Topological analysis of electron densities from Kohn-Sham and subsystem density functional theory

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

Characterization of excited states in time-dependent density functional theory using localized molecular orbitals

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

DFT calculations in the assignment of solid-state NMR and crystal structure elucidation of a lanthanum(iii) complex with dithiocarbamate and phenanthroline

Structure of a novel rare-earth lanthanum(iii) complex resolved by a combination of DFT modelling, NMR spectroscopy, and single crystal XRD.

Frozen density embedding with non-integer subsystems' particle numbers

We extend the frozen density embedding theory to non-integer subsystems' particles numbers. Different features of this formulation are discussed, with special concern for approximate embedding calculations. In particular, we highlight the relation between the non-integer particle-number partition scheme and the resulting embedding errors. Finally, we provide a discussion of the implications of the present theory for the derivative discontinuity issue and the calculation of chemical reactivity descriptors.

On the accuracy of frozen density embedding calculations with hybrid and orbital-dependent functionals for non-bonded interaction energies

We analyze the accuracy of the frozen density embedding (FDE) method, with hybrid and orbital-dependent exchange-correlation functionals, for the calculation of the total interaction energies of weakly interacting systems. Our investigation is motivated by the fact that these approaches require, in addition to the non-additive kinetic energy approximation, also approximate non-additive exact-exchange energies. Despite this further approximation, we find that the hybrid/orbital-dependent FDE approaches can reproduce the total energies with the same accuracy (about 1 mHa) as the one of conventional semi-local functionals. In many cases, thanks to error cancellation effects, hybrid/orbital-dependent approaches yield even the smallest error. A detailed energy-decomposition investigation is presented. Finally, the Becke-exchange functional is found to reproduce accurately the non-additive exact-exchange energies also for non-equilibrium geometries. These performances are rationalized in terms of a reduced-gradient decomposition of the non-additive exchange energy.

Modeling environmental effects on charge density distributions in polar organometallics: validation of embedded cluster models for the methyl lithium crystal

The charge density and its Laplacian at the Li-C and C-H bond critical points and other features of the electron density distribution of the methyl lithium crystal have been compared by density functional methods for (i) the isolated (LiCH(3))(4) tetramer or larger clusters, (ii) for quantum mechanically treated clusters in polarizable continuum model (PCM) surroundings, (iii) for clusters augmented by the periodic electrostatic embedded cluster model (PEECM), and for (iv) the periodic crystal. Comparisons with identical functional and basis sets indicate that both PCM and PEECM embedding of only a tetramer did not fully account for the environmental effect. In contrast, embedding of a full unit cell gave results that were essentially converged to the periodic crystal data. Effects of basis set and exchange correlation functional on the QTAIM bond descriptors are of a comparable order of magnitude as the crystal environmental effects. In this context, embedded cluster computations provide distinct advantages over explicit solid-state calculations with respect to their freedom of the choice of computational and theoretical level. This is demonstrated by embedded MP2 calculations.