Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting

Hu, Wei; Shao, Meiyue; Cepellotti, Andrea; Jornada, Felipe H. da; Lin, Lin; Thicke, Kyle; Yang, Chao; Louie, Steven G.

doi:10.48550/arxiv.1801.09015

Cited by 2 publications

(7 citation statements)

References 19 publications

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“…where the orbitals ϕ i (r) are evaluated on a dense real space grid {r i } Ng i=1 , {r µ } Nµ µ=1 are a subset of these grid points, called the interpolating points, ζ µ (r) are a set of interpolating vectors and N µ = c µ M is the number of interpolating points. Importantly, previous results suggest that c µ is roughly independent of the system size, and a value in the range between 10 − 15 is usually sufficient to reproduce total energies to sub mHa/atom accuracy 42,43,53 . Inserting Eq.…”

Section: Interpolative Separable Density Fittingmentioning

confidence: 93%

“…We could proceed and compute v abkl using the existing ISDF orbital products constructed using the full set of M orbitals. However, it has been found previously that total energies typically converge faster with respect to c µ when ISDF is performed on orbital products containing only the occupied set of orbitals, or at least with one set of occupied orbitals and one set of virtual orbitals 53 . Thus, we instead perform a second ISDF factorization on the 'half-transformed' orbital product set…”

Section: Interpolative Separable Density Fittingmentioning

confidence: 95%

“…49-51, that offers just this. The ISDF approach has so far been applied to speeding up develop a cubic scaling RPA algorithm 52 , speeding up hybrid functional calculations in DFT 42,43 and the computation of excited state properties using the Bethe-Salpether approach 53 . Here our aim is to adapt it to AFQMC.…”

Section: Interpolative Separable Density Fittingmentioning

confidence: 99%

“…The ISDF approach has so far been applied to speeding up develop a cubic scaling RPA algorithm, 52 speeding up hybrid functional calculations in DFT 42,43 and the computation of excited state properties using the Bethe−Salpether approach. 53 Here our aim is to adapt it to AFQMC. We will focus on using the centroidal Veronoi tesselation ISDF developed in ref 43 with our notation and implementation closely following that found in refs 42 and 43.…”

Section: Journal Of Chemical Theory and Computationmentioning

confidence: 99%

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Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting

Malone

Zhang

Morales

2018

J. Chem. Theory Comput.

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We investigate the use of interpolative separable density fitting (ISDF) as a means to reduce the memory bottleneck in auxiliary field quantum Monte Carlo (AFQMC) simulations of real materials in Gaussian basis sets. We find that ISDF can reduce the memory scaling of AFQMC simulations from O(M 4 ) to O(M 2 ). We test these developments by computing the structural properties of Carbon in the diamond phase, comparing to results from existing computational methods and experiment. the choice of approximate exchange correlation functional. Calculating band gaps in semiconductors 1 , discerning different phases in hydrogen under extreme conditions, 2-4 and the systematic description of strongly correlated materials 5 are some well known limitations of DFT. The development of hybrid functionals 6-10 and adaptations of the exchange-correlation functional for strong correlations 11 can sometimes improve results, but require an often adhoc determination of additional parameters.Wavefunction based quantum chemical methods offer an alternative, systematic approach to solving the electronic structure problem directly. Unfortunately, they come with a cost which is often prohibitively large. For example, standard Coupled-Cluster theory (including single and double excitations) scales like the sixth power of the system size, while the exact approach of FCI scales exponentially. Nevertheless, they are increasingly and successfully being applied to problems in solid state physics 12-17 .Quantum Monte Carlo (QMC) methods offer another route to directly solving the manyelectron Schrödinger equation, with often much more favorable scaling. Real space diffusion Monte Carlo 18 is perhaps the most widely used QMC approach to solving electronic structure problems, and can now routinely simulate 100s to 1000s of atoms, making full use of modern supercomputers. 19 In order to overcome the fermionic sign problem, DMC uses a trial wavefunction to impose the fixed-node approximation. Although results for the uniform electron gas suggest that the fixed-node approximation is extremely accurate 20 , it is often difficult to improve the nodes for more realistic systems, where the nodal error can be more significant.Additionally, non-local pseudopotentials, which are eventually necessary for describing heavier elements, are difficult to use and require additional uncontrolled approximations (e.g. the locality approximations 21 ) which are also hard to assess and improve.Phaseless auxiliary field QMC 22,23 (AFQMC) offers an alternative route to overcoming some of these issues. Similar to DMC, it also uses a constraint to remove the fermion sign problem at the expense of a bias 22 , which it implements with a trial wavefunction.Multi-determinant 24,25 , generalized Hartree-Fock 24,26 , and self-consistently determined trial

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Section: Interpolative Separable Density Fittingmentioning

confidence: 93%

Section: Interpolative Separable Density Fittingmentioning

confidence: 95%

Section: Interpolative Separable Density Fittingmentioning

confidence: 99%

Section: Journal Of Chemical Theory and Computationmentioning

confidence: 99%

See 2 more Smart Citations

Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting

Malone

Zhang

Morales

2018

J. Chem. Theory Comput.

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“…The solution of the BSE as described is highly demanding; in recent years several methodological advancements have been introduced to lower the computational cost of performing such BSE calculations. 15,35,36 We will briefly describe our approach, which is implemented in the Gwl code, 37,38 part of the Quantum ESPRESSO distribution. 39,40 We consider only the case of time-reversal symmetric systems, such that the single-particles states can be taken to be real and a complex-conjugate notation can therefore be neglected.…”

Section: Methodsmentioning

confidence: 99%

Koopmans Meets Bethe–Salpeter: Excitonic Optical Spectra without GW

Elliott

Colonna

Marsili

et al. 2019

J. Chem. Theory Comput.

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The Bethe-Salpeter Equation (BSE) can be applied to compute from first-principles optical spectra that include the effects of screened electron-hole interactions. As input, BSE calculations require single-particle states, quasiparticle energy levels and the screened Coulomb interaction, which are typically obtained with many-body perturbation theory, whose cost limits the scope of possible applications. This work tries to address this practical limitation, instead deriving spectral energies from Koopmanscompliant functionals and introducing a new methodology for handling the screened Coulomb interaction. The explicit calculation of the W matrix is bypassed via a direct 1 arXiv:1912.13350v1 [cond-mat.mtrl-sci] 31 Dec 2019 minimization scheme applied on top of a maximally localised Wannier function basis.We validate and benchmark this approach by computing the low-lying excited states of the molecules in Thiel's set, and the optical absorption spectrum of a C 60 fullerene.The results show the same trends as quantum chemical methods and are in excellent agreement with previous simulations carried out at the TD-DFT or G 0 W 0 -BSE level.Conveniently, the new framework reduces the parameter space controlling the accuracy of the calculation, thereby simplifying the simulation of charge-neutral excitations, offering the potential to expand the applicability of first-principles spectroscopies to larger systems of applied interest.

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Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting

Cited by 2 publications

References 19 publications

Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting

Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting

Koopmans Meets Bethe–Salpeter: Excitonic Optical Spectra without GW

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