26 research outputs found
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
We present a new cubic scaling algorithm for the calculation of the RPA
correlation energy. Our scheme splits up the dependence between the occupied
and virtual orbitals in by use of Cauchy's integral formula. This
introduces an additional integral to be carried out, for which we provide a
geometrically convergent quadrature rule. Our scheme also uses the newly
developed Interpolative Separable Density Fitting algorithm to further reduce
the computational cost in a way analogous to that of the Resolution of Identity
method.Comment: 22 pages, 6 figure
Low-Scaling Algorithm for the Random Phase Approximation using Tensor Hypercontraction with k-point Sampling
We present a low-scaling algorithm for the random phase approximation (RPA)
with \textbf{k}-point sampling in the framework of tensor hypercontraction
(THC) for electron repulsion integrals (ERIs). The THC factorization is
obtained via a revised interpolative separable density fitting (ISDF) procedure
with a momentum-dependent auxiliary basis for generic single-particle Bloch
orbitals. Our formulation does not require pre-optimized interpolating points
nor auxiliary bases, and the accuracy is systematically controlled by the
number of interpolating points. The resulting RPA algorithm scales linearly
with the number of \textbf{k}-points and cubically with the system size without
any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA
energy show rapid convergence with respect to the size of the THC auxiliary
basis, suggesting a promising and robust direction to construct efficient
algorithms of higher-order many-body perturbation theories for large-scale
systems.Comment: 35 pages, 6 figure
Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework
Four-center two-electron Coulomb integrals routinely appear in electronic
structure algorithms. The resolution-of-the-identity (RI) is a popular
technique to reduce the computational cost for the numerical evaluation of
these integrals in localized basis-sets codes. Recently, Duchemin and Blase
proposed a separable RI scheme [J. Chem. Phys. 150, 174120 (2019)], which
preserves the accuracy of the standard global RI method with the Coulomb metric
(RI-V) and permits the formulation of cubic-scaling random phase approximation
(RPA) and approaches. Here, we present the implementation of a separable
RI scheme within an all-electron numeric atom-centered orbital framework. We
present comprehensive benchmark results using the Thiel and the GW100 test set.
Our benchmarks include atomization energies from Hartree-Fock, second-order
M{\o}ller-Plesset (MP2), coupled-cluster singles and doubles, RPA and
renormalized second-order perturbation theory as well as quasiparticle energies
from . We found that the separable RI approach reproduces RI-free HF
calculations within 9 meV and MP2 calculations within 1 meV. We have confirmed
that the separable RI error is independent of the system size by including
disordered carbon clusters up to 116 atoms in our benchmarksComment: 16 pages, 8 figure
Complex-valued K-means clustering of interpolative separable density fitting algorithm for large-scale hybrid functional enabled \textit{ab initio} molecular dynamics simulations within plane waves
K-means clustering, as a classic unsupervised machine learning algorithm, is
the key step to select the interpolation sampling points in interpolative
separable density fitting (ISDF) decomposition. Real-valued K-means clustering
for accelerating the ISDF decomposition has been demonstrated for large-scale
hybrid functional enabled \textit{ab initio} molecular dynamics (hybrid AIMD)
simulations within plane-wave basis sets where the Kohn-Sham orbitals are
real-valued. However, it is unclear whether such K-means clustering works for
complex-valued Kohn-Sham orbitals. Here, we apply the K-means clustering into
hybrid AIMD simulations for complex-valued Kohn-Sham orbitals and use an
improved weight function defined as the sum of the square modulus of
complex-valued Kohn-Sham orbitals in K-means clustering. Numerical results
demonstrate that this improved weight function in K-means clustering algorithm
yields smoother and more delocalized interpolation sampling points, resulting
in smoother energy potential, smaller energy drift and longer time steps for
hybrid AIMD simulations compared to the previous weight function used in the
real-valued K-means algorithm. In particular, we find that this improved
algorithm can obtain more accurate oxygen-oxygen radial distribution functions
in liquid water molecules and more accurate power spectrum in crystal silicon
dioxide compared to the previous K-means algorithm. Finally, we describe a
massively parallel implementation of this ISDF decomposition to accelerate
large-scale complex-valued hybrid AIMD simulations containing thousands of
atoms (2,744 atoms), which can scale up to 5,504 CPU cores on modern
supercomputers.Comment: 43 pages, 12 figure