Estimation minimum energy

The minimum energies required to dissociate hydroxyacetone by processes (I), (II), (III), and (IV) are approximately 335, 335, 377, and 377kJmol , respectively (Chowdhury et al 2002b). From the product analysis following hydroxyacetone/air photolysis in broadband experiments (240 20 nm), Orlando et al. (1999) concluded that at most 50% of the photolysis occurred via channel (I). If the estimated minimum energies for the occurrence of dissociation by (I) and (II) are correct, then it would not... 

Due to the noncrystalline, nonequilibrium nature of polymers, a statistical mechanical description is rigorously most correct. Thus, simply hnding a minimum-energy conformation and computing properties is not generally suf-hcient. It is usually necessary to compute ensemble averages, even of molecular properties. The additional work needed on the part of both the researcher to set up the simulation and the computer to run the simulation must be considered. When possible, it is advisable to use group additivity or analytic estimation methods. 

Henkehnan G, Jonsson H. 2000. Improved tangent estimate in the nudged elastic hand method for finding minimum energy paths and saddle points. J Chem Phys 113 9978-9985. 

The probability that an atom will successfully move can be estimated by using Maxwell-Boltzmann statistics. The probability p that an atom will move from one position of minimum energy to an adjacent position is... 

The use of these expressions is effectual only in cases where there is no extensive deviation in the system behavior due to charge transfer overpotential or other kinetic effects.(l) The calculated threshold or thermodynamic energy requirement (2 ) (AG in the previous equation) is often much lower than actually encountered, but is still useful in estimating an approximate or theoretical minimum energy required for electrolysis. Part of the difficulty in applying thermodynamics to many systems of industrial interest may reside in an inability to properly define the activities or nature of the various species involved in the... 

Unfortunately, the two atoms are now in positions that in some sense have given an even worse approximation to the minimum energy state of the molecule than our initial estimate and the calculation is unable to recover and find the true minimum. In short, our calculation has failed miserably because we... 

Bryan and Noonan [98] carried out similar investigations using helium and estimated the minimum energy required to ignite lead azide with a 3 msec delay to be 0.087 cal/cm2, i.e. less than that for blasting gelatine, 0.15cal/cm2, PETN, 0.25 cal/cm2 and tetryl, 0.33 cal/cm2. 

A model of the randomly colling form of polylrll) based on minimum-energy conformers of UpU is described. The blend of conformers is chosen to fit the C—C rotational populations derived in NMR studies of UpU and poly(rU) and to match the experimental unperturbed dimensions of the poly(rU) chain. In addition, estimates of loop closure based on the model are comparable to the sizes of loops most frequently seen In the model oligonucleotides. Approximately 60% of the conformers constituting the model are characterized by stacked, extended C2 -endo ra cmy = tg g+ rotations. 

Similar energy minimization calculations were reported for benzene and p-xylene in silicalite (92). Diffusion coefficients were estimated from minimum energy paths through the pore. The value for benzene, 27.6 kJ/mol, is in good agreement with that of Pickett et al. (91). For the bulkier p-xylene molecule, the activation barrier was predicted to be slightly lower (23 kJ/... 

The conclusion that the free-volume fraction at Tg is not a universal parameter for linear polymers of differing molecular structure can be qualitatively confirmed by the following arguments71. Assume that at temperatures far below Tg polymeric chains are in a state of minimum energy of intramolecular interaction, Le. the fraction of higher-energy ( flexed ) bonds is zeroS4. On the other hand, let the equilibrium fraction of flexed bonds at T> Tg obey the Boltzmann statistics and be a function of Boltzmann s factor e/kT. Thus, the fraction of flexed bonds at Tg can be estimated from the familiar expression ... 

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