Advanced Physical ChemistryG.H. CHENUniversity of Hong Kong培明物
Advanced Physical Chemistry G. H. CHEN University of Hong Kong
Density-Functional TheorySchrOdinger EquationHV=EVWavefunctionHamiltonianH = -(h?/2m)Z,V? + Z, V(r) + Z, Z; e2/riEnergyText Book:Density-FunctionalTheoryforAtoms andMoleculesbyRobertParr&WeitaoYang
SchrÖdinger Equation H y = E y Hamiltonian H = - (h 2 /2me )ii 2 + i V(ri ) + i j e 2 /rij Wavefunction Energy Density-Functional Theory Text Book: Density-Functional Theory for Atoms and Molecules by Robert Parr & Weitao Yang
Hohenberg-Kohn Theorems1st Hohenberg-Kohn Theorem: The external potential V(ris determined, within a trivial additive constant, by theelectron density p(r)Implication: electron density determines every thingE（H)=H+A-H)= Eo+p(r)[u(t)-u'(r)] dr= Eo-p(r)[u(t) -u'(r)] dr.Eo+E<E+E
Hohenberg-Kohn Theorems 1 st 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 p(rsuch that p(r)≥0 and J p(r) dr = NE≤E,[]Implication: Variauon approacn to determine groundstate energy and densityE,[p] = T[p] + Vne[p] + Vee[p]p(t)u(r)dr+FHk[p)Fuk[p]=T[o] +Vee[p]Vee[p]=J[p]+nonclassicalterm(]A)=p(r)u(r)dr+Fuk[p]=E,[p]≥E,[p]
2 nd 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