Correlation interaction

In case of special conditions, viz. internal correlations, interactions can be estimated in addition to the main effects by means of a 2m 1 design. 

With quantum-mechanical methods, the second derivatives of the energy could be used directly for the FF and atomic polar tensors (APT) for the dipole derivatives. Both are standardly computed in most quantum-chemistry programs but for accurate results, moderately large basis sets and/or some accommodation for correlation interaction is needed. Until recently, this has restricted most ab initio studies to modest-sized molecules. 

Density Functional Theory, DFT (B3LYP), CASSCF (Complete Active-State Self-Consistent Field) and MRSD-CI (Multi-Reference Single-Double Correlation Interaction) calculations on the diatomic units AuO, AuO", AuO " and AuO " clearly show that stability of Au-0 bond reduces in this order. This trend is consistent with the molecular orbital diagram of AuO molecule presented in Fig. 10. 

Various structures involving the Re octahedral framework were examined by DFT structural ophmizahon. All ah initio calculations were performed using a commercially available density funchonal code (Material Studio Dmol3 ver3.0, Accelrys, US A), where exchange-correlation interaction was treated by the Perdew-... 

System, basis set and inter-atomic Total correlation Interaction ... 

After the discovery of the relativistic wave equation for the electron by Dirac in 1928, it seems that all the problems in condensed-matter physics become a matter of mathematics. However, the theoretical calculations for surfaces were not practical until the discovery of the density-functional formalism by Hohenberg and Kohn (1964). Although it is already simpler than the Hartree-Fock formalism, the form of the exchange and correlation interactions in it is still too complicated for practical problems. Kohn and Sham (1965) then proposed the local density approximation, which assumes that the exchange and correlation interaction at a point is a universal function of the total electron density at the same point, and uses a semiempirical analytical formula to represent such universal interactions. The resulting equations, the Kohn-Sham equations, are much easier to handle, especially by using modern computers. This method has been the standard approach for first-principles calculations for solid surfaces. 

In particular, V° describes a solute-solute Coulomb and exchange-correlation interaction corrected by an overlap contribution. The effects of the solvent on V° are implicitly included in the values of the transition properties of the two chromophores before the interaction between the two is switched on. These properties can in fact be significantly modified by the reaction field produced by the polarized solvent. In addition, the solvent explicitly enters into the definition of the coupling through the term VIEF of Equation (3.150), which describes the chromophore-solvent-chromophore interaction. 

The DV-Xa molecular orbital (MO) calculations were performed to analyze the Li-K XANES spectra of lithium halides powder. The computational details of the DV-Xa method have been previously described [10]. In this method, the exchange-correlation interaction, Vxcr between electrons is given by the Slater s Xa potential,... 

An expression of the same form was obtained by Felderhof [61] when he analysed the flow perturbation caused by a single particle in terms of the force multipoles theory. Bedeaux [49] pointed out that when the disperse phase concentration approaches the maximum value ([Pg.117]

The Hartree product neglects exchange correlation interactions between molecules. To include proper exchange would make these models inefficient and impractical. 

Vcore(v) is the potential associated with the interaction between valence and core electrons and VexchangeC-v) is the exchange potential between valence electrons. The exchange potential accounts for the repulsive interaction between electrons of like spin (Pauli exclusion principle) and electrons of either spin (correlation interaction). Both of these potentials are experienced in the bulk as well as at the surface. Vdipoie(v) is specific to the surface and arises from charge redistribution at the asymmetric surface. 

More recent work has confirmed these conclusions The counterpoise method leads to an accurate description of the correlated interaction energies in the HF dimer, with the proviso that the basis set is capable of properly describing the physical forces involved . Even with an insufficiently flexible set, the counterpoise-corrected results are more stable with respect to basis set than uncorrected data. 

We will finish this paragraph by stating that the promising and very frequently used density functional theory (DFT) [6] is not generally applicable for molecular complexes. The reason for this is that it does not cover the intersystem correlation interaction energy, approximately equivalent to the classical dispersion energy. The DFT method yields reliable results for H-bonded and ionic clusters but fails completely in London-type clusters where the dispersion energy is dominant. 

The geometries of the isolated bases and base pairs were optimized at the HF/6-31G level and were taken from our paper [11] the non-planarity of bases [38] and base pairs [39] was taken into consideration. The interaction energies [11] of base pairs were constructed as the sum of the HF/6-31G (0.25] interaction energy, MP2/6-31G (0.25) correlation interaction energy and respective deformation energy of bases determined at the HF/6-31G level. Abbreviation 6-3IG (0.25) means that the standard polarization functions in the 6-31G basis set were replaced by more diffuse ones, with an exponent of 0.25. The HF and MP2 interaction energies were corrected for the basis set superposition error. The harmonic vibrational frequencies were determined at the HF/6-31G level [27] and no scaling factors were utilized. 

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