Molecular structure does not easily identify the intricate noncovalent interactions that govern many areas of biology and chemistry, including design new materials drugs. We develop an approach to detect in real space, based on electron density its derivatives. Our reveals underlying chemistry compliments covalent structure. It provides a rich representation van der Waals interactions, hydrogen bonds, steric repulsion small molecules, molecular complexes, solids. Most importantly, method,...

Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering sciences. However, for many predicted properties, there are spectacular failures that can be traced to the delocalization error static correlation commonly used approximations. These errors characterized understood through perspective fractional charges spins introduced recently. Reducing these will open new frontiers applications density theory.

The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis total energy for fractional charges. deviation the correct intrinsic linear behavior in finite systems leads to delocalization localization errors large bulk systems. Functionals whose is convex charges such as local density approximation display incorrect apparent linearity limit, due error. Concave also have calculation, error imposed symmetry. This resolves...

One of the most important challenges in density functional theory (DFT) is proper description fractional charge systems relating to self-interaction error (SIE). Traditionally, SIE has been formulated as a one-electron problem, which addressed several recent functionals. However, these SIE-free functionals, while greatly improving thermochemistry and reaction barriers general, still exhibit many difficulties associated with SIE. Thus we emphasize need surpass this limit shed light on...

The calculation of the band gap by density-functional theory (DFT) is examined considering behavior energy as a function number electrons. It explained that incorrect band-gap prediction with most approximate functionals originates mainly from errors in describing systems fractional charges. Formulas for derivatives respect to electrons are derived, which clarify role optimized effective potentials gap. Calculations recent functional has much improved charges give good and also...

New exchange-correlation functionals that address the important issue of many-electron self-interaction are developed. This is carried out by considering performance functional on systems with fractional numbers electrons at same time as more standard thermochemical tests. The inclusion Coulomb-attenuated exchange in facilitated use adiabatic connection coupled a short-range and long-range splittings. new have good thermochemistry much improved description total energy versus number...

Density functional theory describes matter at the quantum level, but all popular approximations suffer from systematic errors that arise violation of mathematical properties exact functional. We overcame this fundamental limitation by training a neural network on molecular data and fictitious systems with fractional charge spin. The resulting functional, DM21 (DeepMind 21), correctly typical examples artificial delocalization strong correlation performs better than traditional functionals...

Standard approximations for the exchange-correlation functional have been found to give big errors linearity condition of fractional charges, leading delocalization error, and constancy spins, static correlation error. These two conditions are now unified extended states with both charge spin a much more stringent condition: exact energy is plane, linear along coordinate constant line discontinuity at integer. Violation this underlies failure all known approximate functionals describe gaps...

Electronic states with fractional spins arise in systems large static correlation (strongly correlated systems). Such fractional-spin are shown to be ensembles of degenerate ground normal spins. It is proven here that the energy exact functional for a constant, equal comprising pure-spin states. Dramatic deviations from this constancy condition exist all approximate functionals, leading errors strongly systems, such as chemical bond dissociation and band structure Mott insulators. This...

The difficulty of approximate density functionals in describing the energetics Diels-Alder reactions and dimerization aluminum complexes is analyzed. Both these reaction classes involve formation cyclic or bicyclic products, which are found to be underbound by majority considered. We present a consistent view results from perspective delocalization error. This error causes give too low energy for delocalized densities high localized densities, as products. interpretation allows us understand...

We develop a self-interaction-free exchange-correlation functional which is very accurate for thermochemistry and kinetics. This achieved by theoretical construction of the form nonlinear fitting. define simple interpolation adiabatic connection that uses exact exchange, generalized gradient approximation (GGA) meta-GGA functionals. The performance optimized fitting small number empirical parameters. Overall new improves significantly upon hybrids meta-GGAs while correctly describing...

A novel nonempirical scaling correction method is developed to tackle the challenge of band gap prediction in density functional theory. For finite systems largely restores straight-line behavior electronic energy at fractional electron numbers. The can be generally applied a variety mainstream approximations, leading significant improvement prediction. In particular, scaled version modified local approximation predicts gaps with an accuracy consistent for all sizes, ranging from atoms and...

The conventional analysis of Perdew and Levy, Sham Schlüter shows that the functional derivative discontinuity exchange-correlation density plays a critical role in correct prediction bandgaps, or chemical hardness. In recent work by present authors, explicit expressions for bandgap with all common types functionals have been derived without invoking concept energy at all. We here analyze two approaches establish their connection difference. further leads to several important results: (1)...

Manifestations of the derivative discontinuity energy in density functional theory are demonstrated simple systems chemistry and physics.

The electron density of crystals contains all the information required to complete a classification their bonding types. We propose here set three different indexes, flatness, charge transfer, and molecularity, easily obtained from experimental or theoretical density, which give rise in close resemblance classical van Arkel−Ketelaar diagrams.

The long-standing problem of the large overestimation polymer polarizabilities in density-functional theory is reexamined and largely solved using an exact exchange method. We have built accurate optimized effective potential as sum a fixed linear combination basis sets based on our direct optimization This properly develops counteracting depolarization field, it significantly improves recent results from approximate potentials. controversial case hydrogen chains now correctly described...

Delocalization error is one of the most fundamental and dominant errors that plagues presently used density functional approximations. It responsible for a large class problems in theory calculations. For an effective universal alleviation delocalization error, we develop local scaling correction scheme by imposing Perdew-Parr-Levy- Balduz linearity condition to regions system. Our novel applicable various mainstream substantially reduces as exemplified significantly improved description...

The compressibility and thermal expansion of the cubic silicon nitride $(c\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4})$ phase have been investigated by performing in situ x-ray powder-diffraction measurements using synchrotron radiation, complemented with computer simulations means first-principles calculations. bulk $c\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ originates from average both Si-N tetrahedral octahedral compressibilities where polyhedra are less compressible than...

We have developed a second-order perturbation theory (PT) energy functional within density-functional (DFT). Based on PT with the Kohn–Sham (KS) determinant as reference, this new ab initio exchange-correlation includes an exact exchange (EXX) in first order and correlation including all single double excitations from KS reference second order. The explicit dependence of orbitals fits well into our direct minimization approach for optimized effective potential, which is very efficient method...

Charged and neutral oxygen vacancies in the bulk on perfect defective surfaces of MgO are characterized as quantum-mechanical subsystems chemically bonded to host lattice containing most charge left by removed oxygens. Attractors electron density appear inside vacancy, a necessary condition for existence subsystem according atoms molecules theory. The analysis localization function also shows attractors at vacancy sites, which associated basin shared with valence domain nearest This...

In this work the behavior of MP2 for fractional occupations is investigated. The consideration charge gives a simple derivation an expression chemical potential (or derivative energy with respect to number electrons) MP2. A generalized optimized effective formalism (OEP) has been developed in which OEP nonlocal potential, can be applied explicit functionals orbitals and eigenvalues also facilitates evaluation potential. improves upon corresponding Koopmans' theorem Hartree-Fock theory...

We examine the development and investigate performance of exchange-correlation functionals constructed from adiabatic connection. Our method is based on a direct modeling connection curve in coupling-constant space very flexible models. Several different models are investigated construction new families functionals. Also two these (MCY1 MCY2) over wider range systems properties, with comparison made to established Overall, improve upon widely used hybrid generalized gradient approximation...

The random phase approximation (RPA) is thought to be a successful method; however, basic errors have been found that massive implications in the simplest molecular systems. observed successes and failures are rationalized by examining its performance against exact conditions on energy for fractional charges spins. Extremely simple tests reveal RPA method satisfies constancy condition spins leads correct dissociation of closed-shell molecules no static correlation error (such as H${}_{2}$...

In this work, we examine the fractional charge behaviors of doubly hybrid (DH) functionals. By plotting ground-state energies E and energy derivatives for atoms molecules with electron numbers N, directly quantify delocalization errors some representative DH functionals such as B2PLYP, XYG3, XYGJ-OS. Numerical assessments on ionization potentials (IPs), affinities (EAs), fundamental gaps, from either integer number calculations or derivative calculations, are provided. It is shown that XYG3...