Too big, too small or just right? A benchmark assessment of density functional theory for predicting the spatial extent of the electron density of small chemical systems

Abstract

Multipole moments are the first order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory (DFT) prediction of molecular multipole moments thus characterizes errors in modeling the electron density itself, as well as the performance in describing molecules interacting with external electric fields. However, only the lowest non-zero moment is translationally invariant, making the higher order moments origin-dependent. Therefore, instead of using the $3\times 3$ quadrupole moment matrix, we utilize the translationally invariant $3\times 3$ matrix of second cumulants (or spatial variances) of the electron density as the quantity of interest (denoted by $\mathcal{K}$). The principal components of $\mathcal{K}$ are the square of the spatial extent of the electron density along each axis. A benchmark dataset of the prinicpal components of $\mathcal{K}$ for 100 small molecules at the coupled cluster singles and doubles with perturbative triples (CCSD(T)) at the complete basis set (CBS) limit is developed, resulting in 213 independent $\mathcal{K}$ components. The performance of 47 popular and recent density functionals is assessed against this Var213 dataset. Several functionals, especially double hybrids, and also SCAN and SCAN0 yield reliable second cumulants, although some modern, empirically parameterized functionals yield more disappointing performance. The H and Be atoms in particular are challenging for nearly all methods, indicating that future functional development could benefit from inclusion of their density information in training or testing protocols.

References in corpus (16)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Comment on: "Estimating the Hartree-Fock limit from finite basis set calculations" [Jensen F (2005) Theor Chem Acc 113:267]
• A deterministic alternative to the full configuration interaction quantum Monte Carlo method
• How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values
• Fractional spins and static correlation error in density functional theory
• Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method
• SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters
• Semilocal and Hybrid Meta-Generalized Gradient Approximations Based on the Understanding of the Kinetic-Energy-Density Dependence
• Delocalization errors in density functional theory are essentially quadratic in fractional occupation number
• Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections
• Density Functional Theory is Not Straying from the Path toward the Exact Functional
• Third order Møller-Plesset theory made more useful? The role of density functional theory orbitals
• Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H${}_2$
• Beyond the Coulson-Fischer point: Characterizing single excitation CI and TDDFT for excited states in single bond dissociations
• Kohn-Sham Density Functional Theory with Complex, Spin-Restricted Orbitals: Accessing a New Class of Densities without the Symmetry Dilemma
• xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS

Cited by in corpus (2)

• Benchmarking TD-DFT and Wave Function Methods for Oscillator Strengths and Excited-State Dipole Moments
• Revisiting the performance of time-dependent density functional theory for electronic excitations: Assessment of 43 popular and recently developed functionals from rungs one to four