Theory of projected probabilities on non-orthogonal states: Application to electronic populations in molecules

Often it is important to consider the expansion of a quantum state ) in terms of physically meaningful basis states. For example, molecular orbitals can be expressed as linear combinations of atomic orbitals, or vibrational states can be expressed as super positions of local or normal mode eigenstates. In such expansions, it then becomes desirable to determine how much character a quantum state has in one of these basis states. One way of accimplishing this task is to calculate the projected probability of |) on basis state |j). In this paper, we consider this general quantum mechanical problem. If the basis states are orthonormal, then the projected probability of|) on |j) is of course |<|j>|². However, if the basis states are not orthogonal, then this result is no longer valid and one must develop a more general theory to calculate these projected probabilities. An earlier paper used one-dimensional projection operators to initiate this theory and gave closed form results for the case of two non-orthogonal basis states [1]. One- and many-dimensional projection operators, together with linear algebraic techniques, are used to extend this theory to the n non-orthogonal basis state case. Explicit closed form results are given for the two- and three-state cases, and a general algorithm is developed for the case of four or more basis states. Application of the theory is made to atomic populations in three- to six-atom molecules, and comparisons are made to the related work of Mulliken.     

Mass spectra of esters of α-hydroxy and α-methoxy acids

The most abundant fragment produced by electron bombardment of esters of the type R¹R²C(OR³)CO₂R⁴ is the R¹R²C = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm O}\limits^{{\rm + } \cdot } $\end{document}R³ ion. Methyl glycollate (R¹ = R² = R³ = H, R⁴ = Me) eliminates the HCO˙ radical by a complex rearrangement involving the methylenic hydrogen atoms. The methyl and ethyl esters of methoxyacetic acid (R¹ = R² = H, R³ = Me, R⁴ = Me or Et) eliminate formaldehyde by the McLafferty rearrangement.     

Determination of anions in landfill leachates by ion chromatography

Ion chromatography has been used to determine inorganic and organic anions within landfill leachates. Two procedures are operated on split samples which have multiple dilutions and vary in sample treatment: gradient ion-exchange chromatography for inorganic anions and isocratic ion-exclusion chromatography for organic anions. Interference between carbonate and organic acid anions using ion-exclusion chromatography is avoided by treatment with octanesulphonic acid eluent. Using ion-exchange chromatography, the presence of valerate, hexanoate and heptanoate is checked (but not quantified) for a subsample which has been treated to remove chloride; these species are then determined by ion-exclusion chromatography. Analysis of certified standards (10 mg/1 certified VFA standard; Supelco, Bellefonte, PA, USA; 20–150 mg/l inorganic anions, ICMIX1-100, Glen Spectra Reference Materials, Middlesex, UK) gives good agreement (within 5% for organic anions except formate, and within 1% for inorganic anions), with R.S.D. values for all anionic species varying from 0.44–2.23.     

Spectrophotometric methods for the determination of osmium-I Extraction and ultraviolet spectrophotometric determination of osmium tetroxide

An ultraviolet spectrophotometric method is presented for the détermination of milligram quantities of osmium in solutions of uranyl sulphate. Osmium is first oxidised to the octovalent state and the osmium tetroxide which is formed, is selectively extracted with chloroform. The ultraviolet absorption spectrum'of osmium tetroxide in chloroform has a series of absorption bands with peak absorbancies at 282, 289, 297, 304 and 312 mμ and molar absorbancy indexes of 1870, 1760,1640, 1400 and 1000, respectively. For each wavelength, the optimum concentration range for the determination of osmium was evaluated. From 0.4 to 3.3 mg of osmium can be determined with a coefficient of variation of 3%. Of the elements tested only chloride and octovalent ruthenium interfere; however, both of these interferences can be eliminated.     

Spectrophotometric methods for the determination of osmium-II Extraction and determination of osmium in situ with 1.5-diphenylcarbohydrazide

A method has been developed for the spectrophotometric determination of microgram quantities of osmium in uranyl sulphate solutions. The osmium is oxidised to osmium tetroxide, then extracted with chloroform. The extracts are added to an ethanolic solution of 1:5-diphenylcarbohydrazide. A blue-violet coloured reaction product is formed which exhibits maximum absorbancy at 560 mμ. After a period of 2 hr for colour development the molar absorbancy index is about 31,000. Beer's law is adhered to over a range of 30 to 100 μg of osmium with a coefficient of variation of about 4%. A study was made of the effects of foreign substances and only chloride and octovalent ruthenium were found to interfere. Both of these interfering ions can be eliminated.     

Dissociation and ionization effects in atomic absorption spectrochemical analysis

Use of a nitrous oxide-acetylene flame in atomic absorption spectrophotometry reduces or eliminates certain chemical interferences that have been observed in cooler flames. However, ionization increases with temperature, and is significant for some elements in the nitrous oxide-acetylene flame. Ionization can be reduced by adding an easily ionized metal (e.g. alkali metal) to the solution. Elements likely to be determined using the nitrous oxide-acetylene flame which will be significantly ionized are: Al, Ba, Ti, V, Zr, Hf, Nb, Sc, Y, the lanthanides and the actinides. The ionization of an element in the nitrous oxide-acetylene flame can be readily calculated by taking absorption readings, provided that relatively sensitive atom and ion resonance lines are available. This technique possibly could be used to establish ionization potentials or partition functions of those lanthanide elements that are not now well known.     

THE AVAILABILITY OF SOLAR RADIATION BELOW 290 nm AND ITS IMPORTANCE IN PHOTOMODIFICATION OF POLYMERS

Abstract— On a percentage basis, ozone is a very minor component of the atmosphere; at STP it would make a layer only about 2 mm thick. On almost every other basis (biological, meteorological, paleontological, photochemical, etc.) it is a major component, due mainly to the tremendous reduction in solar ultraviolet flux which it causes in the 220–290 nm region. Since no data are available for Λ < 285 nm, a rational basis for estimating the flux reaching the earth's surface in this region is discussed. Variations in ozone concentration are of great importance, and it is possible to have more radiation with Λ < 270 nm fall on a surface in one extreme day than in several years of typical days. Often, persons involved in studies of polymer degradation by sunlight mention that a negligible fraction (1 ppm) of the radiant flux reaching the earth's surface is associated with wavelengths below 290 nm and infer that studies at shorter wavelengths will not be of much practical value. Such inferences are questionable for at least two reasons. (1) The quantum flux density below 290 nm is about 10¹⁶ photons cm^-2 month^-1, so that considerable long-term damage is possible since most of the flux will be absorbed in a layer only a few microns thick. (2) Even if solar radiation below 290 nm were completely absent, the existence of correlations between absorption peaks in the near ultraviolet and visible, and in the infrared with ionization potentials typically 6–12 eV or 200-100 nm) is evidence that we may expect studies in the ultraviolet and extreme ultraviolet (EUV) to provide important clues to the problem of improving the resistance of polymers to sunlight.     

EFFECT OF ULTRAVIOLET RADIATION ON THE ENERGY METABOLISM OF THE CORNEAL EPITHELIUM OF THE RABBIT

The present research was directed at quantifying possible alterations in corneal epithelial metabolic activity secondary to in vivo exposure to ultraviolet radiation (UVR). Microfluorometric energy metabolite assays on microgram (microgram) sized, freeze-dried tissue samples were used as an in vitro means of assessing overall metabolic activity in the epithelium of control rabbit corneas and in the epithelium of UVR-exposed rabbit corneas 2 min after discontinuation of exposure. The specific assays were for glucose, glycogen, adenosine triphosphate (ATP), and phosphocreatine (PCr). The radiant exposures were kept constant at 0.05 J cm-2 for all UVR wavelengths utilized (290, 300, 310 and 360 nm). Experimental UVR exposure conditions served to increase epithelial glucose and glycogen concentrations. Although the epithelial ATP concentrations were unchanged, the epithelial PCr concentrations (a high energy phosphate bond reservoir) decreased as a result of UVR exposure. Overall, the data demonstrate a decrease in corneal epithelial metabolic activity, which may be wavelength-dependent, as a result of UVR exposure. It is suggested that immediate metabolic stress can be responsible for the pattern of epithelial cell loss seen in photokeratitis.