We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consisten
tly defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative, systematically improvable through its clusters extensions, and usable with classical or quantum impurity solvers, depending on the importance of nuclear quantum effects. When tested on models of anharmonic optical and acoustic phonons, we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures.
We derive distance-dependent estimators for two-center and three-center electron repulsion integrals over a short-range Coulomb potential, $textrm{erfc}(omega r_{12})/r_{12}$. These estimators are much tighter than one based on the Schwarz inequality
and can be viewed as a complement to the distance-dependent estimators for four-center short-range Coulomb integrals and for two-center and three-center full Coulomb integrals previously reported. Because the short-range Coulomb potential is commonly used in solid-state calculations, including those with the HSE functional and with our recently introduced range-separated periodic Gaussian density fitting, we test our estimators on a diverse set of periodic systems using a wide range of the range-separation parameter $omega$. These tests demonstrate the robust tightness of our estimators, which are then used with integral screening to calculate periodic three-center short-range Coulomb integrals with linear scaling in system size.
We present ab initio absorption spectra of six three-dimensional semiconductors and insulators calculated using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The spectra are calculate
d efficiently by solving a system of linear equations at each frequency, giving access to an energy range of tens of eV without explicit enumeration of excited states. We assess the impact of Brillouin zone sampling, for which it is hard to achieve convergence due to the cost of EOM-CCSD. Although our most converged spectra exhibit lineshapes that are in good agreement with experiment, they are uniformly shifted to higher energies by about 1 eV. We tentatively attribute this discrepancy to a combination of vibrational effects and the remaining electron correlation, i.e., triple excitations and above.
Despite its reasonable accuracy for ground-state properties of semiconductors and insulators, second-order Moller-Plesset perturbation theory (MP2) significantly underestimates band gaps. Here, we evaluate the band gap predictions of partitioned equa
tion-of-motion MP2 (P-EOM-MP2), which is a second-order approximation to equation-of-motion coupled-cluster theory with single and double excitations. On a test set of elemental and binary semiconductors and insulators, we find that P-EOM-MP2 overestimates band gaps by 0.3 eV on average, which can be compared to the underestimation by 0.6 eV on average exhibited by the G0W0 approximation with a PBE reference. We show that P-EOM-MP2, when interpreted as a Greens function-based theory, has a self-energy that includes all first- and second- order diagrams and a few third-order diagrams. We find that the GW approximation performs better for materials with small gaps and P-EOM-MP2 performs better for materials with large gaps, which we attribute to their superior treatment of screening and exchange, respectively.
Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Randomized iterative methods allow for the estimation of a single dominant eigenvalue at reduced cost by leveraging repeated r
andom sampling and averaging. We present a general approach to extending such methods for the estimation of multiple eigenvalues and demonstrate its performance for problems in quantum chemistry with matrices as large as 28 million by 28 million.
We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in real spac
e and the long-range part in reciprocal space. With a few algorithmic optimizations, we show that this new method -- which we call range-separated GDF (RSGDF) -- scales sublinearly to linearly with the number of $k$-points for small to medium-sized $k$-point meshes that are commonly used in periodic calculations with electron correlation. Numerical results on a few three-dimensional solids show about $10$-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about $10^{-5}~E_{textrm{h}}$ in the converged Hartree-Fock energy with default auxiliary basis sets and can be systematically reduced by increasing the size of the auxiliary basis with little extra work. [The article has been accepted by The Journal of Chemical Physics.]
We introduce vibrational heat-bath configuration interaction (VHCI) as an accurate and efficient method for calculating vibrational eigenstates of anharmonic systems. Inspired by its origin in electronic structure theory, VHCI is a selected CI approa
ch that uses a simple criterion to identify important basis states with a pre-sorted list of anharmonic force constants. Screened second-order perturbation theory and simple extrapolation techniques provide significant improvements to variational energy estimates. We benchmark VHCI on four molecules with 12 to 48 degrees of freedom and use anharmonic potential energy surfaces truncated at fourth and sixth order. For all molecules studied, VHCI produces vibrational spectra of tens or hundreds of states with sub-wavenumber accuracy at low computational cost.
Behaving like atomically-precise two-dimensional quantum wells with non-negligible dielectric contrast, the layered HOIPs have strong electronic interactions leading to tightly bound excitons with binding energies on the order of 500 meV. These stron
g interactions suggest the possibility of larger excitonic complexes like trions and biexcitons, which are hard to study numerically due to the complexity of the layered HOIPs. Here, we propose and parameterize a model Hamiltonian for excitonic complexes in layered HOIPs and we study the correlated eigenfunctions of trions and biexcitons using a combination of diffusion Monte Carlo and very large variational calculations with explicitly correlated Gaussian basis functions. Binding energies and spatial structures of these complexes are presented as a function of the layer thickness. The trion and biexciton of the thinnest layered HOIP have binding energies of 35 meV and 44 meV, respectively, whereas a single exfoliated layer is predicted to have trions and biexcitons with equal binding enegies of 48 meV. We compare our findings to available experimental data and to that of other quasi-two-dimensional materials.
Linear and non-linear spectroscopies are powerful tools used to investigate the energetics and dynamics of electronic excited states of both molecules and crystals. While highly accurate emph{ab initio} calculations of molecular spectra can be perfor
med relatively routinely, extending these calculations to periodic systems is challenging. Here, we present calculations of the linear absorption spectrum and pump-probe two-photon photoemission spectra of the naphthalene crystal using equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). Molecular acene crystals are of interest due to the low-energy multi-exciton singlet states they exhibit, which have been studied extensively as intermediates involved in singlet fission. Our linear absorption spectrum is in good agreement with experiment, predicting a first exciton absorption peak at 4.4 eV, and our two-photon photoemission spectra capture the behavior of multi-exciton states, whose double-excitation character cannot be captured by current methods. The simulated pump-probe spectra provide support for existing interpretations of two-photon photoemission in closely-related acene crystals such as tetracene and pentacene.
The accurate calculation of excited state properties of interacting electrons in the condensed phase is an immense challenge in computational physics. Here, we use state-of-the-art equation-of-motion coupled-cluster theory with single and double exci
tations (EOM-CCSD) to calculate the dynamic structure factor, which can be experimentally measured by inelastic x-ray and electron scattering. Our calculations are performed on the uniform electron gas at densities corresponding to Wigner-Seitz radii of $r_s=5$, 4, and 3 corresponding to the valence electron densities of common metals. We compare our results to those obtained using the random-phase approximation, which is known to provide a reasonable description of the collective plasmon excitation and which resums only a small subset of the polarizability diagrams included in EOM-CCSD. We find that EOM-CCSD, instead of providing a perturbative improvement on the RPA plasmon, predicts a many-state plasmon resonance, where each contributing state has a double-excitation character of 80% or more. This finding amounts to an ab initio treatment of the plasmon linewidth, which is in good quantitative agreement with previous diagrammatic calculations, and highlights the strongly correlated nature of lifetime effects in condensed-phase electronic structure theory.
