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Register a new userAb Initio Bethe-Salpeter Equation Approach to Neutral Excitations in Molecules with Numeric Atom-Centered Orbitals
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The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is a successful approach for calculating the optical gaps and spectra of solids and also for predicting the neutral excitations of small molecules. We here present an all-electron implementation of the GW+BSE formalism for molecules, using numeric atom-centered orbital (NAO) basis sets. We present benchmarks for low-lying excitation energies for a set of small organic molecules, denoted in the literature as Thiels set. Literature reference data based on Gaussian-type orbitals are reproduced to about one meV precision for the molecular benchmark set, when using the same GW quasiparticle energies and basis sets as the input to the BSE calculations. For valence correlation consistent NAO basis sets, as well as for standard NAO basis sets for ground state density-functional theory with extended augmentation functions, we demonstrate excellent convergence of the predicted low-lying excitations to the complete basis set limit. A simple and affordable augmented NAO basis set denoted tier2+aug2 is recommended as a particularly efficient formulation for production calculations. We finally demonstrate that the same convergence properties also apply to linear-response time-dependent density functional theory within the NAO formalism.
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We present first-principles many-body perturbation theory calculations of the quasiparticle electronic structure and of the optical response of HfO$_2$ polymorphs. We use the $GW$ approximation including core electrons by the projector augmented wave (PAW) method and performing a quasiparticle self-consistency also on wavefunctions (QS$GW$). In addition, we solve the Bethe-Salpeter equation on top of $GW$ to calculate optical properties including excitonic effects. For monoclinic HfO$_2$ we find a fundamental band gap of $E_g = 6.33$ eV (with the direct band gap at $E_g^d = 6.41$ eV), and an exciton binding energy of 0.57 eV, which situates the optical gap at $E^o_g = 5.85$ eV. The latter is in the range of spectroscopic ellipsometry (SE) experimental estimates (5.5-6 eV), whereas our electronic band gap is well beyond experimental photoemission (PE) estimates ($< 6$ eV) and previous $GW$ works. Our calculated density of states and optical absorption spectra compare well to raw PE and SE spectra. This suggests that our predictions of both optical and electronic gaps are close to, or at least lower bounds of, the real values.
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 not 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.
In the development of highly efficient photovoltaic cells, solid perovskite systems have demonstrated unprecedented promise, with the figure of merit exceeding nineteen percent of efficiency. In this paper, we investigate the optical and vibrational properties of organometallic cubic perovskite CH3NH3PbI3 using first-principles calculations. For accurate theoretical description, we go beyond conventional density functional theory (DFT), and calculated optical conductivity using relativist quasi-particle (GW) correction. Incorporating these many-body effects, we further solve Bethe-Salpeter equations (BSE) for excitons, and found enhanced optical conductivity near the gap edge. Due to the presence of organic methylammonium cations near the center of the perovskite cell, the system is sensitive to low energy vibrational modes. We estimate the phonon modes of CH3NH3PbI3 using small displacement approach, and further calculate the infrared absorption (IR) spectra. Qualitatively, our calculations of low-energy phonon frequencies are in good agreement with our terahertz measurements. Therefore, for both energy scales (around 2 eV and 0-20 meV), our calculations reveal the importance of many-body effects and their contributions to the desirable optical properties in the cubic organometallic perovskites system.
The accurate prediction of singlet and triplet excitation energies is of significant fundamental interest and is critical for many applications. An area of intense research, most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiels set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relatively to higher level theories. Finally, we find that BSE-TDA calculations built on good DFT starting points, such as those utilizing optimally-tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.
When using atom-centered integration grids, the portion of the grid that belongs to a certain atom also moves when this atom is displaced. In the paper, we investigate the moving-grid effect in the calculation of the harmonic vibrational frequencies when using all-electron full-potential numeric atomic-centered orbitals as the basis set. We find that, unlike the first order derivative (i.e., forces), the moving-grid effect plays an essential role for the second order derivatives (i.e., vibrational frequencies). Further analysis reveals that predominantly diagonal force constant terms are affected, which can be bypassed efficiently by invoking translational symmetry. Our approaches have been demonstrated in both finite (molecules) and extended (periodic) systems.
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