Diffusivity correlation effects

The ionization potential (7.9 eV) falls right outside the bracket of experimental IP s reported for carbon clusters with 40 to 100 atoms (6.42 eV IP 7.87 eV, Ref. 11). Inclusion of correlation effects will lower the calculated ASCF IP by 0.25 to 0.50 eV, so that the corrected IP will be at the upper end of the experimental IP>bracket. Due to the diffuseness of the n orbital from which an electron is removed, the correlation error in the ASCF value will be smaller than in cases where an electron is removed from a well localized bond. In these cases a correction of 1 eV is usually applied. 

A.D. LeClaire and A.B. Lidiard. Correlation effects in diffusion in crystals. Phil. 

Notice that we want to use 2 d-type functions in the basis. This is because for correlated wave functions the d-type functions serve two purposes, which cannot easily be accomplished by one basis function First they serve as polarization functions, polarizing the electron density in the bonding region, a feature that is especially important in 7t-bonded systems. Secondly, they give important contributions to the angular correlation effects, which is very important in linear molecules. Studies of the ANO s shows that the two properties of the d-type functions cannot be incorporated into one function. Hie polarization d is rather diffuse, while the correlating d is a much more contracted function. We therefore prefer to include two d-type functions in the basis set... 

A more sequential approach to the analysis of the systematic error of ab initio methods has been proposed in [14]. The same set of molecules as in [10] has been analyzed there. For this set the series of calculations using the basis sets aug-cc-pVxZ containing both polarization and diffuse functions with the number of exponents x in their respective radial parts up to x = 6 (single zeta x = 1, double zeta - DZ -x = 2, triple zeta - TZ - x = 3, etc.) and with the account of correlation effects in the range of methods from MP2 up to CCSD(T) had been performed and then fitted to the formulae [15-18] ... 

In the general case, correlation effects are present during the diffusion process. This fact implies that... 

Equation 21 is the microscopic equivalent of the Einstein equation (3) and implies that succeeding jumps are uncorrelated. In general, however, backward jumps will take place with a higher probability (the correlation effect [2]), so that eq 21 provides an upper limit of the diffusivity. Alternatively, with known values for D and t, eq 21 allows an estimate of the lower limit of the mean-square jump length [67, 68]. 

When the transverse hopping is diffusive, the effect of tb can only be felt through virtual (perturbative) processes that are faster than the quantum coherence time 1 / 0( ) and in which energy conservation is not required (uncertainty principle). These processes involve pairs of correlated particles in all channels. For instance, a correlated electron-hole pair on one chain can be broken temporarily, one particle hopping to a nearest-neighbor chain (a virtual process) followed a bit later by the other particle, there... 

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