Low-lying excited states by constrained DFT

Abstract

Exploiting the machinery of Constrained Density Functional Theory (CDFT), we propose a variational method for calculating low-lying excited states of molecular systems. We dub this method eXcited CDFT (XCDFT). Excited states are obtained by self-consistently constraining a user-defined population of electrons, N, in the virtual space of a reference set of occupied orbitals. By imposing this population to be N = 1.0, we computed the first excited state of 15 molecules from a test set. Our results show that XCDFT achieves an accuracy in the predicted excitation energy only slightly worse than linear-response time-dependent DFT (TDDFT), but without incurring into problems of variational collapse typical of the more commonly adopted ΔSCF method. In addition, we selected a few challenging processes to test the limits of applicability of XCDFT. We find that in contrast to TDDFT, XCDFT is capable of reproducing energy surfaces featuring conical intersections (azobenzene and H) with correct topology and correct overall energetics also away from the intersection. Venturing to condensed-phase systems, XCDFT reproduces the TDDFT solvatochromic shift of benzaldehyde when it is embedded by a cluster of water molecules. Thus, we find XCDFT to be a competitive method among single-reference methods for computations of excited states in terms of time to solution, rate of convergence, and accuracy of the result.

Capturing multireference excited states by constrained-density-functional theory

“…XCDFT yields excitation energies in semiquantitative agreement with TDDFT and benchmark calculations, however, we noticed [7] that whenever it is required to go beyond a single Slater determinant, spurious contributions from more than singly excited configuration state functions arise degrading the excited state's electronic structure. One particularly deteriorating factor is the resulting significant overlap with the gs KS wavefunction.…”

“…We summarize in Table I excitation energies computed with τ XCDFT along side with available benchmark data [36][37][38][39][40][41]. We find that the performance of τ XCDFT is comparable with XCDFT [7]. However, as we have analyzed above, the character of the states involved are now corrected.…”

“…All XCDFT and τ XCDFT excited state calculations are performed with a development version of the Amsterdam Density Functional (ADF) 2019 program [27]. To assess the performance of τ XCDFT, we consider the lowest excited state for a set of fifteen molecules [7] with the addition of the anthracene, tetracene and fullerene. As describe above (see theory section) we rely on the approximation that the smearing provided by the Fermi-Dirac distribution function is sufficient to account for the fractional occupations resulting from the multireference character of certain excited states.…”

“…In this work, we continue the development of the eXcited Constrained DFT (XCDFT) method [7]. In XCDFT, a variational procedure produces excited states energies and densities of similar quality to the ground states ones for a similarly comparable computational cost.…”

“…The paper is organized as follows: we first describe the theory and implementation of τ XCDFT and clearly show the involved approximations. After a short description of the computational details, needed for the reproducibility of the results, we show results on the same test set considered previously [7], as well as additional complex large molecules, such as anthracene, tetracene and fullerene. These additional large molecular systems are included because the description of their excited states' electronic structure may require more than single excitations from the reference determinant.…”