Nonequilibrium Fermi golden rule for electronic transitions through conical intersections

We consider photoinduced electronic transitions through conical intersections in large molecules. Starting from the linear vibronic model Hamiltonian and treating linear diabatic couplings within the second order cumulant expansion, we have developed a simple analytical expression for the time evolution of electronic populations at finite temperature. The derived expression can be seen as a nonequilibrium generalization of the Fermi golden rule due to a nonequilibrium character of the initial photoinduced nuclear distribution. All parameters in our model are obtained from electronic structure calculations followed by a diabatization procedure. The results of our model are found to agree well with those of quantum dynamics for a test set of systems: fulvene molecule, 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative.     

Multiple boron-boron bonds in neutral molecules: an insight from the extended transition state method and the natural orbitals for chemical valence scheme

We have analyzed the character of B═B and B≡B bonds in the neutral molecules of general form: LHB═BHL (2-L) and LB≡BL (3-L), for various ancillary ligands L attached to the boron center, based on a recently developed method that combines the extended transition state scheme with the theory of natural orbitals for chemical valence (ETS-NOCV). In the case of molecules with the B═B bond, 2-L, we have included L = PMe(3), PF(3), PCl(3), PH(3), C(3)H(4)N(2)═C(NHCH)(2), whereas for molecules containing the B≡B connection, 3-L, the following ligands were considered L = CO, PMe(3), PCl(3), (Me(2)NCH(2)CH(2)O)(2)Ge. The results led us to conclude that use of phosphorus ligands leads to strengthening of the B═B bond by 6.4 kcal/mol (for 2-PMe(3)), by 4.4 (for 2-PF(3)) and by 9.2 (for 2-PH(3)), when compared to a molecule developed on the experimental basis, 2-C(3)H(4)N(2) (ΔE(total) = -118.3 kcal/mol). The ETS scheme has shown that all contributions, that is, (i) orbital interaction ΔE(orb), (ii) Pauli repulsion ΔE(Pauli), and (iii) electrostatic stabilization ΔE(elstat), are important in determining the trend in the B═B bond energies, ΔE(total). ETS-NOCV results revealed that both σ(B═B) and π(B═B) contributions are responsible for the changes in ΔE(orb) values. All considered molecules of the type LB≡BL, 3-L, exhibit a stronger B≡B bond when compared to a double B═B connection in 2-L (|ΔE(total)| is lower by 11.8-42.5 kcal/mol, depending on the molecule). The main reason is a lower Pauli repulsion contribution noted for 3-CO, 3-PMe(3), and 3-PCl(3) molecules. In addition, in the case of 3-PMe(3) and 3-PCl(3), the orbital interaction term is more stabilizing; however, the effect is less pronounced compared to the drop in the Pauli repulsion term. In all of the systems with double and triple boron-boron bonds, the electronic factor (ΔE(orb)) dominates over the electrostatic contribution (ΔE(elstat)). Finally, the strongest B≡B connection was found for 3-Ge [L = (Me(2)NCH(2)CH(2)O)(2)Ge], predominantly as a result of the strongest σ- and π-contributions, despite the highest destabilization originating from the sizable bulkiness of the germanium-containing ligand. The data on energetic stability of multiple boron-boron bonds (relatively high values of bond dissociation energies |ΔE(total)|), suggest that it should be possible to isolate experimentally the novel proposed systems with double B═B bonds, 2-PMe(3), 2-PF(3), 2-PCl(3), and 2-PH(3), and those with triple B≡B connections, 3-PMe(3), 3-Ge, and 3-PCl(3).     

Terahertz spectroscopy of enantiopure and racemic polycrystalline valine

Experimental and computational THz (or far-infrared) spectra of polycrystalline valine samples are reported. The experimental spectra have been measured using THz time-domain spectroscopy. Spectra of the pure enantiomers, both D and L, as well as the dl racemate have been taken at room temperature and low temperature (78 K). The spectra of the pure D and L enantiomers are essentially identical, and they are markedly different from the DL racemate. In addition, a temperature-dependent study of L-valine was undertaken in which the absorption maxima were found to red shift as a function of increasing temperature. The vibrational absorption spectra (frequencies and intensities) were calculated using the harmonic approximation with the Perdew-Burke-Ernzerhof (PBE) functional, localized atomic orbital basis sets, and periodic boundary conditions. The calculated and experimental spectra are in good qualitative agreement. A general method of quantifying the degree to which a calculated mode is intermolecular versus intramolecular is demonstrated, with the intermolecular motions further separated into translational versus rotational/librational motion. This allows straightforward comparison of spectra calculated using different basis sets or other constraints.     

Single dibenzoterrylene molecules in naphthalene and 2,3-dimethylnaphthalene crystals: vibronic spectra

Fluorescence excitation spectra of single dibenzoterrylene (DBT) molecules embedded in naphthalene (N) and 2,3-dimethylnaphthalene (2,3-DMN) crystals were studied at 5 K. The frequencies characterizing the vibronic structure of single DBT molecules in an N crystal agree with the theoretical prediction for the isolated DBT molecule. The 'dipolar' disorder encountered in 2,3-DMN crystals leads to a broad distribution of frequencies of the (0,0) lines of single DBT molecules. Moreover, the observed vibronic frequencies and intensities in the spectrum of DBT in 2,3-DMN crystals are slightly different to those in an N crystal. We conclude that the structure of DBT molecules in a 2,3-DMN crystal is disturbed in comparison with isolated DBT and the main change concerns its central tetracene moiety.     

Distorted fused porphyrin-phthalocyanine conjugates: synthesis and photophysics of supramolecular assembled systems with a pyridylfullerene

In the current work, we report on the synthesis and photophysical features of supramolecular hybrid systems that are based on newly fused porphyrin-phthalocyanine (P-Pc) conjugates and a pyridylfullerene. The ZnP-ZnPc conjugate was synthesized in three steps starting with a Diels-Alder reaction between β-vinylporphyrin and fumaronitrile. The resulting mixture of isomeric adducts was then dehydrogenated to yield the corresponding benzo[b]porphyrin-2(1),2(2)-dicarbonitrile. In the final step, cyclotetramerization with 4-tert-butylphthalonitrile, in the presence of zinc acetate, afforded the bis-metalated conjugate. Selective demetallation of ZnP led to the H(2)P-ZnPc conjugate. For both conjugates steric hindrance is the inception to a bent configuration, which does, however, not preclude enlargement of the π-conjugated system, that is, the porphyrins and the phthalocyanines. The two conjugates coordinate N-(4-pyridyl)fullero[c]pyrrolidine giving rise to the corresponding supramolecular porphyrin-phthalocyanine-fullerene systems. Photophysical measurements corroborate a sequential deactivation in the excited state, namely an initial intramolecular energy transfer from ZnP or H(2)P to ZnPc followed by an intramolecular charge transfer to yield ZnP-(ZnPc)˙(+)-(C(60))˙(-) and H(2)P-(ZnPc)˙(+)-(C(60))˙(-), respectively.     

A Statistical Model for Predicting the Heat Transfer of Solid Particles in Turbulent Flows

The objective of this paper is twofold: (1) to present a statistical model of particle transport and heat transfer in turbulent flows and (2) to examine the performance of this model in various turbulent flows going from a simple flow to a more complicated one. This model is based on a kinetic equation for the probability density function of the particle velocity and temperature distributions in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations performed in various turbulent flows.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.     

Splitting Formulas for Tutte Polynomials

We present two splitting formulas for calculating the Tutte polynomial of a matroid. The first one is for a generalized parallel connection across a 3-point line of two matroids and the second one is applicable to a 3-sum of two matroids. An important tool used is the bipointed Tutte polynomial of a matroid, an extension of the pointed Tutte polynomial introduced by Brylawski.     

Statistical Properties of Unimodal Maps

We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition into topological conjugacy classes, see [ALM]) is not transversely absolutely continuous. As an intermediate step in the proof of the formula, we show that the distribution of the critical orbit is described by the physical measure supported in the chaotic attractor.     

Simulations of energy and switching in AFLCDs with different boundary conditions

Using standard expressions for the various terms in the Gibbs free energy, the switching in antiferroelectric liquid crystal (AFLC) displays is simulated and the time evolution of various energy terms and of the liquid crystal director distributions are calculated. It is shown that when returning from a strong positive voltage to zero, one can reach two types of antiferroelectric state: the normal alternating state with the two bulk polarizations perpendicular to the electrodes and opposite to each other, and the alternative splayed symmetric state with two bulk polarizations parallel to the electrodes and again opposite to each other. The former case gives rise to tri-state switching characteristics, the latter to V-shaped switching. In general strong polar interaction with the alignment layer favours V-shaped switching while weak or no polar interaction give rise to tri-state switching characteristics. Since the V-shaped characteristic has so far only been demonstrated experimentally in ferroelectric liquid crystals (or antiferroelectric liquid crystals being in the ferroelectric state), the difference in AFLCs is discussed and the conditions for continuous switching are modelled. The simulations show that the switching characteristics of the antiferroelectric display can be controlled by the surface parameters.