Quantum Vibronic Effects on the Electronic Properties of Molecular Crystals

Abstract

We present a study of molecular crystals, focused on the effect of nuclear quantum motion and anharmonicity on their electronic properties. We consider a system composed of relatively rigid molecules, a diamondoid crystal, and one composed of floppier molecules, NAI-DMAC, a thermally activated delayed fluorescence compound. We compute fundamental electronic gaps at the density functional theory (DFT) level of theory, with the Perdew−Burke−Erzenhof (PBE) and strongly constrained and approximately normed (SCAN) functionals, by coupling firstprinciples molecular dynamics with a nuclear quantum thermostat. We find a sizable zero-point renormalization (ZPR) of the band gaps, which is much larger in the case of diamondoids (0.6 eV) than for NAI-DMAC (0.22 eV). We show that the frozen phonon (FP) approximation, which neglects intermolecular anharmonic effects, leads to a large error (∼50%) in the calculation of the band gap ZPR. Instead, when using a stochastic method, we obtain results in good agreement with those of our quantum simulations for the diamondoid crystal. However, the agreement is worse for NAI-DMAC where intramolecular anharmonicities contribute to the ZPR. Our results highlight the importance of accurately including nuclear and anharmonic quantum effects to predict the electronic properties of molecular crystals.

Quantum Vibronic Effects on the Excitation Energies of the Nitrogen-Vacancy Center in Diamond

“…FPMD simulations were carried out using the i-PI–Qbox coupling scheme, , where the i-PI package moves the nuclei and the Qbox code provides forces on the nuclei by solving the Kohn–Sham equations. For the stochastic simulations, we generated 200 independent displaced configurations and their antithetic pairs (resulting in 400 configurations) using the PyEPFD package ,, and performed DFT single-point calculations using the Qbox code (see section S3 for further computational details).…”

“…In addition, perturbative methods invoke the rigid ion approximation; i.e., it is assumed that the ionic Hamiltonian depends on only the potential created by each nucleus independently. Although these approximations were shown to be valid for harmonic crystals like diamond, 29,35,36 their applicability has been questioned for isolated molecules, 35,37 molecular crystals, 38,39 or disordered solids. 40 Alternatively, first-principles molecular dynamics (FPMD) simulations can be employed to sample ground-and excitedstate energy surfaces, and these simulations do not utilize harmonic, independent-mode, or quadratic approximations.…”

“…Models based on the QHO yield a Gaussian probability distribution for each phonon mode, and the total probability distribution reduces to a product of independent Gaussian functions. 30,34,39 A Monte Carlo (MC) sampling is employed to sample each mode simultaneously, thus avoiding the need for the single-phonon approximation. 34 To accelerate the convergence of the MC algorithm, Monserrat proposed to sample the thermal lines (TLs) defined by two mean-value positions, σ ν,T and −σ ν,T , for each phonon mode ν, where σ ν,T is the width of the resulting Gaussian function at temperature T. 32 Later, Zacharias and Giustino proposed to consider a specific TL defined by a set of special displacements (SDs): {+σ 1,T , −σ 2,T , +σ 3,T , ..., (−1) N σ N,T }, where N is the total number of phonon modes.…”

“…31,53 The stochastic (TL and MC) and SD methods are a few to several orders of magnitude faster than the FPMD simulations. Various flavors of stochastic methods have been applied to semiconductor crystals, 33 perovskites, 54 isolated molecules, 39 and molecular crystals. 32,38,39 Despite recent efforts to include anharmonicity, 54,55 the performance of these methods in a strongly anharmonic regime is not guaranteed.…”

“…For example, we recently showed that stochastic methods can be applied to molecules and molecular crystals composed of rigid molecules but introduce large errors in the case of floppy molecules and their corresponding molecular crystals. 39 To examine the performance of stochastic methods in accurately computing quantum vibronic effects on the electronic properties of the NV − center, we performed a thermal line (TL) and a Monte Carlo (MC) simulation with a 3…”