Angular Momentum and Euler Angle Conventions in Molecular Spectroscopy

Abstract

Although the theory of angular momentum is treated in almost every textbook on quantum mechanics and molecular spectroscopy, problems are always experienced-especially by the beginner-when formulas from various books and papers are compared. During a survey of all the available relevant textbooks and papers which deal with angular momentum, it was realized that the majority of them can be ordered into two main groups of conventions with two sub classifications each. It is the object of this paper to present these conventions in an unambiguous fashion and to display the relevant formulas in order to facilitate comparisons between various textbooks. However, almost no attention is given to describing the theory of angular momentum, and the textbooks cited below should be consulted for the theoretical background.     

Consistency of the preoperative and intraoperative diagnosis of benign vocal fold lesions

The purpose of this retrospective study was to compare the preoperative and intraoperative diagnosis of benign vocal fold lesions for consistency. The diagnosis was made in 221 consecutive patients with benign vocal fold lesions for which a microlaryngoscopy was carried out in a general ENT-clinic. The preoperative diagnosis was obtained by both white halogen and stroboscopic light. The intraoperative diagnosis was obtained by direct microscopic visualization and palpation of the vocal folds. In 36% of the patients, the preoperative diagnosis was changed intraoperatively. In 31% of the patients, a lesion was missed at the preoperative examination and a lesion was diagnosed only during microlaryngoscopy. Bilateral lesions were found in 53% of the patients preoperatively, and in 82% of the patients intraoperatively. Specially intracordal lesions constituted a diagnostic pitfall. Because the preoperative and intraoperative diagnosis often differed, both the patients and the ENT-surgeon must keep an open mind about what may need to be done at surgery.     

Poly(silarylene–siloxane)polyimides from allyl‐terminated oligoimides and hydride‐functional silarylene–siloxanes via hydrosilylation polymerization

This research was focused on the design and execution of new synthetic routes to low‐temperature‐curable poly(silarylene–siloxane)polyimides. The synthesis of individual oligoimide and silarylene–siloxane blocks was followed by hydrosilylation polymerization to produce crosslinked copolymers. The silarylene–siloxane and polyimide blocks were structurally characterized by IR and ¹H NMR spectroscopy and size exclusion chromatography. The high‐temperature resistance of the copolymers was evaluated through the measurement of heat distortion temperatures (T_HD's) via thermomechanical analysis and by the determination of the weight loss at elevated temperatures via thermogravimetric analysis. Glass‐transition temperatures (T_g's) of the silarylene–siloxane segments were measured by differential scanning calorimetry. Hydrosilylation curing was conducted at 60 °C in the presence of chloroplatinic acid (H₂PtCl₆). The copolymers displayed both high‐temperature resistance and low‐temperature flexibility. We observed T_g of the silarylene–siloxane segment as low as ?77 °C and T_HD of the polyimide segment as high as 323 °C. The influence of various oligoimide molecular weights on the properties of copolymers containing the same silarylene–siloxane was examined. The effect of various silarylene–siloxane molecular weights on the properties of copolymers containing the same oligoimide was also examined. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4922–4932, 2005     

Preparative routes to luminescent mixed-ligand rhenium(I) dicarbonyl complexes

A series of mixed-ligand 2,2'-bipyridine (bpy) and 1,10-phenanthroline (phen) rhenium(I) dicarbonyl complexes that are emissive in fluid solution has been prepared, which includes a new class of the type cis-[Re(CO)2(P-P)(N-N)]+ (where P-P is a chelating diphosphine and N-N is a chelating polypyridine ligand). The four synthetic routes that have been developed rely on either reactive triflate displacement or abstraction of labile chloro ligands, followed by the use of the strong trans-labilizing effect of P donors or direct use of the trans effect of P donors. The spectroscopic, photophysical, and electrochemical properties of these new complexes systematically vary with the net donor ability of the ligands in the coordination sphere, as shown by correlations with Lever's E(L) parameters. Lifetimes and quantum yields of the bipyridine complexes encompass a broad range, 25-1147 ns and ca. 0.002-0.11, respectively.     

Membranous and cartilaginous vocal fold adduction in singing

While vocal fold adduction is an important parameter in speech, relatively little has been known on the adjustment of the vocal fold adduction in singing. This study investigates the possibility of separate adjustments of cartilaginous and membranous vocal fold adduction in singing. Six female and seven male subjects, singers and non-singers, were asked to imitate an instructor in producing four phonation types: "aBducted falsetto" (FaB), "aDducted falsetto" (FaD), "aBducted Chest" (CaB), and "aDducted Chest" (CaD). The phonations were evaluated using videostroboscopy, videokymography (VKG), electroglottography (EGG), and audio recordings. All the subjects showed less posterior (cartilaginous) vocal fold adduction in phonation types FaB and CaB than in FaD and CaD, and less membranous vocal fold adduction (smaller closed quotient) in FaB and FaD than in CaB and CaD. The findings indicate that the exercises enabled the singers to separately manipulate (a) cartilaginous adduction and (b) membranous medialization of the glottis though vocal fold bulging. Membranous adduction (monitored via videokymographic closed quotient) was influenced by both membranous medialization and cartilaginous adduction. Individual control over these types of vocal fold adjustments allows singers to create different vocal timbres.     

Synthese und Charakterisierung neuer intramolekular stickstoffstabilisierter Organoaluminium‐ und Organogalliumalkoxide

Synthesis and Characterization of New Intramolecularly Nitrogen‐stabilized Organoaluminium‐ and Organogallium Alkoxides The intramolecularly nitrogen stabilized organoaluminium alkoxides [Me₂Al{μ‐O(CH₂)₃NMe₂}]₂ ( 1a ), Me₂AlOC₆H₂(CH₂NMe₂)₃‐2,4,6 ( 2a ), [(S)‐Me₂Al{μ‐OCH₂CH(i‐Pr)NH‐i‐Pr}]₂ ( 3a ) and [(S)‐Me₂Al{μ‐OCH₂CH(i‐Pr)NHCH₂Ph}]₂ ( 4 ) are formed by reacting equimolar amounts of AlMe₃ and Me₂N(CH₂)₃OH, C₆H₂[(CH₂NMe₂)₃‐2,4,6]OH, (S)‐i‐PrNHCH(i‐Pr)CH₂OH, or (S)‐PhCH₂NHCH(i‐Pr)CH₂OH, respectively. An excess of AlMe₃ reacts with Me₂N(CH₂)₂OH, Me₂N(CH₂)₃OH, C₆H₂[(CH₂NMe₂)₃‐2,4,6]OH, and (S)‐i‐PrNHCH(i‐Pr)CH₂OH producing the “pick‐a‐back” complexes [Me₂AlO(CH₂)₂NMe₂](AlMe₃) ( 5 ), [Me₂AlO(CH₂)₃NMe₂](AlMe₃) ( 1b ), [Me₂AlOC₆H₂(CH₂NMe₂)₃‐2,4,6](AlMe₃)₂ ( 2b ), and [(S)‐Me₂AlOCH₂CH(i‐Pr)NH‐i‐Pr](AlMe₃) ( 3b ), respectively. The mixed alkyl‐ or alkenylchloroaluminium alkoxides [Me(Cl)Al{μ‐O(CH₂)₂NMe₂}]₂ ( 6 ) and [{CH₂=C(CH₃)}(Cl)Al{μ‐O(CH₂)₂NMe₂}]₂ ( 8 ) are to obtain from Me₂AlCl and Me₂N(CH₂)₂OH and from [Cl₂Al{μ‐O(CH₂)₂NMe₂}]₂ ( 7 ) and CH₂=C(CH₃)MgBr, respectively. The analogous dimethylgallium alkoxides [Me₂Ga{μ‐O(CH₂)₃NMe₂}]₂ ( 9 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)NH‐i‐Pr}]_n ( 10 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)NHCH₂Ph}]_n ( 11 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)N(Me)CH₂Ph}]_n ( 12 ) and [(S)‐Me₂Ga{μ‐OCH₂(C₄H₇NHCH₂Ph)}]_n ( 13 ) result from the equimolar reactions of GaMe₃ with the corresponding alcohols. The new compounds were characterized by elemental analyses, ¹H‐, ¹³C‐ and ²⁷Al‐NMR spectroscopy, and mass spectrometry. Additionally, the structures of 1a , 1b , 2a , 2b , 3a , 5 , 6 and 8 were determined by single crystal X‐ray diffraction.     

Low-temperature infrared and raman studies: XI. The vibrational behaviour of ammonium perchlorate- its phase changes and the rotational freedom of its ions

An infrared, Raman and X-ray diffraction study on NH₄CIO₄. was conducted in the temperature ranges 300 to 17 °K, 300 to 130 °K and 300 to 120 °K respectively. The infrared studies also included the deuterated salt. The spectra are discussed and vibrational assignments made. Changes in the infrared spectra, as well as intensity measurements of the vibrational bands indicate anomalous behaviour in the region 100–110 °K as well as 17–50 °K. Possible reasons for these changes are proposed. The rotational behaviour of the ammonium ion upon cooling and hydrogen bonding are discussed.     

Measurement of formant frequencies and bandwidths in singing

That singers under certain circumstances adjust the articulation of the vocal tract (formant tuning) to enhance acoustic output is both apparent from measurements and understood in theory. The precise effect of a formant on an approaching (retreating) harmonic as the latter varies in frequency during actual singing, however, is difficult to isolate. In this study variations in amplitude of radiated sound components as well as supraglottal and subglottal (esophageal) pressures accompanying the vibrato-related sweep of voice harmonics were used as a basis for estimating the effective center frequencies and bandwidths of the first and second formants.     

On the relation between the dimensions and resonance characteristics of the vocal tract: a study with MRI.

The relation between the spatial configuration of the vocal tract as determined by magnetic resonance imaging (MRI) and the acoustical signal produced was investigated. A male subject carried out a set of phonatory tasks, comprising the utterance of the sustained vowels /i/ and /a/, each in a single articulation, and the vowel /epsilon/ with his larynx positioned variously on a vertical axis. Two- and three-dimensional measurements of the vocal tract were performed. The results of these measurements were used to calculate resonance frequencies, according to predictions from acoustical theory. Finally, calculated frequencies were compared with actually measured resonance frequencies in the audio signal. We found a strong relation between the acoustical signal produced and the spatial configuration for the first resonance frequencies of the articulations of the vowel /epsilon/, and first two resonance frequencies of the vowels /a/ and /i/. The capability to determine accurately vocal tract dimensions is a major advantage of this imaging technique.