Projection angles

Renders-Person, G., An Improved Equation for Calculating Fragment Projection Angles, Proceedings of the Second International Symposium on Ballistics, American Defense Preparedness Association, 1975. 

Cross-Correlated Relaxation for the Measurement of Projection Angles between Tensors I 161... 

The characterisation of the angular dependence of the interaction of two dipole tensors A1 A2 and B B2 is therefore straightforward, namely it depends on the projection angle of the two bonds between A1 and A2 and between B1 and B2. The orientation and magnitude of the chemical shift anisotropy (CSA) tensor, which also can cause cross-correlated relaxation, is not know a priori and therefore needs to be determined experimentally or... 

The dependence of cross-correlated relaxation on the projection angle between the two dipole vectors can be exploited to determine local conformations in ribose rings. 

The size and orientation of the 31P CSA tensor have been calibrated from single-crystal solid state NMR data of barium diethylphosphate [31]. The projection angles 6CHa22 and i between the 1H,13C-dipolar coupling and the components of the 31P-CSA-tensor de-... 

In this example, the projection angle involving the Hn-N bond and Ca-Ha bond is measured. Because the peptide bond is fixed, the relation between CCR rate and the peptide backbone can be directly described by converting the angle 9 to i//. To describe the angular dependance for the dipole-dipole CCR we use the function r = karjf i//) with... 

The relation between the CCR rates and the pseudorotation phase angle can be calculated using the general formula for /dipole-dipole by converting the values of the projection angles into P and i//ln [47] according to... 

All other factors are constants. The angle 9 is the projection angle between bond vectors and is the sole unknown in Eq. 1, and can be readily and precisely determined by measurement of the cross-correlated dipolar relaxation rate. It should be emphasized that 9 is measured directly, without the need of experimental calibration as in the Karplus curve for J-coupling constants for example. 

Another CCR mechanism is the interaction of the magnetic dipole with the chemical shift anisotropy (CSA) tensor, e.g., the interaction with the carbonyl CSA-tensor in proteins. The dipole-CSA CCR-rate is also dependent on the projection angle 9 between the magnetic dipole and CSA tensors ... 

Zincblende structure with top Ga and As atoms rotated into, resp. out of surface, (keeping about constant mutual bond length, rotated by projected angle of 27°) Ga and As back bonds contracted by —2.5% and -3.6%, resp. 

Even fusion with four-membered rings has been achieved, at least with the smaller of the two furan projection angles as in the cyclobutadiene equivalent (32) (72JA8950) the presumably more strained (and antiaromatic ) isomer (33) remains unknown. 

Fig. 6 CCR helps in determining the projection angle between two dipolar interaction vectors...

Fig. 18. Geometry of fan-beam coherent scatter computed tomography. A fan beam is used to illuminate one object slice. The central detector row (in the plane of the drawing) receives the transmitted radiation while the out-of-plane rows receive only scattered radiation. The coordinate represents the projection angle whereas...

Fia. 1.—a. Diagram of Reeves Cl Conformation of the Pyranoside Ring Proposed for Methyl 4,6-Benzylidene-a-D-altropyranoside, with the Hydroxyl Groups Shown on Carbon Atoms 2 and 3. b. Detailed View of Carbon Atoms 2 and 3 with the Hydroxyl Bonds Which Have a Projected Angle of about 180° in the Cl Conformation for This Compound. 

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