Partition function contribution

Data for the 2 CHj C H, Reaction Temperature, Partition Function Contributions, Exponential Term, Logarithm of the Equilibrium Constant... 

When a -0.42 torsional correction to ethane is included we arrive at -30.70 kcal mol 1 which compares with Kistiakowsky s experimental value of Ahyd//298 = -32.58 0.05 kcal mol 1. The discrepancy is well outside the combined error bars of the experiment and the calculation. A calculation by the more recent MM4 force field, however, yields -32.69 kcal mol 1 (Allinger et al., 1996). [For more on the partition function contribution and torsional corrections, see Rogers (2003).]... 

In applying this formula to the determination of the peak absorption coefficient, it is customary to combine with it the rotational partition function contribution kT/hB giving the term hB J/kT, (ref 3, p. 117). This equates to hvpd/IkT in linear and symmetric top molecules and replaces the fimn term in Equation 1.21, with becoming fj. This latter term takes into account the Boltzmann occupancy factor for that state fj = exp — [57(7 + )/kT]... 

The statistical weight matrix constructed from the relative statistical weights permits the calculation of the partition function of a given sequence by matrix multiplication. The partition functions contribute to the evaluation of the conformational sequence probabilities P (i/n/ q> /), i.e. the probability to find a sequence of n residues in a specific conformational state q> starting at the i-th position of the chain. The results of these calculations can graphically be presented in the form of conformational probability profiles. 

Using equations (9), (10), and (11) we find that this factor in the partition function contributes to C%(X)jLk an amount 0.128 at 300 K and 0.236 at 500 K. Using equations (7) and (10) we find that the contribution at 298.15 K to S /Lk is 1.42 the translational contribution is 18.44 so the electronic contribution is about 7% of the total. The electronic contributions must always be evaluated by summation a further example may be found in reference 3. Much information on atomic states and energy levels has been critically evaluated and tabulated. ... 

These results should, of course, be put in perspective. Swain s relationship is not very sensitive to the presence of factors other than zero-point energy [13, 31, 32], and deviations from linear Arrhenius dependences and values of AfJAo < 1 are found, and normally are taken as indicating the presence of tunnelling [2, 36]. Nonetheless a preliminary interpretation of primary isotope effects will be based solely on zero-point energy changes, and the extent to which this needs to be qualified by further consideration of tunnelling or partition-function contributions will be examined later. 

Partition function contributions to AyJAx. An additional feature of the H2-D2 isotope effects of Table 11 is that classical partition-function contributions to A A are readily predicted. At not too low temperatures Qx>JQ.Ui = 4x2, while for the transition state H where X is a heavy atom, Qdjx/Qhjx = 2. It follows that... 

BE = bond increment GE = group increment HFE = Hartree-Fock energy MH = molar heat content MM2, MMP2, MM3, MM4 = molecular mechanics programs PFC = partition function contribution POP = population contribution SE = structural features increment TOR = torsional contribution. 

The partition function contribution, PFC, in equation (2) includes contributions from statistical thermodynamics that consist of the conformational population contribution (POP), the torsional contribution (TOR), and the contributions from translational rotation and a PV term required to convert the energy into enthalpy (T/R) ... 

FF = force field PFC = partition function contribution QM = quantum mechanics VESCF = variable electronegativity self-consistent field. 

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