Publications by authors named "Timothy C Berkelbach"

45 Publications

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

J Chem Phys 2021 Jun;154(21):211105

Department of Chemistry, Columbia University, New York, New York 10027, USA.

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 finite-order perturbation theory 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 this method to estimate the CCSD correlation energy in the combined complete basis set and thermodynamic limits, we find that CCSD recovers 85%-90% of the exact correlation energy at r = 4. We also test the composite approach with the direct random-phase approximation used in place of MP2, yielding a method that is typically (but not always) more cost effective due to the smaller number of orbitals that need to be included in the more expensive CCSD calculation.
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http://dx.doi.org/10.1063/5.0049890DOI Listing
June 2021

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

Phys Rev Lett 2021 May;126(21):216402

Department of Chemistry, Columbia University, New York, New York 10027, USA.

Behaving like atomically precise two-dimensional quantum wells with non-negligible dielectric contrast, the layered hybrid organic-inorganic lead halide perovskites (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 parametrize 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 and 44 meV, respectively, whereas a single exfoliated layer is predicted to have trions and biexcitons with equal binding energies of 48 meV. We compare our findings to available experimental data and to that of other quasi-two-dimensional materials.
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http://dx.doi.org/10.1103/PhysRevLett.126.216402DOI Listing
May 2021

Fast periodic Gaussian density fitting by range separation.

J Chem Phys 2021 Apr;154(13):131104

Department of Chemistry, Columbia University, New York, New York 10027, USA.

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 ten-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about 10E 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.
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http://dx.doi.org/10.1063/5.0046617DOI Listing
April 2021

Vibrational heat-bath configuration interaction.

J Chem Phys 2021 Feb;154(7):074104

Department of Chemistry, Columbia University, New York, New York 10027, USA.

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 12-48 degrees of freedom and use anharmonic potential energy surfaces truncated at fourth and sixth orders. When compared to other methods using the same truncated potentials, VHCI produces vibrational spectra of tens or hundreds of states with sub-wavenumber accuracy at low computational cost.
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http://dx.doi.org/10.1063/5.0035454DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7889291PMC
February 2021

Full-frequency GW without frequency.

J Chem Phys 2021 Jan;154(4):041101

Department of Chemistry, Columbia University, New York, New York 10027, USA.

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), 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 obviates the need for the common "diagonal" approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to O(N), and (4) enables a density-fitted implementation that reduces the scaling to O(N). We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. The new formulation is found to be competitive with conventional O(N) methods based on analytic continuation or contour deformation. 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.
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http://dx.doi.org/10.1063/5.0035141DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7843153PMC
January 2021

Regional Embedding Enables High-Level Quantum Chemistry for Surface Science.

J Phys Chem Lett 2021 Jan 21;12(3):1104-1109. Epub 2021 Jan 21.

Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States.

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, this paper introduces the regional embedding approach, which enables correlated wave function treatments of 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.
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http://dx.doi.org/10.1021/acs.jpclett.0c03274DOI Listing
January 2021

Polytypism, Anisotropic Transport, and Weyl Nodes in the van der Waals Metal TaFeTe.

J Am Chem Soc 2021 Jan 24;143(1):109-113. Epub 2020 Dec 24.

Department of Chemistry, Columbia University, New York, New York 10027, United States.

Layered van der Waals (vdW) materials belonging to the 'Te structure class have recently received intense attention due to their ability to host exotic electronic transport phenomena, such as in-plane transport anisotropy, Weyl nodes, and superconductivity. Here we report two new vdW materials with strongly anisotropic in-plane structures featuring stripes of metallic TaTe and semiconducting FeTe, α-TaFeTe and β-TaFeTe. We find that the structure of α-TaFeTe produces strongly anisotropic in-plane electronic transport (anisotropy ratio of up to 250%), outcompeting all other vdW metals, and demonstrate that it can be mechanically exfoliated to the two-dimensional (2D) limit. We also explore the possibility that broken inversion symmetry in β-TaFeTe produces Weyl points in the electronic band structure. Eight Weyl nodes slightly below the Fermi energy are computationally identified for β-TaFeTe, indicating they may contribute to the transport behavior of this polytype. These findings identify the TaFeTe polytypes as an ideal platform for investigation of 2D transport anisotropy and chiral charge transport as a result of broken symmetry.
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http://dx.doi.org/10.1021/jacs.0c11674DOI Listing
January 2021

Improved Fast Randomized Iteration Approach to Full Configuration Interaction.

J Chem Theory Comput 2020 Sep 11;16(9):5572-5585. Epub 2020 Aug 11.

Department of Chemistry, Columbia University, New York, New York 10027, United States.

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, HO, and N. 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 semistochastic 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.
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http://dx.doi.org/10.1021/acs.jctc.0c00437DOI Listing
September 2020

Recent developments in the PySCF program package.

J Chem Phys 2020 Jul;153(2):024109

Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This 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.
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http://dx.doi.org/10.1063/5.0006074DOI Listing
July 2020

Quantum plasmons and intraband excitons in doped nanoparticles: Insights from quantum chemistry.

J Chem Phys 2020 Jun;152(22):224704

Department of Chemistry, Columbia University, New York, New York 10027, USA.

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. Modeling the excess electrons as interacting electrons confined to a sphere, we find that the excitation evolves from single-particle 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 and electron-hole attraction. In addition, the excitation passes through an intermediate regime where it is best characterized as an intraband exciton. We compare equation-of-motion coupled-cluster theory with those of more affordable single-excitation theories and identify the inclusion of electron-hole interactions as essential to describing the evolution of the excitation. Despite the simplicity of our model, the results are in reasonable agreement with the experimental spectra of doped ZnO nanoparticles at a doping density of 1.4 × 10 cm. Based on our quantum chemistry calculations, we develop a schematic model that captures the dependence of the excitation energy on nanoparticle radius and electron density.
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http://dx.doi.org/10.1063/5.0006429DOI Listing
June 2020

Excitons in Solids from Periodic Equation-of-Motion Coupled-Cluster Theory.

J Chem Theory Comput 2020 May 9;16(5):3095-3103. Epub 2020 Apr 9.

Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States.

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 -points (a 4 × 4 × 4 mesh), corresponds to a canonical EOM-CCSD calculation of 768 electrons in 640 orbitals. We study eight simple main-group semiconductors and insulators, with direct singlet excitation energies in the range of 3 to 15 eV. Our predicted excitation energies exhibit a mean signed error of 0.24 eV and a mean absolute error of 0.27 eV when compared to experimental values. Although this error is similar to that found for EOM-CCSD applied to molecules, it may also reflect the role of vibrational effects, which are neglected in the calculations. Our results support recently proposed revisions of experimental optical gaps for AlP and cubic BN. 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 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.
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http://dx.doi.org/10.1021/acs.jctc.0c00101DOI Listing
May 2020

Linear and Pump-Probe Spectroscopy of Excitons in Molecular Crystals.

J Phys Chem Lett 2020 Mar 5;11(6):2241-2246. Epub 2020 Mar 5.

Department of Chemistry, Columbia University, New York, New York 10027, United States.

Linear and nonlinear spectroscopies are powerful tools used to investigate the energetics and dynamics of electronic excited states of both molecules and crystals. While highly accurate 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 multiexciton 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 qualitative behavior of multiexciton 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 experiments in closely related acene crystals such as tetracene and pentacene.
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http://dx.doi.org/10.1021/acs.jpclett.0c00031DOI Listing
March 2020

Special topic on dynamics of open quantum systems.

J Chem Phys 2020 01;152(2):020401

Institute of Physics, Albert-Ludwig University Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany.

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http://dx.doi.org/10.1063/1.5142731DOI Listing
January 2020

Active space approaches combining coupled-cluster and perturbation theory for ground states and excited states.

Mol Phys 2020 20;118(19-20). Epub 2020 Aug 20.

Department of Chemistry, Columbia University, New York, New York 10027 USA.

We evaluate the performance of approaches that combine coupled-cluster and perturbation theory based on a predefined active space of orbitals. Coupled-cluster theory is used to treat excitations that are internal to the active space and perturbation theory is used for all other excitations, which are at least partially external to the active space. We consider a variety of schemes that differ in how the internal and external excitations are coupled. Such approaches are presented for ground states and excited states within the equation-of-motion formalism. Results are given for the ionization potentials and electron affinities of a test set of small molecules and for the correlation energy and band gap of a few periodic solids.
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http://dx.doi.org/10.1080/00268976.2020.1808726DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7985847PMC
August 2020

Optical Properties of Layered Hybrid Organic-Inorganic Halide Perovskites: A Tight-Binding GW-BSE Study.

J Phys Chem Lett 2019 Oct 2;10(20):6189-6196. Epub 2019 Oct 2.

Department of Chemistry , Columbia University , New York , New York 10027 , United States.

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 AAMX, where controls the thickness of the primarily inorganic perovskite layers. We calculate the mean-field band structure with spin-orbit coupling, quasi-particle corrections within the GW approximation, and optical spectra using the Bethe-Salpeter equation. The model is parametrized by first-principles calculations and classical electrostatic screening, enabling an accurate but cost-effective study of large unit cells and corresponding -dependent properties. A transition of the electronic and optical properties from quasi-two-dimensional behavior to three-dimensional behavior is shown for increasing , and the nonhydrogenic character of the excitonic Rydberg series is analyzed. For methylammonium lead iodide perovskites with butylammonium spacers, our -dependent 1s and 2s exciton energy levels are in good agreement with those from recently reported experiments, and the 1s exciton binding energy is calculated to be 302 meV for = 1, 97 meV for = 5, and 37 meV for = ∞ (bulk MAPbI). A calculation for an exfoliated = 1 bilayer predicts a very large 1s exciton binding energy of 444 meV.
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http://dx.doi.org/10.1021/acs.jpclett.9b02491DOI Listing
October 2019

Large Band Edge Tunability in Colloidal Nanoplatelets.

Nano Lett 2019 10 1;19(10):7124-7129. Epub 2019 Oct 1.

Center for Nanoscale Materials , Argonne National Laboratory , Argonne , Illinois 60439 , United States.

We study the impact of organic surface ligands on the electronic structure and electronic band edge energies of quasi-two-dimensional (2D) colloidal cadmium selenide nanoplatelets (NPLs) using density functional theory. We show how control of the ligand and ligand-NPL interface dipoles results in large band edge energy shifts, over a range of 5 eV for common organic ligands with a minor effect on the NPL band gaps. Using a model self-energy to account for the dielectric contrast and an effective mass model of the excitons, we show that the band edge tunability of NPLs together with the strong dependence of the optical band gap on NPL thickness can lead to favorable photochemical and optoelectronic properties.
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http://dx.doi.org/10.1021/acs.nanolett.9b02645DOI Listing
October 2019

Dielectric disorder in two-dimensional materials.

Nat Nanotechnol 2019 Sep 19;14(9):832-837. Epub 2019 Aug 19.

Department of Physics, University of Regensburg, Regensburg, Germany.

Understanding and controlling disorder is key to nanotechnology and materials science. Traditionally, disorder is attributed to local fluctuations of inherent material properties such as chemical and structural composition, doping or strain. Here, we present a fundamentally new source of disorder in nanoscale systems that is based entirely on the local changes of the Coulomb interaction due to fluctuations of the external dielectric environment. Using two-dimensional semiconductors as prototypes, we experimentally monitor dielectric disorder by probing the statistics and correlations of the exciton resonances, and theoretically analyse the influence of external screening and phonon scattering. Even moderate fluctuations of the dielectric environment are shown to induce large variations of the bandgap and exciton binding energies up to the 100 meV range, often making it a dominant source of inhomogeneities. As a consequence, dielectric disorder has strong implications for both the optical and transport properties of nanoscale materials and their heterostructures.
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http://dx.doi.org/10.1038/s41565-019-0520-0DOI Listing
September 2019

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

J Chem Theory Comput 2019 Sep 26;15(9):4834-4850. Epub 2019 Aug 26.

Department of Chemistry , Columbia University , New York , New York 10027 , United States.

We introduce a family of methods for the full configuration interaction problem in quantum chemistry, based on the fast randomized iteration (FRI) framework [Lim, L.-H.; Weare, J. , , 547; DOI: 10.1137/15M1040827 ]. 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 11-45 times more statistically efficient than the multinomial FCI-FRI scheme, which is in turn 1.4-178 times more statistically efficient than the original FCIQMC algorithm.
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http://dx.doi.org/10.1021/acs.jctc.9b00422DOI Listing
September 2019

Many-body simulation of two-dimensional electronic spectroscopy of excitons and trions in monolayer transition metal dichalcogenides.

Nat Commun 2019 Jul 31;10(1):3419. Epub 2019 Jul 31.

Department of Chemistry, Columbia University, New York, NY, 10027, USA.

Indications of coherently interacting excitons and trions in doped transition metal dichalcogenides have been measured as quantum beats in two-dimensional electronic spectroscopy, but the microscopic principles underlying the optical signals of exciton-trion coherence remain to be clarified. Here we present calculations of two-dimensional spectra of such monolayers based on a microscopic many-body formalism. We use a parameterized band structure and a static model dielectric function, although a full ab initio implementation of our formalism is possible in principle. Our simulated spectra are in excellent agreement with experiments, including the quantum beats, while revealing the interplay between excitons and trions in molybdenum- and tungsten-based transition metal dichalcogenides. Quantum beats are confirmed to unambiguously reflect the exciton-trion coherence time in molybdenum compounds, but are shown to provide a lower bound to the coherence time for tungsten analogues due to a destructive interference from coexisting singlet and triplet trions.
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http://dx.doi.org/10.1038/s41467-019-11497-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6668418PMC
July 2019

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

Phys Rev Lett 2019 Jun;122(22):226402

Department of Chemistry, Columbia University, New York, New York 10027 USA.

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 (RPA), 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.
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http://dx.doi.org/10.1103/PhysRevLett.122.226402DOI Listing
June 2019

Vertex Corrections to the Polarizability Do Not Improve the GW Approximation for the Ionization Potential of Molecules.

J Chem Theory Comput 2019 May 16;15(5):2925-2932. Epub 2019 Apr 16.

Department of Chemistry , Columbia University , New York , New York 10027 , United States.

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.
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http://dx.doi.org/10.1021/acs.jctc.8b00995DOI Listing
May 2019

Communication: Random-phase approximation excitation energies from approximate equation-of-motion coupled-cluster doubles.

J Chem Phys 2018 Jul;149(4):041103

Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA.

The ground-state correlation energy calculated in the random-phase approximation (RPA) is known to be identical to that calculated using a subset of terms appearing in coupled-cluster theory with double excitations (CCD). In particular, for particle-hole (ph) RPA this equivalence requires keeping only those terms that generate time-independent ring diagrams, and for particle-particle (pp) RPA it requires keeping only those terms that generate ladder diagrams. Here I show that these identities extend to excitation energies, for which those calculated in each RPA are identical to those calculated using approximations to equation-of-motion coupled-cluster theory with double excitations (EOM-CCD). The equivalence requires three approximations to EOM-CCD: first, the ground-state CCD amplitudes are obtained from the ring-CCD or ladder-CCD equations (the same as for the correlation energy); second, the EOM eigenvalue problem is truncated to the minimal subspace, which is one particle + one hole for ph-RPA and two particles or two holes for pp-RPA; third, the similarity transformation of the Fock operator must be neglected, as it corresponds to a Brueckner-like dressing of the single-particle propagator, which is not present in the conventional RPA.
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http://dx.doi.org/10.1063/1.5032314DOI Listing
July 2018

On the Relation between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation.

J Chem Theory Comput 2018 Aug 6;14(8):4224-4236. Epub 2018 Aug 6.

Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States.

We discuss the analytic and diagrammatic structure of ionization potential (IP) and electron affinity (EA) equation-of-motion coupled-cluster (EOM-CC) theory, in order to put it on equal footing with the prevalent GW approximation. The comparison is most straightforward for the time-ordered one-particle Green's function, and we show that the Green's function calculated by EOM-CC with single and double excitations (EOM-CCSD) includes fewer ring diagrams at higher order than does the GW approximation, due to the former's unbalanced treatment of time-ordering. However, the EOM-CCSD Green's function contains a large number of vertex corrections, including ladder diagrams, mixed ring-ladder diagrams, and exchange diagrams. By including triple excitations, the EOM-CCSDT Green's function includes all diagrams contained in the GW approximation, along with many high-order vertex corrections. In the same language, we discuss a number of common approximations to the EOM-CCSD equations, many of which can be classified as elimination of diagrams. Finally, we present numerical results by calculating the principal charged excitations energies of the molecules contained in the so-called GW100 test set [ J. Chem. Theory Comput. 2015 , 11 , 5665 - 5687 ]. We argue that (in molecules) exchange is as important as screening, advocating for a Hartree-Fock reference and second-order exchange in the self-energy.
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http://dx.doi.org/10.1021/acs.jctc.8b00455DOI Listing
August 2018

Linear and nonlinear spectroscopy from quantum master equations.

J Chem Phys 2017 Dec;147(24):244109

Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA.

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.
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http://dx.doi.org/10.1063/1.5006824DOI Listing
December 2017

Gaussian and plane-wave mixed density fitting for periodic systems.

J Chem Phys 2017 Oct;147(16):164119

Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

We introduce a mixed density fitting scheme that uses both a Gaussian and a plane-wave fitting basis to accurately evaluate electron repulsion integrals in crystalline systems. We use this scheme to enable efficient all-electron Gaussian based periodic density functional and Hartree-Fock calculations.
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http://dx.doi.org/10.1063/1.4998644DOI Listing
October 2017

Coulomb engineering of the bandgap and excitons in two-dimensional materials.

Nat Commun 2017 05 4;8:15251. Epub 2017 May 4.

Departments of Physics and Electrical Engineering, Columbia University, New York, New York 10027, USA.

The ability to control the size of the electronic bandgap is an integral part of solid-state technology. Atomically thin two-dimensional crystals offer a new approach for tuning the energies of the electronic states based on the unusual strength of the Coulomb interaction in these materials and its environmental sensitivity. Here, we show that by engineering the surrounding dielectric environment, one can tune the electronic bandgap and the exciton binding energy in monolayers of WS and WSe by hundreds of meV. We exploit this behaviour to present an in-plane dielectric heterostructure with a spatially dependent bandgap, as an initial step towards the creation of diverse lateral junctions with nanoscale resolution.
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http://dx.doi.org/10.1038/ncomms15251DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5418602PMC
May 2017

Gaussian-Based Coupled-Cluster Theory for the Ground-State and Band Structure of Solids.

J Chem Theory Comput 2017 Mar 1;13(3):1209-1218. Epub 2017 Mar 1.

Department of Chemistry and James Franck Institute, University of Chicago , Chicago, Illinois 60637, United States.

We present the results of Gaussian-based ground-state and excited-state equation-of-motion coupled-cluster theory with single and double excitations for three-dimensional solids. We focus on diamond and silicon, which are paradigmatic covalent semiconductors. In addition to ground-state properties (the lattice constant, bulk modulus, and cohesive energy), we compute the quasiparticle band structure and band gap. We sample the Brillouin zone with up to 64 k-points using norm-conserving pseudopotentials and polarized double- and triple-ζ basis sets, leading to canonical coupled-cluster calculations with as many as 256 electrons in 2176 orbitals.
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http://dx.doi.org/10.1021/acs.jctc.7b00049DOI Listing
March 2017

On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics.

J Chem Phys 2016 Apr;144(15):154106

Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA.

Well-defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Padé resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Padé-resummed master equations with numerically exact results in the context of the spin-boson model demonstrates that the proposed criteria correctly demarcate the regions of parameter space where the Padé approximation is reliable. The applicability analysis we present is not confined to the specifics of the Hamiltonian under consideration and should provide guidelines for other classes of resummation techniques.
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http://dx.doi.org/10.1063/1.4946809DOI Listing
April 2016

Extending the applicability of Redfield theories into highly non-Markovian regimes.

J Chem Phys 2015 Nov;143(19):194108

Department of Chemistry, Columbia University, New York, New York 10027, USA.

We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna-Matthews-Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.
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http://dx.doi.org/10.1063/1.4935443DOI Listing
November 2015

Observation of Excitonic Rydberg States in Monolayer MoS2 and WS2 by Photoluminescence Excitation Spectroscopy.

Nano Lett 2015 May 3;15(5):2992-7. Epub 2015 Apr 3.

§Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, United States.

We have identified excited exciton states in monolayers of MoS2 and WS2 supported on fused silica by means of photoluminescence excitation spectroscopy. In monolayer WS2, the positions of the excited A exciton states imply an exciton binding energy of 0.32 eV. In monolayer MoS2, excited exciton transitions are observed at energies of 2.24 and 2.34 eV. Assigning these states to the B exciton Rydberg series yields an exciton binding energy of 0.44 eV.
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http://dx.doi.org/10.1021/nl504868pDOI Listing
May 2015
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