Properties of dentin, enamel and their junction, studied with Brillouin scattering and compared to Raman microscopy.

OBJECTIVE: Dentin, enamel and the transition zone, called the dentin-enamel junction (DEJ), have an organization and properties that play a critical role in tooth resilience and in stopping the propagation of cracks. Understanding their chemical and micro-biomechanical properties is then of foremost importance. The aim of this study is to apply Brillouin microscopy on a complex biological structure, that is, the DEJ, and to compare these results with those obtained with Raman microscopy. DESIGN: Both techniques allow noncontact measurements at the microscopic scale. Brillouin microscopy is based on the interaction between acoustic phonons and laser photons and gives a relation between the frequency shift of the scattered light and the stiffness of the sample. Raman spectra contain peaks related to specific chemical bonds. RESULTS: Comparison of the Brillouin and Raman cartographies reveals correlations between mechanical and chemical properties. Indeed, the shapes of the phosphate content and stiffness curves are similar. The two spectroscopies give compatible values for the mean distance between two tubules, i.e., 4-6 µm. Moreover, for the first time, the daily cross striations of enamel could be studied, indicating a relationship between the variation in the phosphate concentration and the variation in the rigidity within the enamel prisms. CONCLUSIONS: We demonstrate here the possibility of using Brillouin scattering microscopy to both study complex biological materials such as the enamel-dentin junction and visualize secondary structures. Correlations between the chemical composition and mechanical properties could help in better understanding the tissue histology.

Semiclassical initial value representation: From Møller to Miller. II.

As shown by W. H. Miller in a seminal article [J. Chem. Phys. 53, 3578 (1970)], the most convenient and accurate semiclassical (SC) theory of molecular scattering in action-angle coordinates is based on the initial value representation (IVR) and the use of shifted angles, which are different from the natural angles usually used in the quantum and classical treatments. Here, we show for an inelastic molecular collision that the initial and final shifted angles define three-segment classical paths that are exactly those involved in the classical-limit of Tannor-Weeks quantum scattering theory [J. Chem. Phys. 98, 3884 (1993)], provided that the translational wave packets |g+⟩ and |g-⟩ into play in this theory are both taken at |0⟩. Assuming this to be the case, using van Vleck propagators, and applying the stationary phase approximation, Miller's SCIVR expression of S-matrix elements is found, with an additional cut-off factor canceling the energetically forbidden transition probabilities. This factor, however, is close to unity in most practical cases. Furthermore, these developments show that the Møller operators underlie Miller's formulation, thus confirming, for molecular collisions, the results recently established in the simpler case of light-induced rotational transitions [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. Last but not least, we show, based on the previous results, that for processes involving long-range anisotropic forces, implementing the Skinner-Miller method [Chem. Phys. Lett. 300, 20 (1999)] in shifted coordinates makes its predictions both easier and more accurate than in natural coordinates.

An efficient algorithm for capturing quantum effects in classical reactive scattering: application to D + H+3 → H2D+ + H.

Motivated by a recent semiclassical analysis of chemical reaction thresholds [Bonnet et al., J. Chem. Phys., 2022, 157, 094114], we present an efficient algorithm for including zero-point energy (ZPE) effects in classical reactive scattering. The algorithm is an extension of the quasi-classical trajectory (QCT) Gaussian binning method. We apply it to the astrophysically important D + H+3 reaction, where there are significant quantum effects and where application of other methods is problematic [Braunstein et al., Phys. Chem. Chem. Phys., 2022, 24, 5489]. The rate constants computed with the new, general algorithm closely match recent Ring Polymer Molecular Dynamics (RPMD) [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] and experimentally derived [Bowen et al., J. Chem. Phys., 2021, 154, 084307] ones spanning ∼4 orders of magnitude from 70 to 1500 K.

An Experimental and Theoretical Investigation of the Gas-Phase C(3P) + N2O Reaction. Low Temperature Rate Constants and Astrochemical Implications.

The reaction between atomic carbon in its ground electronic state, C(3P), and nitrous oxide, N2O, has been studied below room temperature due to its potential importance for astrochemistry, with both species considered to be present at high abundance levels in a range of interstellar environments. On the experimental side, we measured rate constants for this reaction over the 50-296 K range using a continuous supersonic flow reactor. C(3P) atoms were generated by the pulsed photolysis of carbon tetrabromide at 266 nm and were detected by pulsed laser-induced fluorescence at 115.8 nm. Additional measurements allowing the major product channels to be elucidated were also performed. On the theoretical side, statistical rate theory was used to calculate low temperature rate constants. These calculations employed the results of new electronic structure calculations of the 3A″ potential energy surface of CNNO and provided a basis to extrapolate the measured rate constants to lower temperatures and pressures. The rate constant was found to increase monotonically as the temperature falls (kC(3P)+N2O (296 K) = (3.4 ± 0.3) × 10-11 cm3 s-1), reaching a value of kC(3P)+N2O (50 K) = (7.9 ± 0.8) × 10-11 cm3 s-1 at 50 K. As current astrochemical models do not include the C + N2O reaction, we tested the influence of this process on interstellar N2O and other related species using a gas-grain model of dense interstellar clouds. These simulations predict that N2O abundances decrease significantly at intermediate times (103 - 105 years) when gas-phase C(3P) abundances are high.

Capturing quantum effects with quasi-classical trajectories in the D + H+3 → H2D+ + H reaction.

We present quasi-classical trajectory (QCT) cross sections, rate constants, and product state distributions for the D + H+3 → H2D+ + H reaction. Using the same H+4 potential surface, the rate constants obtained from several QCT-based methods correcting for zero-point effects by Gaussian binning the product H2D+ are compared to ring polymer molecular dynamics (RPMD) rate constants [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] which include quantum effects and to recent experimentally derived rate constants [Bowen et al., J. Chem. Phys., 2021, 154, 084307]. QCT with standard binning predicts rate constants that increase slowly as the temperature decreases from 1500 to 100 K. In contrast, the RPMD rate constants decrease rapidly with decreasing temperature. By 100 K, the QCT standard binning rate constant is more than 3 orders of magnitude larger than the RPMD rate constant. We show that QCT with Gaussian binning and proper normalization captures the zero-point effects and reproduces the RPMD rate constants over a large temperature range. Furthermore, the simple technique of counting only reactive trajectories with vibrational energy above the product zero-point energy matches the RPMD results well down to ∼300 K. The present Gaussian binned rate constants are in fair agreement with new experimentally derived rate constants from 100 to 1500 K. However, because the Gaussian binned rate constants do not include tunneling, important at lower temperatures, and the RPMD and experimentally derived rate constants have significant differences, the roles of the competing effects of zero-point energy, internal excitation of the H+3, and quantum tunneling are not simple and require further study for a consistent picture of the dynamics. Since rate constants for complex forming reactions, such as the title reaction, are difficult to converge with RPMD, alternative QCT-based methods, which include quantum effects and in addition provide product state distributions as described here, are highly desirable.

Semiclassical descriptions of rotational transitions in natural and shifted angles: Analysis of unexpected results.

In the semiclassical theory of rotational transitions, S-matrix elements are expressed as integrals over initial and final angles of probability amplitudes calculated along the classical paths joining these angles, before final passage to an initial value representation [W. H. Miller, J. Phys. Chem. A 105, 2942 (2001)]. These angles can be either natural angles fixing the orientation of the rotor or angles shifted with respect to the previous ones so as to vary only within the interaction region causing the transitions. The two approaches, however, were recently shown to lead to different predictions. While the theory in natural angles lacks precision and exhibits unphysical behavior, the theory in shifted angles is much more accurate and physically well behaved [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. The present work is devoted to the analysis of this unexpected finding.

Ab initio molecular dynamics of hydrogen on tungsten surfaces.

The dissociation process of hydrogen molecules on W(110) was studied using density functional theory and classical molecular dynamics. We have calculated the dissociation probability for molecules with energies below 300 meV and analyzed the dynamics of the adsorption process. Our results show that the fate of each trajectory is determined at distances relatively far from the surface, at roughly 2-2.5 Å. This distance varies slightly with the initial kinetic energy of the molecule. Part of our simulations include van der Waals dispersion effects in the interaction between molecule and surface. We present a comparison between these results and other theoretical and experimental results previously published. The inclusion of the van der Waals term provokes an increase in the far-distance attraction that is compensated by a stronger repulsion at short distances. The combination of both effects appreciably decreases the value of the dissociation probability. The successful comparison of our results with experimental information confirms that the methodology employed can be considered as a rich and accurate instrument to study the dissociation of hydrogen on surfaces.

Semiclassical initial value representation: From Møller to Miller.

The initial value representation (IVR) was proposed five decades ago by Miller [J. Chem. Phys. 53, 3578 (1970)] in order to improve the feasibility and accuracy of semiclassical (SC) scattering calculations. Møller operators, which play a fundamental role in quantum scattering theory, do not appear in his formulation based on action-angle coordinates. These operators were introduced much later by Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)] in SC-IVR calculations performed in Cartesian coordinates within the Tannor and Weeks [J. Chem. Phys. 98, 3884 (1993)] formulation of quantum scattering theory. Remarkably, Møller operators were found to boost the numerical efficiency of SC-IVR calculations. The purpose of this work is to show within a simple model of light-induced rotational transitions that, in fact, Møller operators were already underlying Miller's pioneering formulation. In line with the results of Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)], removing the action of these operators in Miller's theory strongly decreases its numerical efficiency.

When classical trajectories get to quantum accuracy: II. The scattering of rotationally excited H2 on Pd(111).

The classical trajectory method in a quantum spirit assigns statistical weights to classical paths on the basis of two semiclassical corrections: Gaussian binning and the adiabaticity correction. This approach was recently applied to the heterogeneous gas-surface reaction between H2 in its internal ground state and Pd(111) surface e.g. [A. Rodríguez-Fernández et al., J. Phys. Chem. Lett., 2019, 10, 7629]. Its predictions of the sticking and state-resolved reflection probabilities were found to be in surprisingly good agreement with those of exact quantum time-dependent calculations where standard quasi-classical trajectory calculations failed. We show in this work that the quality of the previous calculations is maintained or even improved when H2 is rotationally excited.

Experimental and theoretical studies of the N(2D) + H2 and D2 reactions.

This study reports the results of an experimental and theoretical investigation of the N(2D) + H2 and N(2D) + D2 reactions at room temperature and below. On the experimental side, a supersonic flow (Laval nozzle) reactor was employed to measure rate constants for these processes at temperatures as low as 127 K. N(2D) was produced indirectly by pulsed laser photolysis and these atoms were detected directly by pulsed laser induced fluorescence in the vacuum ultraviolet wavelength region. On the theoretical side, two different approaches were used to calculate rate constants for these reactions; a statistical quantum mechanical (SQM) method and a quasi-classical trajectory capture model including a semi-classical correction for tunneling (SC-Capture). This work is described in the context of previous studies, while the discrepancies between both experiment and theory, as well as between the theoretical results themselves are discussed.

Experimental and Theoretical Study of the O(1D) + HD Reaction.

This work addresses the kinetics and dynamics of the gas-phase reaction between O(1D) and HD molecules down to low temperature. Here, measurements were performed by using a supersonic flow (Laval nozzle) reactor coupled with pulsed laser photolysis for O(1D) production and pulsed-laser-induced fluorescence for O(1D) detection to obtain rate constants over the 50-300 K range. Additionally, temperature-dependent branching ratios (OD + H/OH + D) were obtained experimentally by comparison of the H/D atom atom yields with those of a reference reaction. In parallel, theoretical rate constants and branching ratios were calculated by using three different techniques; mean potential phase space theory (MPPST), the statistical quantum mechanical method (SQM), and ring polymer molecular dynamics (RPMD). Although the agreement between experimental and theoretical rate constants is reasonably good, with differences not exceeding 30% over the entire temperature range, the theoretical branching ratios derived by the MPPST and SQM methods are as much as 50% larger than the experimental ones. These results are presented in the context of earlier work, while the possible origins of the discrepancies between experiment and theory are discussed.

The Intricate Dynamics of the Si(3P) + OH(X2Π) Reaction.

The dynamics of the Si(3P) + OH(X2Π) → SiO(X1Σ+,v',j') + H(2S) reaction is investigated by means of the quasi-classical trajectory method on the electronic ground state X2A' potential energy surface in the 10-2-1 eV collision energy range. Although the reaction involves the formation of a long-lived intermediate complex, a high probability for back-dissociation to the reactants is found because of inefficient intravibrational redistribution of energy among the complex modes. At low collision energies, the reactive events are governed by a dynamics with mixed direct/indirect features. As the collision energy increases, the intermediate complex lifetime increases and final state distributions are found to be in reasonable agreement with statistical predictions obtained using the mean potential phase space theory, thus highlighting the indirect character of the process. These rich and puzzling dynamical features are in line with what has been previously observed for the S(3P) + OH(X2Π) reaction.

The dynamics of the C(1D)+H2/D2/HD reactions at low temperature.

We present results of a theoretical investigation on the dynamics of the C(1D)+H2 reaction and the corresponding isotopic variants in which the carbon atom collides either with D2 or HD. Statistical techniques have been tested in comparison with the recent experimental information at low temperature (T < 300 K) and exact quantum mechanical calculations reported on the title reactions in an attempt to establish their possible complex-forming character. Our study includes the calculation of probabilities, rotational distributions, integral cross sections, differential cross sections, and rate constants. Previous quantum mechanical results have been extended here to complete the analysis of the underlying mechanisms which govern the collision process.

A combined theoretical and experimental investigation of the kinetics and dynamics of the O(1D) + D2 reaction at low temperature.

The O(1D) + H2 reaction is a prototype for simple atom-diatom insertion type mechanisms considered to involve deep potential wells. While exact quantum mechanical methods can be applied to describe the dynamics, such calculations are challenging given the numerous bound quantum states involved. Consequently, efforts have been made to develop alternative theoretical strategies to portray accurately the reactive process. Here we report an experimental and theoretical investigation of the O(1D) + D2 reaction over the 50-296 K range. The calculations employ three conceptually different approaches - mean potential phase space theory, the statistical quantum mechanical method and ring polymer molecular dynamics. The calculated rate constants are in excellent agreement over the entire temperature range, exhibiting only weak temperature dependence. The agreement between experiment and theory is also very good, with discrepancies smaller than 26%. Taken together, the present and previous theoretical results validate the hypothesis that long-lived complex formation dominates the reaction dynamics at low temperature.

Simulation of the experimental imaging results for the OH + CHD3 reaction with a simple and accurate theoretical approach.

The OH + CHD3 reaction is among the largest one ever studied at the high-resolution level permitted by imaging techniques [B. Zhang et al., J. Phys. Chem. A, 2005, 109, 8989]. This process involves eighteen configuration space coordinates, which are large enough to make exact quantum scattering calculations beyond reach. Moreover, freezing some degrees-of-freedom in order to render these calculations feasible may lead to unrealistic predictions. However, we have found it possible to reproduce for the first time the pair-correlated measurements of Zhang et al. at a nearly quantitative level by means of full-dimensional classical trajectory calculations in a quantum spirit on a recent ab initio potential energy surface. These calculations combine the classical description of the dynamics, well suited to polyatomic systems, with Bohr quantization of both reagent and product vibrational motions. While this pseudo-quantization is exactly imposed to the reagents, it is approximately imposed to the products in a first step through energy-based Gaussian binning (1GB). In a second step, we show that the original action-based Gaussian binning (GB), long thought to be inapplicable in practice to polyatomic reactions, yields in fact results comparable in accuracy and numerical cost to those obtained by means of 1GB, provided that Gaussian weights are properly widened. This new finding clearly extends the scope of GB in theoretical reactive scattering.

Vegetable oil hybrid films cross-linked at the air-water interface: formation kinetics and physical characterization.

Vegetable oil based hybrid films were developed thanks to a novel solvent- and heating-free method at the air-water interface using silylated castor oil cross-linked via a sol-gel reaction. To understand the mechanism of the hybrid film formation, the reaction kinetics was studied in detail by using complementary techniques: rheology, thermogravimetric analysis, and infrared spectroscopy. The mechanical properties of the final films were investigated using nano-indentation, whereas their structure was studied using a combination of wide-angle X-ray scattering, electron diffraction, and atomic force microscopy. We found that solid and transparent films form in 24 hours and, by changing the silica precursor to castor oil ratio, their mechanical properties are tunable in the MPa-range by about a factor of twenty. In addition to that, a possible optimization of the cross-linking reaction with different catalysts was explored, and finally cytotoxicity tests were performed on fibroblasts proving the absence of film toxicity. The results of this work pave the way to a straightforward synthesis of castor-oil films with tunable mechanical properties: hybrid films cross-linked at the air-water interface combine an easy and cheap spreading protocol with the features of their thermal history optimized for possible future micro/nano drug loading, thus representing excellent candidates for the replacement of non-environmentally friendly petroleum-based materials.

Theoretical Study of the Pair-Correlated F + CHD3(v = 0,ν1 = 1) Reaction: Effect of CH Stretching Vibrational Excitation.

The F + CHD3(v) reaction is a benchmark system in polyatomic reactions. Theoretical/experimental comparisons have been reported in recent years that present some controversies, specifically the role of the reactant CH stretching vibrational excitation, CHD3(ν1 = 1), on the reactivity of both isotope channels, DF(v) + CHD2(v') and HF(v) + CD3(v'). However, in many cases, these comparisons are not made on an equal footing. Previous theoretical studies were concerned with overall reactivity of each isotope channel, while fine velocity map imaging experiments provided results in a product pair-correlated manner. In order to shed some light on these controversies, we perform here a pair-correlated theory/experiment comparison for the title reaction, using quasi-classical trajectory calculations on a full dimensional potential energy surface. When these calculations are analyzed in a quantum spirit, i.e., by discarding those trajectories whose results do not meet quantum-mechanical requirements and aiming to reproduce stringent experimental constraints, some of the discrepancies on overall reactivity and the effect of the CH vibrational excitation are now resolved. Agreement with the available experimental studies, though still qualitative in some aspects, has noticeably improved.

S((1)D) + ortho-D2 Reaction Dynamics at Low Collision Energies: Complementary Crossed Molecular Beam Experiments and Theoretical Investigations.

The excitation function of the S((1)D) + D2 reaction was determined in a crossed molecular beam apparatus for collision energies ranging from 1817 to 47 J mol(-1) in the near-cold regime. A very good overall agreement was found between experimental data and the theoretical results obtained using the ab initio potential energy surface built by Ho and coworkers and different methods: time-independent quantum dynamics (QM), semiclassical mean potential capture theory (sc-MPCT), and quasi-classical trajectories (QCT). The general trend of the experimental excitation function is well reproduced in most of the range by a simple capture calculation with an R(-6) dispersion potential. The present results are discussed in the light of previous studies on the isotopic variants S((1)D) + H2 and HD.

Quantum state-resolved differential cross sections for complex-forming chemical reactions: Asymmetry is the rule, symmetry the exception.

We argue that statistical theories are generally unable to accurately predict state-resolved differential cross sections for triatomic bimolecular reactions studied in beam experiments, even in the idealized limit where the dynamics are fully chaotic. The basic reason is that quenching of interferences between partial waves is less efficient than intuitively expected, especially around the poles.