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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Theoretical Study of the Phenoxy Radical Recombination with the O( 3 P) Atom, Phenyl plus Molecular Oxygen Revisited

Quantum chemical calculations of the C 6 H 5 O 2 potential energy surface (PES) were carried out to study the mechanism of the phenoxy + O( 3 P) and phenyl + O 2 reactions. CASPT2(15e,13o)/CBS//CASSCF(15e,13o)/DZP multi-reference calculations were utilized to map out the minimum energy path for the entrance channels of the phenoxy + O( 3 P) reaction. Stationary points on the C 6 H 5 O 2 PES were explored at the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311++G** level for the species with a single-reference character of the wave function and at the CASPT2(15e,13o)/CBS//B3LYP/6-311++G** level of theory for the species with a multi-reference character of the wave function. Conventional, variational, and variable reaction coordinate transition state theories were employed in Rice-Ramsperger-Kassel-Marcus Master Equation calculations to assess temperature- and pressure-dependent phenomenological rate constants and product branching ratios. Here, the main bimolecular product channels of the phenoxy + O( 3 P) reaction are concluded to be para/ortho-benzoquinone + H, 2,4-cyclopentadienone + HCO, and, at high temperatures, also phenyl + O 2 . The main bimolecular product channels of the phenyl + O 2 reaction include 2,4-cyclopentadienone + HCO at lower temperatures, and phenoxy + O( 3 P) at higher temperatures. Both for the phenoxy + O( 3 P) and phenyl + O 2 reactions, the collisional stabilization of peroxybenzene at low temperatures and high pressures competes with the bimolecular product channels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Rate Coefficients for OH + NO (+N 2 ) in the Fall-off Regime and the Impact of Water Vapor

The termolecular, association reaction between OH and NO is a source of nitrous acid (HONO), an important atmospheric trace gas. Rate coefficients for the title reaction as recommended by evaluation panels differ substantially at the temperatures and pressures that prevail in the Earth’s boundary layer where the reaction is in the fall-off regime between low- and high-pressure limiting rate coefficients. Using pulsed laser methods for generation and detection of OH, we have reinvestigated the kinetics of the title reaction at pressures of 22–743 Torr (1 Torr = 1.333 hPa) and temperatures (273, 298, and 333 K) in pure N 2 and in N 2 –H 2 O bath gases. In situ optical absorption measurements were used to rule out any bias due to NO 2 or HONO impurities. Our rate coefficients (k 1 ) in N 2 bath gas are parametrized in terms of low-pressure (k o ) and high-pressure (k ∞ ) rate coefficients and a fall-off parameter (F C ) with k 1,0 N 2 = 7.24 × 10 –31 (T/300 K) –2.17 cm 6 molecule –2 s –1 , k 1,∞ = 3.3 × 10 –12 (T/300 K) –3 cm 3 molecule –1 s –1 , and F C = 0.53. Used with the “Troe” expression for termolecular reactions, these parameters accurately reproduce the current data in the fall-off regime and also capture literature rate coefficients at extrapolated temperatures. The presence of water vapor was found to enhance the rate coefficients of the title reaction significantly. The low-pressure limiting rate coefficient in H 2 O bath gas is a factor 5–6 larger than in N 2 , at room temperature (k 1,o H 2 O = 4.55 × 10 –30 (T/300 K) –4.85 cm 6 molecule –2 s –1 ) indicating that H 2 O is much more efficient in quenching the association complex HONO* through collisional energy transfer. Based on measurements in N 2 –H 2 O mixtures, a parametrization of k 1 including both N 2 and H 2 O as third-body quenchers was derived. Neglecting the effect of H 2 O results, e.g., in an underestimation of k 1 by >10% in the tropical boundary layer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Association Kinetics for Perfluorinated n -Alkyl Radicals

Radical-radical reaction channels are important in the pyrolysis and oxidation chemistry of perfluoroalkyl substances (PFAS). In particular, unimolecular dissociation reactions within unbranched n-perfluoroalkyl chains, and their corresponding reverse barrierless association reactions, are expected to be significant contributors to the gas-phase thermal decomposition of families of species such as perfluorinated carboxylic acids and perfluorinated sulfonic acids. Unfortunately, experimental data for these reactions are scarce and uncertain. Furthermore, obtaining reliable theoretical predictions for such reactions is a laborious and computationally intensive task. Here, in this work, the chemical kinetics of the various association/decomposition reactions producing/decomposing the C 2 -C 4 series of unbranched n-perfluoroalkanes (C 2 F 6 , C 3 F 8 , and C 4 F 10 ) are examined using state-of-the-art ab initio transition-state-theory-based master-equation calculations. The variable-reaction-coordinate transition-state theory (VRC-TST) formalism is employed in computing the microcanonical and canonical rates for the association reactions. Reaction thermochemistry is obtained via composite quantum chemistry calculations and the laddering of error-canceling reaction schemes via a connectivity-based hierarchy approach employing ANL1/ANL0-style reference energies. Lennard-Jones collision model parameters for the considered systems were estimated by a direct dynamics approach, and collisional energy transfer parameters were obtained from analogies to systems of similar size and heavy-atom connectivity. A one-dimensional master equation approach was used to convert the microcanonical rate coefficients from the VRC-TST analysis into temperature- and pressure-dependent rate constants for the association reactions and the reverse dissociation reactions. The data are reported in standardized formats for usage in comprehensive chemical kinetic models for PFAS thermal destruction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Mechanism, Thermochemistry, and Kinetics for the CH + N 2 Reaction Leading to Prompt NO Formation in Combustion

Here, the reaction of CH + N 2 forming H + NCN is a remarkable example of activation of the nitrogen triple bond and is an important source of prompt NO in combustion. The reaction pathway is complex and proceeds through two competing mechanisms: a cyclic addition channel initiated by c-HC(NN) and a chain-addition channel initiated by HCNN, both of which eventually form HNCN prior to dissociation to H + NCN. This work reinvestigates this reaction with composite coupled cluster protocols, including a novel spin-flip equation of motion coupled cluster scheme, combined with pragmatic two-dimensional master equation simulations of the resulting rate coefficients. These improved calculations predict the CH + N 2 rate coefficient between the two more recent previous theoretical results and reduce the uncertainties of the best theoretical models of this reaction to less than a factor of 1.3. Additionally, we provide a closer theoretical investigation of the simultaneous dependence of the CH + N 2 rate coefficient on pressure and temperature, and affirm that collisionally stabilized HNCN, another potential source of prompt NO, emerges as an appreciable product of this reaction under conditions relevant to automotive internal combustion engines and aircraft gas turbine engines.

Nguyen, Thanh Lam [Univ. of Florida, Gainesville, ↗
DOE OSTI2024

Utilizing Quantum Cascade Lasers for Ultranarrow Velocity Resolution and Quantum-State Selectivity in Molecular Beam Scattering and Spectroscopy

Here, we demonstrate the capability of a narrow linewidth quantum cascade laser (QCL) to selectively excite a very narrow velocity range of nitric oxide (σ ≤ 7(3) m/s) with a pure ro-vibrational quantum state. By implementing a counter-propagating geometry, the molecules are selectively excited according to the Doppler shift of the ro-vibrational transition frequency such that the velocity width associated with the excited molecules depends only on the QCL linewidth. We demonstrate a velocity distribution limited by the effective linewidth of our free-running QCL (Γ = 3.2 MHz). Our development provides a cost-effective, flexible approach to resolve quantum-state selective chemical dynamics with excellent velocity resolution in a wide variety of molecules with infrared-active transitions. This technique has been formulated to provide ultrahigh collisional energy resolution in molecular beams to delineate final quantum-state product pairs in studies of molecular collisions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Structure of Gas Phase Monohydrated Nicotine: Implications for Nicotine’s Native Structure in the Acetylcholine Binding Protein

In this work, we report a joint experimental–theoretical study of the never reported before structure and infrared spectra of gas phase monohydrated nicotine (NIC) and nornicotine (NOR) and use them to assign their protonation sites. NIC’s biological activity is strongly affected by its protonation site, namely, the pyrrolidine (Pyrro-NICH + , anticipated active form) and pyridine (Pyri-NICH + ) forms; however, these have yet to be directly experimentally determined in either the nicotinic acetylcholine receptor (nAChR, no water present) or the acetylcholine-binding protein (AChBP, a single water molecule is present) but can only be inferred to be Pyrro-NICH + from the intermolecular distance to the neighboring residues (i.e., tryptophan). Our temperature-controlled double ion trap infrared spectroscopic experiments assisted by the collisional stripping method and high-level theoretical calculations yield the protonation ratio of Pyri:Pyrro = 8:2 at 240 K for the gas phase NICH + ···(H 2 O) complex, which resembles the molecular cluster present in the AChBP. Therefore, a single water molecule in the gas phase enhances this ratio in NICH + relative to the 3:2 for the nonhydrated gas phase NICH + in a trend that contrasts with the almost exclusive presence of Pyrro-NICH + in aqueous solution. In contrast, the Pyri-NORH + protomer is exclusively observed, a fact that may correlate with its weaker biological activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Long-Range Interaction between Molecules with Electronic Degeneracy: Beyond the Born–Oppenheimer Approximation

Long-range intermolecular interaction plays an essential role in (ultra)cold collisions. For monomers with degenerate electronic states, an accurate description of the long-range interaction can be challenging due to the potential breakdown of the Born–Oppenheimer approximation. In this work, we developed a general method to construct long-range interaction potential energy surfaces (IPESs) between arbitrary molecules using the degenerate perturbation theory of Schrödinger. To further simplify the application of this method, a group-theoretical method is introduced to identify nonzero components of electrostatic properties of monomers, especially for the nonlinear molecules. To demonstrate this approach, we report the long-range IPESs of the O( 3 P)–OH( 2 Π) and OH( 2 Π)–OH( 2 Π) systems. The excellent agreement with ab initio calculations in large separations, even near electronic degeneracies, confirms the accuracy of our approach. The method is expected to lay the groundwork for the accurate investigation of (ultra)cold collisional dynamics involving open-shell species.

ab initio calculations↗
DOE OSTI2020

Effects of Global and Regional Dust Storms on the Martian Hot O Corona and Photochemical Loss

Here, we examine for the first time the effects of both global and regional dust storms on the formation of the Martian hot O corona and associated photochemical loss of O. Our study is conducted by utilizing our integrated model framework, which couples our Martian hot O corona model with a multifluid magnetohydrodynamic model for Mars for the dusty and clear atmospheric condition cases. We present our results with the most up-to-date cross sections for the O( 3 P )-CO 2 collisions. The main effect of dust storms on the ionosphere is the upward shift of the ionosphere on the dayside, which results in an increase in production of hot O at all altitudes above the ionospheric peak. However, the dust-induced inflation of the neutral upper atmosphere results in an enhancement in collisional loss of hot O and thus effectively suppresses the hot O density, reducing the global photochemical loss rate by ~28% for the global dust storm scenario. The relative density structure of the hot O corona does not show any significant changes, while its magnitude decreases at all altitudes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Hydraulic Modeling of Induced and Propagated Fractures: Analysis of Flow and Pressure Data From Hydromechanical Experiments in the COSC-1 Deep Borehole in Crystalline Rock Near Åre, Sweden

To characterize the coupled hydromechanical behavior of rock fractures, the step-rate injection method for fracture in-situ properties (SIMFIP) was conducted with a specialized downhole probe developed by Guglielmi et.al. In June 2019, a field campaign was carried out near Åre, Sweden, where the SIMFIP probe was applied in the Collisional Orogeny in the Scandinavian Caledonides-1 scientific borehole to understand the dynamics of injection-induced fracture initiation, fracture opening, and shearing due to water injection-withdrawal in a borehole interval isolated by two packers. Three intervals were investigated at ~500 m depth: (a) an unfractured section (intact rock), (b) a section with non-conductive fractures, and (c) a section with hydraulically conductive fractures. Pressure, injection flow rate, and borehole wall displacement were simultaneously measured during the tests. In the present study, the geometry of the induced fracture and deformation of existing fractures at different time stages of the tests are determined based on a hydrologic model by using the measured pressure and flow data during each time stage of the experiment. A numerical model for the fluid flow within the fracture and the packed-off borehole interval is implemented within COMSOL Multiphysics. By matching model simulations with observed data for all three sections, estimates of the induced and propagated fractures' radius and aperture at successive time stages have been obtained in each case. We could also determine the non-linear relationship between fracture aperture and pressure for values above fracture opening pressures. The model results provide insights for the understanding of pressure-induced fracture initiation and propagation in crystalline rock.

58 GEOSCIENCES↗
DOE OSTI2021

Interplay Between Crustal‐Scale Thrusting, High Metamorphic Heating Rates, and the Development of Inverted Thermal‐Metamorphic Gradients: Numerical Models and Examples From the Caledonides of Northern Scotland

Abstract Understanding the processes that produce high prograde metamorphic heating rates and the development of inverted metamorphic sequences in collisional thrust belts remains a fundamental challenge for tectonics and metamorphic petrology. New 2D finite element models of crustal‐scale thrusts with variable slip rates (10, 20, 35, 50 km Myr −1 ) are used to examine how thrust sheet emplacement contributes to these processes. In the models, average prograde heating rates of 31–118 °C Myr −1 are observed in the footwall, with maximum transient heating rates of ∼167 °C Myr −1 occurring at the highest slip rate. Also, thrust sheet emplacement produces an inverted thermal gradient in the model footwall. At slip rates of 10 km Myr −1 , heating magnitudes >200 °C are observed >7 km structurally beneath the thrust plane. At slip rates of 20–50 km Myr −1 , models produce thermal penetration depths of 4–5 km for similar heating magnitudes. Petrologically determined heating rates for thrust footwalls in the Scandian orogenic wedge of northern Scotland mostly yield rates consistent with model results (10–230 °C Myr −1 ). The model‐derived magnitude of inverted thermal gradients is also similar to those indicated in texturally determined deformation temperature transects across the Scandian orogenic wedge (100 °C–180 °C). Combined, these results indicate that high heating rates can be produced by fault slip at typical plate velocities. Additionally, this implies that crustal‐scale thrusts are likely to produce inverted metamorphic sequences in most systems, provided that P‐T conditions during slip allow for metamorphic or recrystallization processes that would preserve evidence for such features.

Thigpen, J. Ryan↗
DOE OSTI2023

Important ice processes are missed by the Community Earth System Model (CESM) in Southern Ocean mixed–phase clouds: Bridging SOCRATES observations to model developments

Global climate models (GCMs) are challenged by difficulties in simulating cloud phase and cloud radiative effect over the Southern Ocean (SO). Some of the new generation GCMs predict too much liquid and too little ice in mixed-phase clouds. This misrepresentation of cloud phase in GCMs results in weaker negative cloud feedback over the SO and a higher climate sensitivity. Based on a model comparison with observational data obtained during the Southern Ocean Cloud Radiation and Aerosol Transport Experimental Study (SOCRATES), this study addresses a key uncertainty in the Community Earth System Model version 2 (CESM2) related to cloud phase, namely ice formation in pristine remote SO clouds. It is found that sea spray organic aerosols (SSOA) are the most important type of ice nucleating particles (INPs) over the SO with concentrations one order of magnitude higher than those of dust INPs based on measurements and CESM2 simulations. Secondary ice production (SIP) which includes riming splintering, rain droplet shattering, and ice-ice collisional fragmentation as implemented in CESM2 is the dominant ice production process in moderately cold clouds with cloud temperatures greater than –20°C. SIP enhances the in-cloud ice number concentrations (Ni) by 1-3 orders of magnitude and predicts more mixed-phase (with percentage occurrence increased from 15% to 21%), in better agreement with the observations. Finally, this study highlights the importance of accurately representing cloud phase over the pristine remote SO by considering the ice nucleation of SSOA and SIP processes, which are currently missing in most GCM cloud microphysics parameterizations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

An Efficient Bayesian Approach to Learning Droplet Collision Kernels: Proof of Concept Using “Cloudy,” a New n -Moment Bulk Microphysics Scheme

The small-scale microphysical processes governing the formation of precipitation particles cannot be resolved explicitly by cloud resolving and climate models. Instead, they are represented by microphysics schemes that are based on a combination of theoretical knowledge, statistical assumptions, and fitting to data (“tuning”). Historically, tuning was done in an ad hoc fashion, leading to parameter choices that are not explainable or repeatable. Recent work has treated it as an inverse problem that can be solved by Bayesian inference. The posterior distribution of the parameters given the data—the solution of Bayesian inference—is found through computationally expensive sampling methods, which require over $\mathcal{O}$(10 5 ) evaluations of the forward model; this is prohibitive for many models. We present a proof of concept of Bayesian learning applied to a new bulk microphysics scheme named “Cloudy,” using the recently developed Calibrate-Emulate-Sample (CES) algorithm. Cloudy models collision-coalescence and collisional breakup of cloud droplets with an adjustable number of prognostic moments and with easily modifiable assumptions for the cloud droplet mass distribution and the collision kernel. The CES algorithm uses machine learning tools to accelerate Bayesian inference by reducing the number of forward evaluations needed to $\mathcal{O}$(10 2 ). It also exhibits a smoothing effect when forward evaluations are polluted by noise. In a suite of perfect-model experiments, we show that CES enables computationally efficient Bayesian inference of parameters in Cloudy from noisy observations of moments of the droplet mass distribution. In an additional imperfect-model experiment, a collision kernel parameter is successfully learned from output generated by a Lagrangian particle-based microphysics model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Evaluating the Collision‐Coalescence Process in Idealized Cloud Convection Using Large‐Eddy Simulations With Lagrangian Microphysics

Drizzle initiation through the collision and coalescence of cloud droplets plays a crucial role in warm cloud precipitation. Recent theoretical studies suggest that the influence of collisional growth on the droplet size distribution can be quantified by a non-dimensional drizzle number (Dz). Here, large-eddy simulations with Lagrangian microphysics are employed to evaluate the theory by simulating a tall convection-cloud chamber under various conditions. Results show that the smaller the Dz, the larger the impact of collisions on the right tail of the droplet size distribution, consistent with the theory. The simulations confirm that the collision rate can be estimated from the droplet size distribution interacting only with cloud droplets of the same size at the mode radius. This suggests that the idealized theory can be a useful tool to design a cloud chamber for drizzle investigation, as well as to represent drizzle formation in models of real atmospheric clouds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Probing atomic physics at ultrahigh pressure using laser-driven implosions

Abstract Spectroscopic measurements of dense plasmas at billions of atmospheres provide tests to our fundamental understanding of how matter behaves at extreme conditions. Developing reliable atomic physics models at these conditions, benchmarked by experimental data, is crucial to an improved understanding of radiation transport in both stars and inertial fusion targets. However, detailed spectroscopic measurements at these conditions are rare, and traditional collisional-radiative equilibrium models, based on isolated-atom calculations and ad hoc continuum lowering models, have proved questionable at and beyond solid density. Here we report time-integrated and time-resolved x-ray spectroscopy measurements at several billion atmospheres using laser-driven implosions of Cu-doped targets. We use the imploding shell and its hot core at stagnation to probe the spectral changes of Cu-doped witness layer. These measurements indicate the necessity and viability of modeling dense plasmas with self-consistent methods like density-functional theory, which impact the accuracy of radiation transport simulations used to describe stellar evolution and the design of inertial fusion targets.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Automating data analysis for hydrogen/deuterium exchange mass spectrometry using data-independent acquisition methodology

We present a hydrogen/deuterium exchange workflow coupled to tandem mass spectrometry (HX-MS 2 ) that supports the acquisition of peptide fragment ions alongside their peptide precursors. The approach enables true auto-curation of HX data by mining a rich set of deuterated fragments, generated by collisional-induced dissociation (CID), to simultaneously confirm the peptide ID and authenticate MS 1 -based deuteration calculations. The high redundancy provided by the fragments supports a confidence assessment of deuterium calculations using a combinatorial strategy. The approach requires data-independent acquisition (DIA) methods that are available on most MS platforms, making the switch to HX-MS 2 straightforward. Importantly, we find that HX-DIA enables a proteomics-grade approach and wide-spread applications. Considerable time is saved through auto-curation and complex samples can now be characterized and at higher throughput. We illustrate these advantages in a drug binding analysis of the ultra-large protein kinase DNA-PKcs, isolated directly from mammalian cells.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Femtosecond electronic structure response to high intensity XFEL pulses probed by iron X-ray emission spectroscopy

We report the time-resolved femtosecond evolution of the K-shell X-ray emission spectra of iron during high intensity illumination of X-rays in a micron-sized focused hard X-ray free electron laser (XFEL) beam. Detailed pulse length dependent measurements revealed that rapid spectral energy shift and broadening started within the first 10 fs of the X-ray illumination at intensity levels between 10 17 and 10 18 W cm -2 . We attribute these spectral changes to the rapid evolution of high-density photoelectron mediated secondary collisional ionization processes upon the absorption of the incident XFEL radiation. These fast electronic processes, occurring at timescales well within the typical XFEL pulse durations (i.e., tens of fs), set the boundary conditions of the pulse intensity and sample parameters where the widely-accepted ‘probe-before-destroy’ measurement strategy can be adopted for electronic-structure related XFEL experiments.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Effect of Auger recombination on transient optical properties in XUV and soft X-ray irradiated silicon nitride

Spatially encoded measurements of transient optical transmissivity became a standard tool for temporal diagnostics of free-electron-laser (FEL) pulses, as well as for the arrival time measurements in X-ray pump and optical probe experiments. The modern experimental techniques can measure changes in optical coefficients with a temporal resolution better than 10 fs. This, in an ideal case, would imply a similar resolution for the temporal pulse properties and the arrival time jitter between the FEL and optical laser pulses. However, carrier transport within the material and out of its surface, as well as carrier recombination may, in addition, significantly decrease the number of carriers. This would strongly affect the transient optical properties, making the diagnostic measurement inaccurate. Below we analyze in detail the effects of those processes on the optical properties of XUV and soft X-ray irradiated Si 3 N 4 , on sub-picosecond timescales. Si 3 N 4 is a wide-gap insulating material widely used for FEL pulse diagnostics. Theoretical predictions are compared with the published results of two experiments at FERMI and LCLS facilities, and with our own recent measurement. The comparison indicates that three body Auger recombination strongly affects the optical response of Si 3 N 4 after its collisional ionization stops. By deconvolving the contribution of Auger recombination, in future applications one could regain a high temporal resolution for the reconstruction of the FEL pulse properties measured with a Si 3 N 4 -based diagnostics tool.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Ultraviolet spectroscopy of pressurized and supercritical carbon dioxide

Abstract Carbon dioxide (CO 2 ) is prevalent in planetary atmospheres and sees use in a variety of industrial applications. Despite its ubiquitous nature, its photochemistry remains poorly understood. In this work we explore the density dependence of pressurized and supercritical CO 2 electronic absorption spectra by vacuum ultraviolet spectroscopy over the wavelength range 1455-2000 Å. We show that the lowest absorption band transition energy is unaffected by a density increase up to and beyond the thermodynamic critical point (137 bar, 308 K). However, the diffuse vibrational structure inherent to the spectrum gradually decreases in magnitude. This effect cannot be explained solely by collisional broadening and/or dimerization. We suggest that at high densities close proximity of neighboring CO 2 molecules with a variety of orientations perturbs the multiple monomer electronic state potential energy surfaces, facilitating coupling between binding and dissociative states. We estimate a critical radius of ~4.1 Å necessary to cause such perturbations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗