Photochemical Reactions in Oriented Systems

Modification of chemical reactions through the use of constrained and/or organized media has attracted a great deal of attention recently. Results from our laboratory in this direction which include a study of photochemical reactions in solid state and in cyclodextrins are presented here. A study of solid state photochemical behavior of coumarins has provided information regarding subtler aspects of topochemical postulates of photodimerization. Results pertaining to geometrical criteria for photodimerization and "chloro" as a crystal engineering group are discussed. As a part of an attempt to correlate chemical reactivity with molecular packing in the solid state, photooxidation of diarylthioketones in the solid state has been investigated. The observed differences in the reactivity of these crystals are rationalized in terms of crystal packing. Though cyclodextrins have been extensively studied, very few photochemical reactions involving molecules complexed to cyclodextrins have been examined. In this connection, the utility of cyclodextrins in bringing about selectivity in photochemical reactions through the study of excited state behavior of olefins and aryl alkyl ketones has been demonstrated in our laboratory.

A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

X-ray studies on crystalline complexes involving amino acids. IV. The structure of L-arginine L-ascorbate

L-Arginine ascorbate, C6HIsN40+.C6H706, a 1"1 crystalline complex between the amino acid arginineand the vitamin ascorbic acid, crystallizes in the monoclinic space group P21 with two formula units in a cell of dimensions a = 5.060 (8), b = 9.977 (9), c = 15.330 (13) A, fl = 97.5 (2) °. The structure was solved by the symbolic addition procedure and refined to an R of 0.067 for 1501 photographically observed reflec- tions. The conformation of the arginine molecule in the structure is different from any observed so far. The present structure provides the first description of the ascorbate anion unaffected by the geometrical constraints and disturbances imposed by the requirements of metal coordination. The lactone group and the deprotonated enediol group in the anion are planar and the side chain assumes a conformation which appears to be sterically the most favourable. In the crystals, the arginine molecules and the ascorbate anions aggregate separately into alternating layers. The molecules in the arginine layer are held together by interactions involving a-amino and ~t-carboxylate groups, a situation analogous to that found in proteins. The two layers of unlike molecules are interconnected primarily through the interactions of the side-chain guanidyl group of arginine with the ascorbate ion. These involve a specific ion-pair interaction accompanied by two convergent hydrogen bonds and another pair of nearly parallel hydrogen bonds.

Structural phase transition study of the morphotropic phase boundary compositions of Na0.5Bi0.5TiO3-PbTiO3

Neutron, synchrotron x-ray powder diffraction and dielectric studies have been performed for morphotropic phase boundary (MPB) compositions of the (1 - x )Na1/2Bi1/2TiO3-xPbTiO(3) system. At room temperature, the MPB compositions (0.10 < x <= 0.15) consist of a mixture of rhombohedral (space group R3c) and tetragonal ( space group P4mm) structures with the fraction of tetragonal phase increasing with increasing PbTiO3 content. On heating, while the rhombohedral phase just outside the MPB region, i.e. x = 0.10, transforms directly to a cubic phase, the rhombohedral phase of the MPB compositions transforms gradually to a tetragonal phase, until interrupted by a rhombohedral-cubic phase transition. The correspondence of the dielectric anomalies with the structural transitions of the different compositions has been examined and compared with earlier reports.

Wave analysis of sound decay in rectangular rooms

The decay of sound in a rectangular room is analyzed for various boundary conditions on one of its walls. It is shown that the decay of the sound-intensity level is in general nonlinear. But for specific areas and impedances of the material it is possible to obtain a linear initial decay. It is also shown that the coefficients derived from the initial decay rates neither correspond to the predictions of Sabine's or Eyring's geometrical theories nor to the normal coefficients of Morse's wave theory. The dependence of the coefficients on the area of the material is discussed. The influence of the real and the imaginary parts of the specific acoustic impedance of the material on the coefficients is also discussed. Finally, the existence of a linear initial decay corresponding to the decay of a diffuse field in the case of a highly absorbing material partially covering a wall is explained on the basis of modal coupling.

A note on the application of a radiation condition for a source in a rotating stratified fluid

The motion due to an oscillatory point source in a rotating stratified fluid has been studied by Sarma & Naidu (1972) by using threefold Fourier transforms. The solution obtained by them in the hyperbolic case is wrong since they did not make use of any radiation condition, which is always necessary to get the correct solution. Whenever the motion is created by a source, the condition of radiation is that the sources must remain sources, not sinks of energy and no energy may be radiated from infinity into the prescribed singularities of the field. The purpose of the present note is to explain how Lighthill's (1960) radiation condition can be applied in the hyperbolic case to pick the correct solution. Further, the solution thus obtained is reiterated by an alternative procedure using Sommerfeld's (1964) radiation condition.

Computational Studies on Bimetallic Clusters

The chemical and physical properties of bimetallic clusters have attracted considerable attention due to the potential technological applications of mixed-metal systems. It is of fundamental interests to study clusters because they are the link between atomic surface and bulk properties. More information of metal-metal bond in small clusters can be hence released. The studies in my thesis mainly focus on the two different kinds of bimetallic clusters: the clusters consisting of extraordinary shaped all metal four-membered rings and a series of sodium auride clusters. As described in most general organic chemistry books nowadays, a group of compounds are classified as aromatic compounds because of their remarkable stabilities, particular geometrical and energetic properties and so on. The notation of aromaticity is essentially qualitative. More recently, the connection has been made between aromaticity and energetic and magnetic properties. Also, the discussions of the aromatic nature of molecular rings are no longer limited to organic compounds obeying the Hückel’s rule. In our research, we mainly applied the GIMIC method to several bimetallic clusters at the CCSD level, and compared the results with those obtained by using chemical shift based methods. The magnetically induced ring currents can be generated easily by employing GIMIC method, and the nature of aromaticity for each system can be therefore clarified. We performed intensive quantum chemical calculations to explore the characters of the anionic sodium auride clusters and the corresponding neutral clusters since it has been fascinating in investigating molecules with gold atom involved due to its distinctive physical and chemical properties. As small gold clusters, the sodium auride clusters seem to form planar structures. With the addition of a negative charge, the gold atom in anionic clusters prefers to carry the charge and orients itself away from other gold atoms. As a result, the energetically lowest isomer for an anionic cluster is distinguished from the one for the corresponding neutral cluster. Mostly importantly, we presented a comprehensive strategy of ab initio applications to computationally implement the experimental photoelectron spectra.

Structure of a new crystal form of 2-{[3-(trifluoromethyl)phenyl]amino}benzoic acid (flufenamic acid)

C14Ht0F3NO2, P2.Jc, a = 12.523 (4), b = 7.868(6), c = 12.874 (3)A, fl = 95.2 (2) ° , O,,, = 1.47 (4), D e = 1.47 Mg m -3, Z = 4. Final R = 0.074 for 2255 observed reflections. The carboxyl group and the phenyl ring bearing the carboxyl group are nearly coplanar whereas the two phenyl rings are inclined with respect to each other at 52.8 ° . The difference between the two polymorphs of flufenamic acid lies in the geometrical disposition of the [3-(trifluoromethyl)- phenyl]amino moiety with respect to the benzoic acid moiety. As in other fenamate structures, the carboxyl group and the imino N atom are connected through an intramolecular hydrogen bond; also, pairs of centrosymmetrically related molecules are connected through hydrogen bonds involving carboxyl groups.

Uniformity of film thickness on rotating planetary planar substrates

For the purposes of obtaining a number of components with nearly identical thickness distributions over the substrate area and of minimizing the inhomogeneities of the film, it is logical to presume that a substrate rotating on its own axis and revolving around another axis will give more uniformity in film thickness than a substrate only revolving around one axis. In relation to the practical applications, an investigation has been undertaken to study the refinement that can be achieved by using a planar planetary substrate holder. It is shown theoretically that the use of the planetary substrate holder under ideal conditions of source and geometry does not offer any further improvement in uniformity of thickness over the conventional rotary work-holder. It is also shown that the geometrical parameters alone have little influence over the uniformity achieved on a planetary substrate, because of the complex cyclidal motion of any point on it. However, for any given geometry, a non-integral speed ratio of the planetary substrate and the work-holder shows considerably less variation in thickness over the substrate area.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Radiative transfer, interception and scattering in coniferous forests : models and applications for production ecology and remote sensing

This work develops methods to account for shoot structure in models of coniferous canopy radiative transfer. Shoot structure, as it varies along the light gradient inside canopy, affects the efficiency of light interception per unit needle area, foliage biomass, or foliage nitrogen. The clumping of needles in the shoot volume also causes a notable amount of multiple scattering of light within coniferous shoots. The effect of shoot structure on light interception is treated in the context of canopy level photosynthesis and resource use models, and the phenomenon of within-shoot multiple scattering in the context of physical canopy reflectance models for remote sensing purposes. Light interception. A method for estimating the amount of PAR (Photosynthetically Active Radiation) intercepted by a conifer shoot is presented. The method combines modelling of the directional distribution of radiation above canopy, fish-eye photographs taken at shoot locations to measure canopy gap fraction, and geometrical measurements of shoot orientation and structure. Data on light availability, shoot and needle structure and nitrogen content has been collected from canopies of Pacific silver fir (Abies amabilis (Dougl.) Forbes) and Norway spruce (Picea abies (L.) Karst.). Shoot structure acclimated to light gradient inside canopy so that more shaded shoots have better light interception efficiency. Light interception efficiency of shoots varied about two-fold per needle area, about four-fold per needle dry mass, and about five-fold per nitrogen content. Comparison of fertilized and control stands of Norway spruce indicated that light interception efficiency is not greatly affected by fertilization. Light scattering. Structure of coniferous shoots gives rise to multiple scattering of light between the needles of the shoot. Using geometric models of shoots, multiple scattering was studied by photon tracing simulations. Based on simulation results, the dependence of the scattering coefficient of shoot from the scattering coefficient of needles is shown to follow a simple one-parameter model. The single parameter, termed the recollision probability, describes the level of clumping of the needles in the shoot, is wavelength independent, and can be connected to previously used clumping indices. By using the recollision probability to correct for the within-shoot multiple scattering, canopy radiative transfer models which have used leaves as basic elements can use shoots as basic elements, and thus be applied for coniferous forests. Preliminary testing of this approach seems to explain, at least partially, why coniferous forests appear darker than broadleaved forests in satellite data.

Wave analysis of sound decay in rectangular rooms

The decay of sound in a rectangular room is analyzed for various boundary conditions on one of its walls. It is shown that the decay of the sound-intensity level is in general nonlinear. But for specific areas and impedances of the material it is possible to obtain a linear initial decay. It is also shown that the coefficients derived from the initial decay rates neither correspond to the predictions of Sabine's or Eyring's geometrical theories nor to the normal coefficients of Morse's wave theory. The dependence of the coefficients on the area of the material is discussed. The influence of the real and the imaginary parts of the specific acoustic impedance of the material on the coefficients is also discussed. Finally, the existence of a linear initial decay corresponding to the decay of a diffuse field in the case of a highly absorbing material partially covering a wall is explained on the basis of modal coupling.

Characteristics of Proportional Weirs

A theorem termed the Geometrical Continuity Theorem is enunciated and proven. This theorem throws light on the aspects of the continuity of the proportional portion with the base weir portion. These two portions constitute the profile of a proportional weir. A weir of this type with circular bottom is designed. The theorem is used to establish the continuity at the junction of the proportional and the base weir portions of this weir. The coordinates of the weir profile are obtained by numerical methods and are furnished in tabular form for ready use by designers. The discharge passing through the weir is a linear function of the head. The verification of the assumed linear discharge-head relation is furnished for one of the three weirs with which experiments were conducted. The coefficient of discharge for this typical weir is found to be a constant with a value of 0.59.

Fourier transform of the collagen triple-helical structure and its significance

The Fourier transforms of the collagen molecular structure have been calculated taking into consideration various side chain atoms, as well as the presence of bound water molecules. There is no significant change in the calculated intensity distribution on including the side chain atoms of non-imino-acid residues. Taking into account the presence of about two bound water molecules per tripeptide unit, the agreement with the observed x-ray pattern is slightly improved. Fourier transforms have also been calculated for the detailed molecular geometries proposed from other laboratories. It is found that there are no major differences between them, as compared to our structure, either in the positions of peak intensity or in the intensity distribution. Hence it is not possible to judge the relative merits of the various molecular geometries for the collagen triple helix from a comparison of the calculated transforms with the meagre data available from its x-ray fibre pattern. It is also concluded that the collagen molecular structure should be regarded as a somewhat flexible chain structure, capable of adapting itself to the requirements of the different side groups which occur in each local region.

The structure of phosphacymantrene

Proton NMR spectra of phosphacymantrene (π-phospholyl manganese tricarbonyl) orientated in the nematic phases of liquid crystals have been investigated. The derived H-H and H-P direct dipolar coupling constants have been used to determine the relative proton-proton and proton-phosphorus distances. A comparison of the geometrical data of various 5-membered aromatic heterocycles shows that the relative distances between the protons closest to the heteroatom increase with the van der Waals radius of the heteroatom. The results suggest that NMR spectroscopy of orientated molecules can be used to determine van der Waals radii.