TDDFT in Chemistry and Biochemistry III - TDDFT.org

Implementation Using Molecular Basis SetsLCAO expansion of KS orbitalsϕ p (r, σ) = ∑ µ C µpσχ µ (r)Response equations are transformed into finite-dimensional linearequations, amenable to matrix algebra techniques;Atomic orbitals are atom-centered, mostly contracted CartesianGaussian-type orbitals (CGTOs),χ µ (r) = ∑ d c d x i y j z k e −ζ d (r−R µ) 2 ;Atomic orbitals form a local, non-orthogonal basis set;Integrals over CGTOs can be evaluated analytically using Gaussianproduct theorem and recursion w.r.t. l = i + j + k;Basis set parameters (c d , ζ d ) tabulated, several hierarchies of basissets of increasing size (Pople, Dunning, Ahlrichs, etc.) available.Dmitrij Rappoport (Harvard U.) TDDFT in Chemistry III TDDFT Winter School 2010 16 / 22