arXiv subjects

Timothy C. Berkelbach

Publications and source records attributed to Timothy C. Berkelbach.

At least 73 records · Page 4Linked to original sources

arXiv2021

Fast periodic Gaussian density fitting by range separation

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 space 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.]

physics.chem-ph↗

arXiv2021

Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches

Coupled-cluster theory with single and double excitations (CCSD) is a promising ab initio method for the electronic structure of three-dimensional metals, for which second-order perturbation theory (MP2) diverges in the thermodynamic limit. However, due to the high cost and poor convergence of CCSD with respect to basis size, applying CCSD to periodic systems often leads to large basis set errors. In a common "composite" method, MP2 is used to recover the missing dynamical correlation energy through a focal-point correction, but the inadequacy of MP2 for metals raises questions about this approach. Here we describe how high-energy excitations treated by MP2 can be "downfolded" into a low-energy active space to be treated by CCSD. Comparing how the composite and downfolding approaches perform for the uniform electron gas, we find that the latter converges more quickly with respect to the basis set size. Nonetheless, the composite approach is surprisingly accurate because it removes the problematic MP2 treatment of double excitations near the Fermi surface. Using the method to estimate the CCSD correlation energy in the combined complete basis set and thermodynamic limits, we find CCSD recovers over 90% of the exact correlation energy at $r_s=4$. We also test the composite and downfolding approaches with the random-phase approximation used in place of MP2, yielding a method that is more effective but more expensive.

cond-mat.mtrl-sci↗

arXiv2020

Vibrational Heat-Bath Configuration Interaction

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 approach 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.

physics.chem-ph↗

arXiv2020

Simulations of Trions and Biexcitons in Layered Hybrid Organic-Inorganic Lead Halide Perovskites

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 strong 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.

cond-mat.mtrl-sci↗

arXiv2020

Regional Embedding Enables High-Level Quantum Chemistry for Surface Science

Compared to common density functionals, ab initio wave function methods can provide greater reliability and accuracy, which could prove useful when modeling adsorbates or defects of otherwise periodic systems. However, the breaking of translational symmetry necessitates large supercells that are often prohibitive for correlated wave function methods. As an alternative, we introduce the regional embedding approach, which enables correlated wave function treatments of only a target fragment of interest through small, fragment-localized orbital spaces constructed using a simple overlap criterion. Applications to the adsorption of water on lithium hydride, hexagonal boron nitride, and graphene substrates show that regional embedding combined with focal point corrections can provide converged CCSD(T) (coupled cluster) adsorption energies with very small fragment sizes.

cond-mat.mtrl-sci↗

arXiv2020

Full-Frequency GW without Frequency

Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as $O(N^6)$ where $N$ is the size of the system. Here we introduce a new formulation of the full-frequency GW approximation by exactly recasting it as an eigenvalue problem in an expanded space. This new formulation (1) avoids the use of time or frequency grids, (2) naturally precludes the common "diagonal" approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to $O(N^5)$, and (4) enables a density-fitted implementation that reduces the scaling to $O(N^4)$. We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. In this new formulation, the relation of the GW approximation to configuration interaction, coupled-cluster theory, and the algebraic diagrammatic construction is made especially apparent, providing a new direction for improvements to the GW approximation.

cond-mat.mtrl-sci↗

arXiv2020

Improved Fast Randomized Iteration Approach to Full Configuration Interaction

We present three modifications to our recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) and investigate their effects on the method's performance for Ne, H$_2$O, and N$_2$. The initiator approximation, originally developed for full configuration interaction quantum Monte Carlo, significantly reduces statistical error in FCI-FRI when few samples are used in compression operations, enabling its application to larger chemical systems. The semi-stochastic extension, which involves exactly preserving a fixed subset of elements in each compression, improves statistical efficiency in some cases but reduces it in others. We also developed a new approach to sampling excitations that yields consistent improvements in statistical efficiency and reductions in computational cost. We discuss possible strategies based on our findings for improving the performance of stochastic quantum chemistry methods more generally.

physics.comp-ph↗

arXiv2020

Recent developments in the PySCF program package

PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science.

physics.chem-ph↗

arXiv2020

Excitons in solids from periodic equation-of-motion coupled-cluster theory

We present an ab initio study of electronically excited states of three-dimensional solids using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The explicit use of translational symmetry, as implemented via Brillouin zone sampling and momentum conservation, is responsible for a large reduction in cost. Our largest system studied, which samples the Brillouin zone using 64 k-points (a 4x4x4 mesh) corresponds to a canonical EOM-CCSD calculation of 768 electrons in 640 orbitals. We study eight simple semiconductors and insulators, with direct singlet excitation energies in the range of 3 to 15 eV. Our predicted excitation energies exhibit a mean absolute error of 0.27 eV when compared to experiment. We furthermore calculate the energy of excitons with nonzero momentum and compare the exciton dispersion of LiF with experimental data from inelastic X-ray scattering. By calculating excitation energies under strain, we extract hydrostatic deformation potentials in order to quantify the strength of interactions between excitons and acoustic phonons. Our results indicate that coupled-cluster theory is a promising method for the accurate study of a variety of exciton phenomena in solids.

cond-mat.mtrl-sci↗

arXiv2019

A unification of the Holstein polaron and dynamic disorder pictures of charge transport in organic semiconductors

We present a unified and nonperturbative method for calculating spectral and transport properties of Hamiltonians with simultaneous Holstein (diagonal) and Peierls (off-diagonal) electron-phonon coupling. Our approach is motivated by the separation of energy scales in semiconducting organic molecular cystals, in which electrons couple to high-frequency intramolecular Holstein modes and to low-frequency intermolecular Peierls modes. We treat Peierls modes as quasi-classical dynamic disorder, while Holstein modes are included with a Lang-Firsov polaron transformation and no narrow-band approximation. Our method reduces to the popular polaron picture due to Holstein coupling and the dynamic disorder picture due to Peierls coupling. We derive an expression for efficient numerical evaluation of the frequency-resolved optical conductivity based on the Kubo formula and obtain the DC mobility from its zero-frequency component. We also use our method to calculate the electron-addition Green's function corresponding to the inverse photoemission spectrum. For realistic parameters, temperature-dependent DC mobility is largely determined by the Peierls-induced dynamic disorder with minor quantitative corrections due to polaronic band-narrowing, and an activated regime is not observed at relevant temperatures. In contrast, for frequency-resolved observables, a quantum mechanical treatment of the Holstein coupling is qualitatively important for capturing the phonon replica satellite structure.

cond-mat.mtrl-sci↗

arXiv2019

Ab Initio Linear and Pump-Probe Spectroscopy of Excitons in Molecular Crystals

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 performed 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.

cond-mat.mtrl-sci↗

arXiv2019

Thickness-dependent optical properties of layered hybrid organic-inorganic halide perovskites: A tight-binding GW-BSE study

We present a many-body calculation of the band structure and optical spectrum of the layered hybrid organic-inorganic halide perovskites in the Ruddlesden-Popper phase with the general formula A$^{'}_{2}$A$_{n-1}$M$_{n}$X$_{3n+1}$, focusing specifically on the lead iodide family. We calculate the mean-field band structure with spin-orbit coupling, quasiparticle corrections within the GW approximation, and optical spectra using the Bethe-Salpeter equation. The model is parameterized by first-principles calculations and classical electrostatic screening, enabling an accurate but cost-effective study of large unit cells and corresponding thickness-dependent properties. A transition of the electronic and optical properties from quasi-two-dimensional behavior to three-dimensional behavior is shown for increasing $n$ and the nonhydrogenic character of the excitonic Rydberg series is analyzed. The thickness-dependent 1s and 2s exciton energy levels are in good agreement with recently reported experiments and the 1s exciton binding energy is calculated to be 302 meV for $n=1$, 97 meV for $n=5$, and 37 meV for $n=\infty$ (bulk MAPbI3).

cond-mat.mtrl-sci↗

arXiv2019

Coupled-cluster impurity solvers for dynamical mean-field theory

We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest coupled cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.

cond-mat.str-el↗

arXiv2019

Quantum plasmons and intraband excitons in doped nanoparticles: Failure of the Tamm-Dancoff approximation and importance of electron-hole attraction

We use excited-state quantum chemistry techniques to investigate the intraband absorption of doped semiconductor nanoparticles as a function of doping density, nanoparticle radius, and material properties. The excess electrons are modeled as interacting particles confined in a sphere. We compare the predictions of various single-excitation theories, including time-dependent Hartree-Fock, the random-phase approximation, and configuration interaction with single excitations. We find that time-dependent Hartree-Fock most accurately describes the character of the excitation, as compared to equation-of-motion coupled-cluster theory with single and double excitations. The excitation evolves from confinement-dominated, to excitonic, to plasmonic with increasing number of electrons at fixed density, and the threshold number of electrons to produce a plasmon increases with density due to quantum confinement. Exchange integrals (attractive electron-hole interactions) are essential to properly describe excitons, and de-excitations (i.e.~avoidance of the Tamm-Dancoff approximation) are essential to properly describe plasmons. We propose a schematic model whose analytic solutions closely reproduce our numerical calculations. Our results are in good agreement with experimental spectra of doped ZnO nanoparticles at a doping density of $1.4\times 10^{20}$ cm$^{-3}$.

cond-mat.mes-hall↗

arXiv2019

Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error using Fast Randomized Iteration

We introduce a family of methods for the full configuration interaction problem in quantum chemistry, based on the fast randomized iteration (FRI) framework [L.-H. Lim and J. Weare, SIAM Rev. 59, 547 (2017)]. These methods, which we term "FCI-FRI," stochastically impose sparsity during iterations of the power method and can be viewed as a generalization of full configuration interaction quantum Monte Carlo (FCIQMC) without walkers. In addition to the multinomial scheme commonly used to sample excitations in FCIQMC, we present a systematic scheme where excitations are not sampled independently. Performing ground-state calculations on five small molecules at fixed cost, we find that the systematic FCI-FRI scheme is 11 to 45 times more statistically efficient than the multinomial FCI-FRI scheme, which is in turn 1.4 to 178 times more statistically efficient than the original FCIQMC algorithm.

physics.chem-ph↗

arXiv2019

Ab Initio Lifetime and Concomitant Double-Excitation Character of Plasmons at Metallic Densities

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 excitations (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.

physics.chem-ph↗

arXiv2019

Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules

The $GW$ approximation is based on the neglect of vertex corrections, which appear in the exact self-energy and the exact polarizability. Here, we investigate the importance of vertex corrections in the polarizability only. We calculate the polarizability with equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD), which rigorously includes a large class of diagrammatically-defined vertex corrections beyond the random phase approximation (RPA). As is well-known, the frequency-dependent polarizability predicted by EOM-CCSD is quite different and generally more accurate than that predicted by the RPA. We evaluate the effect of these vertex corrections on a test set of 20 atoms and molecules. When using a Hartree-Fock reference, ionization potentials predicted by the $GW$ approximation with the RPA polarizability are typically overestimated with a mean absolute error of 0.3 eV. However, those predicted with a vertex-corrected polarizability are typically underestimated with an increased mean absolute error of 0.5 eV. This result suggests that vertex corrections in the self-energy cannot be neglected, at least for molecules. We also assess the behavior of eigenvalue self-consistency in vertex-corrected $GW$ calculations, finding a further worsening of the predicted ionization potentials.

cond-mat.mtrl-sci↗

arXiv2018

Many-Body Simulation of Two-Dimensional Electronic Spectroscopy of Excitons and Trions in Monolayer Transition-Metal Dichalcogenides

We present a many-body formalism for the simulation of time-resolved nonlinear spectroscopy and apply it to study the coherent interaction between excitons and trions in doped transition-metal dichalcogenides. Although the formalism can be straightforwardly applied in a first-principles manner, for simplicity we use a parameterized band structure and a static model dielectric function, both of which can be obtained from a calculation using the $GW$ approximation. Our simulation results shed light on the interplay between singlet and triplet trions in molybdenum- and tungsten-based compounds. Our two-dimensional electronic spectra are in excellent agreement with recent experiments and we accurately reproduce the beating of a cross-peak signal indicative of quantum coherence between excitons and trions. Although we confirm that the quantum beats in molybdenum-based monolayers unambigously reflect the exciton-trion coherence time, they are shown here to provide a lower-bound to the coherence time of tungsten analogues due to a destructive interference emerging from coexisting singlet and triplet trions.

cond-mat.mtrl-sci↗