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1. Generalized Einstein relations between absorption and emission spectra at thermodynamic equilibrium

   https://doi.org/10.1073/pnas.2410280121  

   Ryu, Jisu; Yeola, Sarang; Jonas, David M (September 2024, Proceedings of the National Academy of Sciences)

   We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes’ shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes’ shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive. 

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2. Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

   https://doi.org/10.1021/acs.jpcb.4c01401  

   Myers, Christopher A; Lu, Shao-Yu; Shedge, Sapana; Pyuskulyan, Arthur; Donahoe, Katherine; Khanna, Ajay; Shi, Liang; Isborn, Christine M (June 2024, The Journal of Physical Chemistry B)

   The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore–solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore–solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening. 

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3. Time-resolved vibronic spectra with nuclear–electronic orbital time-dependent configuration interaction

   https://doi.org/10.1063/5.0243394  

   Garner, Scott M; Upadhyay, Shiv; Li, Xiaosong; Hammes-Schiffer, Sharon (January 2025, The Journal of Chemical Physics)

   Time-resolved spectroscopy is an important tool for probing photochemically induced nonequilibrium dynamics and energy transfer. Herein, a method is developed for the ab initio simulation of vibronic spectra and dynamical processes. This framework utilizes the recently developed nuclear–electronic orbital time-dependent configuration interaction (NEO-TDCI) approach, which treats all electrons and specified nuclei quantum mechanically on the same footing. A strategy is presented for calculating time-resolved vibrational and electronic absorption spectra from any initial condition. Although this strategy is general for any TDCI implementation, utilizing the NEO framework allows for the explicit inclusion of quantized nuclei, as illustrated through the calculation of vibrationally hot spectra. Time-resolved spectra produced by either vibrational or electronic Rabi oscillations capture ground-state absorption, stimulated emission, and excited-state absorption between vibronic states. This methodology provides the foundation for fully ab initio simulations of multidimensional spectroscopic experiments. 

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4. Enhancing the resolution of ¹ H and ¹³ C solid-state NMR spectra by reduction of anisotropic bulk magnetic susceptibility broadening

   https://doi.org/10.1039/C7CP04223J  

   Hanrahan, Michael P.; Venkatesh, Amrit; Carnahan, Scott L.; Calahan, Julie L.; Lubach, Joseph W.; Munson, Eric J.; Rossini, Aaron J. (January 2017, Phys. Chem. Chem. Phys.)

   We demonstrate that natural isotopic abundance 2D heteronuclear correlation (HETCOR) solid-state NMR spectra can be used to significantly reduce or eliminate the broadening of 1 H and 13 C solid-state NMR spectra of organic solids due to anisotropic bulk magnetic susceptibility (ABMS). ABMS often manifests in solids with aromatic groups, such as active pharmaceutical ingredients (APIs), and inhomogeneously broadens the NMR peaks of all nuclei in the sample. Inhomogeneous peaks with full widths at half maximum (FWHM) of ∼1 ppm typically result from ABMS broadening and the low spectral resolution impedes the analysis of solid-state NMR spectra. ABMS broadening of solid-state NMR spectra has previously been eliminated using 2D multiple-quantum correlation experiments, or by performing NMR experiments on diluted materials or single crystals. However, these experiments are often infeasible due to their poor sensitivity and/or provide limited gains in resolution. 2D 1 H– 13 C HETCOR experiments have previously been applied to reduce susceptibility broadening in paramagnetic solids and we show that this strategy can significantly reduce ABMS broadening in diamagnetic organic solids. Comparisons of 1D solid-state NMR spectra and 1 H and 13 C solid-state NMR spectra obtained from 2D 1 H– 13 C HETCOR NMR spectra show that the HETCOR spectrum directly increases resolution by a factor of 1.5 to 8. The direct gain in resolution is determined by the ratio of the inhomogeneous 13 C/ 1 H linewidth to the homogeneous 1 H linewidth, with the former depending on the magnitude of the ABMS broadening and the strength of the applied field and the latter on the efficiency of homonuclear decoupling. The direct gains in resolution obtained using the 2D HETCOR experiments are better than that obtained by dilution. For solids with long proton longitudinal relaxation times, dynamic nuclear polarization (DNP) was applied to enhance sensitivity and enable the acquisition of 2D 1 H– 13 C HETCOR NMR spectra. 2D 1 H– 13 C HETCOR experiments were applied to resolve and partially assign the NMR signals of the form I and form II polymorphs of aspirin in a sample containing both forms. These findings have important implications for ultra-high field NMR experiments, optimization of decoupling schemes and assessment of the fundamental limits on the resolution of solid-state NMR spectra. 

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5. High‐Frequency Waves Driven by Agyrotropic Electrons Near the Electron Diffusion Region

   https://doi.org/10.1029/2020GL087111  

   Dokgo, Kyunghwan; Hwang, Kyoung‐Joo; Burch, James L.; Yoon, Peter H.; Graham, Daniel B.; Li, Wenya (March 2020, Geophysical Research Letters)

   Abstract National Aeronautics and Space Administration's Magnetosphere Multiscale mission reveals that agyrotropic electrons and intense waves are prevalently present in the electron diffusion region. Prompted by two distinct Magnetosphere Multiscale observations, this letter investigates by theoretical means and the properties of agyrotropic electron beam‐plasma instability and explains the origin of different structures in the wave spectra. The difference is owing to the fact that in one instance, a continuous beam mode is excited, while in the other, discrete Bernstein modes are excited, and the excitation of one mode versus the other depends on physical input parameters, which are consistent with observations. Analyses of dispersion relations show that the growing mode becomes discrete when the maximum growth rate is lower than the electron cyclotron frequency. Making use of particle‐in‐cell simulations, we found that the broadening anglein the gyroangle space is also an important factor controlling the growth rate. Ramifications of the present finding are also discussed. 

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