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H y = E y

Density-Functional Theory. H y = E y. Schr Ö dinger Equation. Wavefunction. Hamiltonian H = - ( h 2 /2m e )  i  i 2 +  i V(r i ) +  i  j e 2 /r ij. Energy. Text Book: Density-Functional Theory for Atoms and Molecules by Robert Parr & Weitao Yang.

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H y = E y

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  1. Density-Functional Theory Hy = Ey SchrÖdinger Equation Wavefunction Hamiltonian H = - (h2/2me)ii2+ iV(ri) + ije2/rij Energy Text Book: Density-Functional Theory for Atoms and Molecules by Robert Parr & Weitao Yang

  2. Hohenberg-Kohn Theorems 1st Hohenberg-Kohn Theorem: The external potential V(r) is determined, within a trivial additive constant, by the electron density r(r). Implication: electron density determines every thing.

  3. 2nd Hohenberg-Kohn Theorem: For a trial density r’(r), such that r’(r) 0 and  r’(r) dr = N, E0 Ev[r’(r)] Implication: Variation approach to determine ground state energy and density.

  4. Kohn-Sham Equation eiyi

  5. Database: 1. C.L. Yaws, Chemical Properties Handbook, (McGraw-Hill, New York, 1999) 2. D.R. Lide, CRC Handbook of Chemistry and Physics, 3rd ed. (CRC Press, Boca Raton, FL, 2000) 3. J.B . Pedley, R.D. Naylor, S.P. Kirby, Thermochemical data of organic compounds, 2nd ed. (Chapman and Hall, New York, 1986) Differences of heat of formation in three references for same compound are less than 1 kcal/mol; and error bars are all less than 1kcal/mol Selected Data: 180 small- or medium-size organic molecules HKU, 06/11/2013

  6. MAD=22.6 kcal/mol

  7. Hu, Wang, Wong & Chen, J. Chem. Phys. (Comm) (2003) B3LYP/6-311+G(d,p) B3LYP/6-311+G(3df,2p) MAD=22.6 kcal/mol MAD=11.6 kcal/mol MAD=1.59 kcal/mol MAD=1.45 kcal/mol

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