Three-body correlation

Correlation Functions in Open Systems. II. Two- and Three-Body Correlations. 

Three-Body Correlation Effects in Third-Order Reduced... 

Three-Body Correlation Effects in Third-Order Reduced Density Matrices Table 1 Graph representation of elements of RDM s and related quantities... 

The decomposition just described shows clearly that the pure two-, three-,. . . body correlation terms in the 2-, 3-,. .. RDM s are, , . .. etc. These terms will... 

Three-body correlation effects in third-order reduced density matrices... 

Three-Body Correlation Ejfects in Third-Order Reduced Density Matrices Table 3 Contribution (X 1Q2) of the different correlation matrices to some relevant elements... 

The three-body correlation energy17 is therefore specified by... 

U. Baffle, L. Ulivi, M. Zoppi, and F. Barocchi. The three-body correlation spectral moments in depolarized interaction induced light scattering of Hj at 297 K. Chem. Phys. Lett., 755 559-564 (1987). 

D. P. Shelton, G. C. Tabisz, F. Barocchi, and M. Zoppi. The three-body correlation spectrum in collision induced light scattering by isotropic molecular gases. Molec. Phys., 4(5 21-31 (1982). 

We may also readily calculate corrections to the IBI approximation, obtaining as a bonus a more precise definition of its limits of validity. First-order corrections have two origins, the three-body correlation function and the effect of a third body on the two-body correlation function. 

The three-body correlation function requires us to evaluate... 

The effective interaction diameter approximation also allows the three-body correlation and perturbed two-body dynamics terms to be written... 

Fernandez A, Colubri A, Berry RS (2002) Three-body correlations in protein folding The... 

Fig. 3.6 Number of backbone hydrogen bonds plotted against the number of three-body correlations (C3) extracted from representative FM trajectory capturing the wrapping/folding dynamics for the thermophilic variant of protein G...

There are two results in the data reported in Table 2 which I find both striking and surprising. Unexpectedly it appears that the largest error of 3D which occurs in the elements simultaneously involving the homo and the lumo is not due to the omission of three-body correlation effects, as the developments of Nakatsuji and Yasuda [15,16] seemed to imply, but is rather a result of subtracing instead of adding this three-body contribution to the joint effects of the one- and the two-body contributions. That is, in the FCI calculation and for these elements, the three correlation matrices practically cancel each... 

Over the years there have been important progress in finding trial functions substantially more accurate then the pair product form for homogeneous systems [12,13]. Within the generalized Feynman-Kac formalism, it is possible to systematically improve a given trial function [13,14]. The first corrections to the pair product action with plane wave orbitals are a three-body correlation term which modifies the correlation part of the trial function (Jastrow) and a backfiow transformation which changes the orbitals and therefore the nodal structure (or the phase) of the trial function [14]. The new trial function has the form... 

As mentioned above, a set of experimental data does not necessarily correspond to a unique molecular structure. Moreover, even unphysical structures may be consistent with a set of experimental data. It is therefore necessary to carefully choose a set of constraints to limit the number of possible structures. The uniqueness theorem of statistical mechanics [30, 31] provides a guide to the number and type of constraints that should be appfied in the RMC method in order to get a unique structure [32]. For systems in which only two- and three-body forces are important, the uniqueness theorem states that a given set of pair correlation function and three-body correlation function determines aU the higher correlation functions. In other words, assuming that only two- and three-body forces are important, the RMC method must be implemented along with constraints that describe the three-body correlations [27]. 

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