We present a method to efficiently combine the computation of electron-electron and electron-phonon self-energies, which enables the evaluation of electron-phonon coupling at the $G_0W_0$ level of theory for systems with hundreds of atoms. In additio
n, our approach, which is a generalization of a method recently proposed for molecules [J. Chem. Theory Comput. 2018, 14, 6269-6275], enables the inclusion of non-adiabatic and temperature effects at no additional computational cost. We present results for diamond and defects in diamond and discuss the importance of numerically accurate $G_0W_0$ band structures to obtain robust predictions of zero point renormalization (ZPR) of band gaps, and of the inclusion of non-adiabatic effect to accurately compute the ZPR of defect states in the band gap.
Optically and magnetically active point defects in semiconductors are interesting platforms for the development of solid-state quantum technologies. Their optical properties are usually probed by measuring photoluminescence spectra, which provide inf
ormation on excitation energies and on the interaction of electrons with lattice vibrations. We present a combined computational and experimental study of photoluminescence spectra of defects in diamond and SiC, aimed at assessing the validity of theoretical and numerical approximations used in first principles calculations, including the use of the Franck-Condon principle and the displaced harmonic oscillator approximation. We focus on prototypical examples of solid-state qubits, the divacancy centers in SiC and the nitrogen-vacancy in diamond, and we report computed photoluminescence spectra as a function of temperature that are in very good agreement with the measured ones. As expected we find that the use of hybrid functionals leads to more accurate results than semilocal functionals. Interestingly our calculations show that constrained density functional theory (CDFT) and time-dependent hybrid DFT perform equally well in describing the excited state potential energy surface of triplet states; our findings indicate that CDFT, a relatively cheap computational approach, is sufficiently accurate for the calculations of photoluminescence spectra of the defects studied here. Finally, we find that only by correcting for finite-size effects and extrapolating to the dilute limit, one can obtain a good agreement between theory and experiment. Our results provide a detailed validation protocol of first principles calculations of photoluminescence spectra, necessary both for the interpretation of experiments and for robust predictions of the electronic properties of point defects in semiconductors.
Quantum computers hold promise to greatly improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable on classical architectures. Here, we discuss computational fram
eworks to carry out electronic structure calculations of solids on noisy intermediate scale quantum computers using embedding theories and effective many-body Hamiltonians. We focus on a specific class of materials, i.e., spin defects in solids, which are promising systems to build future quantum technologies, e.g., computers, sensors and devices for quantum communications. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear within reach.
We study the effect of quantum vibronic coupling on the electronic properties of carbon allotropes, including molecules and solids, by combining path integral first principles molecular dynamics (FPMD) with a colored noise thermostat. In addition to
avoiding several approximations commonly adopted in calculations of electron-phonon coupling, our approach only adds a moderate computational cost to FPMD simulations and hence it is applicable to large supercells, such as those required to describe amorphous solids. We predict the effect of electron-phonon coupling on the fundamental gap of amorphous carbon, and we show that in diamond the zero-phonon renormalization of the band gap is larger than previously reported.
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We present a
detailed derivation of a quantum embedding theory recently introduced, which is based on the definition of effective Hamiltonians. The effect of the environment on a chosen active space is accounted for through screened Coulomb interactions evaluated using density functional theory. Importantly, the random phase approximation is not required and the evaluation of virtual electronic orbitals is circumvented with algorithms previously developed in the context of calculations based on many-body perturbation theory. In addition, we generalize the quantum embedding theory to active spaces composed of orbitals that are not eigenstates of Kohn-Sham Hamiltonians. Finally, we report results for spin defects in semiconductors.
Accurate and efficient calculations of absorption spectra of molecules and materials are essential for the understanding and rational design of broad classes of systems. Solving the Bethe-Salpeter equation (BSE) for electron-hole pairs usually yields
accurate predictions of absorption spectra, but it is computationally expensive, especially if thermal averages of spectra computed for multiple configurations are required. We present a method based on machine learning to evaluate a key quantity entering the definition of absorption spectra: the dielectric screening. We show that our approach yields a model for the screening that is transferable between multiple configurations sampled during first principles molecular dynamics simulations; hence it leads to a substantial improvement in the efficiency of calculations of finite temperature spectra. We obtained computational gains of one to two orders of magnitude for systems with 50 to 500 atoms, including liquids, solids, nanostructures, and solid/liquid interfaces. Importantly, the models of dielectric screening derived here may be used not only in the solution of the BSE but also in developing functionals for time-dependent density functional theory (TDDFT) calculations of homogeneous and heterogeneous systems. Overall, our work provides a strategy to combine machine learning with electronic structure calculations to accelerate first principles simulations of excited-state properties.
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power
of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environment. Here we present a quantum embedding theory for the calculation of strongly-correlated electronic states of active regions, with the rest of the system described within density functional theory. We demonstrate the accuracy and effectiveness of the approach by investigating several defect quantum bits in semiconductors that are of great interest for quantum information technologies. We perform calculations on quantum computers and show that they yield results in agreement with those obtained with exact diagonalization on classical architectures, paving the way to simulations of realistic materials on near-term quantum computers.
We present a method to compute optical spectra and exciton binding energies of molecules and solids based on the solution of the Bethe-Salpeter equation (BSE) and the calculation of the screened Coulomb interaction in finite field. The method does no
t require the explicit evaluation of dielectric matrices nor of virtual electronic states, and can be easily applied without resorting to the random phase approximation. In addition it utilizes localized orbitals obtained from Bloch states using bisection techniques, thus greatly reducing the complexity of the calculation and enabling the efficient use of hybrid functionals to obtain single particle wavefunctions. We report exciton binding energies of several molecules and absorption spectra of condensed systems of unprecedented size, including water and ice samples with hundreds of atoms.
We derive a dielectric-dependent hybrid functional which accurately describes the electronic properties of heterogeneous interfaces and surfaces, as well as those of three- and two-dimensional bulk solids. The functional, which does not contain any a
djustable parameter, is a generalization of self-consistent hybrid functionals introduced for homogeneous solids, where the screened Coulomb interaction is defined using a spatially varying, local dielectric function. The latter is determined self-consistently using density functional calculations in finite electric fields. We present results for the band gaps and dielectric constants of 3D and 2D bulk materials, and band offsets for interfaces, showing an accuracy comparable to that of GW calculations.
We describe a finite-field approach to compute density response functions, which allows for efficient $G_0W_0$ and $G_0W_0Gamma_0$ calculations beyond the random phase approximation. The method is easily applicable to density functional calculations
performed with hybrid functionals. We present results for the electronic properties of molecules and solids and we discuss a general scheme to overcome slow convergence of quasiparticle energies obtained from $G_0W_0Gamma_0$ calculations, as a function of the basis set used to represent the dielectric matrix.
