The symmetry of molecular polarization tensors

Polarization tensors are discussed in terms of their intrinsic symmetry group which is a direct product of the point group and the subgroup of the permutation group relevant to the experiment. The study of these latter groups is simplified by use of the isomorphism with certain point groups and permutations of suffixes can be visualized by rotations and reflections of the vertices of various objects in space. The approach unites the previous treatments and provides a means of constructing the bases for the irreducible tensor components. The difficulties introduced by Laplace's equation are explained and the information obtainable from induced birefringence experiments (Kerr and Cotton–Mouton effects) discussed for various systems.     

Nuclear‐Spin‐Induced Cotton–Mouton Effect in a Strong External Magnetic Field

Novel, high‐sensitivity and high‐resolution spectroscopic methods can provide site‐specific nuclear information by exploiting nuclear magneto‐optic properties. We present a first‐principles electronic structure formulation of the recently proposed nuclear‐spin‐induced Cotton–Mouton effect in a strong external magnetic field (NSCM‐B). In NSCM‐B, ellipticity is induced in a linearly polarized light beam, which can be attributed to both the dependence of the symmetric dynamic polarizability on the external magnetic field and the nuclear magnetic moment, as well as the temperature‐dependent partial alignment of the molecules due to the magnetic fields. Quantum‐chemical calculations of NSCM‐B were conducted for a series of molecular liquids. The overall order of magnitude of the induced ellipticities is predicted to be 10^?11–10^?6 rad T^?1 M ^?1 cm^?1 for fully spin‐polarized nuclei. In particular, liquid‐state heavy‐atom systems should be promising for experiments in the Voigt setup.     

Birefringence studies in non-dipolar liquids

Measurements of the Kerr effect and Cotton—Mouton effect of a series of non-dipolar, axially-symmetric, diamagnetic molecules have been made at 25°C and 632.8 nm. The static orientational correlation functions for these liquids were drawn from depolarised Rayleigh scattering studies and the derived magnetic anisotropies are in good agreement with literature data.     

A theory of field-induced birefringence applicable to systems of large molecules

We consider a molecule in an external constant field interacting with a linearly polarized photon. When the field is chosen to be magnetic and directed along the wave vector of the photon (longitudinal), we find that the time dependence of the state function implies a rotation of the plane of polarization of the photon characteristic of the Faraday effect. Similarly when the field is transverse, the time evolution of the state corresponds to the Kerr effect in the case of an electric, and the Cotton—Mouton effect in the case of a magnetic field. The theory is applicable to a dilute system of freely oriented molecules of any size: the long-wavelength approximation is not invoked. The general procedure for averaging over all molecular orientations is carried out explicitly in the case of the Faraday effect.     

Chiroptical properties of steroid 1,3-diaxial diols in the presence of [Mo2(OAc)4]

Summary Bidentate complexes of dimolybdenum tetraacetate with 1,3-diaxial diols show Cotton effects around 490–540 nm (CD band I), 400–440 nm (II), 350–380 nm (III), 320 nm (IV) and 280 nm (V). The sign of the Cotton effect II can be predicted by a proposed sector rule. It seems that from the Cotton effects for cyclic 1,3-diols the absolute configurations or conformations can be obtained.A part of this material was presented at III-rd International Conference on CD Spectroscopy [1]     

Measuring internal energy deposition in collisional activation using hydrated ion nanocalorimetry to obtain peptide dissociation energies and entropies

The internal energy deposited in both on- and off-resonance collisional activation in Fourier transform ion cyclotron resonance mass spectrometry is measured with ion nanocalorimetry and is used to obtain information about the dissociation energy and entropy of a protonated peptide. Activation of Na⁺(H₂O)₃₀ results in sequential loss of water molecules, and the internal energy of the activated ion can be obtained from the abundances of the product ions. Information about internal energy deposition in on-resonance collisional activation of protonated peptides is inferred from dissociation data obtained under identical conditions for hydrated ions that have similar m/z and degrees-of-freedom. From experimental internal energy deposition curves and Rice-Ramsperger-Kassel-Marcus (RRKM) theory, dissociation data as a function of collision energy for protonated leucine enkephalin, which has a comparable m/z and degrees-of-freedom as Na⁺(H₂O)₃₀, are modeled. The threshold dissociation energies and entropies are correlated for data acquired at a single time point, resulting in a relatively wide range of threshold dissociation energies (1.1 to 1.7 eV) that can fit these data. However, this range of values could be significantly reduced by fitting data acquired at different dissociation times. By measuring the internal energy of an activated ion, the number of fitting parameters necessary to obtain information about the dissociation parameters by modeling these data is reduced and could result in improved accuracy for such methods.     

Axial chirality of donor-donor, donor-acceptor, and tethered 1,1'-binaphthyls: a theoretical revisit with dynamics trajectories

The circular dichroism (CD) spectra of (R)-2,2'-dimethoxy-1,1'-binaphthyl (DD) and its untethered and tethered donor-acceptor analogues (DA and DA7-DA9) were investigated experimentally and theoretically. The experimental CD spectra of DD and DA resembled each other in several aspects, displaying a positive-positive-negative Cotton effect pattern in the (1)L(b)-(1)L(a) region and a strong negative couplet at the (1)B(b) band, but significantly differed in transition energy and rotatory strength. The couplet amplitude (A) of the main band was 1.6 times larger in DA than in DD, despite the comparable extinction coefficients and seemingly analogous conformations. An additional positive Cotton effect was observed at the CT (CT) band for donor-acceptor binaphthyl DA. Our theoretical prediction of the CD spectra of binaphthyls involves three sequential first principle quantum mechanics (QM) calculations. Thus, the geometry optimizations of a series of conformers with varying dihedral angles were performed by the dispersion-corrected DFT-D method using the B97-D functional and the TZV2P basis set. The potential curve as a function of the dihedral angle (θ) was obtained by using the SCS-MP2/TZVPP single-point energy calculations with and without application of the solvent correction. The CD spectrum of each conformer was independently calculated by the second-order approximate coupled cluster calculation (CC2 method) using the TZVPP basis sets and the resolution of the identity (RI-J) approximation. The (net) theoretical CD spectrum was obtained by averaging over all possible conformers, where the dynamics trajectories based on the relative SCS-MP2 energies were taken into account. By using 17 possible conformers at θ varying from 50 to 130° by 5° intervals, the experimental CD spectra were successfully reproduced in a quantitative manner, enabling us to characterize properly almost all of the important spectral features and chiroptical properties. The two-state model, reported previously, turned out to have led to the right answer with wrong reasons. The couplet sign and amplitude A are critical functions of θ and can be used not only for (qualitatively) determining the absolute configuration but also for quantitatively analyzing the binaphthyl conformations. The angle dependence of A was already argued in the classical coupled oscillator and exciton chirality theories to provide reasonable structure elucidations but only in a qualitative or semiquantitative manner. Our method is able to predict the A value quantitatively as a function of θ. For tethered binaphthyls DA7-DA9, particular care should be exercised in the conformational assessment based on the classical treatment because the amplitude A was shown to be significantly affected by the existence of the tether itself. In the present method, the couplet amplitude A was nicely related to the dihedral angle θ of DA and DD by the state-of-the-art ab initio calculations, enabling us to gain the quantitative information about the conformation of axially chiral binaphthyls. The Cotton effect at the CT band also serves as a complementary clue for elucidating the conformation of donor-acceptor binaphthyls.     

Electron and positron pair emission by low energy positron impact on surfaces

The emission of electron pairs from surfaces has the power to reveal details about the electron–electron interaction in condensed matter. This process, stimulated by a primary electron or photon beam, has been studied both in experiment and theory over the last two decades. An additional pathway, namely positron–electron pair emission, holds the promise to provide additional information. It is based on the notion that the Pauli exclusion principle does not need to be considered for this process.We have commissioned a laboratory based positron source and performed a systematic study on a variety of solid surfaces. In a symmetric emission geometry we can explore the fact that positron and electron are distinguishable particles. Following fundamental symmetry arguments we have to expect that the available energy is shared unequally among positron and electron. Experimentally we observe such a behavior for all materials studied. We find an universal feature for all materials in the sense that on average the positron carries a larger fraction of the available energy. This is qualitatively accounted for by a simplified scattering model. Numerical results, which we obtained by a microscopic theory of positron–electron emission from surfaces, reveal however that there are also cases in which the electron carries more energy. Whether the positron or the electron is more energetic depends on details of the bound electron state and of the emission geometry. The coincidence intensity is strongly material dependent and there exists an almost monotonic relation between the singles and coincidence intensity. These results resemble the findings obtained in electron and photon stimulated electron pair emission. An additional reaction channel is the emission of an electron pair upon positron impact. We will discuss the energy distributions and the material dependence of the coincidence signal which shows similar features as those for positron–electron pairs.     

Atomic Motions in Molecular Crystals from Diffraction Measurements

The information provided by modern crystal structure analyses is not limited to the atomic arrangement. It also includes, for each atom, a set of quantities known as anisotropic Gaussian displacement parameters (ADP's), which provide information about averaged displacements of atoms from their mean positions. From analysis of these quantities, conclusions can be drawn about the rigid-body motion of molecules, about large-amplitude internal molecular motions, and about the identification of any disorder present in the crystals as being mainly dynamic or mainly static in nature. For some crystals, such analyses yield energy barriers to rotation of rigid molecules or molecular fragments that are in good agreement with values obtained by other physical methods.     

Is the original Kissinger equation obsolete today?

The original Kissinger, Friedman, and modified Kissinger–Akahira–Sunose (KAS) methodologies were used to evaluate the apparent activation energy of theoretically simulated complex processes consisting of two overlapping independent JMA-like (Johnson–Mehl–Avrami-like) subprocesses. Three overlay series were studied, each representing one of the basic conceptual types of peak overlap. It was shown that, in the case of complex processes, both the tested isoconversion methods (KAS and Friedman) provide good qualitative information about the activation energies of the involved overlapping signals. However, from the quantitative point of view, the data are not easy to interpret, and deconvolution procedures are necessary for meaningful results to be obtained. On the other hand, in most cases, the apparent activation energy determined by the original Kissinger equation for the overlapped dominant peak corresponded very well to the true values determined for the sole processes. This suggests large robustness of the Kissinger methodology that even nowadays may be considered very advantageous and utilized in kinetic analysis of complex processes.     

Arrhenius plots for activation energy of atomization in graphite-furnace atomic-absorption spectrometry

Activation energy plots drawn by use of various Arrhenius-type equations for atomization reactions in graphite-furnace atomic-absorption spectrometry (GFAAS) do not give reliable kinetic information about the atomization mechanism of the analyte element beyond a few data-points located near the very beginning of the absorbance signal profile. These plots are non-linear if they are drawn with data points near the maximum of the absorbance signal profile. This paper presents two Arrhenius-type equations which give linear plots over a long range of data-points, and hence reliable values for the activation energy. Also, a simple method is proposed for calculating the activation energy from the data-points anywhere from the initial appearance of the absorbance signal to its maximum. Activation energy values given by these two equations and by the method of calculation are compared with each other and with those given by the commonly used methods. The calculated activation energy values obtained can be used to verify those obtained experimentally. The three proposed methods also provide reliable kinetic information on atom-formation reactions in GFAAS. A mechanism for the atomization of copper, based on the experimentally determined activation energy and reaction order is proposed.     

Dual Upconverted and Downconverted Circularly Polarized Luminescence in Donor–Acceptor Assemblies

Through mimicking both the chiral and energy transfer in an artificial self‐assembled system, not only was chiral transfer realized but also a dual upconverted and downconverted energy transfer system was created that emit circularly polarized luminescence. The individual chiral π‐gelator can self‐assemble into a nanofiber exhibiting supramolecular chirality and circularly polarized luminescence (CPL). In the presence of an achiral sensitizer Pd^II octaethylporphyrin derivative, both chirality transfer from chiral gelator to achiral sensitizer and triplet‐triplet energy transfer from excited sensitizer to chiral gelator could be realized. Upconverted CPL could be observed through a triplet–triplet annihilation photon upconversion (TTA‐UC), while downconverted CPL could be obtained from chirality‐transfer‐induced emission of the achiral sensitizer. The interplay between chiral energy acceptor and achiral sensitizer promoted the communication of chiral and excited energy information.     

Localization and coherent dynamics of excitons in the two-dimensional optical spectrum of molecular J-aggregates

Two-dimensional optical spectra of J-aggregates at low temperature provide a large amount of information about the nature and dynamics of exciton states that is hidden in conventional broad band pump-probe spectra. By using numerical simulations, we study the two-dimensional absorption spectrum and find that it is dominated by a V-shaped negative peak and a blueshifted elliptic positive peak. We demonstrate a simple method to derive the energy dependence of the exciton localization size from the distance between these two features in the zero waiting time experiment. When the waiting time is turned on, the V peak is filled with an extra positive peak resulting from population relaxation. From the time evolution of this peak, energy dependent relaxation rates can be obtained. The oscillations of coherent contributions to the two-dimensional spectrum are not damped by inhomogeneous mechanisms and can be seen clearly.     

Optical rotatory dispersion of indoline alkaloids with keto groups

The optical rotatory dispersion curves of a series of indolines, N(a)-acetyl-indolines and N(a)-methoxycarbonyl-indolines containing keto groups have been measured. It has been shown that the absolute stereochemistry of N(a)-acetyl-indolines containing keto groups can still be determined from the character of the Cotton Effect due to the aromatic chromophore, the ketone Cotton Effect however being more difficult to interpret. The use of N(a)-methoxycarbonyl-indoline and indoline chromophores is dangerous due to the complex nature of the Cotton Effect of the former and the overlapping of that of the latter with the ketone Cotton Effect.     

Nuclear magnetic resonance studies on microstructure of ethylene copolymers. VI. Carbon-13 spectra of ethylene–vinyl acetate copolymers

The 22.6-MHz Fourier-transform noise-decoupled ¹³C (carbon-13) NMR spectra of several ethylene–vinyl acetate (E–VA) copolymers were obtained. We found that triad information on monomer placement can be deduced from carbonyl resonances, triad and pentad information can be deduced from methine carbon resonances, and triad information is available from the methylene carbon resonances. The random comonomer distributions in E–VA polymerizations were demonstrated up to pentad placements. In addition, the use of model-compound data in the analysis of copolymer spectra was shown.     

Surface Tension Calculations for Liquid Metals

Abstract

We present a class of models for the surface of a liquid metal, which may be part of an electrochemical interface. The particles of the system, for the purpose of derivation of thermodynamic properties, are the charged ion cores, while the energy of the electrons is evaluated using the electron density functional formalism, previously principally applied to solids. An expression for the surface energy U^s , defined as the energy required to create unit area of surface by separation of a volume of homogeneous metal into two parts, is derived (Eqs. 18–20). The surface tension γ is obtained by differentiating the Helmholtz free energy with respect to the area of the system, keeping volume and particle number constant (Eqs. 27–37). The surface tension is also equal to the difference between the free energy of the system containing a surface and the free energy of a reference system. It thus defines a surface energy through the Gibbs-Helmholtz equation, and this surface energy is shown to be identical to U^s .

The expressions for U^s and γ are made explicit (Eqs. 45–57) by insertion of particular assumptions for the ion-density profile, the electron-density profile, the interionic interaction and pair distribution function, and the electronic energy. Only information about bulk liquid metal is used. The parameter in the electron-density profile is obtained by minimizing the surface energy. The simplest assumption for the interionic interaction, hard-sphere and Coulombic repulsions, requires a choice for the hard-sphere diameter, which is made such that the pressure of bulk metals is given correctly (52–55). For the alkali metals, the surface tension calculated from this model is about half the experimental value in each case, while calculated surface energies are too high (1/5 too high for Cs, but three times too high for Li). For the electrical potential difference between the inside and the outside of a metal, and for the electrochemical potential, agreement with experiment is good. The main reason for the disagreements in the other properties is traced to the simple form used for the ion pair distribution function.     

Synthesis and Rheological Investigation ofModel Symmetric 3-Arm Star Polyethylene简

A variety of linear and 3-arm star polyethylene （PE） model polymers covering a wide range of molecular weight are synthesized by the living polymerization of butadiene and the subsequent hydrogenation. Several rheological parameters of these model linear and 3-arm star PE samples are analyzed for detecting the long chain branching （LCB） structure. It is found that the analyses based on zero shear viscosity, vGP plot and flow activation energy are very sensitive to the 3-arm star PEs. The information on the presence of LCB can be obtained with these methods even for low molecular weight samples, which can not be determined by GPC-MALLS. However the information about the LCB structure can not be obtained by the rheological methods alone.     

Remarks on detecting high-energy deuterium–tritium fusion gamma rays using a gas Cherenkov detector

As fusion ignition conditions are approached using the national ignition facility (NIF), independent high-bandwidth gamma-ray fusion burn measurements become essential complements to information obtained from neutron diagnostics. The 16.75-MeV gamma rays that accompany deuterium–tritium (d+t) fusion can be detected using a high-bandwidth gaseous carbon dioxide Cherenkov threshold detector. The detection energy threshold was set by the CO₂ gas pressure. A 1-GHz detector system was fielded successfully at the Omega laser facility, demonstrating unambiguous detection of high-energy fusion gamma rays from high-yield d+t implosions. An experiment to detect the ∼12.5 MeV d–t fusion gamma ray is described.     

Electronic states and structural stability of supported Au clusters

The quantized energy levels of electrons in supported nanometer-size Au clusters have been resolved at room temperature using field emission techniques. By studying the time dependence of the electron emission current from an individual supported cluster, information about the structural stability of the cluster can also be obtained. Studies show abrupt jumps between different emission rates that are revisited as time progresses. This phenomenon can be attributed to a rearrangement of the cluster structure and/or orientation on the substrate and provides new evidence of multiple ‘isomeric’ structures for small clusters of metallic atoms.     

An algorithm for geometry optimization without analytical gradients

A numerical algorithm for locating both minima and transition states designed for use in the ab initio program package GAUSSIAN 82 is presented. It is based on the RFO method of Simons and coworkers and is effectively the numerical version of an analytical algorithm (OPT = EF) previously published in this journal. The algorithm is designed to make maximum use of external second derivative information obtained from prior optimizations at lower levels of theory. It can be used with any wave function for which an energy can be calculated and is about two to three times faster than the default DFP algorithm (OPT = FP) supplied with GAUSSIAN 82.