Local Descriptors of Dynamic and Nondynamic Correlation

Abstract

Quantitatively accurate electronic structure calculations rely on the proper description of electron correlation. A judicious choice of the approximate quantum chemistry method depends upon the importance of dynamic and nondynamic correlation, which is usually assesed by scalar measures. Existing measures of electron correlation do not consider separately the regions of the Cartesian space where dynamic or nondynamic correlation are most important. We introduce real-space descriptors of dynamic and nondynamic electron correlation that admit orbital decomposition. Integration of the local descriptors yields global numbers that can be used to quantify dynamic and nondynamic correlation. Illustrative examples over different chemical systems with varying electron correlation regimes are used to demonstrate the capabilities of the local descriptors. Since the expressions only require orbitals and occupation numbers, they can be readily applied in the context of local correlation methods, hybrid methods, density matrix functional theory, and fractional-occupancy density functional theory.

Rapid Detection of Strong Correlation with Machine Learning for Transition-Metal Complex High-Throughput Screening

“…where larger I ND values can be used as an indicator of MR character 33, [63][64]70 . The ratio, 67 r ND , of the I ND to the total correlation (i.e., I D +I ND ) has been proposed by Martin and coworkers as a size-intensive MR diagnostic:…”

“…We curated a dataset of 4,865 mononuclear octahedral transitionmetal complexes generated in six prior studies [71][72][73][74][75][76] using fixed-occupation DFT geometry optimizations in TeraChem [94][95] automated with molSimplify [96][97] . All sets used the same high- We automated the calculation of FT-DFT 66 MR diagnostics [63][64][65] Table S22). The FT-DFT calculations employed the recommended 104 temperature for B3LYP (9000 K) with Fermi-Dirac smearing and were initiated from fixed-occupation DFT wavefunctions [71][72][73][74][75][76] when available (Supporting Information Text S4 and Tables S22-S23).…”

The role of topology in organic molecules: origin and comparison of the radical character in linear and cyclic oligoacenes and related oligomers

“…Some global diagnostics exist in the literature like 25,26 or A λ , 27 but they are based on costly calculations which might hamper the judicious choice of single-or multi-reference electronic structure methods for large systems or for a fast screening of compounds. Note also that only very recently local descriptors of electron correlation have appeared 28 too.…”

Comprehensive benchmarking of density matrix functional approximations

“…[23][24][25][26][27] Despite the success, the account of dynamic correlation still poses a great challenge for DMFAs 2,14,23 and calls for means to separate dynamic and nondynamic correlation within DMFT. 22,28,29 The development of more accurate DMFAs also depends on appropriate benchmark tests and, to our knowledge, only a recent paper addresses the validation of most DMFAs in the literature, comparing their performance in the energy calculation of few-electron systems with different electron correlation. 23 Since functionals are mostly used to calculate the electronic energy of chemical systems, it does not strike as a surprise that the energy usually serves as a yardstick in benchmarking DMFAs.…”