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 Su 1 state of H2. Analysis of the eigenvalue problem for the excitation energies as well as direct derivation of the exchange-correlation ~xc! kernel f xc(r,r8,v) 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 f xc(r,r8,v), which is revealed in a different behavior of the various matrix elements K1c ,1c xc ~between the highest occupied Kohn–Sham molecular orbital c1 and virtual MOs cc) as a function of the bond distance R~H–H!. The effect of nonlocality of f xc(r,r8) is modeled by using different expressions for the corresponding matrix elements of different orbitals. Asymptotically corrected ALDA ~ALDA-AC! expressions for the matrix elements K12,12 xc(st)