Comparison of quantum Monte Carlo with time-dependent and static density-functional theory calculations of diamondoid excitation energies and Stokes shifts

Abstract

We compute the absorption and emission energies and hence Stokes shifts of small diamondoids as a function of size using different theoretical approaches, including density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations. The absorption spectra of these molecules are also investigated by time-dependent DFT and compared with experiment. We analyze the structural distortion and formation of a self-trapped exciton in the excited state, and we study the effects of these on the Stokes shift as a function of size. Compared to recent experiments, QMC overestimates the excitation energies by about 0.8(1) eV on average. Benefiting from a cancellation of errors, the optical gaps obtained in DFT calculations with the B3LYP functional are in better agreement with experiment. It is also shown that time-dependent B3LYP calculations can reproduce most of the features found in the experimental spectra. According to our calculations, the structures of diamondoids in the excited state show a distortion which is hardly noticeable compared to that found for methane. As the number of diamond cages is increased, the distortion mechanism abruptly changes character. We have shown that the Stokes shift is size dependent and decreases with the number of diamond cages. If we neglect orbital symmetry effects on the optical excitations, the rate of decrease in the Stokes shift is, on average, 0.1 eV per cage for small diamondoids.

Quantum nuclear dynamics in the photophysics of diamondoids

“…Our calculations yield substantial redshifts of 650, 550 and 490 meV for adamantane, diamantane and triamantane, respectively, reflecting significant structural relaxations upon photoexcitation. with the calculations of Marsusi et al 21 (Supplementary Note 1) reduces the discrepancy between experimental and Quantum Monte Carlo-calculated optical gaps from 0.8 to 0.3 eV. This difference is within the error bar estimated by Marsusi et al 21 , and is of the order of the difference between DMC data and GW calculations of the ionization potentials 32 .…”

“…with the calculations of Marsusi et al 21 (Supplementary Note 1) reduces the discrepancy between experimental and Quantum Monte Carlo-calculated optical gaps from 0.8 to 0.3 eV. This difference is within the error bar estimated by Marsusi et al 21 , and is of the order of the difference between DMC data and GW calculations of the ionization potentials 32 . This result identifies the change in quantum nuclear energy upon photoexcitation as the missing physics in previous attempts at explaining the optical properties of diamondoids 6,21,33 .…”

“…In this work, we demonstrate the remarkable role played by nuclear quantum motion in the fundamental photophysics of the diamondoids. Previous many-body Quantum Monte Carlo calculations 6,21 have found the onset of optical absorption to be almost an electronvolt higher than measured in experiments, and it has been suggested that vibronic effects may be responsible for the discrepancy 21 . Here, we combine first-principles calculations with Monte Carlo integration techniques to show that not only does the nuclear motion substantially renormalize the calculated optical gaps but also that vibronic couplings dramatically modify the absorption lineshapes, even at zero temperature.…”

Size and shape dependent photoluminescence and excited state decay rates of diamondoids

“…[8][9][10][11][12][13][14][15] In particular, the observation of photoluminescence (PL) in reduced-dimensional semiconductor systems, which otherwise exhibit an indirect band gap, like Si and C (diamond), opens possibilities to tailor their optical properties and to interface with already existing technologies. [2][3][4] However, despite numerous studies, [2][3][4]16,17 the fundamental photophysical processes in such systems still are not fully understood. In order to gain a deeper insight into these processes, it is desirable to perform experiments under idealized conditions, i.e.…”

“…high excitation energies with respect to the optical gap [E gap ]) caused the spectrum to be completely congested, thus lacking any vibrational fine structure, making it difficult to compare with calculations. 16 The optical properties of gas phase polymantanes have so far only been investigated with absorption spectroscopy. 2 This study showed that the basic shape (1-, 2-, & 3-dimensional) of the diamondoids is reflected in the overall shape of its absorption spectrum.…”