Correlation coupling

If we compare results obtained with the same basis sets with the three coupled cluster models CCS, CC2 and CCSD, we find similar trends as observed in Refs. [22,45] The CCS model underestimates strongly the static hyperpolarizabilities and their dispersion. The results are usually of similar quality as those obtained with SCF. For methane, the CCS static hyperpolarizabilities are intermediate between the SCF and the CCSD values obtained in the same basis set. In Ref. [45] the CCS percentage dispersion contribution to the third harmonic generation (THG) hyperpolarizability of methane was found to be slightly smaller than for SCF, both underestimating significantly the dispersion obtained with the correlated coupled cluster models CC2 and CCSD. Accordingly the CCS dispersion coeflBcients listed in Table 3 are substantially smaller than the respective CCSD results obtained in the same basis sets. 

Other data were obtained from subcooled water flowing through small tubes (0.08-0.12 in. or 0.2 to 0.3 cm in diameter) at pressures ranging from 290 to 2,900 psia (2.0 to 20 MPa) (Povarnin and Semenov, 1960). This correlation, coupling the pressure effect with local subcooling, is in the form... 

Very active research has been devoted to the development of complexity measures that would allow the quantitative characterization of a complex system. In the present context, complexity is not just described by the number of states, the multiplicity of a system, as defined in information science, or by the characteristics of the graphs representing a molecule or an assembly of molecules, or by structural complexity. Complexity implies and results from multiple components and interactions between them with integration, i.e. long range correlation, coupling and feedback. It is interaction between components that makes the whole more than the sum of the parts and leads to collective properties. Thus, the complexity of an organized system involves three basic features ... 

Keywords explicit-r12 correlation coupled-cluster methods higher-order excitations... 

Shiozaki, T., Kamiya, M., Hirata, S., Valeev, E.F. Equations of explicitly-correlated coupled-cluster methods. Phys. Chem. Chem. Phys. 2008, 10, 3358-70. 

Neiss, C., Hattig, C. Frequency-dependent nonlinear optical properties with explicitly correlated coupled-cluster response theory using the CCSD(R12) model. J. Chem. Phys. 2007, 126, 154101. 

Noga, J., Valiron, P., Klopper, W. The accuracy of atomization energies from explicitly correlated coupled-cluster calculations. J. Chem. Phys. 2001, 115, 2022-32. 

Noga, J., Kedzuch, S., Simunek, J., Ten-no, S. Explicitly correlated coupled cluster F12 theory with single and double excitations. J. Chem. Phys. 2008, 128, 174103. 

Tew, D.P., Klopper, W., Hattig, C. A diagonal orbital-invariant explicitly-correlated coupled-cluster method. Chem. Phys. Lett. 2008, 452, 326-32. 

Kohn, A., Richings, G.W., Tew, D.P. Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence. J. Chem. Phys. 2008, 129, 201103. 

Previous attempts to calculate bond energies in tin compounds employed levels of theory that were inadequate to provide accurate results. As discussed above, accurate bond energies require the use of either composite ah initio methods or methods employing a high level of electron correlation coupled with isogyric reactions to minimize basis set truncation and other systematic errors. Consequently, the results reported by Basch [46,96], which use a number of imcorrected ah initio methods or with very simple corrections (i.e., across-the-board energy corrections by finite amounts), are unhkely to be particularly accurate. 

The first observation of spin-polarization in PS I was reported by Blankenship et al.273 in 1975 (for review see reference 274). Spectra at higher mw frequencies allowed the assignment Aj to a quinone in the radical pair.275276 Interestingly, two sequential RPs were observed277,278 resulting from P q A, and P o FeS" showing that kinetic information about forward ET can be extracted in addition to relaxation and polarization decay. Furthermore, the relative orientation of AT and Aj- could be deduced, the analysis is based on the correlated coupled radical pair (CCRP) concept.279 281... 

Internal ligand relaxation allows the removal of strain possibly imposed on the ligands by the receptor during correlation-coupled refinement but usually yields suboptimal models. Therefore, correlation-coupled receptor minimization followed by unconstrained ligand relaxation is repeated several times until a highly correlated pseudoreceptor model is obtained in the relaxed state (designated ligand equilibration). 

In 1964 Molodozhnikov and co-workers (137) reported the isolation of several diterpenoid alkaloids from the shrub Spiraea japonica L. fil. of the Roseaceae family. Later Goto and co-workers (138) examined alkaloids of the same plant (Japanese name Shimotsuke ) and isolated 10 new alkaloids. The structures of 3 of these, spiradine A (152), spiradine B (153), and spiradine C (154) have been determined by chemical correlations coupled with a single-crystal X-ray analysis (139) of spiradine A methiodide (155). 

This is our new equation for the single-site density distributions which generalizes the LMBW equation (2) to polyatomic fluids, below called a site-site LMBW (SS-LMBW) equation [47]. As distinct from the site-site DFT approaches [20-24], the SS-LMBW equation properly treats the short- and long-range correlations coupled in the site-site direct correlation function Cy (r2, rs). The SS-LMBW theory also differs from the RISM approach to inhomogeneous polyatomic fluids derived within the density functional formalism by Chandler et al. [25,26]. In Equations (3.7) and (3.13) of Ref. [26] for the site density profiles p (r), the orientational averaging with the intramolecular matrix (r 12)... 

When double resonance experiments are used to determine relative signs of coupling constants a set of unequivocally correlated couplings can be obtained. In the case of Me(,Pb2 a suggestion, (545) based on... 

As was already mentioned, the generalized transport coefficients (fc, z) and (a(k, z), describing the dynamic cross-correlation coupling, tend to zero in the hydrodynamic limit. However, if a wavenumber k is finite they can contribute significantly to the dynamic behavior of the system. 

Explicitly Correlated Coupled Cluster R12 Calculations (J. Noga P. Valiron)... 

THIS PROGRAM USES THE WELL-KNOWK SOUDERS AMD BROWN CORRELATION COUPLED WITH LIQUID SURGE CAPACITY TO SIZE LIQUID-VAPOR SEPARATORS. 

COSY-90 Correlating coupled homonuclear spins. Typically used for correlating protons coupled over 2- or 3-bonds, but may be... 

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