Hartree-Fock model exchange energy

Hartree-Fock model, exchange energy, 1 6 Hartree-Fock study, 1 313 hydrogen-bonded systems, 1 313 hydrogenic model problem, 1 161 hyperfine coupling constants, 2 162... 

B3LYP Model. A Hybrid Density Functional Model which improves on the Local Density Model by accounting explicitly for non-uniformity in electron distributions, and which also incorporates the Exchange Energy from the Hartree-Fock Model. The B3LYP model involves three adjustable parameters. 

Hybrid density functional models = density functional models which incorporate the exchange energy from the Hartree-Fock model. 

Tab. 12.1. Total interaction energies Ei of the multiply-hydrogen-bonded complex in Fig. 12.2 in kJ mol. BHLYP is a hybrid density functional which features 50% admixture of exact Hartree-Fock-type exchange, AMI and PM3 are semi-empirical models, which are an efficient approximation to the Hartree-Fock method, and CCSD is a coupled-cluster model.

The choice of = g ni,n = nirij implies the Hartree-Fock model, and optimization of the occupation numbers and natural orbitals with this choice indeed returns the HF wave function, i.e. the HF wave function cannot be improved by allowing fractional occupation numbers. The /(n /iy) function is usually set equal to n,ny, since this is just the Coulomb interaction, and the exchange-correlation part is modelled by g(ni,rij)P Modelling the exchange-correlation energy by a g(tii/ij) function is stiU in its infancy. 

It was this observation which gave rise to so-called hybrid derrsity ftmctional models, such as the B3LYP model. Here, the Hartree-Fock exchange energy is added to the exchange energy from a partictrlar density functional model with one or more adjustable parameters. 

Calculations based on the continuum dielectric model have been performed by the hydrated electron in the limit of zero cavity size (19). The general treatment is based on a variational calculation using hydrogenic type wave functions for the ground and the first excited states. This treatment is based on a Hartree Fock scheme, where the Coulomb and exchange interaction of the excess electron with the medium are replaced by the polarization energy of a continuous dielectric. The results obtained are summarized in Table V. The fair agreement obtained with... 

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