Accurate Theoretical Description of the 1La and 1Lb Excited States in Acenes Using the All Order Constricted Variational Density Functional Theory Method and the Local Density Approximation

We present the results of calculations on the vertical singlet L-1(a) and L-1(b) excitation energies in acenes within time dependent density functional theory (TDDFT), second order constricted variational DFT (CV(2)-DFT), and all order constricted variational DFT (CV(infinity)-DFT) using the local density approximation LDA(VWN). For the linear acenes it is shown that the application of the Tamm-Dancoff (TD) approximation to TDDFT (TDDFT-TD) substantially improves the agreement with experiment compared to pure TDDFT. This improvement leads to the correct ordering of the L-1(a) and L-1(b) excitation energies in naphthalene. As TDDFT-TD is equivalent to the second order CV(2)-TD method one might hope for further improvements by going to all orders in CV(infinity)-TD. Indeed, for linear acenes the application of the CV(infinity)-TD method brings the agreement with experiment to within 0.1 eV for both types of excitations using the simple LDA functional. The CV(infinity)-TD method based on LDA is also shown to be accurate for 15 nonlinear acenes with root-mean-square deviations of 0.24 eV for L-1(a) and 0.17 eV for L-1(b).