A determination of the free-energy difference between two diastereomeric ion-pairs

1969 ◽  
pp. 35 ◽  
Author(s):  
G. A. Knudsen ◽  
B. Franzus ◽  
J. H. Surridge
Keyword(s):  
Free Energy ◽  
Ion Pairs ◽  
Energy Difference ◽  
Free Energy Difference

Conformational analysis of 1,4-disubstituted cyclohexanes. III. trans-1,4-Di(trifluoroacetoxy)cyclohexane

1969 ◽  
Vol 47 (3) ◽  
pp. 429-431 ◽  
Author(s):  
Gordon Wood ◽  
E. P. Woo ◽  
M. H. Miskow
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Free Energy ◽  
Magnetic Resonance ◽  
Low Temperature ◽  
Conformational Analysis ◽  
Integration Method ◽  
Standard Free Energy ◽  
Energy Difference ◽  
Free Energy Difference ◽  
Conformational Free Energy

By the low temperature nuclear magnetic resonance integration method the standard free energy difference between the diequatorial and the diaxial forms of 1-H,4-H-trans-1,4-di(trifluoroacetoxy)-cyclohexane-d8 was found to be 77 ± 5 cal/mole. The conformational free energy (−ΔG0) of the trifluoroacetoxy group in the monosubstituted cyclohexane was 485 ± 4 cal/mole at the same temperature. The non-additivity of the −ΔG0 values is discussed in terms of transannular electrostatic interaction.

A comprehensive computational examination of transannular Diels–Alder reactions of unsubstituted C14 trienes — Barriers, template effects, and the Curtin–Hammett principle

2001 ◽  
Vol 79 (8) ◽  
pp. 1284-1292 ◽  
Author(s):  
Saul Wolfe ◽  
Anthony V Buckley ◽  
Noham Weinberg
Keyword(s):  
Free Energy ◽  
Energy Difference ◽  
Diels Alder ◽  
Molecular Orbital Calculations ◽  
Free Energy Difference ◽  
Molecular Mechanics Calculations ◽  
Geometrical Isomers ◽  
Free Energy Of Activation ◽  
Transition Structures ◽  
Cyclic Compounds

A combination of MM3-level molecular mechanics calculations and PM3-level semiempirical molecular orbital calculations has been employed, in conjunction with an algorithm for the comprehensive conformational analysis of cyclic compounds, to obtain 1202 unique 1,3,9-cyclotetradecatriene conformations, distributed over the six possible geometrical isomers, and 70 unique transannular Diels–Alder transition structures leading to the six possible stereoisomeric tricyclic olefins. A kinetic analysis that takes into account all minima of a given geometrical isomer and all transition structures leading to the same tricyclic product leads to a free energy of activation that is almost the same as the free energy difference between the lowest minimum and the lowest transition structure (the Curtin–Hammett principle). A substantial template effect, mainly entropic in origin, is found when the transannular reactions are compared to the Diels–Alder reactions of the cognate 2,4-hexatrienes with the 2-butenes. Although the cyclization of the trans-cis-trans triene favours the cis-anti-cis over the trans-anti-trans product by more than 20 kcal mol–1, the situation is reversed in the acyclic reaction. A cyclic triene that can cyclize directly to a trans-anti-trans tricycle can therefore be proposed.Key words: molecular models, Deslongchamps, Takahashi, trans-anti-trans tricycle, MM3, PM3, transition states.

Applying Bi-directional Jarzynski Methods to Quasi-equilibrium States

2010 ◽  
Vol 63 (3) ◽  
pp. 357 ◽  
Author(s):  
James C. Reid ◽  
Stephen R. Williams ◽  
Debra J. Searles
Keyword(s):  
Free Energy ◽  
Recent Work ◽  
Glassy State ◽  
Energy Difference ◽  
Fundamental Importance ◽  
Energy Measurement ◽  
Quasi Equilibrium ◽  
Major Advance ◽  
Free Energy Difference ◽  
Jarzynski Equality

Measuring free energy differences between states is of fundamental importance to understanding and predicting the behaviour of thermodynamic systems. The Jarzynski equality provides a method for measuring free energy differences using non-equilibrium work paths and represents a major advance of modern thermodynamics. Recent work has extended the theory by using work paths in both directions between the states to improve the accuracy of the free energy measurement. It has also been shown that the Jarzynski equality can be adapted to measure the free energy of quasi-equilibrium systems such as glasses. Here we combine these advances to accurately measure the free energy difference between a glassy state and equilibrium using bi-directional methods. For this system however, the result is not as accurate as that achieved using the work evaluated in a single direction.

Nucleation & Growth of Precipitates in Transformations Driven by Diffusion

1997 ◽  
Vol 481 ◽  
Author(s):  
N. Clavaguera ◽  
M.T. Clavaguera-Mora
Keyword(s):  
Free Energy ◽  
Calculated Data ◽  
Energy Difference ◽  
Calphad Approach ◽  
Free Energies ◽  
Free Energy Difference ◽  
Diffusion Controlled ◽  
The Matrix ◽  
Rapidly Solidified ◽  
Selection Of

ABSTRACTA theoretical analysis of the transformation kinetics which accounts for nuclei, either prequenched or created homogeneously, and whose growth are controlled by diffusion is presented. The change in growth habit intervening during the transformation is analysed in terms of the evolution of the free energy difference between the precipitate and the matrix at the interface, ΔG1. In the Avrami formalism, this quantity accounts for the competition between interface and diffusion controlled growth whereas the nucleation events are driven by the free energy difference between the precipitate and the bulk matrix. Competition and selection of precipitate phases in highly undercooled melts using the CALPHAD approach for the evaluation of the free energies and the changes in diffusivity with concentration are analysed. Experimental vs. calculated data are discussed in some rapidly solidified metallic systems.

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