H y = E y Density-Functional Theory SchrÖdinger Equation Wavefunction Hamiltonian H = - (h2/2me)ii2 + i V(ri) + i j e2/rij Energy Text Book: Density-Functional Theory for Atoms and Molecules by Robert Parr & Weitao Yang

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.

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.

Kohn-Sham Equation ei yi

1. C.L. Yaws, Chemical Properties Handbook, 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

MAD=22.6 kcal/mol

B3LYP/6-311+G(d,p) B3LYP/6-311+G(3df,2p) 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