Coordination temperature dependence

Noncartesian coordinates. Temperature dependent material properties... 

On heating (7.529) it dimerises to a 4-coordinate cyclodiphosphazane (7.530). It also undergoes the very interesting reaction (7.523) to yield a derivative containing two P atoms, one of which is 4-coordinate and the other 5-coordinate. Temperature-dependent NMR spectra indicate this phosphorane may be in equilibrium with 3- and 4-coordinate derivatives (7.531) [6,13,14]. 

Free energy calculations rely on the following thermodynamic perturbation theory [6-8]. Consider a system A described by the energy function = 17 + T. 17 = 17 (r ) is the potential energy, which depends on the coordinates = (Fi, r, , r ), and T is the kinetic energy, which (in a Cartesian coordinate system) depends on the velocities v. For concreteness, the system could be made up of a biomolecule in solution. We limit ourselves (mostly) to a classical mechanical description for simplicity and reasons of space. In the canonical thermodynamic ensemble (constant N, volume V, temperature T), the classical partition function Z is proportional to the configurational integral Q, which in a Cartesian coordinate system is... 

Magnetic measurements of PuFi, between 4.2 and 300 K are consistent at high temperatures with older measurements (10-12). The large temperature dependent diamagnetism observed earlier was not found. Up to 100 K the susceptibility is nearly temperature independent with a value of X ip 2940 x 10-6 emu. The Curie-Weiss behavior near room temperature indicates population of a higher first excited state. The structure of PuFi, is isomorphic with that of UFi, (13), where two different sets of actinide atoms are 8-fold coordinated by a distorted antiprism. 

Four strongly downshifted signals in each spectrum, between 50 and 110 ppm, were assigned to the four CB protons of the cysteines coordinating the Fe ". The contact shifts of the protons reflect the coordination of cysteine to the Fe " of the antiferromagnetically coupled Fe "-Fe" pair as the cysteine protons sense the spin down orientation of the Fe " (S = ) site. This is supported by the observation that the temperature dependence of the cysteine H" protons (measured between 276 and 308 K) follows Curie behavior (decreasing contact shift with increasing temperature). 

The partial differential equations describing the catalyst particle are discretized with central finite difference formulae with respect to the spatial coordinate [50]. Typically, around 10-20 discretization points are enough for the particle. The ordinary differential equations (ODEs) created are solved with respect to time together with the ODEs of the bulk phase. Since the system is stiff, the computer code of Hindmarsh [51] is used as the ODE solver. In general, the simulations progressed without numerical problems. The final values of the rate constants, along with their temperature dependencies, can be obtained with nonlinear regression analysis. The differential equations were solved in situ with the backward... 

Table 3.5. The number of degrees of freedom in translation, rotation and vibrations of the reacting molecules and the transition state in the gas phase reaction of CO and O2 and the temperature dependence these modes contribute to the partition function. Note that one of the modes of the transition state complex is the reaction coordinate, so that only six vibrational modes are listed.

In a recent paper we used the temperature sequence of EXAFS measurements of the reduced catalyst In H2 to determine the temperature dependence of the disorder. (7 ) Comparable data was obtained for Ft metal over the same temperature range. The analysis proceeded by fitting the 1st coordination shell catalyst data to a 2-shell model In which the 1st shell was assumed to be that part of the Ft cluster... 

Combines sensitivity of EPR and high resolution of NMR to probe ligand superhyperfine interactions For paramagnetic proteins enhanced chemical shift resolution, contact and dipolar shifts, spin delocalization, magnetic coupling from temperature dependence of shifts Identification of ligands coordinated to a metal centre... 

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