Density functions energy

Johnson, B. G., Frisch, M. J., 1993, Analytic Second Derivatives of the Gradient-Corrected Density Functional Energy. Effect of Quadrature Weight Derivatives , Chem. Phys. Lett., 216, 133. 

W. Wu, S. J. Zhong, S. Shaik, Chem. Phys. Lett. 292, 7 (1998). VBDFT(s) A Hiickel-Type Semi-empirical Valence Bond Method Scaled to Density Functional Energies. Application to Linear Polyenes. 

Weinert M, Davenport JW (1992) Eractional occupations and density-functional energies and forces. Phys Rev B 45(23) 13709-13712... 

Next, the trial density functional energy (4.396) will be optimized in the tight of variational principle (4.392) as prescribed by the HK2 theorem. The combined result of the HK theorems will eventually fiinush the new quantum energy expression of multi-electroiuc systems beyond the exponential wall of the wave function. 

Because of its computational efficiency and good results for molecular properties, the MP2 method is one of the two most commonly used methods for including correlation effects on molecular ground-state equilibrium properties. (The other widely used method is the density-functional method—Section 16.5.) Also, in perhaps the most accurate form of density-functional theory, the MP2 correlation energy (16.13) is multiplied by an empirical constant and added to the density functional energy to give improved results see the discussion of double-hybrid functionals in Section 16.5. 

Type Semi-empirical Valence Bond Method Scaled to Density Functional Energies. Applications to Linear Polyene. 

This way the density functional character for the terms involved in the molecular energies is emphasized. For example, the energy of the atom A in the considered molecule associates with the density functional energy... 

The univocity of the relation between the external potential applied to the electronic system and the electronic density is provided by the Hohenberg-Kohn Theorems, see the Volume I of this five-volume book dedicated to quantum nanochemistry (Putz, 2016a). Moreover, one of the theorems also states the inequality relation between a density functional energy of any electronic state, E[p and the true functional energy of the fundamental electronic state of the system, i [p, namely as... 

Wei W, Zhong SJ, Shark S (1998) VBDFT(s) a Huckel-type semi-empirical valence bond method scaled to density functional energies. Application to linear polyenes. Chem Phys Lett 292 7-14... 

Wu W, Shaik S (1999) VB-DPT a nonempirical hybrid method combining valence bond theory and density functional energies. Chem Phys Lett 301 37 2... 

Analytic Second Derivatives of the Gradient-corrected Density Functional Energy. 

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