Vertical and adiabatic excitations in anthracene from quantum Monte Carlo: Constrained energy minimization for structural and electronic excited-state properties in the JAGP ansatz

Abstract

We study the ionization energy, electron affinity, and the π → π(∗) ((1)La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the (1)La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral (1)La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.

Excitation energies from diffusion Monte Carlo using selected configuration interaction nodes

“…(7) 7. 35(2) 7.37(2) 7.30(1) 0.07(2) exDMC 7.36(1) 7. 35(1) 7.30(1) 0.06(1) Max(B) 0.05(1) 0.06(2) 0.02(1) 3 A 2 (n → 3p) sCI(4) 9.27(1) 9.28(1) 9.28(1) 0.01(1) sCI(5) 9.31(1) 9.32(1) 9.31(1) 0.01(1) sCI(6) 9.33(1) 9.31(1) 9.28(1) 0.05(1) sCI (7) 9.30(2) 9.34(2) 9.28(1) 0.06(2) exDMC 9.33(1) 9.32(1) 9.28(1) 0.05(2) Max(B) 0.06(1) 0.06(2) 0.03(1) 3 A 1 (n → 3s) sCI(4) 9.59(1) 9.58(1) 9.58(1) 0.01(1) sCI(5) 9.61(1) 9.60(1) 9.58(1) 0.03(1) sCI(6) 9.62(1) 9.59(1) 9.58(1) 0.04(1) sCI (7) 9.61(3) 9.60(2) 9.57(1) 0.04(3) exDMC 9.63(1) 9.60(1) 9.59(1) 0.04(2) Max(B) 0.04(1) 0.02(1) 0.02 (1) have a Rydberg character, hence exhibiting a strong basis set sensitivity.…”

Fate of the open-shell singlet ground state in the experimentally accessible acenes: A quantum Monte Carlo study

“…To optimize the previously described JSD and JDD wave functions, the λ i, j coefficients are constrained at a fixed rank of the geminal matrix, and diagonalized at each energy minimization step to get new MOs. This scheme has already been employed in the QMC calculation of the low-lying energy spectrum of the anthracene molecule 49 , and in the Ref. 52 for the energy optimization of diradical molecules.…”

Evaluating theGWApproximation with CCSD(T) for Charged Excitations Across the Oligoacenes

“…[2][3][4][5] In addition, acenes and other polycyclic aromatic hydrocarbons are abundant in the universe and their properties are of importance to astrophysics. Charged excitations, namely excited states associated with electron addition and removal, have been well-studied for acene molecules with a variety of computational approaches, including density functional theory (DFT), many-body perturbation theory (MBPT), and wavefunction-based quantum chemistry methods, [9][10][11] and hence constitute an excellent benchmark case for the development and refinement of methods. Additionally, aspects of charged excitations for acenes are still not entirely understood.…”