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At least 145 records · Page 8

HȮ 2 + HȮ 2 : High level theory and the role of singlet channels

At low temperatures and high pressures, the HȮ 2 + HȮ 2 reaction is an important reaction in combustion. There are significant unresolved discrepancies between prior theoretical and experimental studies of this reaction. It has generally been presumed to occur as an abstraction on the triplet surface to produce H 2 O 2 + 3 O 2 . Here, we employ a combination of high-level electronic structure theory (the ANL0 composite method or multi-reference methods as appropriate), sophisticated transition state theory (vibrationally adiabatic torsions, variational, and variable reaction coordinate), and master equation analyses to predict the thermal kinetics on the H 2 O 4 surface. Notably, this analysis suggests a significant branching to HȮ 3 + ȮH near 1000 K via reaction on the singlet surface. This channel does not appear to have been considered in prior combustion models. HȮ 3 itself is a metastable complex (bound by only 3 kcal mol -1 ) that rapidly dissociates to ȮH + 3 O 2 . Thus, the net reaction for this channel, HȮ 2 + HȮ 2 → ȮH + ȮH + O 2 , converts two low reactivity HȮ 2 radicals into two highly reactive ȮH radicals. The ramifications of these newly derived rate expressions are highlighted through kinetic modeling studies of H 2 , CH 3 OH, $\textit{n}$-heptane, and isooctane oxidation; all at the high pressures of relevance to combustion devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of a micro-scale dislocation pileup on the atomic-scale multi-variant phase transformation and twinning

In this paper, we perform concurrent atomistic–continuum (CAC) simulations to assess the contribution of the internal stress induced by the microscale dislocation pileup at an atomically structured interface to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) the pileup-induced internal stress concentration profile follows neither the classical Eshelby model nor the super-dislocation model alone, but a combination of them; (c) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape. The two variants of the hexagonal phases form a twin with respect to each other; (d) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (e) the microscale dislocation pileup-induced internal shear stress and the structural change at the atomic-scale interface reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. In conclusion, the gained knowledge will advance our understanding of how the multi-phase material behaves in many complex physical processes, such as the synthesis of multi-phase high-entropy alloys or superhard ceramics under high-pressure torsion, deep mantle earthquakes in geophysics, and so on, which all involve dislocation slip, PTs, twinning, and their interactions across from the atomistic to the microscale and beyond.

36 MATERIALS SCIENCE↗

Effect of curvature on extensional stiffness matrix of 2-D braided composite tubes

In the micromechanical analysis of braided composite tubes, the effects of curvature are often ignored. This approach is acceptable for thin-walled tubes with a large radius. However, in case of small diameter thick-walled tubes, such an approach may lead to inaccurate results. Therefore, it is of interest to determine when the curvature effects of tubular geometry become important in micromechanics. In this study, the extensional stiffness matrix of 2-D braided composite tubes was calculated using a curved unit-cell. The periodicity was imposed in circumferential and longitudinal directions of the tube. The extensional stiffness coefficients were calculated by simulating an internal pressure test, uniaxial tensile test, and torsion test. The obtained stiffness coefficients were compared to those obtained using a flat unit-cell. The results of curved unit-cell were different from that of flat unit-cell. The differences in stiffness coefficients, calculated using curved and flat unit cells were as high as 13%.

42 ENGINEERING↗

Pilgrim : A thermal rate constant calculator and a chemical kinetics simulator

Pilgrim is a program written in Python and designed to use direct dynamics in the calculation of thermal rate constants of chemical reactions by the variational transition state theory (VTST), based on electronic structure calculations for the potential energy surface. Pilgrim can also simulate reaction mechanisms using kinetic Monte Carlo (KMC). For reaction processes with many elementary steps, the rate constant of each of these steps can be calculated by means of conventional transition state theory (TST) or by using VTST. In the current version, Pilgrim can evaluate thermal rates using the canonical version of reaction-path VTST, which requires the calculation of the minimum energy path (MEP) associated with each elementary step or transition structure. Multi-dimensional quantum effects can be incorporated through the small-curvature tunneling (SCT) approximation. These methodologies are available both for reactions involving a single structure of the reactants and the transition state and also for reactions involving flexible molecules with multiple conformations of the reactant and/or of the transition state. For systems with many conformers, the program can evaluate each of the elementary reaction rate constants by multipath canonical VTST or multi-structural VTST. Moreover, the reactant can be unimolecular or bimolecular. Torsional anharmonicity can be incorporated through either the MSTor or the Q2DTor programs. Dual-level calculations are also available in Pilgrim: automatic high-level single-point energies can be used to correct the energy of reactants, transition states, products, and MEP points using the interpolated single-point energies (ISPE) algorithm. When the rate constants of all the chemical processes of interest are known, by means of their calculation using Pilgrim or alternatively through analytical fits to the rate constants as functions of temperature, it is possible to simulate a multistep mechanism under specified laboratory conditions using KMC. Finally, this algorithm allows performing a kinetic simulation to monitor the evolution of each chemical species with time and obtain the product yields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fused perylene diimide-based polymeric acceptors with different $\mathcal{π}$-conjugation and molecular conformation in all polymer solar cells

Two perylene diimide (PDI) based polymeric acceptors, PFPDIBT-TT2F and PFPDIT-TT2F, which consist of fused-PDI moieties (FPDIBT and FPDIT) and 3,3'-difluoro-2,2'-bithiophene (TT2F) units, has been designed and synthesized. Compared with the unfused-PDI polymer (PPDI-TT2F) as the control molecule, the influence of structural conformation and π-conjugation extension on the performance of all-polymer solar cells has been investigated. Due to both the extended π-conjugation and the torsional polymer skeleton, the device adopting PFPDIT-TT2F achieved an obviously improved PCE of 5.11% comparing with the devices using the other two polymeric acceptors. This study demonstrates that the fused PDIs bridged by a thiophene enables both extended π-conjugation and twisted molecular conformation, and the latter plays a dominant role in the improvement of device performance.

42 ENGINEERING↗

Effect of melt shearing on D -mannitol crystal twisting in the presence of small molecule and macromolecular additives

Here, many molecular crystals grow as twisted lamellae from the melt when the driving force is high, but the mechanisms governing the spontaneous formation of helicoidal crystallites are varied and those operative in particular cases are difficult to identify. Polyvinylpyrrolidone (PVP) induces the crystallization of D-mannitol as banded spherulites comprised of twisted fibrils emanating radially from spherulite nucleation centers. The molecular weight of the PVP phase affects the twisting pitch, P, (rotation of the crystallite by 180°), in D-mannitol thin films crystallized from the melt. At a relatively high crystallization temperature (T c =130°C), P was sensitive to the PVP molecular weight, ranging from 390±20 μm for D-mannitol films incorporating 15 wt% 10 kDa PVP to 20±3 μm for the same weight of 1300 kDa PVP. Magnitudes of complex viscosities, |η*|, of D-mannitol/PVP melts measured via small-amplitude oscillatory shearing were strongly dependent on the PVP molecular weight, but were not correlated to P(T). Instead, P was sensitive to the dynamic PVP chain conformation during D-mannitol crystallization. Under steady torsional shear, P decreased from~30 μm to~8μm with increasing shear rates from 0.01 to 100 s -1 for D-mannitol films crystallized at 130°C in the presence of 15 wt% 10 or 1300 kDa PVP. Shear forces decrease the entanglement density of polymer chains while orienting the chains along the stream lines of the viscometric flow, indicating that the conformations of macromolecular additives can affect the pitch of banded spherulites. By contrast, P in D-mannitol twisted by D-sorbitol was independent of shear rate.

36 MATERIALS SCIENCE↗

Polyconvex neural network models of thermoelasticity

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. Here, in this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

N-heterocyclic carbene platinum-butadiyne Click/iClick complexes. Towards blue-violet phosphorescence

By employing two different methods, namely, Click and iClick, a series of four trans-NHC-Pt(II) triazole-acetylide complexes containing benzyl (3a), methylnaphthalene (3b), methylanthracene (3c), and phenyl (3d) substituents at the terminal triazole ring were synthesized and characterized. The traditional click approach involves first synthesizing a triazole-acetylene and then attaching to the Pt ion. In the iClick approach, the triazole is formed via cycloaddition by combining a trans-platinum butadiyne with the corresponding organic azide. The complexes were interrogated to determine the effects of conjugation and ligand substituent on their photophysical properties. Complex 3a exhibits a photoluminescence lifetime of 4.3 μs at 77 K. Ascribed to emission from conformers differing due to the torsion of the aryl acetylide ligands, employing different excitation wavelengths results in different emission spectra. Complex 3a emits in the violet region with CIE coordinates of (0.159, 0.021) under 290 nm excitation and shifts to CIE coordinates of (0.161, 0.019) under 320 nm excitation. Finally, complex 3d, having a photoluminescence lifetime of 13.1 μs at room temperature, emits in the sky-blue region with CIE coordinates of (0.237, 0.355).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Aeroelastic oscillations of a pitching flexible wing with structural geometric nonlinearities: Theory and numerical simulation

In this paper, we focus on the derivation of an analytical model of the aeroelastic dynamics of an elastically mounted flexible wing. This equations of motion obtained serve to help understand the behaviour of the aeroelastic wind tunnel setup in question, which consists of a rectangular wing with a uniform NACA 0012 airfoil profile, whose base is free to rotate rigidly about a longitudinal axis. Of particular interest are the structural geometric nonlinearities primarily introduced by the coupling between the rigid body pitch degree-of-freedom and the continuous system. A coupled system of partial differential equations (PDEs) coupled with an ordinary differential equation (ODE) describing axial-bending-bending-torsion-pitch motion is derived using Hamilton's principle. A finite dimensional approximation of the system of coupled differential equations is obtained using the Galerkin method, leading to a system of coupled nonlinear ODEs. Subsequently, these nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Adopting a linear unsteady aerodynamic model, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. Finally, the behaviour of the limit cycle oscillations is primarily influenced by the structural geometric nonlinear terms in the coupled system of PDEs and ODE.

42 ENGINEERING↗

Uncertainty evaluation for twist drilling stability model

This paper describes the first uncertainty analysis for drilling stability using a frequency-domain drilling stability model. The stability model inputs include: the modal parameters for the torsional-axial vibration mode from the twist drill-holder-spindle axial frequency response function; and the mechanistic coefficients that relate the torque and thrust force to chip area for the selected drill-workpiece material combination. Furthermore, Monte Carlo simulation is applied to propagate the input uncertainties to output uncertainty in the predicted stability map, which separates stable from unstable (chatter) zones in the spindle speed-chip width parameter space. Additionally, the mean stability boundary and its 95% confidence intervals are determined for five cases: varying all four inputs simultaneously and varying them individually. This enables the individual sensitivities to be compared. Experimental results from drilling tests are included for comparison to the prediction. Additionally, Matlab code is provided to implement the stability model and Monte Carlo uncertainty analysis.

42 ENGINEERING↗

Systematic exploration of the thermochemistry for a set of peroxy hydroperoxy-alkyl radicals

Here, the thermochemistry of peroxy hydroperoxy-alkyl ($\overline{O}$OQOOH) radicals has a significant influence on the reactivity of fuels and on the formation of highly oxygenated molecules (HOMs) in the atmosphere. Theoretical characterization of these radicals can be arduous due to their molecular size and complex fundamental interactions, such as hydrogen-bonding and torsional anharmonicity, and difficult to validate in the absence of any direct experimental thermochemical data. In this work, we systematically explore the thermochemistry of a set of $\overline{O}$OQOOH radicals with five increasingly affordable approaches with considerations for these interactions. In doing so, we present a novel conformer selection approach suited to predict properties at combustion temperatures. As a corollary, we also highlight the shortcomings in the standard choice of the ground conformer as the reference. The set of molecules is comprised of 149 C 2 -C 8 $\overline{O}$OQOOH radicals, selected to encompass a wide variety of branching and substitution patterns. Comparisons amongst the approaches help quantify the errors arising from various simplifying assumptions. For the largest of these radicals, and with the most affordable approach, final predictions of Gibbs energies are assigned a 2 σ uncertainty of 4 kcal mol -1 in the negative temperature coefficient region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of the integral length scales of turbulent inflows on wind turbine loads

As wind turbines become larger, the fluctuations in the inflow become increasingly influential in the turbine structural loading. These fluctuations are characterized by the integral length scale, which represents the average size of the largest energy-containing turbulent eddies. Current design standards neglect the varying integral length scales that characterize inflows of wind turbines in operation. Using large-eddy simulations, we generate turbulent inflows of varying integral length scales and quantify the loads of the IEA 15-MW reference wind turbine. Results illustrate that the impact of turbulence on rotor and tower loads is up to 10 times greater than the impact of the mean shear profile. Increasing integral length scales from 0.3x to 0.5x the rotor diameter reduces blade root flapwise moments and rotor and tower loads. Increasing integral length scales from 0.5x to 1.7x the rotor diameter increases the rotor aerodynamic thrust force and the blade root flapwise shear loads and decreases the tower base torsional moment and the tilting and yawing rotor aerodynamic moments. Additionally, turbulence intensity has a greater impact on wind turbine loads than integral length scales. In conclusion, findings indicate that design standards should consider varying integral length scales for accurate wind turbine loading characterization in turbulent inflow conditions.

17 WIND ENERGY↗

Fracture toughness evaluation for Zr-4 clad tubing structure with pellet inserts

Applying fracture mechanics approach to spent nuclear fuel (SNF) system reliability investigation is warranted due to the inherent flaws and hydride structures existed in a SNF system after nuclear reactor operation. However, none of the existing fracture toughness data deal with fuel cladding specific geometry or spent fuel material conditions, such as cladding structure with the pellet-inserts and the associated pellet clad mechanical interactions induced mixed-mode damage mechanisms. Thus, the development of an intrinsic fracture mechanics approach that is suitable for SNF materials is needed. Due to thin wall and small dimension of clad tubing structure, the spiral notch torsion test (SNTT) method of small specimen approach was used to estimate the clad tubing structure fracture toughness. The estimated fracture toughness for Zr-4 cladding with alumina-pellet inserts are presented in this report. For SNTT samples with a short or medium crack length, between 5.4-mm and 8-mm, the estimate JIQ upon fracture initiation for the baseline Zr-4 cladding is at 50 kJ/m2 with 2-sigma uncertainty of 3.26 kJ/m2, and the associated KIQ is at 67.46 MPa√m. For SNTT samples with a long crack length, around 13-mm, the crack initialization is deviated from that of the Mode-I tensile fracture and appears to be a mixed-mode fracture of Mode I – tensile stress and Mode III – out of plane shear stress; the estimated JMQ is at 18.9 kJ/m2, the associated KMQ is at 41.4 MPa√m.

36 MATERIALS SCIENCE↗

Rotating Alfvén waves in rotating plasmas

Angular momentum coupling between a rotating magnetized plasma and torsional Alfvén waves carrying orbital angular momentum (OAM) is examined. It is demonstrated not only that rotation is the source of Fresnel–Faraday rotation – or orbital Faraday rotation effects – for OAM-carrying Alfvén waves, but also that angular momentum from an OAM-carrying Alfvén wave can be transferred to a rotating plasma through the inverse process. For the direct process, the transverse structure angular rotation frequency is derived by considering the dispersion relation for modes with opposite OAM content. For the inverse process, the torque exerted on the plasma is derived as a function of wave and plasma parameters.

Physics↗

Controlling Symmetry Breaking Charge Transfer in BODIPY Pairs

Symmetry breaking charge transfer (SBCT) is a process in which a pair of identical chromophores absorb a photon and use its energy to transfer an electron from one chromophore to the other, breaking the symmetry of the chromophore pair. This excited state phenomenon is observed in photosynthetic organisms where it enables efficient formation of separated charges that ultimately catalyze biosynthesis. SBCT has also been proposed as a means for developing photovoltaics and photocatalytic systems that operate with minimal energy loss. It is known that SBCT in both biological and artificial systems is in part made possible by the local environment in which it occurs, which can move to stabilize the asymmetric SBCT state. However, how environmental degrees of freedom act in concert with steric and structural constraints placed on a chromophore pair to dictate its ability to generate long-lived charge pairs via SBCT remain open topics of investigation. In this work we compare a broad series of dipyrrin dimers that are linked by distinct bridging groups to discern how the spatial separation and mutual orientation of linked chromophores and the structural flexibility of their linker each impact SBCT efficiency. Across this material set, we observe a general trend that SBCT is accelerated as the spatial separation between dimer chromophores decreases, consistent with the expectation that the electronic coupling between these units varies exponentially with their separation. However, one key observation is that the rate of charge recombination following SBCT was found to slow with decreasing interchromophore separation, rather than speed up. This stems from an enhancement of the dimers’ structural rigidity due to increasing steric repulsion as the length of their linker shrinks. This rigidity further inhibits charge recombination in systems where symmetry has already enforced zero HOMO-LUMO overlap. Additionally, for the forward transfer the active torsion is shown to increase LUMO-LUMO coupling, allowing for faster SBCT within bridging groups. Further, by understanding trends for how rates of SBCT and charge recombination depend on a dimer’s internal structure and their environment, we identify design guidelines for creating artificial systems for driving sustained light-induced charge separation. Such systems can find application in solar energy technologies and photocatalytic applications but can serve as a model for light-induced charge separation in biological systems.

14 SOLAR ENERGY↗

Coordination Chemistry and Photoluminescence of Sm(II) Dibenzo-24-crown-8 Complexes

Three Sm(II) dibenzo-24-crown-8 (db24c8) complexes were synthesized in anhydrous, air-free conditions via the reaction of SmI 2 with db24c8 and tetrabutylammonium tetraphenylborate ([TBA][BPh 4 ]; where needed) in acetonitrile (CH 3 CN), dimethoxyethane (DME), and tetrahydrofuran (THF) to yield [Sm(db24c8)(CH 3 CN) 2 ][BPh 4 ][I]·CH 3 CN, [Sm(db24c8)(DME)]I 2 , and [Sm(db24c8)(THF) 2 ]I 2 , respectively. In each case, a 10-coordinate, staggered dodecahedral (2:6:2) environment is formed around the Sm 2+ center that is completed by either two solvent molecules (CH 3 CN or THF) or one bidentate solvent molecule (DME). Inner-sphere solvent molecules can be excluded by reacting SmI 2 with db24c8 in 1:3 THF:toluene to yield Sm(db24c8)I 2 . Here, this molecule features a distorted, eight-coordinate, hexagonal pyramidal Sm 2+ metal center, where the coordinated db24c8 molecule shows a torsion angle unexpectedly close to the 180° antiperiplanar arrangement and two uncoordinated db24c8 oxygen atoms. Solution UV–vis–NIR measurements demonstrate that Sm 2+ is a good size match for the cavity of various db24c8 conformations and that Eu 2+ and Yb 2+ exhibit competition between acetonitrile solvation and the Eu 2+ and Yb 2+ /db24c8 complexes in solution. During excitation by 546 nm light, both [Sm(db24c8)(DME)]I 2 and [Sm(db24c8)(THF) 2 ]I 2 exhibit mixed 5d → 4f and 4f → 4f emission at 20 °C and exclusively 4f → 4f at −180 °C, whereas Sm(db24c8)I 2 only shows 5d → 4f emission regardless of temperature. Photoluminescence from [Sm(db24c8)(CH 3 CN) 2 ][BPh 4 ][I]·CH 3 CN is quenched.

Cations↗

CoarsenConf: Equivariant Coarsening with Aggregated Attention for Molecular Conformer Generation

Molecular conformer generation (MCG) is an important task in cheminformatics and drug discovery. The ability to efficiently generate low-energy 3D structures can avoid expensive quantum mechanical simulations, leading to accelerated virtual screenings and enhanced structural exploration. Several generative models have been developed for MCG, but many struggle to consistently produce high-quality conformers for meaningful downstream applications. To address these issues, we introduce CoarsenConf, which coarse-grains molecular graphs based on torsional angles and integrates them into an SE(3)-equivariant hierarchical variational autoencoder. Through equivariant coarse-graining, we aggregate the fine-grained atomic coordinates of subgraphs connected via rotatable bonds, creating a variable-length coarse-grained latent representation. Our model uses a novel aggregated attention mechanism to restore fine-grained coordinates from the coarse-grained latent representation, enabling efficient generation of accurate conformers. Furthermore, we evaluate the chemical and biochemical quality of our generated conformers on multiple downstream applications, including property prediction and large-scale oracle-based protein docking. Overall, CoarsenConf generates more accurate conformer ensembles compared to prior generative models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonadiabatic Dynamics of Photoexcited cis-Stilbene Using Ab Initio Multiple Spawning

The photochemistry of cis-stilbene proceeds through two pathways: cis-trans isomerization and ring closure to 4a,4b-dihydrophenanthrene (DHP). Despite serving for many decades as a model system for photoisomerization, the photodynamics of cis-stilbene is still not fully understood. In this work, we use ab initio multiple spawning on a SA-2-CASSCF(2,2) potential energy surface to simulate the nonadiabatic dynamics of isolated cis-stilbene. We find the cyclization (to DHP and cis-stilbene) and isomerization (to trans- and cis-stilbene) reaction coordinates to be orthogonal; branching between the two pathways is determined on the S1 excited state within 150 fs of photoexcitation. Furthermore ,trajectory basis functions (TBFs) undergoing cyclization decay rapidly to the ground state in 250 fs, while TBFs moving along the isomerization coordinate remain on the excited state longer, with the majority decaying between 300 and 500 fs. We observe three avoided crossing regions in the dynamics: two along the isomerization coordinate (displaying pyramidalization and migration of an ethylenic hydrogen or phenyl group), and one DHP-like conical intersection along the cyclization coordinate. The isomeric form of the vibrationally hot photoproducts (as determined by measurement 2 ps after photoexcitation) is determined within less than 50 fs of decay to the ground state mediated by passage through a conical intersection. Excess vibrational energy of ground state cis- and trans-stilbene is channelled into phenyl torsions (with mostly opposing directionality). Finally, our simulations are validated by direct comparison to experiment for the absorption spectrum, branching ratio of the three photoproducts (44:52:4 cis-stilbene:trans-stilbene:DHP), and excited state lifetime (520 ± 40 fs).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗