Length-energy correlation constants

Whether a particular metal is known to crystallize in only a close-packed or body-centered cubic form, or in both, we are therefore able to calculate, from its vaporization enthalpy, the bond enthalpy term (M-M) for bonds of a known length d, and so, using the equation (M-M) = Ad -, we can calculate the value of A for that metal. Values of length-energy correlation constants, A, calculated thus are listed in Table 1, with other relevant data. From these we can, in turn, calculate the enthalpies of all of the metal-metal bonds in (homonuclear) cluster compounds of these metals, if their structures, and so their bond lengths, have been determined. 

Table 1. The idealized structures (bee, hep or fee), enthalpies of atomization, Af/f M(g) kJmol, metal-metal bond lengths,

Stals, J., Rev. Pure Appl. Chem., 1970, 20, 1 (extensive discussion of bond length, bond order, stretching force constants, and bond energy correlations). 

K = equillibrium folding constant n = number of molecules N = chain length P = correlation coefficient R = gas constant T = temperature ACp = change in heat capacity AG = free energy of folding AH = Van t Hoff enthalpy of folding AS = entropy of folding 6 = ellipticity o = mean-square error. 

FIG. 12 Inverse effective correlation length in units of the lattice constant a = 4.26 A as a function of temperature the extrapolated transition temperature Tq = 25.02 0.08 K, as obtained independently from energy cumulants, is marked by a dotted line. Full lines correspond to a fit assuming a simple hnear dependence + C l - r/FqI expected near Tq for a first-order transition, whereas dashed... 

Inclusion of electron correlation normally lowers the force constants, since the correlation energy increases as a function of bond length. This usually means that vibrational frequencies decrease, although there are exceptions (vibrational frequencies also depend on off-diagonal force constants). The values calculated at the MP2 and CCSD(T) levels are shown in Tables 11.14 and 11.15. 

The active space used for both systems in these calculations is sufficiently large to incorporate important core-core, core-valence, and valence-valence electron correlation, and hence should be capable of providing a reliable estimate of Wj- In addition to the P,T-odd interaction constant Wd, we also compute ground to excited state transition energies, the ionization potential, dipole moment (pe), ground state equilibrium bond length and vibrational frequency (ov) for the YbF and pe for the BaF molecule. 

Crystal structure correlations explore relationships between reactivity and actual structural parameters such as bond lengths and angles. Reactivity measured in terms of rate and equilibrium constants allows us to introduce the energy dimension directly, because these constants translate directly into... 

Several groups have applied theoretical and quantum chemical calculations to many aspects of the phenanthrolines over the past two decades. The -electron distributions in all the phenanthrolines have been determined, and they are generally in accord with the known chemical reactions of the molecules.37 Resonance energies of 1,7- and 1,10-phenanthrolines have been calculated and compared with those of 7-aminoquinoline and 8-aminoquinoline, respectively.38 Calculations applied to 1,10-phenanthroline and methyl-substituted derivatives have been correlated with their reduction potentials39 and ionization constants.40 Bond lengths for most of the phenanthrolines have been computed.41... 

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