Perspective: Fifty years of density-functional theory in chemical physics

Ab Initio Optimized Effective Potentials for Real Molecules in Optical Cavities: Photon Contributions to the Molecular Ground State

We introduce a simple scheme to efficiently compute photon exchange-correlation contributions due to the coupling to transversal photons as formulated in the newly developed quantum-electrodynamical density-functional theory (QEDFT).1-5 Our construction employs the optimized-effective potential (OEP) approach by means of the Sternheimer equation to avoid the explicit calculation of unoccupied states. We demonstrate the efficiency of the scheme by applying it to an exactly solvable GaAs quantum ring model system, a single azulene molecule, and chains of sodium dimers, all located in optical cavities and described in full real space. While the first example is a two-dimensional system and allows to benchmark the employed approximations, the latter two examples demonstrate that the correlated electron-photon interaction appreciably distorts the ground-state electronic structure of a real molecule. By using this scheme, we not only construct typical electronic observables, such as the electronic ground-state density, but also illustrate how photon observables, such as the photon number, and mixed electron-photon observables, for example, electron-photon correlation functions, become accessible in a density-functional theory (DFT) framework. This work constitutes the first three-dimensional ab initio calculation within the new QEDFT formalism and thus opens up a new computational route for the ab initio study of correlated electron-photon systems in quantum cavities.

How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry

Static polarizabilities are the first response of the electron density to electric fields, and offer a formally exact measure of the accuracy of excited states. We have developed a benchmark database of polarizabilities and have assessed the performance of 60 popular and recent functionals in predicting them.

A theoretical study of new representatives of closed- and open-circle benzofuran and benzocyclopentadienone oligomers

Strain energies for oxa[n]circulene species relative to the unstrained tetraoxa[8]circulene.

Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT

Decomposition of the exact time-dependent exchange–correlation potential offers a new starting point to build approximations with memory.

Steric charge

Steric charge is an informative descriptor providing novel insights to appreciate the steric effect and stereoselectivity for chemical processes and transformations.

A meta-GGA level screened range-separated hybrid functional by employing short range Hartree–Fock with a long range semilocal functional

The range-separated hybrid density functionals are very successful in describing a wide range of molecular and solid-state properties accurately.

‘Diet GMTKN55’ offers accelerated benchmarking through a representative subset approach

The GMTKN55 benchmarking protocol allows comprehensive analysis and ranking of density functional approximations with diverse chemical behaviours. This work reports diet versions of GMTKN55 which reproduce key properties of the full protocol at substantially reduced numerical cost. ‘Diet GMTKN55’ can thus be used for benchmarking expensive methods, or in combination with solid state benchmarks.

Mechanistic insights into hydrodeoxygenation of phenol on bimetallic phosphide catalysts

Different binding modes of the reactant on different catalysts determine the hydrodeoxygenation selectivity.

Infrared spectroscopy of gas phase alpha hydroxy carboxylic acid homo and hetero dimers

New gas phase infrared spectroscopy is reported for an aromatic alpha hydroxy carboxylic acid homo dimer of 9-hydroxy-9-fluorene carboxylic acid (9HFCA)₂, and the hetero dimer of 9HFCA with glycolic acid.

ANI-1, A data set of 20 million calculated off-equilibrium conformations for organic molecules

One of the grand challenges in modern theoretical chemistry is designing and implementing approximations that expedite ab initio methods without loss of accuracy. Machine learning (ML) methods are emerging as a powerful approach to constructing various forms of transferable atomistic potentials. They have been successfully applied in a variety of applications in chemistry, biology, catalysis, and solid-state physics. However, these models are heavily dependent on the quality and quantity of data used in their fitting. Fitting highly flexible ML potentials, such as neural networks, comes at a cost: a vast amount of reference data is required to properly train these models. We address this need by providing access to a large computational DFT database, which consists of more than 20 M off equilibrium conformations for 57,462 small organic molecules. We believe it will become a new standard benchmark for comparison of current and future methods in the ML potential community.

Computational Chemistry: The Fate of Current Methods and Future Challenges

"Where do we go from here?" is the underlying question regarding the future (perhaps foreseeable) developments in computational chemistry. Although this young discipline has already permeated practically all of chemistry, it is likely to become even more powerful with the rapid development of computational hard- and software.

Computational methods for 2D materials: discovery, property characterization, and application design

The discovery of two-dimensional (2D) materials comes at a time when computational methods are mature and can predict novel 2D materials, characterize their properties, and guide the design of 2D materials for applications. This article reviews the recent progress in computational approaches for 2D materials research. We discuss the computational techniques and provide an overview of the ongoing research in the field. We begin with an overview of known 2D materials, common computational methods, and available cyber infrastructures. We then move onto the discovery of novel 2D materials, discussing the stability criteria for 2D materials, computational methods for structure prediction, and interactions of monolayers with electrochemical and gaseous environments. Next, we describe the computational characterization of the 2D materials' electronic, optical, magnetic, and superconducting properties and the response of the properties under applied mechanical strain and electrical fields. From there, we move on to discuss the structure and properties of defects in 2D materials, and describe methods for 2D materials device simulations. We conclude by providing an outlook on the needs and challenges for future developments in the field of computational research for 2D materials.

Determination of trace metal concentration in compost, DAP, and TSP fertilizers by neutron activation analysis (NAA) and insights from density functional theory calculations

Leaching of toxic metals from fertilizers is a growing concern in an agricultural country like Bangladesh due to the serious consequences in health and food chain. Fertilizers used in farming fields and nurseries (plant sales outlet) in the mid-southern part of Bangladesh were collected for the determination of toxic metals. This study employed the neutron activation method and a relative standardization approach. Three standard/certified reference materials, namely NIST coal fly ash 1633b, IAEA-Soil-7, and IAEA-SL-1 (lake sediment), were considered for elemental quantification. Concentration of As (2.63-16.73 mg/kg), Cr (40.93-261.77 mg/kg), Sb (0.47-63.58 mg/kg), Th (1.44-19.16 mg/kg), and U (1.90-209.41 mg/kg) were determined in fertilizers. High concentrations of Cr, Sb, and U were detected in some compost and phosphate fertilizers (TSP and diammonium phosphate (DAP)) in comparison with the IAEA/European market standard and other studies. Quantum mechanical calculations were performed to understand the molecular level interaction of CrO₃, Sb₂O₃, and AsO₃, with DAP by employing density functional theory with the B3LYP/SDD level of theory. Our results indicated that CrO₃ and Sb₂O₃ have strong binding affinity with DAP compared to AsO₃, which supports the experimental results. These compounds attached to the phosphate group through covalent-like bonding with oxygen. The frontier molecular orbital calculation indicated that HOMO-LUMO gap of the AsO₃-DAP (5.46 eV) and Sb₂O₃-DAP (6.48 eV) complexes are relatively lower than the CrO₃-DAP, which indicates that As and Sb oxides are chemically more prone to attach with the phosphate group of DAP fertilizer.

Electronic-Structure Origin of Cation Disorder in Transition-Metal Oxides

Cation disorder is an important design criterion for technologically relevant transition-metal (TM) oxides, such as radiation-tolerant ceramics and Li-ion battery electrodes. In this Letter, we use a combination of first-principles calculations, normal mode analysis, and band-structure arguments to pinpoint a specific electronic-structure effect that influences the stability of disordered phases. We find that the electronic configuration of a TM ion determines to what extent the structural energy is affected by site distortions. This mechanism explains the stability of disordered phases with large ionic radius differences and provides a concrete guideline for the discovery of novel disordered compositions.

Ab Initio QM/MM Modeling of the Rate-Limiting Proton Transfer Step in the Deamination of Tryptamine by Aromatic Amine Dehydrogenase

Aromatic amine dehydrogenase (AADH) and related enzymes are at the heart of debates on the roles of quantum tunneling and protein dynamics in catalysis. The reaction of tryptamine in AADH involves significant quantum tunneling in the rate-limiting proton transfer step, shown by large H/D primary kinetic isotope effects (KIEs), with unusual temperature dependence. We apply correlated ab initio combined quantum mechanics/molecular mechanics (QM/MM) methods, at levels up to local coupled cluster theory (LCCSD(T)/(aug)-cc-pVTZ), to calculate accurate potential energy surfaces for this reaction, which are necessary for quantitative analysis of tunneling contributions and reaction dynamics. Different levels of QM/MM treatment are tested. Multiple pathways are calculated with fully flexible transition state optimization by the climbing-image nudged elastic band method at the density functional QM/MM level. The average LCCSD(T) potential energy barriers to proton transfer are 16.7 and 14.0 kcal/mol for proton transfer to the two carboxylate atoms of the catalytic base, Asp128β. The results show that two similar, but distinct pathways are energetically accessible. These two pathways have different barriers, exothermicity and curvature, and should be considered in analyses of the temperature dependence of reaction and KIEs in AADH and other enzymes. These results provide a benchmark for this prototypical enzyme reaction and will be useful for developing empirical models, and analyzing experimental data, to distinguish between different conceptual models of enzyme catalysis.

Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory

Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.

Practical Density Functionals beyond the Overdelocalization-Underbinding Zero-Sum Game

Density functional theory (DFT) uses a density functional approximation (DFA) to add electron correlation to mean-field electronic structure calculations. Standard strategies (generalized gradient approximations GGAs, meta-GGAs, hybrids, etc.) for building DFAs, no matter whether based on exact constraints or empirical parametrization, all face a zero-sum game between overdelocalization (fractional charge error, FC) and underestimation of covalent bonding (fractional spin error, FS). This work presents an alternative strategy. Practical "Rung 3.5" ingredients are used to implement insights from hyper-GGA DFAs that reduce both FS and FC errors. Prototypes of this strategy qualitatively improve FS and FC error over 40 years of standard DFAs while maintaining low cost and practical evaluation of properties. Numerical results ranging from transition metal thermochemistry to absorbance peaks and excited-state geometry optimizations highlight this strategy's promise and indicate areas requiring further development.

The nature of three-body interactions in DFT: Exchange and polarization effects

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar₂-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy

From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully nonlocal. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard density functional theory (DFT) functionals, are captured by the highly nonlocal structure, which goes beyond the "Jacob's ladder" framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.

Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches

Our general framework for the simulation of vibrational signatures in electronic spectra has been extended to treat one large-amplitude motion (LAM) at the anharmonic level, coupled to the other small-amplitude motions (SAM) treated as harmonic. The coupling between LAM and SAM is minimized thanks to the use of delocalized internal coordinates, which are built automatically from the molecular topology. General LAMs can be employed, ranging from intrinsic reaction coordinates to rigid or flexible paths based on the distinguished coordinate approach. The anharmonic model is based on a fully numerical method based on the discrete variable representation (DVR) theory, supporting different types of boundary conditions. The inclusion of this model in a general-purpose electronic structure code makes available to the user a large panel of quantum chemistry models, for both isolated and condensed phases. The flexibility and reliability of the new framework are illustrated by some case studies, covering various types of LAMs, ranging from a small test case, the photoelectron spectrum of ammonia, to larger systems, such as phenylanthracene and cyclobutanone.

Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?

The development of approximate exchange-correlation functionals is critical for modern density functional theory. A recent analysis of atomic systems suggested that some modern functionals are straying from the path toward the exact functional because electron densities are becoming less accurate while energies are becoming more accurate since the year 2000. To investigate this trend for more chemically relevant systems, the electron densities in the bonding regions and the atomization energies are analyzed for a series of diatomic molecules with 90 different functionals. For hybrid generalized gradient approximation functionals developed since the year 2000, the errors in densities and atomization energies are decoupled; the accuracy of the energies remains relatively consistent while the accuracy of the densities varies significantly. Such decoupling is not observed for generalized gradient and meta-generalized gradient approximation functionals. Analysis of electron densities in bonding regions is found to be important for the evaluation of functionals for chemical systems.