Correlation strength

A close estimate of the dynamic correlation energy was obtained by a simple formula in terms of pair populations and correlation contributions within and between localized molecular orbitals. The orbital and orbital-pair correlation strengths rapidly decrease with the distance between the orbitals in a pair. For instance, the total valence correlation energy of diamond per carbon atom, estimated as 164 mh, is the result of 84 mh from intra-orbital contributions, 74.5 mh from inter-orbital closest neighbors contributions, and 6.1 mh from interorbital vicinal contributions. The rapid decay of the orbital correlation contributions with the distance between the localized orbitals explains the near-... 

It is worth noting that the chosen A and A satisfy the constraints in Eqs. (78) and (90). Moreover, the expression (94) also holds true for systems where the largest occupation deviates significantly from one, indicating that it may possibly be vahd for arbitrary correlation strengths [76]. 

Since all the m /2 have values between 0 and 1, there is another possible measurement of the correlation strength ... 

In discotic phases the orientation of the molecules is perpendicular to the molecular plane. Here, the columns can be arranged in a nematic or columnar manner. In the nematic phase the molecules possess a centre of gravity randomly ordered, but with the short molecular axis of each molecule more or less parallel. In the columnar phase, beside the preferable orientation of the short molecular axes, the disc-like molecules are ordered forming columns. Depending on the correlation strength between he columns these phases can be subdivided into ordered or disordered. A third possibility is to have a thermodynamically preferable position of the columns in the mesophase, like in a hexagonal cell. Additionally, a tilt of the columns is also possible. 

In addition, comparison to solutions of the Hubbard and PPP models including electron correlation shows the VB wave function to be a more accurate initial approximation than the Hartree Fock solution at the correlation strengths likely to be encountered in realistic semiempirical models. In spite of the qualitative superiority of the VB wave function, systematic computational approaches to more accurate treatment of correlation are still most readily achieved when starting from the independent particle limit, but the correlated wave functions thus built up are likely to be interpretable in valence bond terms. 

The fineness modulus was developed in an effort to correlate strength of concrete in terms of its component sizes. The fineness modulus is simply the sum of the percentages coarser in a given sieve-analysis divided by 100. In concrete work, fineness modulus is applied to the aggregate and the following Tyler Standard Scale sieves are used 100, 48, 28, 14, 8, 4, and 3/Vin., 3/4-in., and iy2-in. mesh. By using this series of sieves each sieve has a clear width opening double that of the next finest sieve, or one-half that of. the next coarsest sieve. 

Table 2 Charge fluctuation <(An,2))corr and correlation strength parameters A , in pentalene (55) and...

Results for the Hubbard model In Fig. 4, we display the dependence of a on the chain length for different values of 7/t, for uniform (Fig. 4a) and dimerized (Fig. 4b) Hubbard chains. The polarizability decreases with increasing correlation strength in both... 

For fixed electron correlation strength, Eh increases with increasing 5 (Fig. 15). This implies that the larger the 6 value, the more excitonic-like is the lowest charge excitation. 

Thus, y (0 s are calculated every Ax interval (or time-segment) with a time resolution determined according to the interval in which the trajectory data are stored [16], In Equation 8.17, is the a-component of the ith atom velocity vector in the case of PMD simulations while )°a is the a-component in the case of reference equilibrium MD simulations without perturbations, i.e., a set of UMD simulations. Therefore, shows the relative correlation strength in comparison to the reference correlation Vj (Equation 8.18), which is the average within the Lth Ax time-segment over the latter UMD simulations numbers of trajectories). The present way to calculate the velocity correlation is to find the fundamental frequencies without combination tones in each Ax time-segment. 

Fig. 6, (top) Hole-concentration p (=1 - x) dependence of the effective number of carriers Neff for Lai-xSrxTiOa and Yi-xCaxTiOa [74], (bottom) The parameter C as a function of the electron correlation strength, where C is the rate at which the Drude-like response changes with bandfilling [64]... 

In the intermediate correlation strength system, Ca3Ru202, Raman Scattering results reveal a metal-insulator transition to an antiferromagnetic phase below Tm 50 K, as evidenced by the development of a large charge gap... 

Shogenov, V. N., Kozlov, G. V, Gazaev, M.A., Shustov, G. B., Mikitaev,A. K. (1985). The Correlation Strength-Notch Length in Polycarbonate-Polyarylate Blend Fihns. sokomolek. Soed. B, 27(4), 244-245. 

Feldman and Beaudoin correlated strength and modulus of elasticity for several systems over a wide range of porosities. The systems included pastes hydrated at room temperature, autoclaved cement paste with and without additions of fly ash, and those obtained by other workers. Porosity was obtained by measurement of solid volume by a helium pycnometric technique and apparent volume, through the application of Archimedes principle. 

The study of resonance enhancements of is very important for a better knowledge of electronic structure (e.g. position and width of two photon states normally unaccessible by usual spectroscopic techniques) and for a better comprehension of electron-electron interaction in these systems. In fact the theoretical calculation of Hayden and Mele (1985) show that with increasing electron-electron correlation strength a crossover of two and one photon states occurs. It means, that for large electron-electron interactions two photon state lies below one photon state as it was observed. 

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