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Visualizing atomic sizes and molecular shapes with the classical turning surface of the Kohn-Sham potential.

ABSTRACT: The Kohn-Sham potential [Formula: see text] is the effective multiplicative operator in a noninteracting Schrödinger equation that reproduces the ground-state density of a real (interacting) system. The sizes and shapes of atoms, molecules, and solids can be defined in terms of Kohn-Sham potentials in a nonarbitrary way that accords with chemical intuition and can be implemented efficiently, permitting a natural pictorial representation for chemistry and condensed-matter physics. Let [Formula: see text] be the maximum occupied orbital energy of the noninteracting electrons. Then the equation [Formula: see text] defines the surface at which classical electrons with energy [Formula: see text] would be turned back and thus determines the surface of any electronic object. Atomic and ionic radii defined in this manner agree well with empirical estimates, show regular chemical trends, and allow one to identify the type of chemical bonding between two given atoms by comparing the actual internuclear distance to the sum of atomic radii. The molecular surfaces can be fused (for a covalent bond), seamed (ionic bond), necked (hydrogen bond), or divided (van der Waals bond). This contribution extends the pioneering work of Z.-Z. Yang et al. [Yang ZZ, Davidson ER (1997) Int J Quantum Chem 62:47-53; Zhao DX, et al. (2018) Mol Phys 116:969-977] by our consideration of the Kohn-Sham potential, protomolecules, doubly negative atomic ions, a bond-type parameter, seamed and necked molecular surfaces, and a more extensive table of atomic and ionic radii that are fully consistent with expected periodic trends.

SUBMITTER: Ospadov E

PROVIDER: S-EPMC6294941 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Bypassing the Kohn-Sham equations with machine learning.

Project description:Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.Machine learning allows electronic structure calculations to access larger system sizes and, in dynamical simulations, longer time scales. Here, the authors perform such a simulation using a machine-learned density functional that avoids direct solution of the Kohn-Sham equations.

| S-EPMC5636838 | biostudies-other

From Kohn-Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential.

Project description:Accurately describing excited states within Kohn-Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

| S-EPMC8363072 | biostudies-literature

Revisiting Artifacts of Kohn-Sham Density Functionals for Biosimulation.

Project description:We revisit the problem of unphysical charge density delocalization/fractionalization induced by the self-interaction error of common approximate Kohn-Sham (KS) density functional theory functionals on simulation of small to medium-sized proteins in a vacuum. Aside from producing unphysical electron densities and total energies, the vanishing of the HOMO-LUMO gap associated with the unphysical charge delocalization leads to an unphysical low-energy spectrum and catastrophic failure of most popular solvers for the KS self-consistent field (SCF) problem. We apply a robust quasi-Newton SCF solver [ Phys. Chem. Chem. Phys. 2024, 26, 6557] to obtain solutions for some of these difficult cases. The anatomy of the charge delocalization is revealed by the natural deformation orbitals obtained from the density matrix difference between the Hartree-Fock and KS solutions; the charge delocalization not only can occur between charged fragments (such as in zwitterionic polypeptides) but also involves neutral fragments. The vanishing-gap phenomenon and troublesome SCF convergence are both attributed to the unphysical KS Fock operator eigenspectra of molecular fragments (e.g., amino acids or their side chains). Analysis of amino acid pairs suggests that the unphysical charge delocalization can be partially ameliorated by the use of some range-separated hybrid functionals but not by semilocal or standard hybrid functionals. Last, we demonstrate that solutions without the unphysical charge delocalization can be located even for semilocal KS functionals highly prone to such defects, but such solutions have non-Aufbau character and are unstable with respect to mixing of the non-overlapping "frontier" orbitals. Caution should be exercised when unexpectedly small (or vanishing) HOMO-LUMO gaps and atypical SCF convergence patterns (e.g., oscillatory) are observed in KS DFT simulations in any context (bio or otherwise).

| S-EPMC11325537 | biostudies-literature

Rapidly predicting Kohn-Sham total energy using data-centric AI.

Project description:Predicting material properties by solving the Kohn-Sham (KS) equation, which is the basis of modern computational approaches to electronic structures, has provided significant improvements in materials sciences. Despite its contributions, both DFT and DFTB calculations are limited by the number of electrons and atoms that translate into increasingly longer run-times. In this work we introduce a novel, data-centric machine learning framework that is used to rapidly and accurately predicate the KS total energy of anatase [Formula: see text] nanoparticles (NPs) at different temperatures using only a small amount of theoretical data. The proposed framework that we call co-modeling eliminates the need for experimental data and is general enough to be used over any NPs to determine electronic structure and, consequently, more efficiently study physical and chemical properties. We include a web service to demonstrate the effectiveness of our approach.

| S-EPMC9402589 | biostudies-literature

Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn-Sham Calculations.

Project description:Quasiparticle energies and fundamental band gaps in particular are critical properties of molecules and materials. It was rigorously established that the generalized Kohn-Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn-Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over 40 systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the ( N - 1)-electron systems. Results show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. This work highlights the pathway to quasiparticle and excitation energies from ground density functional calculations.

| S-EPMC6445661 | biostudies-literature

Energy decomposition analysis of single bonds within Kohn-Sham density functional theory.

Project description:An energy decomposition analysis (EDA) for single chemical bonds is presented within the framework of Kohn-Sham density functional theory based on spin projection equations that are exact within wave function theory. Chemical bond energies can then be understood in terms of stabilization caused by spin-coupling augmented by dispersion, polarization, and charge transfer in competition with destabilizing Pauli repulsions. The EDA reveals distinguishing features of chemical bonds ranging across nonpolar, polar, ionic, and charge-shift bonds. The effect of electron correlation is assessed by comparison with Hartree-Fock results. Substituent effects are illustrated by comparing the C-C bond in ethane against that in bis(diamantane), and dispersion stabilization in the latter is quantified. Finally, three metal-metal bonds in experimentally characterized compounds are examined: a [Formula: see text]-[Formula: see text] dimer, the [Formula: see text]-[Formula: see text] bond in dizincocene, and the Mn-Mn bond in dimanganese decacarbonyl.

| S-EPMC5715786 | biostudies-literature

Beyond Kohn-Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory.

Project description:A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn-Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections.

| S-EPMC5793875 | biostudies-literature

The Nature of Nonclassical Carbonyl Ligands Explained by Kohn-Sham Molecular Orbital Theory.

Project description:When carbonyl ligands coordinate to transition metals, their bond distance either increases (classical) or decreases (nonclassical) with respect to the bond length in the isolated CO molecule. C-O expansion can easily be understood by π-back-donation, which results in a population of the CO's π*-antibonding orbital and hence a weakening of its bond. Nonclassical carbonyl ligands are less straightforward to explain, and their nature is still subject of an ongoing debate. In this work, we studied five isoelectronic octahedral complexes, namely Fe(CO)6 2+ , Mn(CO)6 + , Cr(CO)6 , V(CO)6 - and Ti(CO)6 2- , at the ZORA-BLYP/TZ2P level of theory to explain this nonclassical behavior in the framework of Kohn-Sham molecular orbital theory. We show that there are two competing forces that affect the C-O bond length, namely electrostatic interactions (favoring C-O contraction) and π-back-donation (favoring C-O expansion). It is a balance between those two terms that determines whether the carbonyl is classical or nonclassical. By further decomposing the electrostatic interaction ΔVelstat into four fundamental terms, we are able to rationalize why ΔVelstat gives rise to the nonclassical behavior, leading to new insights into the driving forces behind C-O contraction.

| S-EPMC7756819 | biostudies-literature

Nature of the Ru-NO Coordination Bond: Kohn-Sham Molecular Orbital and Energy Decomposition Analysis.

Project description:We have analyzed structure, stability, and Ru-NO bonding of the trans-[RuCl(NO)(NH3)4]2+ complex by using relativistic density functional theory. First, we focus on the bond dissociation energies associated with the three canonical dissociation modes leading to [RuCl(NH3)4]++NO+, [RuCl(NH3)4]2++NO, and [RuCl(NH3)4]3++NO-. The main objective is to understand the Ru-NO+ bonding mechanism in the conceptual framework of Kohn-Sham molecular orbital theory in combination with a quantitative energy decomposition analysis. In our analyses, we have addressed the importance of the synergism between Ru-NO+ σ-donation and π-backdonation as well as the so-called negative trans influence of the Cl- ligand on the Ru-NO bond. For completeness, the Ru-NO+ bonding mechanism is compared with that of the corresponding Ru-CO bond.

| S-EPMC5474663 | biostudies-literature

Post-Kohn-Sham Random-Phase Approximation and Correction Terms in the Expectation-Value Coupled-Cluster Formulation.

Project description:Using expectation-value coupled-cluster theory and many-body perturbation theory (MBPT), we formulate a series of corrections to the post-Kohn-Sham (post-KS) random-phase approximation (RPA) energy. The beyond-RPA terms are of two types: those accounting for the non-Hartree-Fock reference and those introducing the coupled-cluster doubles non-ring contractions. The contributions of the former type, introduced via the semicanonical orbital basis, drastically reduce the binding strength in noncovalent systems. The good accuracy is recovered by the attractive third-order doubles correction referred to as Ec2g. The existing RPA approaches based on KS orbitals neglect most of the proposed corrections but can perform well thanks to error cancellation. The proposed method accounts for every contribution in the state-of-the-art renormalized second-order perturbation theory (rPT2) approach but adds additional terms which initially contribute in the third order of MBPT. The cost of energy evaluation scales as noniterative O(N4) in the implementation with low-rank tensor decomposition. The numerical tests of the proposed approach demonstrate accurate results for noncovalent dimers of polar molecules and for the challenging many-body noncovalent cluster of CH4···(H2O)20.

| S-EPMC10569055 | biostudies-literature

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