libreta: Computerized Optimization and Code Synthesis for Electron Repulsion Integral Evaluation

Abstract

A new library called libreta for the evaluation of electron repulsion integrals (ERIs) over segmented and contracted Gaussian functions is developed. Our libreta is optimized from three aspects: (1) The Obara-Saika, Dupuis-Rys-King, and McMurchie-Davidson method are all employed. The recurrence relations involved are optimized by tree-search for each combination of angular momenta, and in the best case, 50% of the intermediates can be eliminated to reduce the computational cost. (2) The optimized codes for recurrence relations are combined with different contraction orders, each of which is suitable for ERIs of different angular momenta and contraction patterns. In practice, libreta will determine and use the best scheme to evaluate each ERI. (3) libreta is also optimized at the coding level. For example, with common subexpression elimination and local memory access, the performance can be increased by about 6% and 20%, respectively. The performance was compared with libint2. For both popular segmented and contracted basis sets, libreta can be faster than libint2 by 7.2-912.0%. For basis sets of heavy elements that contain Gaussian basis functions of large contraction degrees, the performance can be increased 20-30 times. We also tested the performance of libreta in direct self-consistent field (SCF) calculations and compared it with NWChem. In most cases, the average time for one SCF iteration by libreta is less than NWChem by 144.2-495.9%. Finally, we discuss the origin of redundancies occurring in the recurrence relations and derive an upper bound of the least number of intermediates required to be calculated in a McMurchie-Davidson recurrence, which is confirmed by ours as well as previous authors' results. We expect that libreta can become a useful tool for theoretical and computational chemists to develop their own algorithms rapidly.

Group 14 Central Atoms and Halogen Bonding in Different Dielectric Environments: How Germanium Outperforms Silicon

“…The potentials have been computed on the 0.001 au isodensity surface, and the maximum potential at the σ-hole (V s,max ), minimum at the lone pair (V s,min ) on the base have been determined from G09 generated wavefunction (.wfn) files using the Multiwfn software. [53][54][55] Analyses of the electron densities to obtain point charges (by so-called natural population analyses) has been carried out using the Natural Bond Orbital (NBO) program [56] as implemented in the G09 suite. Those NBO point charges are useful for the qualitative discussions, despite claims that they tend to exaggerate the ionic character of polar covalent bonds.…”

Molecular design of long intra‐annular nitrogen chains: 3H‐tetrazolo[1,5‐d]tetrazole‐based high‐energy‐density materials

“…The values of α, β and γ are À0.0064, 241.42, and À3.43, respectively. The σ + 2 and υ, calculated by molecule surface analysis with Multiwfn 3.7 program [39,40], were listed in the Supplementary Information.…”

Atomic Charges, Surface Electrostatic Potential Analysis, and Bond Order Analysis on Nitriles and Isocyanides

“…In order to analyze the molecular electrostatic surfaces and bonding features, the global and local electrostatic extrema, and the molecular surface electrostatic potential (ESP) maps [21][22][23][24][25] were evaluated with Multiwfn 3.7 (dev) [26] and pictured by VMD 1.9.2 [27]. The ESP evaluation code based on the LIBRETA electron repulsion integral library developed by Zhang in 2018 [28] is employed in this work. Moreover, Hirshfeld population analyses [29][30][31] and ADCH fragment charges [32,33] were performed using build-in sphericalized atomic densities in free states, and Laplacian bond order (LBO) [34] and fuzzy bond order (FBO) [35] analyses were carried out by means of the embedded methods in Multiwfn 3.7 (dev).…”