Adiabatic connection formula

The relativistic adiabatic connection formula is based on a modified Hamiltonian H g) in which not only the electron-photon coupling strength is multiplied by the dimensionless scaling parameter g but also a g-dependent, multiplicative, external potential is introduced. 

Although the adiabatic connection formula of Eq. (8) justifies a certain amount of Hartree-Fock mixing, there are situations in which a should vanish. In a spin-restricted description of the molecule Hj at infinite bond length (Sect. 4) the Hartree-Fock or A = 0 hole is equally distributed over both atoms, and is independent of the electron s position. But the hole for any finite A, however small, is entirely localized on the electron s atom, so no amount of Hartree-Fock mixing is acceptable in this case. 

Nagy, A. (1995). Coordinate scaling and adiabatic connection formula for ensembles of fractionally occupied excited states, Ini. J. Quantum Chem. 56, 225-228. 

The starting point for the proposed new approach is an exact formula [238], [239], based on the adiabatic connection formula and the zero-temperature fluctuation-dissipation theorem, relating the groundstate xc energy to the inter-... 

Adiabatic connection formula, 409 Basis Set Superposition Error (BSSE), 67 Cubic response function, 261 ... 

This adiabatic connection formula [49] is very useful for calculating expectation values using the interaction picture. In the corresponding Gellman-law expression in Hilbert space [50] there is an extra denominator that takes care of the phase of the wavefunction. 

Substitution of these expressions into the adiabatic connection formula of Eq. (29)... 

The idea of mixing density functional approximations with exact (Hartree-Fock-Uke) exchange rests on theoretical considerations involving the adiabatic connection formula... 

The adiabatic connection formula is at the root of the ACMs. This formula is usually expressed in the form ... 

Several gradient corrected exchange [28-30] and correlation [31-34] functionals have been proposed. In our study we use different combinations of those of Becke [28] and Perdew and Wang [30] for the exchange and the functionals proposed by Perdew [31] and Proynov [34] for the correlation. Recently, Becke [29] has introduced the so-called hybrid functional that is based on the "adiabatic connection" formula [35], Because of its reliability, largely validated in the literature [36-38], we employ in our work also the B3LYP functional which uses the Becke gradient... 

The connection between these two components of the exchange-correlation energy is achieved by means of the so-called adiabatic connection formula (ACE),... 

Adiabatic approximation, 53, 56 Adiabatic connection formula, 409 Adiabatic Connection Model (ACM), 187 Aliasing, in pseudospectral methods, 174 Allowed reaction, Woodward-Hoffmann rules, 356... 

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