Cumulant correlation energy

The two-particle cumulant is a correlation increment. It describes Coulomb correlation, since the Fermi correlation is already contained in the description in terms of only. In terms of the cumulants, the energy expectation value can be written... 

The correlation energy of a 2n electron system is in general larger in absolute value than that of the system with one less electron. Therefore, the quantity (Et — Ec) is positive and tends to compensate the error AEt. On the other hand, the same argument, applied to the calculation of electron affinities (the change in energy produced by the capture of an electron in an empty orbital (pt), suggests that the errors —AEt and E — Et) should cumulate rather than cancel. 

The next most rapid type of motion is identified with deliberate imprecision as defect diffusion . It is closely similar to the fairly rapid vibrational excursions of limited angular extent that are considered in the theory presented above. Motions of this type can arise either from cumulative low energy distortions of bond angle within one set of potential energy minima, or from thermally accessible local changes of the rotationally isomeric states of a few bonds. The latter changes will probably be correlated, in order to satisfy the... 

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... 

To summarize the theory dynamic correlations are described by the unitary operator exp A acting on a suitable reference funchon, where A consists of excitation operators of the form (4). We employ a cumulant decomposition to evaluate all expressions in the energy and amphtude equations. Since we are applying the cumulant decomposition after the first commutator (the term linear in the amplimdes), we call this theory linearized canonical transformation theory, by analogy with the coupled-cluster usage of the term. The key features of the hnearized CT theory are summarized and compared with other theories in Table II. 

In the frame of CSTPM, the following dynamics parameters of the cascade system components can be experimentally measured the spin label rotation correlation time and spin relaxation parameters, the fluorescence and phosphorescence polarization correlation times, the singlet and triplet state quenching rate constants, the rate constant of photoisomerization, and the rate constant of the triplet-triplet energy transfer. This set of parameters is a cumulative characteristic of the dynamic state of biomembranes in the wide range of the probes amplitude and characteristic time. 

In figs. 24 and 25 we indicate the individual and cumulative effects on the spin observables of the various corrections discussed in this section. In particular, we stress those which have been studied at higher energies. The first-order NRIA predictions for 500 MeV p + Ca and 800 MeV p + Pb elastic scattering spin observables are shown by the dotted curves in figs. 24 and 25, respectively. Predictions in which correlations, medium corrections, and the EMSO potential are successively added to the calculations are indicated by the dashed, dashed-dotted, and solid curves, respectively. For 800 MeV... 

Figure 10. Correlation of angular diversity and energy diversity. Symmetric configurations ciuster near the origin, and D <20% irregular configurations near D = D 100%. There is also a statistical cumulation around 50%. The plot indicates that...

In energy domain, the cumulative reaction probability can also be calculated employing flux correlation functions [3, 4] ... 

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