. Our combined experimental, electronic structure, and microcanonical kinetics modelling investigations provide compelling evidence that three-body collisions of molecular hydrogen with long-lived reaction intermediates accessed through intersystem crossing are prevalent deep inside molecular clouds. This concept might be exportable to reactions involving polycyclic aromatic hydrocarbons thus affording a versatile machinery to complex organics via third-body stabilizations of bimolecular collision complexes deep inside cold molecular clouds.

astrochemistry↗

DOE OSTI2025

MolViewSpec: a Mol* extension for describing and sharing molecular visualizations

Data visualization is a pivotal component of a structural biologist’s arsenal. The Mol* Viewer makes molecular visualizations available to broader audiences via most web browsers. While Mol* provides a wide range of functionality, it has a steep learning curve and is only available via a JavaScript interface. To enhance the accessibility and usability of web-based molecular visualization, we introduce MolViewSpec (molstar.org/mol-view-spec), a standardized approach for defining molecular visualizations that decouples the definition of complex molecular scenes from their rendering. Scene definition can include references to commonly used structural, volumetric, and annotation data formats together with a description of how the data should be visualized and paired with optional annotations specifying colors, labels, measurements, and custom 3D geometries. Developed as an open standard, this solution paves the way for broader interoperability and support across different programming languages and molecular viewers, enabling more streamlined, standardized, and reproducible visual molecular analyses. MolViewSpec is freely available as a Mol* extension and a standalone Python package.

Midlik, Adam [European Bioinformatics Institute (U↗

DOE OSTI2024

Constraining dark matter-proton scattering from molecular cloud ionization

Optically dense clouds in the interstellar medium composed predominantly of molecular hydrogen, known as molecular clouds, are sensitive to energy injection in the form of photon absorption, cosmic-ray scattering, and dark matter (DM) scattering. The ionization rates in dense molecular clouds are heavily constrained by observations of abundances of various molecular tracers. Recent studies have set constraints on the DM-electron scattering cross section using measurements of ionization rates in dense molecular clouds. Here we calculate the analogous bounds on the DM-proton cross section using the molecular Migdal effect, recently adapted from the neutron scattering literature to the DM context. These bounds may be the strongest limits on a strongly coupled DM subfraction, and represent the first application of the Migdal effect to astrophysical systems. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2023

One dimensional temperature measurements by resonantly ionized photoemission thermometry of molecular nitrogen

This paper presents an extensive parameter study of a non-intrusive and non-seeded laser diagnostic method for measuring one dimensional (1D) rotational temperature of molecular nitrogen (N 2 ) at 165 - 450 K. Compared to previous efforts using molecular oxygen, here resonantly ionized and photoelectron induced fluorescence of molecular nitrogen for thermometry (N 2 RIPT) was demonstrated. The RIPT signal is generated by directly probing various rotational levels within the rovibrational absorption band of N 2 , corresponding to the 3-photon transition of N 2 ( X 1 Σ g + , v =0→ b 1 Π u , v ′ =6) near 285 nm, without involving collisional effects of molecular oxygen and nitrogen. The photoionized N 2 produces strong first negative band of N 2 + ( B 2 Σ u + − X 2 Σ g + ) near 390 nm, 420 nm, and 425 nm. Boltzmann analyses of various discrete fluorescence emission lines yield rotational temperatures of molecular nitrogen. By empirically choosing multiple rotational levels within the absorption band, non-scanning thermometry can be accurately achieved for molecular nitrogen. It is demonstrated that the N 2 RIPT technique can measure 1D temperature profile up to ∼5 cm in length within a pure N 2 environment. Multiple wavelengths are thoroughly analyzed and listed that are accurate for RIPT for various temperature ranges.

McCord, Walker (ORCID:0000000179747550)↗

DOE OSTI2025

Tabletop soft x-ray absorption spectroscopy for molecular fingerprinting

For applications related to nuclear security, safeguards, and nonproliferation, it is often critical to know the molecular compositions of lanthanide- and actinide-containing samples. Spectroscopy is a widely used tool that looks at the interaction between light and matter: Different species absorb or emit light at unique wavelengths which act as signatures. However, there is a limited number of tools that can achieve high-sensitivity, accurate measurements of lanthanide and actinide molecular compositions. Candidate methods include mass spectrometry, which usually destroys at least part of the sample and requires complicated stoichiometry to guess the original sample’s molecular compositions; optical spectroscopies, which have great atomic but limited molecular sensitivities or other drawbacks which make sensing molecules difficult like limited light sources or strong absorption in the atmosphere; and nuclear spectroscopies (gamma, neutron) which also have limited sources and long (>minute) collection times. As such, the purpose of our research is to develop a new tool to better distinguish between subtle differences in molecules containing lanthanides and actinides. Soft x-ray spectroscopy is sensitive to molecular form and is minimally intrusive/nondestructive to the sample. However, soft x-ray light with sufficient brightness for spectroscopy is typically limited to user-facilities like synchrotrons or free electron lasers, where beamtimes are competitive, and work with radiological materials may be difficult or entirely prohibited. To overcome this issue, our Team has developed a custom tabletop laser-driven, soft x-ray light source which employs high harmonic generation (HHG). Soft x-ray spectroscopy can distinguish between subtly different molecules, in the spectral range which we need to study these heavy elements. A tabletop system provides an effective and affordable tool to find both the elemental and chemical specificity of lanthanide and samples. Creating a light source in the soft x-ray spectrum is difficult because these wavelengths in the range 5-20 nm (20-350 eV photon energies) only penetrate several 100s of nm in most solid materials and only reflect well in shallow, grazing incident angles. The results are applicable to nuclear forensics, because molecular fingerprinting of lanthanide and actinide samples can be used to back out the origin and processing method of nuclear materials (Skrodzki, et al.).

36 MATERIALS SCIENCE↗

DOE OSTI2022

A lipidomics platform to analyze the fatty acid compositions of non-polar and polar lipid molecular species from plant tissues: Examples from developing seeds and seedlings of pennycress (Thlaspi arvense)

The lipidome comprises the total content of molecular species of each lipid class, and is measured using the analytical techniques of lipidomics. Many liquid chromatography-mass spectrometry (LC-MS) methods have previously been described to characterize the lipidome. However, many lipidomic approaches may not fully uncover the subtleties of lipid molecular species, such as the full fatty acid (FA) composition of certain lipid classes. Here, we describe a stepwise targeted lipidomics approach to characterize the polar and non-polar lipid classes using complementary LC-MS methods. Our “polar” method measures 260 molecular species across 12 polar lipid classes, and is performed using hydrophilic interaction chromatography (HILIC) on a NH2 column to separate lipid classes by their headgroup. Our “non-polar” method measures 254 molecular species across three non-polar lipid classes, separating molecular species on their FA characteristics by reverse phase (RP) chromatography on a C30 column. Five different extraction methods were compared, with an MTBE-based extraction chosen for the final lipidomics workflow. A state-of-the-art strategy to determine and relatively quantify the FA composition of triacylglycerols is also described. This lipidomics workflow was applied to developing, mature, and germinated pennycress seeds/seedlings and found unexpected changes among several lipid molecular species. During development, diacylglycerols predominantly contained long chain length FAs, which contrasted with the very long chain FAs of triacylglycerols in mature seeds. Potential metabolic explanations are discussed. The lack of very long chain fatty acids in diacylglycerols of germinating seeds may indicate very long chain FAs, such as erucic acid, are preferentially channeled into beta-oxidation for energy production.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1976

Calculations of molecular ionization energies using a self-consistent-charge Hartree-Fock-Slater method

A numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented. Molecular wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atomlike problems. Binding energies and wavefunctions for the molecules are generated using a discrete variational method for a given molecular potential. In the self-consistent-charge (SCC) approximation to the complete self-consistent-field (SCF) method, results of a Mulliken population analysis of the molecular eigenfunctions are used in each iteration to produce 'atomic' occupation numbers. The simplest SCC potential is then obtained from overlapping spherical atomlike charge distributions. Molecular ionization energies are calculated using the transition-state procedure; results are given for CO, H2O, H2S, AlCl, InCl, and the Ni5O surface complex. Agreement between experimental and theoretical ionization energies for the free-molecule valence levels is generally within 1 eV. The simple SCC procedure gives a reasonably good approximation to the molecular potential, as shown by comparison with experiment, and with complete SCF calculations for CO, H2O, and H2S.

Rosen, A.↗

NASA NTRS1977

Distribution of molecular weight in glyceride polymerizates or aggregates of them after contact with lunar grains

An attempt is made to report on experiments in which a molecular-weight increase was determined in thin layers of triglyceride-containing glycerides after thin-layer contact for two years with lunar topsoil grains at 25 C without any thermal activation. It is noted that solidification was observed on both dielectric grains and metal-rich areas and that changes in viscosity and molecular weights were first detected by solidification of surface layers. Gel permeation chromatography is described which detected a general shift of the Gaussian distribution of the molecular-weight data toward generally higher molecular weights as well as an increase in mean molecular weight. Reaction mechanisms are considered, and results of spectrographic analysis are cited which support the interpretations of the molecular-weight data.

Asunmaa, S. K.↗

NASA NTRS1982

Ultrahigh molecular weight aromatic siloxane polymers

The condensation of a diol with a silane in toluene yields a silphenylene-siloxane polymer. The reaction of stiochiometric amounts of the diol and silane produced products with molecular weights in the range 2.0 - 6.0 x 10 to the 5th power. The molecular weight of the product was greatly increased by a multistep technique. The methodology for synthesis of high molecular weight polymers using a two step procedure was refined. Polymers with weight average molecular weights in excess of 1.0 x 10 to the 6th power produced by this method. Two more reactive silanes, bis(pyrrolidinyl)dimethylsilane and bis(gamma butyrolactam)dimethylsilane, are compared with the dimethyleminodimethylsilane in ability to advance the molecular weight of the prepolymer. The polymers produced are characterized by intrinsic viscosity in tetrahydrofuran. Weight and number average molecular weights and polydispersity are determined by gel permeation chromatography.

Ludwick, L. M.↗

NASA NTRS1986

An optical imaging and polarimetric study of the Lynds 723 and Barnard 335 molecular outflow regions

Optical polarization measurements are reported for a sample of stars viewed through the periphery of two dense molecular clouds, Barnard 335 and Lynds 723. These observations suggest that the direction of the magnetic field threading these clouds lies along position angle 111 + or - 4 deg for B335 and 90 + or - 8 deg for L723. In each case, the deduced field direction is approximately parallel to the direction defined by a collimated bipolar molecular outflow driven by a highly obscured FIR source. R, I, and H-alpha CCD images of these regions reveal knots of optical emission apparently associated with the molecular outflows. In the case of L723, two emission features are found within the blueshifted wing of the molecular outflow; along with the FIR source, these knots define a position angle nearly identical to that of the molecular flow. For B335, the observed emission knot lies in the redshifted wing of the molecular outflow along a position angle approximately equal to that of the flow.

Vrba, F. J.↗

NASA NTRS1988

Submillimeter and far-infrared line observations of M17 SW - A clumpy molecular cloud penetrated by ultraviolet radiation

Millimeter, submillimeter, and far-IR spectroscopic observations of the M17 SW star formation region are reported. Strong forbidden C II 158 micron and CO J = 7 - 6 line emission arises in an H II region/molecular cloud interface of several pc thickness. Weaker forbidden C II emission appears to be extended over 15 pc throughout the molecular cloud. CO J = 14 - 13 and forbidden O I 145 micron spectra indicate high temperatures and densities for both molecular and atomic gas in the interface. The results require the molecular cloud near the interface to be clumpy or filamentary. The extended forbidden C II emission throughout the molecular cloud has a level around 20 times higher than expected from a single molecular cloud interface exposed to an ultraviolet radiation field typical of the solar neighborhood. The high gas temperature of molecular material in the UV-illuminated interface region suggests that CO self-shielding and heating of CO by photoelectrons are important.

Stutzki, J.↗

NASA NTRS1990

Unbound molecular complexes in M33

The HI content of the nearby spiral galaxy M33 (d approx. 0.8 Mpc) has been the subject of many detailed studies (most recently Deul and van der Hulst 1987), but similar data on the molecular gas component has been lacking. This galaxy is currently undergoing vigorous high-mass star formation, as evidenced by the many OB associations and HII regions, and so is expected to possess at least some molecular gas. Interferometric studies have detected molecular clouds similar to Galactic Giant Molecular Clouds (GMCs) (Boulanger et al. 1988; Wilson et al. 1988). Researchers have recently mapped the nuclear region of M33 in the CO J=1-0 line with a 12 m telescope (half power beam width 55 inches approx. 210 pc) out to a radius of 3.5 minutes in order to trace the detailed distribution of the molecular gas. The resulting map reveals six large complexes with diameters of 200 to 400 pc. Interferometer observations of these regions have resolved them into individual molecular clouds similar to Galactic GMCs (Wilson et al. 1988). The complexes shown are much larger than individual Galactic GMCs (Sanders, Scoville, and Solomon 1985), but are somewhat smaller on average than the large associations seen in the grand-design spiral galaxy M51 (Rand and Kulkarni 1989). If we extend the velocity-diameter relation observed for Galactic GMCs to these larger structures, the predicted velocity widths are a factor of 1.5 to 3 times greater than the observed full-width half-maximum velocities (13 to 29 km (s-1). The peak brightness temperatures are approx. 0.2 K, at least a factor of 10 lower than what is observed for Galactic GMCs. If these large structures are made up of objects similar to Galactic GMCs, the area filling factor of the small clouds is roughly 10 percent. These results suggest that these complexes are not very large GMCs, but rather are associations of many individual GMCs or GMCs embedded in a diffuse gas component.

Wilson, Christine D.↗

NASA NTRS1990

Spatial variation of the physical conditions of molecular gas in galaxies

Multi-line studies of CO-12, CO-13, C-18O, HCN, and HCO(+) at 3 mm, 1.3 mm, and 0.8 mm using the Institute for Radio Astronomy in the Millimeter range (IRAM) 30 m telescope, with the IRAM superconductor insulator superconductor (SIS) receivers and the Max Planck Institute for External Physics (MPE) 350 GHz SIS receiver, show that the densities and temperatures of molecular gas in external galaxies change significantly with position. CO-12 measures the densities and temperature of diffuse interclump molecular gas, but not the bulk of the molecular gas. Simple one-component models, with or without external heating, cannot account for the weakness of the CO-12 J = 3 to 2 line relative to J = 2 to 1 and J = 1 to 0. CO-12 does not trace the bulk of the molecular gas, and optical depth effects obviate a straightforward interpretation of CO-12 data. Instead, researchers turned to the optically thin CO isotopes and other molecular species. Isotopic CO lines measure the bulk of the molecular gas, and HCN and HCO(+) pick out denser regions. Researchers find a warm ridge of gas in IC 342 (Eckart et al. 1989), denser gas in the starburst nucleus of IC 342, and a possible hot-spot in NGC 2903. In IC 342, NGC 2146, and NGC 6764, the CO-13 J = 2 to 1 line is subthermally populated, implying gas densities less than or equal to 10(exp 4) cm(-3).

Jackson, James M.↗