E.J. Baerends

Excitation energies of dissociating H2: a problematic case for the adiabatic approximation of time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is applied for calculation of the excitation energies of the dissociating H2 molecule. The standard TDDFT method of adiabatic local density approximation (ALDA) totally fails to reproduce the potential curve for the lowest excited singlet 1Σu+ state of H2. Analysis of the eigenvalue problem for the excitation energies as well as direct derivation of the exchange-correlation (xc) kernel fxc(r,r′,ω) shows that ALDA fails due to breakdown of its simple spatially local approximation for the kernel. The analysis indicates a complex structure of the function fxc(r,r′,ω), which is revealed in a different behavior of the various matrix elements K1c,1cxc (between the highest occupied Kohn–Sham molecular orbital ψ1 and virtual MOs ψc) as a function of the bond distance R(H–H). The effect of nonlocality of fxc(r,r′) is modeled by using different expressions for the corresponding matrix elements of different orbitals. Asymptotically corrected ALDA (ALDA-AC) expressions...