Structure of Multi-State Correlation in Electronic Systems

Beyond the Hohenberg-Kohn density functional theory for the ground state, it has been established that the Hamiltonian matrix for a finite number (N) of lowest eigenstates is a matrix density functional. Its fundamental variable─the matrix density D(r)─can be represented by, or mapped to, a set of auxiliary, multiconfigurational wave functions expressed as a linear combination of no more than N2 determinant configurations. The latter defines a minimal active space (MAS), which naturally leads to the introduction of the correlation matrix functional, responsible for the electronic correlation effects outside the MAS. In this study, we report a set of rigorous conditions in the Hamiltonian matrix functional, derived by enforcing the symmetry of a Hilbert subspace, namely the subspace invariance property. We further establish a fundamental theorem on the correlation matrix functional. That is, given the correlation functional for a single state in the N-dimensional subspace, all elements of the correlation matrix functional for the entire subspace are uniquely determined. These findings reveal the intricate structure of electronic correlation within the Hilbert subspace of lowest eigenstates and suggest a promising direction for efficient simulation of excited states.

Correcting Dispersion Corrections with Density-Corrected DFT

Almost all empirical parametrizations of dispersion corrections in DFT use only energy errors, thereby mixing functional and density-driven errors. We introduce density and dispersion-corrected DFT (D2C-DFT), a dual-calibration approach that accounts for density delocalization errors when parametrizing dispersion interactions. We simply exclude density-sensitive reactions from the training data. We find a significant reduction in both errors and variation among several semilocal functionals and their global hybrids when tailored dispersion corrections are employed with Hartree-Fock densities.

The Determination of Free Energy of Hydration of Water Ions from First Principles

We model the autoionization of water by determining the free energy of hydration of the major intermediate species of water ions. We represent the smallest ions─the hydroxide ion OH-, the hydronium ion H3O+, and the Zundel ion H5O2+─by bonded models and the more extended ionic structures by strong nonbonded interactions (e.g., the Eigen H9O4+ = H3O+ + 3(H2O) and the Stoyanov H13O6+ = H5O2+ + 4(H2O)). Our models are faithful to the precise QM energies and their components to within 1% or less. Using the calculated free energies and atomization energies, we compute the pKa of pure water from first principles as a consistency check and arrive at a value within 1.3 log units of the experimental one. From these calculations, we conclude that the hydronium ion, and its hydrated state, the Eigen cation, are the dominant species in the water autoionization process.

Stochastic density functional theory combined with Langevin dynamics for warm dense matter

This study overviews and extends a recently developed stochastic finite-temperature Kohn-Sham density functional theory to study warm dense matter using Langevin dynamics, specifically under periodic boundary conditions. The method's algorithmic complexity exhibits nearly linear scaling with system size and is inversely proportional to the temperature. Additionally, a linear-scaling stochastic approach is introduced to assess the Kubo-Greenwood conductivity, demonstrating exceptional stability for dc conductivity. Utilizing the developed tools, we investigate the equation of state, radial distribution, and electronic conductivity of hydrogen at a temperature of 30 000 K. As for the radial distribution functions, we reveal a transition of hydrogen from gaslike to liquidlike behavior as its density exceeds 4g/cm^{3}. As for the electronic conductivity as a function of the density, we identified a remarkable isosbestic point at frequencies around 7 eV, which may be an additional signature of a gas-liquid transition in hydrogen at 30 000 K.

Correlation consistent basis sets designed for density functional theory: Third-row atoms (Ga-Br)

The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga-Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn-Sham limit is improved relative to other basis sets where convergence to the Kohn-Sham limit is typically not observed.

Constructing Mixed Density Functionals for Describing Dissociative Chemisorption on Metal Surfaces: Basic Principles

The production of a majority of chemicals involves heterogeneous catalysis at some stage, and the rates of many heterogeneously catalyzed processes are governed by transition states for dissociative chemisorption on metals. Accurate values of barrier heights for dissociative chemisorption on metals are therefore important to benchmarking electronic structure theory in general and density functionals in particular. Such accurate barriers can be obtained using the semiempirical specific reaction parameter (SRP) approach to density functional theory. However, this approach has thus far been rather ad hoc in its choice of the generic expression of the SRP functional to be used, and there is a need for better heuristic approaches to determining the mixing parameters contained in such expressions. Here we address these two issues. We investigate the ability of several mixed, parametrized density functional expressions combining exchange at the generalized gradient approximation (GGA) level with either GGA or nonlocal correlation to reproduce barrier heights for dissociative chemisorption on metal surfaces. For this, seven expressions of such mixed density functionals are tested on a database consisting of results for 16 systems taken from a recently published slightly larger database called SBH17. Three expressions are derived that exhibit high tunability and use correlation functionals that are either of the PBE GGA form or of one of two limiting nonlocal forms also describing the attractive van der Waals interaction in an approximate way. We also find that, for mixed density functionals incorporating GGA correlation, the optimum fraction of repulsive RPBE GGA exchange obtained with a specific GGA density functional is correlated with the charge-transfer parameter, which is equal to the difference in the work function of the metal surface and the electron affinity of the molecule. However, the correlation is generally not large and not large enough to obtain accurate guesses of the mixing parameter for the systems considered, suggesting that it does not give rise to a very effective search strategy.

Recent Advancements in Mechanistic Studies of Palladium- and Nickel-Catalyzed Ethylene Copolymerization with Polar Monomers

The introduction of polar functional groups into polyolefin chain structures creates opportunities to enhance specific properties, such as adhesion, dyeability, printability, compatibility, thermal stability, and electrical conductivity, which widen the range of potential applications for these modified materials. Transition metal catalysts, especially late transition metals, have proven to be highly effective in copolymerization processes due to their reduced Lewis acidity and electrophilicity. However, when compared to the significant progress and summary of synthetic methods, there is a distinct lack of a comprehensive summary of mechanistic studies pertaining to the catalytic systems involved in ethylene copolymerization catalyzed by palladium and nickel catalysts. In this review, we have provided a comprehensive summary of the latest developments in mechanistic studies of ethylene copolymerization with polar monomers catalyzed by late-transition-metal complexes. Experimental and computational methods were employed to conduct a detailed investigation of these organic and organometallic systems. It is mainly focused on ligand substitution, changes in binding modes, ethylene/polar monomer insertion, chelate opening, and β-H elimination. Factors that control the catalytic activity, molecular weight, comonomer incorporation ratios, and branch content are analyzed, these include steric repulsions between ligands and monomers, electronic effects arising from both ligands and monomers, and so on.

Nonlocal Functionals Inspired by the Strongly Interacting Limit of DFT: Exact Constraints and Implementation

Capturing strong correlation effects remains a key challenge for the development of improved exchange-correlation (XC) functionals in density functional theory. The recently proposed multiple radii functional (MRF) [J. Phys. Chem. Lett. 2017, 8, 2799; J. Chem. Theory Comput. 2019, 15, 3580] was designed to capture strong correlation effects seamlessly, as its mathematical structure draws from that of the exact XC functional in the limit of infinite correlations. The MRF functional provides a framework for building approximations along the density-fixed adiabatic connection, delivers accurate XC energy densities in the standard DFT gauge (same as that of the exact exchange energy density), and is free of one-electron self-interaction errors. To facilitate the development of XC functionals based on the MRF, we examine the behavior of the MRF functional when applied to uniform and scaled densities and consider how it can be made exact for the uniform electron gas. These theoretical insights are then used to build improved forms for the fluctuation function, an object that defines XC energy densities within the MRF framework. We also show how the MRF fluctuation function for physical correlation can be easily readjusted to accurately capture the XC functional in the limit of infinite correlations, demonstrating the versatility of MRF for building approximations for different correlation regimes. We describe the implementation of MRF using densities expanded on Gaussian basis sets, which improves the efficiency of previous grid-based MRF implementations.

Better performance of Hartree-Fock over DFT: a quantum mechanical investigation on pyridinium benzimidazolate types of zwitterions in the light of localization/delocalization issues

CONTEXT

With the advent of fast computing facilities, combined with rapid emerges of many new and intricate quantum mechanical functionals, computations with pure Hartree-Fock (HF) theory are now-a-days regarded as trivial or obsolete, or even considered as not reliable by many researchers. Consequently, current trends in computational chemistry show extensive use of post-HF theories for smaller molecular systems and various DFT methods for organic and inorganic chemistry related problems (larger molecules/systems). In this contribution, I have tried to show that sometimes, HF might be more suitable over DFT methodologies in addressing structure-property correlations. Molecules studied here were previously synthesized by Boyd in 1966 and important experimental data were produced by Alcalde and co-workers in 1987. Comparison of computed and experimental results clearly shows that HF method was more effective in reproducing the experimental data compared to especially the DFT methodologies. Reliability of HF method was further assured from the very similar results shown by the CCSD, CASSCF, CISD and QCISD methods. Current study also indicates that the localization issue associated with HF proved to be advantageous over delocalization issue of DFT based methodologies, in correctly describing the structure-property correlation for zwitterion systems.

METHODS

All computations were performed with Gaussian 09. A wide-range of quantum mechanical methodologies, HF, B3LYP, CAM-B3LYP, BMK, B3PW91, TPSSh, LC-ωPBE, M06-2X, M06-HF, ωB97xD, MP2, CASSCF, CCSD, QCISD, CISD and semi-empirical methods like, Huckel, CNDO, AM1, PM3MM and PM6, were used for investigations.

Simulating Highly Activated Sticking of H2 on Al(110): Quantum versus Quasi-Classical Dynamics

We evaluate the importance of quantum effects on the sticking of H₂ on Al(110) for conditions that are close to those of molecular beam experiments that have been done on this system. Calculations with the quasi-classical trajectory (QCT) method and with quantum dynamics (QD) are performed using a model in which only motion in the six molecular degrees of freedom is allowed. The potential energy surface used has a minimum barrier height close to the value recently obtained with the quantum Monte Carlo method. Monte Carlo averaging over the initial rovibrational states allowed the QD calculations to be done with an order of magnitude smaller computational expense. The sticking probability curve computed with QD is shifted to lower energies relative to the QCT curve by 0.21 to 0.05 kcal/mol, with the highest shift obtained for the lowest incidence energy. Quantum effects are therefore expected to play a small role in calculations that would evaluate the accuracy of electronic structure methods for determining the minimum barrier height to dissociative chemisorption for H₂ + Al(110) on the basis of the standard procedure for comparing results of theory with molecular beam experiments.

Computational evaluation of bioactive compounds from Viscum album (mistletoe) as inhibitors of p63 for pancreatic cancer treatment

Pancreatic ductal adenocarcinoma is an aggressive malignancy usually detectable at the advanced stage, with a 5-year survival rate of less than 8%. It has been reported that a gene called tumor-protein 63 (TP63) is expressed in an aggressive form of pancreatic cancer with a squamous signature. Thus, inhibiting the activity of p63 can be a means of treating and managing PDA. Different studies have shown that plant constituents are rich and can be a promising source for discovering drug candidates. The extract from mistletoe (Viscum album) is known to contain anticancer compounds; however, the specific molecular mechanism of the bioactive compounds is unknown. This study examines the pancreatic cancer therapeutic potential of the bioactive compounds in the flavonoid and phenolic acid constituents of mistletoe by adopting structural bioinformatics and advanced theoretical chemistry techniques via molecular docking, molecular dynamics simulation, molecular mechanics/generalized Born surface area (MM/GBSA) calculations, pharmacokinetic analysis, and density functional theory analysis. The six best compounds from the flavonoid constituent with the highest binding affinity ranging from -6.8 kcal/mol to -6.7 kcal/mol were selected with the control gemcitabine (-5.5 kcal/mol) for further computational analysis after molecular docking. Furthermore, MM/GBSA calculation showed the highest binding energy for the selected docked compounds, which validates their inhibitory potential. Hence, the molecular dynamics simulation, post-simulation analysis, pharmacokinetics model, and DFT results showed that mistletoe compounds are reliable due to their stable interaction with the target protein and drug-likeness properties.Communicated by Ramaswamy H. Sarma.

Perspectives on weak interactions in complex materials at different length scales

Nanocomposite materials consist of nanometer-sized quantum objects such as atoms, molecules, voids or nanoparticles embedded in a host material. These quantum objects can be exploited as a super-structure, which can be designed to create material properties targeted for specific applications. For electromagnetism, such targeted properties include field enhancements around the bandgap of a semiconductor used for solar cells, directional decay in topological insulators, high kinetic inductance in superconducting circuits, and many more. Despite very different application areas, all of these properties are united by the common aim of exploiting collective interaction effects between quantum objects. The literature on the topic spreads over very many different disciplines and scientific communities. In this review, we present a cross-disciplinary overview of different approaches for the creation, analysis and theoretical description of nanocomposites with applications related to electromagnetic properties.

Emergence of Wigner oscillations in a model of real time cooling process: a time-dependent density-functional theory approach

Friedel and Wigner oscillations are well known phenomena occurring in quantum systems. Specifically, in a system composed byNconfined fermions, the former are characterized by the presence ofN/2peaks in the density distributions, whereas the last byNpeaks. Here, we considerN = 2 fermions harmonically confined in one-dimensional quantum dots. It is known that the transition from the Friedel to the Wigner oscillations is induced by the increment of interaction between the fermions. The increment of temperature, on the other hand, acts on eliminating the oscillations. In this context, by employing a time-dependent density-functional theory formalism, we here obtain the emergence of Wigner oscillations in a model which simulates a real time cooling process.

SBH17: Benchmark Database of Barrier Heights for Dissociative Chemisorption on Transition Metal Surfaces

Accurate barriers for rate controlling elementary reactions on metal surfaces are key to understanding, controlling, and predicting the rate of heterogeneously catalyzed processes. While barrier heights for gas phase reactions have been extensively benchmarked, dissociative chemisorption barriers for the reactions of molecules on metal surfaces have received much less attention. The first database called SBH10 and containing 10 entries was recently constructed based on the specific reaction parameter approach to density functional theory (SRP-DFT) and experimental results. We have now constructed a new and improved database (SBH17) containing 17 entries based on SRP-DFT and experiments. For this new SBH17 benchmark study, we have tested three algorithms (high, medium, and light) for calculating barrier heights for dissociative chemisorption on metals, which we have named for the amount of computational effort involved in their use. We test the performance of 14 density functionals at the GGA, GGA+vdW-DF, and meta-GGA rungs. Our results show that, in contrast with the previous SBH10 study where the BEEF-vdW-DF2 functional seemed to be most accurate, the workhorse functional PBE and the MS2 density functional are the most accurate of the GGA and meta-GGA functionals tested. Of the GGA+vdW functionals tested, the SRP32-vdW-DF1 functional is the most accurate. Additionally, we found that the medium algorithm is accurate enough for assessing the performance of the density functionals tested, while it avoids geometry optimizations of minimum barrier geometries for each density functional tested. The medium algorithm does require metal lattice constants and interlayer distances that are optimized separately for each functional. While these are avoided in the light algorithm, this algorithm is found not to give a reliable description of functional performance. The combination of relative ease of use and demonstrated reliability of the medium algorithm will likely pave the way for incorporation of the SBH17 database in larger databases used for testing new density functionals and electronic structure methods.

Improved proton-transfer barriers with van der Waals density functionals: Role of repulsive non-local correlation

Proton-transfer (PT) between organic complexes is a common and important biochemical process. Unfortunately, PT energy barriers are difficult to accurately predict using density functional theory (DFT); in particular, using the generalized gradient approximation (GGA) tends to underestimate PT barriers. Moreover, PT typically occurs in environments where dispersion forces contribute to the cohesion of the system; thus, a suitable exchange-correlation functional should accurately describe both dispersion forces and PT barriers. This paper provides benchmark results for the PT barriers of several density functionals including several variants of the van der Waals density functional (vdW-DF).The benchmark set comprises small organic molecules with inter- and intra-molecular PT. The results show that replacing GGA correlation with a fully non-local vdW-DF correlation increases the PT barriers, making it closer to the quantum chemical reference values.In contrast, including non-local correlations with the Vydrov-Voorhis (VV) method or dispersion-corrections at the DFT-D3 or the Tkatchenko-Scheffler (TS) levelhas barely any impact on the PT barriers.Hybrid functionals also increase and improve the energies,resulting in excellent performance of hybrid versions of the van der Waals density functionals vdW-DF-cx and vdW-DF2-B86R. For the formic acid dimer PT system, we analyzed the GGA exchange and non-local correlation contributions. The analysis shows that the repulsive part of the non-local correlation kernel plays a key role in the PT energy barriers predicted with vdW-DF.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

Mechanisms, Challenges, and Opportunities of Dual Ni/Photoredox-Catalyzed C(sp2)-C(sp3) Cross-Couplings

The merging of photoredox and nickel catalysis has revolutionized the field of C-C cross-coupling. However, in comparison to the development of synthetic methods, detailed mechanistic investigations of these catalytic systems are lagging. To improve the mechanistic understanding, computational tools have emerged as powerful tools to elucidate the factors controlling reactivity and selectivity in these complex catalytic transformations. Based on the reported computational studies, it appears that the mechanistic picture of catalytic systems is not generally applicable, but is rather dependent on the specific choice of substrate, ligands, photocatalysts, etc. Given the complexity of these systems, the need for more accurate computational methods, readily available and user-friendly dynamics simulation tools, and data-driven approaches is clear in order to understand at the molecular level the mechanisms of these transformations. In particular, we anticipate that such improvement of theoretical methods will become crucial to advance the understanding of excited-state properties and dynamics of key species, as well as to enable faster and unbiased exploration of reaction pathways. Further, with greater collaboration between computational, experimental, and spectroscopic communities, the mechanistic investigation of photoredox/Ni dual-catalytic reactions is expected to thrive quickly, facilitating the design of novel catalytic systems and promoting our understanding of the reaction selectivity.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

Poisoning density functional theory with benchmark sets of difficult systems

Large benchmark sets like GMTKN55 [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] let us analyse the performance of density functional theory over a diverse range of systems and bonding types. However, assessing over a large and diverse set can miss cases where approaches fail badly, and can give a misleading sense of security. To this end we introduce a series of 'poison' benchmark sets, P30-5, P30-10 and P30-20, comprising systems with up to 5, 10 and 20 atoms, respectively. These sets represent the most difficult-to-model systems in GMTKN55. We expect them to be useful in developing new approximations, identifying weak points in existing ones, and to aid in selecting appropriate DFAs for computational studies involving difficult physics, e.g. catalysis.

Thermal excitation signals in the inhomogeneous warm dense electron gas

We investigate the emergence of electronic excitations from the inhomogeneous electronic structure at warm dense matter parameters based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They include satellite signals around the standard plasmon feature, transformation of plasmons to optical modes, and double-plasmon modes. These modes exhibit a pronounced dependence on the temperature. This makes them potentially invaluable for the diagnostics of plasma parameters in the warm dense matter regime. We demonstrate that these modes can be probed with present experimental techniques.

Catalytic properties of the ferryl ion in the solid state: a computational review

This review summarises the last findings in the emerging field of heterogeneous catalytic oxidation of light alkanes by ferryl species supported on solid-state systems such as the conversion of methane into methanol by FeO-MOF74.

Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light-matter coupling

Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit and the infinite-frequency as well as the homogeneous limit, and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows us to extend the ansatz to the full minimal-coupling problem and to nonadiabatic situations. Finally, we provide a simple local density-type functional that takes the strong coupling to the transverse photon degrees of freedom into account and includes the correct frequency and polarization dependence. This QEDFT functional accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.

Density Functional Calculations Based on the Exponential Ansatz

This work explores the application of the singles-based exponential ansatz to density functional calculations. In contrast to the standard approach where Kohn-Sham (KS) orbitals are determined prior to computing molecular quantities of interest, we consider the single-reference Hartree-Fock wave function as a starting point. Applying the exponential ansatz to this single reference gives an auxiliary wave function that is employed to calculate the electronic properties of the system. This wave function is determined self-consistently through the standard KS Hamiltonian but evaluated over the Hartree-Fock molecular orbital basis. By using spin-symmetry breaking, we recover size-consistent results free of unphysical fractional charges in the dissociation limit. Our method shows consistency with standard KS density functional calculations when the system geometry is similar to the equilibrium one or in repulsive configurations. For moderately long distances between atoms, not at dissociation, because of self-interaction the exponential ansatz may give instabilities in the form of large cluster amplitudes. To avoid these, this work introduces a relatively simple regularization method that preserves size-consistency and penalizes high amplitudes of the cluster operator, whereas the results remain physically meaningful. We also present the time-dependent extension of our theory and show that it can feature quantum states where multiple electrons are excited.

Analysis of atomic Pauli potentials and their large-Z limit

Modeling the Pauli energy, the contribution to the kinetic energy caused by Pauli statistics, without using orbitals is the open problem of orbital-free density functional theory. An important aspect of this problem is correctly reproducing the Pauli potential, the response of the Pauli kinetic energy to a change in density. We analyze the behavior of the Pauli potential of non-relativistic neutral atoms under Lieb-Simon scaling-the process of taking nuclear charge and particle number to infinity, in which the kinetic energy tends to the Thomas-Fermi limit. We do this by mathematical analysis of the near-nuclear region and by calculating the exact orbital-dependent Pauli potential using the approach of Levy and Ouyang for closed-shell atoms out to element Z = 976. In rough analogy to Lieb and Simon's own findings for the charge density, we find that the potential does not converge smoothly to the Thomas-Fermi limit on a point-by-point basis but separates into several distinct regions of behavior. Near the nucleus, the potential approaches a constant given by the difference in energy between the lowest and highest occupied eigenvalues. We discover a transition region in the outer core where the potential deviates unexpectedly and predictably from both the Thomas-Fermi potential and the gradient expansion correction to it. These results may provide insight into the semi-classical description of Pauli statistics and new constraints to aid the improvement of orbital-free density functional theory functionals.

The relevance of electronic perturbations in the warm dense electron gas

Warm dense matter (WDM) has emerged as one of the frontiers of both experimental physics and theoretical physics and is a challenging traditional concept of plasma, atomic, and condensed-matter physics. While it has become common practice to model correlated electrons in WDM within the framework of Kohn-Sham density functional theory, quantitative benchmarks of exchange-correlation (XC) functionals under WDM conditions are yet incomplete. Here, we present the first assessment of common XC functionals against exact path-integral Monte Carlo calculations of the harmonically perturbed thermal electron gas. This system is directly related to the numerical modeling of x-ray scattering experiments on warm dense samples. Our assessment yields the parameter space where common XC functionals are applicable. More importantly, we pinpoint where the tested XC functionals fail when perturbations on the electronic structure are imposed. We indicate the lack of XC functionals that take into account the needs of WDM physics in terms of perturbed electronic structures.

Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches

Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Electronic-structure methods for materials design

The accuracy and efficiency of electronic-structure methods to understand, predict and design the properties of materials has driven a new paradigm in research. Simulations can greatly accelerate the identification, characterization and optimization of materials, with this acceleration driven by continuous progress in theory, algorithms and hardware, and by adaptation of concepts and tools from computer science. Nevertheless, the capability to identify and characterize materials relies on the predictive accuracy of the underlying physical descriptions, and on the ability to capture the complexity of realistic systems. We provide here an overview of electronic-structure methods, of their application to the prediction of materials properties, and of the different strategies employed towards the broader goals of materials design and discovery.

Analysis of the relative stability of lithium halide crystal structures: Density functional theory and classical models

All lithium halides exist in the rock salt crystal structure under ambient conditions. In contrast, common lithium halide classical force fields more often predict wurtzite as the stable structure. This failure of classical models severely limits their range of application in molecular simulations of crystal nucleation and growth. Employing high accuracy density functional theory (DFT) together with classical models, we examine the relative stability of seven candidate crystal structures for lithium halides. We give a detailed examination of the influence of DFT inputs, including the exchange-correlation functional, basis set, and dispersion correction. We show that a high-accuracy basis set, along with an accurate description of dispersion, is necessary to ensure prediction of the correct rock salt structure, with lattice energies in good agreement with the experiment. We also find excellent agreement between the DFT-calculated rock salt lattice parameters and experiment when using the TMTPSS-rVV10 exchange-correlation functional and a large basis set. Detailed analysis shows that dispersion interactions play a key role in the stability of rock salt over closely competing structures. Hartree-Fock calculations, where dispersion interactions are absent, predict the rock salt structure only for LiF, while LiCl, LiBr, and LiI are more stable as wurtzite crystals, consistent with radius ratio rules. Anion-anion second shell dispersion interactions overcome the radius ratio rules to tip the structural balance to rock salt. We show that classical models can be made qualitatively correct in their structural predictions by simply scaling up the pairwise additive dispersion terms, indicating a pathway toward better lithium halide force fields.

Effects of Structural Dynamics on Charge Carrier Transfer in B-DNA: A Combined MD and RT-TDDFT Study

Hole transfer along the axis of duplex DNA has been the focus of physical chemistry research for decades, with implications in diverse fields, from nanotechnology to cell oxidative damage. Computational approaches are particularly amenable for this problem, to complement experimental data for interpretation of transfer mechanisms. To be predictive, computational results need to account for the inherent mobility of biological molecules during the time frame of experimental measurements. Here, we address the structural variability of B-DNA and its effects on hole transfer in a combined molecular dynamics (MD) and real-time time-dependent density functional theory (RT-TDDFT) study. Our results show that quantities that characterize the charge transfer process, such as the time-dependent dipole moment and hole population at a specific site, are sensitive to structural changes that occur on the nanosecond time scale. We extend the range of physical properties for which such a correlation has been observed, further establishing the fact that quantitative computational data on charge transfer properties should include statistical averages. Furthermore, we use the RT-TDDFT results to assess an efficient tight-binding method suitable for high-throughput predictions. We demonstrate that charge transfer, although affected by structural variability, on average, remains strong in AA and GG dimers.

Low-Order Scaling G0W0 by Pair Atomic Density Fitting

We derive a low-scaling G0W0 algorithm for molecules using pair atomic density fitting (PADF) and an imaginary time representation of the Green's function and describe its implementation in the Slater type orbital (STO)-based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-ζ (TZ) plus double polarization quality. Also owing to a very small prefactor, a G0W0 calculation for the largest of these clusters takes only 240 CPU hours with these settings. We assess the accuracy of our algorithm for HOMO and LUMO energies in the GW100 database. With errors of 0.24 eV for HOMO energies on the quadruple-ζ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-type basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF approach of accurately representing diffuse atomic orbital (AO) products. We speculate that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented double-ζ (DZ) quality is decreasing with system size. On the augmented DZ level, we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.

Mean-field density matrix decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.

Deriving approximate functionals with asymptotics

Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB expansion in one dimension, and modern approaches to asymptotic expansions. A mathematical framework for analyzing asymptotic behavior for the sums of energies unites both corrections to the gradient expansion of DFT and hyperasymptotics of sums. Simple examples are given for the model problem of orbital-free DFT in one dimension. In some cases, errors can be made as small as 10-32 Hartree suggesting that, if these new ingredients can be applied, they might produce approximate functionals that are much more accurate than those in current use. A variation of the Euler-Maclaurin formula generalizes previous results.

Quantum chemical accuracy from density functional approximations via machine learning

Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol-1 with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol-1) on test data. Moreover, density-based Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness of Δ-DFT  is highlighted by correcting "on the fly" DFT-based molecular dynamics (MD) simulations of resorcinol (C6H4(OH)2) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT  facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to the leading order (-0.221Z^5/3 and -0.021Z ln Z, respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to E_x(N, Z) ≈ -0.354N^2/3Z (as known before only for Z ≫ N ≫ 1) and E_c ≈ -0.02N ln N. These asymptotic estimates are most correct for atomic ions with large N and Z ≫ N, but we find that they are qualitatively and semi-quantitatively correct even for small N and N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely predictive approximate density functionals should be designed to recover the correct asymptotics. It is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.

Double hybrid DFT calculations with Slater type orbitals

On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange- and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems.

Disorder-robust bands from anisotropic orbitals in a coordination polymer semiconductor

While the effects of structural disorder on the electronic properties of solids are poorly understood, it is widely accepted that spatially isotropic orbitals lead to robustness against disorder. In this paper, we use first-principles calculations to show that a cluster of occupied bands in the coordination polymer semiconductor β-copper(I) thiocyanate undergo relatively little fluctuation in the presence of thermal disorder-a surprising finding given that these bands are composed of spatially anisotropic d-orbitals. Analysis with the tight-binding method and a stochastic network model suggests that the robustness of these bands to the thermal disorder can be traced to the way in which these orbitals are aligned with respect to each other. This special alignment causes strong inverse statistical correlations between orbital-orbital distances, making these bands robust to random fluctuations of these distances. As well as proving that disorder-robust electronic properties can be achieved even with anisotropic orbitals, our results provide a concrete example of when simple 'averaging' methods can be used to treat thermal disorder in electronic structure calculations.

Ion energy-loss characteristics and friction in a free-electron gas at warm dense matter and nonideal dense plasma conditions

We investigate the energy-loss characteristics of an ion in warm dense matter (WDM) and dense plasmas concentrating on the influence of electronic correlations. The basis for our analysis is a recently developed ab initio quantum Monte Carlo- (QMC) based machine learning representation of the static local field correction (LFC) [Dornheim et al., J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013], which provides an accurate description of the dynamical density response function of the electron gas at the considered parameters. We focus on the polarization-induced stopping power due to free electrons, the friction function, and the straggling rate. In addition, we compute the friction coefficient which constitutes a key quantity for the adequate Langevin dynamics simulation of ions. Considering typical experimental WDM parameters with partially degenerate electrons, we find that the friction coefficient is of the order of γ/ω_{pi}=0.01, where ω_{pi} is the ionic plasma frequency. This analysis is performed by comparing QMC-based data to results from the random-phase approximation (RPA), the Mermin dielectric function, and the Singwi-Tosi-Land-Sjölander (STLS) approximation. It is revealed that the widely used relaxation time approximation (Mermin dielectric function) has severe limitations regarding the description of the energy loss of ions in a correlated partially degenerate electrons gas. Moreover, by comparing QMC-based data with the results obtained using STLS, we find that the ion energy-loss properties are not sensitive to the inaccuracy of the static local field correction (LFC) at large wave numbers, k/k_{F}>2 (with k_{F} being the Fermi wave number), but that a correct description of the static LFC at k/k_{F}≲1.5 is important.

Leading correction to the local density approximation of the kinetic energy in one dimension

A mathematical framework is constructed for the sum of the lowest N eigenvalues of a potential. Exactness is illustrated on several one-dimensional systems (harmonic oscillator, particle in a box, and Poschl-Teller well). Semiclassical expansion yields the leading corrections for finite systems, identifying the error in common gradient expansions in density functional theory. Some singularities can be avoided when evaluating the correction to the leading term. Correcting the error in the gradient expansion greatly improves accuracy. The relevance to practical density functional calculations is discussed.

A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals

We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Møller-Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of [Formula: see text], our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.