Chapter 7
Density Functional Calculations
My other hope is that...a basically new ab initio treatment capable of giving
chemically accurate results a priori, is achieved soon.
M.J.S. Dewar,A Semiempirical Life, 1992.AbstractDensity functional theory is based on the two Hohenberg–Kohn theo-
rems, which state that the ground-state properties of an atom or molecule are
determined by its electron density function, and that a trial electron density must
give an energy greater than or equal to the true energy (the latter theorem is true
only if the exact functional could be used). In the Kohn–Sham approach the energy
of a system is formulated as a deviation from the energy of an idealized system with
noninteracting electrons. From the energy equation, by minimizing the energy with
respect to the Kohn–Sham orbitals the Kohn–Sham equations can be derived,
analogously to the Hartree–Fock equations. Finding good functionals is the main
problem in DFT. Various levels of DFT and new functionals are discussed. The
mutually related concepts of electronic chemical potential, electronegativity, hard-
ness, softness, and the Fukui function are exemplified.
7.1 Perspective..............................................................
We have seen three broad techniques for calculating the geometries and energies
of molecules: molecular mechanics (Chapter 3), ab initio methods (Chapter 5), and
semiempirical methods (Chapters 4 and 6). Molecular mechanics is based on a
balls-and-springs model of molecules. Ab initio methods are based on the subtler
model of the quantum mechanical molecule, which we treat mathematically starting
with the Schr€odinger equation. Semiempirical methods, from simpler ones like the
H€uckel and extended H€uckel theories (Chapter 4) to the more complex SCF
semiempirical theories (Chapter 6), are also based on the Schr€odinger equation,
and in fact their “empirical” aspect comes from the desire to avoid the mathematical
E.G. Lewars,Computational Chemistry,
DOI 10.1007/978-90-481-3862-3_7,#Springer ScienceþBusiness Media B.V. 2011
445