Low-scaling analytical gradients for the direct random phase approximation using an atomic orbital formalism.

We present an atomic orbital formalism to obtain analytical gradients within the random phase approximation for calculating first-order properties. Our approach allows exploiting sparsity in the electronic structure in order to reduce the computational complexity. Furthermore, we introduce Cholesky decomposed densities to remove the redundancies present in atomic orbital basis sets, making our method a competitive alternative to canonical theories also for small molecules. The approach is presented in a general framework that allows extending the methodology to other correlation methods. Beyond showing the validity and accuracy of our approach and the approximations used in this work, we demonstrate the efficiency of our method by computing nuclear gradients for systems with up to 600 atoms and 5000 basis functions.

Efficient calculation of beyond RPA correlation energies in the dielectric matrix formalism.

We present efficient methods to calculate beyond random phase approximation (RPA) correlation energies for molecular systems with up to 500 atoms. To reduce the computational cost, we employ the resolution-of-the-identity and a double-Laplace transform of the non-interacting polarization propagator in conjunction with an atomic orbital formalism. Further improvements are achieved using integral screening and the introduction of Cholesky decomposed densities. Our methods are applicable to the dielectric matrix formalism of RPA including second-order screened exchange (RPA-SOSEX), the RPA electron-hole time-dependent Hartree-Fock (RPA-eh-TDHF) approximation, and RPA renormalized perturbation theory using an approximate exchange kernel (RPA-AXK). We give an application of our methodology by presenting RPA-SOSEX benchmark results for the L7 test set of large, dispersion dominated molecules, yielding a mean absolute error below 1 kcal/mol. The present work enables calculating beyond RPA correlation energies for significantly larger molecules than possible to date, thereby extending the applicability of these methods to a wider range of chemical systems.

Short-range second order screened exchange correction to RPA correlation energies.

Direct random phase approximation (RPA) correlation energies have become increasingly popular as a post-Kohn-Sham correction, due to significant improvements over DFT calculations for properties such as long-range dispersion effects, which are problematic in conventional density functional theory. On the other hand, RPA still has various weaknesses, such as unsatisfactory results for non-isogyric processes. This can in parts be attributed to the self-correlation present in RPA correlation energies, leading to significant self-interaction errors. Therefore a variety of schemes have been devised to include exchange in the calculation of RPA correlation energies in order to correct this shortcoming. One of the most popular RPA plus exchange schemes is the second order screened exchange (SOSEX) correction. RPA + SOSEX delivers more accurate absolute correlation energies and also improves upon RPA for non-isogyric processes. On the other hand, RPA + SOSEX barrier heights are worse than those obtained from plain RPA calculations. To combine the benefits of RPA correlation energies and the SOSEX correction, we introduce a short-range RPA + SOSEX correction. Proof of concept calculations and benchmarks showing the advantages of our method are presented.

Screening methods for linear-scaling short-range hybrid calculations on CPU and GPU architectures.

We present screening schemes that allow for efficient, linear-scaling short-range exchange calculations employing Gaussian basis sets for both CPU and GPU architectures. They are based on the LinK [C. Ochsenfeld et al., J. Chem. Phys. 109, 1663 (1998)] and PreLinK [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 138, 134114 (2013)] methods, but account for the decay introduced by the attenuated Coulomb operator in short-range hybrid density functionals. Furthermore, we discuss the implementation of short-range electron repulsion integrals on GPUs. The introduction of our screening methods allows for speedups of up to a factor 7.8 as compared to the underlying linear-scaling algorithm, while retaining full numerical control over the accuracy. With the increasing number of short-range hybrid functionals, our new schemes will allow for significant computational savings on CPU and GPU architectures.

Low-Scaling Self-Consistent Minimization of a Density Matrix Based Random Phase Approximation Method in the Atomic Orbital Space.

An efficient minimization of the random phase approximation (RPA) energy with respect to the one-particle density matrix in the atomic orbital space is presented. The problem of imposing full self-consistency on functionals depending on the potential itself is bypassed by approximating the RPA Hamiltonian on the basis of the well-known Hartree-Fock Hamiltonian making our self-consistent RPA method completely parameter-free. It is shown that the new method not only outperforms post-Kohn-Sham RPA in describing noncovalent interactions but also gives accurate dipole moments demonstrating the high quality of the calculated densities. Furthermore, the main drawback of atomic orbital based methods, in increasing the prefactor as compared to their canonical counterparts, is overcome by introducing Cholesky decomposed projectors allowing the use of large basis sets. Exploiting the locality of atomic and/or Cholesky orbitals enables us to present a self-consistent RPA method which shows asymptotically quadratic scaling opening the door for calculations on large molecular systems.

Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

Molecular dynamics studies on the DNA-binding process of ERG.

The ETS family of transcription factors regulate gene targets by binding to a core GGAA DNA-sequence. The ETS factor ERG is required for homeostasis and lineage-specific functions in endothelial cells, some subset of haemopoietic cells and chondrocytes; its ectopic expression is linked to oncogenesis in multiple tissues. To date details of the DNA-binding process of ERG including DNA-sequence recognition outside the core GGAA-sequence are largely unknown. We combined available structural and experimental data to perform molecular dynamics simulations to study the DNA-binding process of ERG. In particular we were able to reproduce the ERG DNA-complex with a DNA-binding simulation starting in an unbound configuration with a final root-mean-square-deviation (RMSD) of 2.1 Å to the core ETS domain DNA-complex crystal structure. This allowed us to elucidate the relevance of amino acids involved in the formation of the ERG DNA-complex and to identify Arg385 as a novel key residue in the DNA-binding process. Moreover we were able to show that water-mediated hydrogen bonds are present between ERG and DNA in our simulations and that those interactions have the potential to achieve sequence recognition outside the GGAA core DNA-sequence. The methodology employed in this study shows the promising capabilities of modern molecular dynamics simulations in the field of protein DNA-interactions.