arXiv subjects

Timothy C. Berkelbach

Publications and source records attributed to Timothy C. Berkelbach.

At least 55 records · Page 3Linked to original sources

arXiv2022

Understanding and eliminating spurious modes in variational Monte Carlo using collective variables

The use of neural network parametrizations to represent the ground state in variational Monte Carlo (VMC) calculations has generated intense interest in recent years. However, as we demonstrate in the context of the periodic Heisenberg spin chain, this approach can produce unreliable wave function approximations. One of the most obvious signs of failure is the occurrence of random, persistent spikes in the energy estimate during training. These energy spikes are caused by regions of configuration space that are over-represented by the wave function density, which are called ``spurious modes'' in the machine learning literature. After exploring these spurious modes in detail, we demonstrate that a collective-variable-based penalization yields a substantially more robust training procedure, preventing the formation of spurious modes and improving the accuracy of energy estimates. Because the penalization scheme is cheap to implement and is not specific to the particular model studied here, it can be extended to other applications of VMC where a reasonable choice of collective variable is available.

physics.chem-ph↗

arXiv2022

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of strongly correlated molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods -- including heat-bath CI, the density matrix renormalization group approach, and FCIQMC -- to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.

physics.comp-ph↗

arXiv2022

Excitons and their Fine Structure in Lead Halide Perovskite Nanocrystals from Atomistic GW/BSE Calculations

Atomistically detailed computational studies of nanocrystals, such as those derived from the promising lead-halide perovskites, are challenging due to the large number of atoms and lack of symmetries to exploit. Here, focusing on methylammonium lead iodide nanocrystals, we combine a real-space tight binding model with the GW approximation to the self-energy and obtain exciton wavefunctions and absorption spectra via solutions of the associated Bethe-Salpeter equation. We find that the size dependence of carrier confinement, dielectric contrast, electron-hole exchange, and exciton binding energies has a strong impact on the lowest excitation energy, which can be tuned by almost 1 eV over the diameter range of 2-6 nm. Our calculated excitation energies are about 0.2 eV higher than experimentally measured photoluminescence, and they display the same qualitative size dependence. Focusing on the fine structure of the band-edge excitons, we find that the lowest-lying exciton is spectroscopically dark and about 20-30 meV lower in energy than the higher-lying triplet of bright states, whose degeneracy is slightly broken by crystal field effects.

cond-mat.mtrl-sci↗

arXiv2022

Anharmonic Lattice Dynamics from Vibrational Dynamical Mean-Field Theory

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-consistently 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 cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects), and can be combined with existing low-level diagrammatic theories of anharmonicity. 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 test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH+VDMFT approach.

cond-mat.mtrl-sci↗

arXiv2022

Accurate thermochemistry of covalent and ionic solids from spin-component-scaled MP2

We study the performance of spin-component-scaled second-order Møller-Plesset perturbation theory (SCS-MP2) for the prediction of the lattice constant, bulk modulus, and cohesive energy of 12 simple, three-dimensional, covalent and ionic semiconductors and insulators. We find that SCS-MP2 and the simpler scaled opposite-spin MP2 (SOS-MP2) yield predictions that are significantly improved over the already good performance of MP2. Specifically, when compared to experimental values with zero-point vibrational corrections, SCS-MP2 (SOS-MP2) yields mean absolute errors of 0.015 (0.017) Å for the lattice constant, 3.8 (3.7) GPa for the bulk modulus, and 0.06 (0.08) eV for the cohesive energy, which are smaller than those of leading density functionals by about a factor of two or more. We consider a reparameterization of the spin scaling parameters and find that the optimal parameters for these solids are very similar to those already in common use in molecular quantum chemistry, suggesting good transferability and reliable future applications to surface chemistry on insulators.

cond-mat.mtrl-sci↗

arXiv2022

Integral-direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal

We present an algorithm and implementation of integral-direct, density-fitted Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) for periodic systems. The new code eliminates the formerly prohibitive storage requirements and allows us to study systems one order of magnitude larger than before at the periodic MP2 level. We demonstrate the significance of the development by studying the benzene crystal in both the thermodynamic limit and the complete basis set limit, for which we predict an MP2 cohesive energy of $-72.8$ kJ/mol, which is about $10$--$15$ kJ/mol larger in magnitude than all previously reported MP2 calculations. Compared to the best theoretical estimate from literature, several modified MP2 models approach chemical accuracy in the predicted cohesive energy of the benzene crystal and hence may be promising cost-effective choices for future applications on molecular crystals.

physics.chem-ph↗

arXiv2022

Conductivity of an electron coupled to anharmonic phonons

We study the impact of phonon anharmonicity on the electronic dynamics of soft materials using a nonperturbative quantum-classical approach. The method is applied to a one-dimensional model of doped organic semiconductors with low-frequency intermolecular lattice phonons. We find that anharmonicity that leads to phonon hardening increases the mobility and anharmonicity that leads to phonon softening decreases the mobility. We also test various approximations, including the use of adiabatic phonon disorder, an effective harmonic model with temperature-dependent frequencies, and the Boltzmann transport equation with second-order perturbation theory scattering rates. Overall, we find surprisingly good agreement between all methods but that accounting for phonon anharmonicity is important for accurate prediction of electronic transport including both quantitative mobility values and their qualitative temperature dependence. For the model studied, phonon lifetime effects have relatively little impact on carrier transport, but the effective frequency shift due to anharmonicity is essential. In cases with highly asymmetric, non-Gaussian disorder, an effective harmonic model cannot quantitatively reproduce mobilities or finite-frequency conductivity, and this is especially true for acoustic phonons.

cond-mat.mtrl-sci↗

arXiv2022

The normal state of attractive Fermi gases from coupled-cluster theory

We introduce coupled-cluster (CC) theory for the numerical study of the normal state of two-component, dilute Fermi gases with attractive, short-range interactions at zero temperature. We focus on CC theory with double excitations (CCD) and discuss its close relationship with -- and improvement upon -- the t-matrix approximation, i.e., the resummation of ladder diagrams via a random-phase approximation. We further discuss its relationship with Chevy's variational wavefunction ansatz for the Fermi polaron and argue that CCD is its natural extension to nonzero minority species concentrations. Studying normal state energetics for a range of interaction strengths below and above unitarity, we find that CCD yields good agreement with fixed-node diffusion Monte Carlo. We find that CCD does not converge for small polarizations and large interaction strengths, which we speculatively attribute to the nascent instability to a superfluid state.

cond-mat.quant-gas↗

arXiv2022

Ground-state properties of metallic solids from ab initio coupled-cluster theory

Metallic solids are a challenging target for wavefunction-based electronic structure theories and have not been studied in great detail by such methods. Here, we use coupled-cluster theory with single and double excitations (CCSD) to study the structure of solid lithium and aluminum using optimized Gaussian basis sets. We calculate the equilibrium lattice constant, bulk modulus, and cohesive energy and compare them to experimental values, finding accuracy comparable to common density functionals. Because the quantum chemical "gold standard" CCSD(T) (CCSD with perturbative triple excitations) is inapplicable to metals in the thermodynamic limit, we test two approximate improvements to CCSD, which are found to improve the predicted cohesive energies.

cond-mat.mtrl-sci↗

arXiv2022

Approximating matrix eigenvalues by subspace iteration with repeated random sparsification

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by leveraging repeated random sampling and averaging. We present a general approach to extending such methods for the estimation of multiple eigenvalues and demonstrate its performance for several benchmark problems in quantum chemistry.

math.NA↗

arXiv2022

Dark-exciton driven energy funneling into dielectric inhomogeneities in two-dimensional semiconductors

The optoelectronic and transport properties of two-dimensional transition metal dichalcogenide semiconductors (2D TMDs) are highly susceptible to external perturbation, enabling precise tailoring of material function through post-synthetic modifications. Here we show that nanoscale inhomogeneities known as nanobubbles can be used for both strain and, less invasively, dielectric tuning of exciton transport in bilayer tungsten disulfide (WSe2). We use ultrasensitive spatiotemporally resolved optical scattering microscopy to directly image exciton transport, revealing that dielectric nanobubbles are surprisingly efficient at funneling and trapping excitons at room temperature, even though the energies of the bright excitons are negligibly affected. Our observations suggest that exciton funneling in dielectric inhomogeneities is driven by momentum-indirect (dark) excitons whose energies are more sensitive to dielectric perturbations than bright excitons. These results reveal a new pathway to control exciton transport in 2D semiconductors with exceptional spatial and energetic precision using dielectric engineering of dark state energetic landscapes.

cond-mat.mes-hall↗

arXiv2022

Correlation-consistent Gaussian basis sets for solids made simple

The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis sets commonly used in molecular simulation show significant linear dependencies when used in close-packed solids, leading to severe numerical issues that hamper the convergence to the complete basis set (CBS) limit, especially in correlated calculations. In this work, we revisit Dunning's strategy for construction of correlation-consistent basis sets and examine the relationship between accuracy and numerical stability in periodic settings. Specifically, we find that limiting the number of primitive functions avoids the appearance of problematic small exponents while still providing smooth convergence to the CBS limit. As an example, we generate double-, triple-, and quadruple-zeta correlation-consistent Gaussian basis sets for periodic calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets cover the main-group elements from the first three rows of the periodic table. Especially for atoms on the left side of the periodic table, our basis sets are less diffuse than those used in molecular calculations. We verify the fast and reliable convergence to the CBS limit in both Hartree-Fock and post-Hartree-Fock (MP2) calculations, using a diverse test set of $19$ semiconductors and insulators.

physics.chem-ph↗

arXiv2021

Linear free energy relationships in electrostatic catalysis

The use of electric fields to modify chemical reactions is a promising, emerging technique in catalysis. However, there exist few guiding principles, and rational design requires assumptions about the transition state or explicit atomistic calculations. Here, we present a linear free energy relationship, familiar in other areas of physical organic chemistry, that microscopically relates field-induced changes in the activation energy to those in the reaction energy, connecting kinetic and thermodynamic behaviors. We verify our theory using first-principles electronic structure calculations of a symmetric S$_\mathrm{N}$2 reaction and the dehalogenation of an aryl halide on gold surfaces and observe hallmarks of linear free energy relationships, such as the shifting to early and late transition states. We also report and explain a counterintuitive case, where the constant of proportionality relating the activation and reaction energies is negative, such that stabilizing the product increases the activation energy, i.e., opposite of the Bell-Evans-Polanyi principle.

physics.chem-ph↗

arXiv2021

Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations

The Bethe-Salpeter equation (BSE) that results from the GW approximation to the self-energy is a frequency-dependent (nonlinear) eigenvalue problem due to the dynamically screened Coulomb interaction between electrons and holes. The computational time required for a numerically exact treatment of this frequency dependence is $O(N^6)$, where $N$ is the system size. To avoid the common static screening approximation, we show that the full-frequency dynamical BSE can be exactly reformulated as a frequency-independent eigenvalue problem in an expanded space of single and double excitations. When combined with an iterative eigensolver and the density fitting approximation to the electron repulsion integrals, this reformulation yields a dynamical BSE algorithm whose computational time is $O(N^5)$, which we verify numerically. Furthermore, the reformulation provides direct access to excited states with dominant double excitation character, which are completely absent in the spectrum of the statically screened BSE. We study the $2^1A_\mathrm{g}$ state of butadiene, hexatriene, and octatetraene and find that GW/BSE overestimates the excitation energy by about 1.5-2 eV and significantly underestimates the double excitation character.

cond-mat.mtrl-sci↗

arXiv2021

A simplified GW/BSE approach for charged and neutral excitation energies of large molecules and nanomaterials

Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [S. Grimme, J. Chem. Phys. \textbf{138}, 244104 (2013)], we describe a simplified approach to excited state calculations within the GW approximation to the self-energy and the Bethe-Salpeter equation (BSE), which we call sGW/sBSE. The primary simplification to the electron repulsion integrals yields the same structure as with tensor hypercontraction, such that our method has a storage requirement that grows quadratically with system size and computational timing that grows cubically with system size. The performance of sGW is tested on the ionization potential of the molecules in the GW100 test set, for which it differs from \textit{ab intio} GW calculations by only 0.2 eV. The performance of sBSE (based on sGW input) is tested on the excitation energies of molecules in the Thiel set, for which it differs from \textit{ab intio} GW/BSE calculations by about 0.5 eV. As examples of the systems that can be routinely studied with sGW/sBSE, we calculate the band gap and excitation energy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in 4678 spatial orbitals and the absorption spectra of two large organic dye molecules with hundreds of atoms.

cond-mat.mes-hall↗

arXiv2021

Tight distance-dependent estimators for screening two-center and three-center short-range Coulomb integrals over Gaussian basis functions

We derive distance-dependent estimators for two-center and three-center electron repulsion integrals over a short-range Coulomb potential, $\textrm{erfc}(ωr_{12})/r_{12}$. 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 $ω$. 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.

physics.chem-ph↗

arXiv2021

Absorption Spectra of Solids from Periodic Equation-of-Motion Coupled-Cluster Theory

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 calculated 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.

physics.chem-ph↗

arXiv2021

Improving MP2 band gaps with low-scaling approximations to EOM-CCSD

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 equation-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 Green's 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.

cond-mat.mtrl-sci↗