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The Pauli kinetic energy functional and its functional derivative, termed Pauli potential, play a crucial role in the successful implementation of orbital-free density functional theory for electronic structure calculations. However, the exact forms of these two quantities are not known. Therefore, perforce, one employs the approximate forms for the Pauli functional or Pauli potential for performing orbital-free density functional calculations. In the present study, we developed a feed-forward neural network-based representation for the Pauli potential using a 1-dimensional (1-D) model system. We expanded density in terms of basis functions, and the coefficients of the expansion were used as input to a feed-forward neural network. Using the neural network-based representation of the Pauli potential, we calculated the ground-state densities of the 1-D model system by solving the Euler equation. We calculated the Pauli kinetic energy using the neural network-based Pauli potential employing the exact relation between the Pauli kinetic energy functional and the potential. The sum of the neural network-based Pauli kinetic energy and the von Weizsäcker kinetic energy resulted in an accurate estimation of the total kinetic energy. The approach presented in this paper can be employed for the calculation of Pauli potential and Pauli kinetic energy, obviating the need for a functional derivative. The present study is an important step in the advancement of application of machine learning-based techniques toward the orbital-free density functional theory-based methods. [ABSTRACT FROM AUTHOR]

Recent measurements of the third harmonic scattering responses of molecules have given a new impetus for computing molecular second hyperpolarizabilities (γ) and for deducing structure–property relationships. This paper has employed a variety of wavefunction and density functional theory methods to evaluate the second hyperpolarizability of the p-nitroaniline prototypical push-pull π-conjugated molecule, addressing also numerical aspects, such as the selection of an integration grid and the impact of the order of differentiation vs the achievable accuracy by using the Romberg quadrature. The reliability of the different methods has been assessed by comparison to reference Coupled-Cluster Singles and Doubles with perturbative treatment of the Triples results. On the one hand, among wavefunction methods, the MP2 scheme offers the best accuracy/cost ratio for computing the static γ. On the other hand, using density functional theory, γ remains a challenging property to compute because all conventional, global hybrid or range-separated hybrid, exchange–correlation functionals underestimate static γ values by at least 15%. Even tuning the range-separating parameter to minimize the delocalization errors does not enable to improve the γ values. Nevertheless, the original double-hybrid B2-PLYP functional, which benefits from 27% of PT2 correlation and 53% Hartree–Fock exchange, provides accurate estimates of static γ values. Unfortunately, the best performing exchange–correlation functionals for γ are not necessarily reliable for the first hyperpolarizability, β, and vice versa. In fact, the β of p-nitroaniline (pNA) could be predicted, with a good accuracy, with several hybrid exchange–correlation functionals (including by tuning the range-separating parameter), but these systematically underestimate γ. As for γ, the MP2 wavefunction method remains the best compromise to evaluate the first hyperpolarizability of pNA at low computational cost. [ABSTRACT FROM AUTHOR]

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 method or dispersion-corrections at the DFT-D3 or the Tkatchenko–Scheffler level has barely any impact on the PT barriers. Hybrid functionals also increase and improve the energies, resulting in an excellent performance of hybrid versions of 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. [ABSTRACT FROM AUTHOR]

Model Hamiltonians with long-range interaction yield energies are corrected taking into account the universal behavior of the electron–electron interaction at a short range. Although the intention of this paper is to explore the foundations of using density functionals combined with range separation, the approximations presented can be used without them, as illustrated by a calculation on harmonium. In the regime, when the model system approaches the Coulomb system, they allow the calculation of ground states, excited states, and properties, without making use of the Hohenberg–Kohn theorem. Asymptotically, the technique is improvable and allows for error estimates that can validate the results. Some considerations for correcting the errors of finite basis sets in this spirit are also presented. Being related to the present understanding of density functional approximations, the results are comparable to those obtained with the latter, as long as these are accurate. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid density functional valence bond method based on unpaired electron density, called λ-DFVB(U), is presented, which is a combination of the valence bond self-consistent field (VBSCF) method and Kohn–Sham density functional theory. In λ-DFVB(U), the double-counting error of electron correlation is mitigated by a linear decomposition of the electron–electron interaction using a parameter λ, which is a function of an index based on the number of effectively unpaired electrons. In addition, λ-DFVB(U) is based on the approximation that correlation functionals in KS-DFT only cover dynamic correlation and exchange functionals mimic some amount of static correlation. Furthermore, effective spin densities constructed from unpaired density are used to address the symmetry dilemma problem in λ-DFVB(U). The method is applied to test calculations of atomization energies, atomic excitation energies, and reaction barriers. It is shown that the accuracy of λ-DFVB(U) is comparable to that of CASPT2, while its computational cost is approximately the same as VBSCF. [ABSTRACT FROM AUTHOR]

The research presented in the paper concerns the elastic properties of struvite. The article combines theoretical and experimental research. Experimental studies were carried out on struvite single crystals grown in sodium metasilicate gel by single diffusion. This unique method leads to obtaining crystals of sufficiently large size to conduct, for the first time, experimental measurement of elastic properties of monocrystalline struvite. Using the nanoindentation method, the Ez = 29.1 ± 0.7 GPa value of the component of Young's modulus was determined for a struvite single crystal. In addition, the elastic constants C11, C22, and C33 were determined using micro-Brillouin spectroscopy. Theoretical calculations of the abovementioned properties have been carried out by employing density functional theory methods. Scaling of the theoretical elastic constants leads to obtaining good agreement with the experimental values. Values of the Ex and Ey components of the Young's modulus, not available from the experimental nanoindentation technique, have been determined theoretically as 23 GPa and 27 GPa, respectively. Differences in the values of elastic components and Young's modulus components are related to the layered crystal structure of struvite and directional character of the hydrogen-bonding pattern. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (χ) and hardness (η) directly reflect the energy–density relationship via the chemical potential ∂E/∂N and we thus hypothesized that they probe universality. We studied χ and η for atoms Z = 1–36 using 50 diverse functionals covering all major classes. Very few functionals describe both χ and η well. η benefits from error cancellation, whereas χ is marred by error propagation from IP and EA; thus, almost all standard GGA and hybrid functionals display a plateau in the MAE at ∼0.2 eV–0.3 eV for η. In contrast, variable performance for χ indicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional, we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes "non-universality" and large dependency on exact exchange. Thus, we argue that performance for χ for the same systems is a hallmark of an important aspect of universality by probing ∂E/∂N. With this metric, B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD are the most "universal" among the tested functionals. B98 and B97-1 are accurate for very diverse metal–ligand bonds, supporting that a balanced description of ∂E/∂N and ∂E2/∂N2, via χ and η, is probably a first simple probe of universality. [ABSTRACT FROM AUTHOR]

Machine learning (ML) has demonstrated its potential usefulness for the development of density functional theory methods. In this work, we construct an ML model to correct the density functional approximations, which adopts semilocal descriptors of electron density and density derivative and is trained by accurate reference data of relative and absolute energies. The resulting ML-corrected functional is tested on a comprehensive dataset including various types of energetic properties. Particularly, the ML-corrected Becke's three parameters and the Lee–Yang–Parr correlation (B3LYP) functional achieves a substantial improvement over the original B3LYP on the prediction of total energies of atoms and molecules and atomization energies, and a marginal improvement on the prediction of ionization potentials, electron affinities, and bond dissociation energies; whereas, it preserves the same level of accuracy for isomerization energies and reaction barrier heights. The ML-corrected functional allows for fully self-consistent-field calculation with similar efficiency to the parent functional. This study highlights the progress of building an ML correction toward achieving a functional that performs uniformly better than B3LYP. [ABSTRACT FROM AUTHOR]

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within the Kohn–Sham density functional theory for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of the warm dense matter. Generated by laser-induced compression and heating in the laboratory, the warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing with the exact quantum Monte Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used, compared with the previously reported results for the PBE, PBEsol, local-density approximation, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy. [ABSTRACT FROM AUTHOR]

Quantum chemical calculations on atomistic systems have evolved into a standard approach to studying molecular matter. These calculations often involve a significant amount of manual input and expertise, although most of this effort could be automated, which would alleviate the need for expertise in software and hardware accessibility. Here, we present the AutoRXN workflow, an automated workflow for exploratory high-throughput electronic structure calculations of molecular systems, in which (i) density functional theory methods are exploited to deliver minimum and transition-state structures and corresponding energies and properties, (ii) coupled cluster calculations are then launched for optimized structures to provide more accurate energy and property estimates, and (iii) multi-reference diagnostics are evaluated to back check the coupled cluster results and subject them to automated multi-configurational calculations for potential multi-configurational cases. All calculations are carried out in a cloud environment and support massive computational campaigns. Key features of all components of the AutoRXN workflow are autonomy, stability, and minimum operator interference. We highlight the AutoRXN workflow with the example of an autonomous reaction mechanism exploration of the mode of action of a homogeneous catalyst for the asymmetric reduction of ketones. [ABSTRACT FROM AUTHOR]

Artificial intelligence-enhanced quantum mechanical method 1 (AIQM1) is a general-purpose method that was shown to achieve high accuracy for many applications with a speed close to its baseline semiempirical quantum mechanical (SQM) method ODM2*. Here, we evaluate the hitherto unknown performance of out-of-the-box AIQM1 without any refitting for reaction barrier heights on eight datasets, including a total of ∼24 thousand reactions. This evaluation shows that AIQM1's accuracy strongly depends on the type of transition state and ranges from excellent for rotation barriers to poor for, e.g., pericyclic reactions. AIQM1 clearly outperforms its baseline ODM2* method and, even more so, a popular universal potential, ANI-1ccx. Overall, however, AIQM1 accuracy largely remains similar to SQM methods (and B3LYP/6-31G* for most reaction types) suggesting that it is desirable to focus on improving AIQM1 performance for barrier heights in the future. We also show that the built-in uncertainty quantification helps in identifying confident predictions. The accuracy of confident AIQM1 predictions is approaching the level of popular density functional theory methods for most reaction types. Encouragingly, AIQM1 is rather robust for transition state optimizations, even for the type of reactions it struggles with the most. Single-point calculations with high-level methods on AIQM1-optimized geometries can be used to significantly improve barrier heights, which cannot be said for its baseline ODM2* method. [ABSTRACT FROM AUTHOR]

Surface platinum hydride structures may exist and play a potentially important role during electrocatalysis and cathodic corrosion of Pt(111). Earlier work on platinum hydrides suggests that Pt may form clusters with multiple equivalents of hydrogen. Here, using thermodynamic methods and density functional theory, we compared several surface hydride structures on Pt(111). The structures contain multiple monolayers of hydrogen in or near the surface Pt layer. The hydrogen in these structures may bind the subsurface or reconstruct the surface both in the set of initial configurations and in the resulting (meta)stable structures. Multilayer stable configurations share one monolayer of subsurface H stacking between the top two Pt layers. The structure containing two monolayers (MLs) of H is formed at −0.29 V vs normal hydrogen electrode, is locally stable with respect to configurations with similar H densities, and binds H neutrally. Structures with 3 and 4 ML H form at −0.36 and −0.44 V, respectively, which correspond reasonably well to the experimental onset potential of cathodic corrosion on Pt(111). For the 3 ML configuration, the top Pt layer is reconstructed by interstitial H atoms to form a well-ordered structure with Pt atoms surrounded by four, five, or six H atoms in roughly square-planar and octahedral coordination patterns. Our work provides insight into the operando surface state during low-potential reduction reactions on Pt(111) and shows a plausible precursor for cathodic corrosion. [ABSTRACT FROM AUTHOR]

A systematic study is made of the accuracy and efficiency of a number of existing quadrature schemes for molecular Kohn–Sham Density-Functional Theory (DFT) using 408 molecules and 254 chemical reactions. Included are the fixed SG-x (x = 0–3) grids of Gill et al., Dasgupta, and Herbert, the 3-zone grids of Treutler and Ahlrichs, a fixed five-zone grid implemented in Molpro, and a new adaptive grid scheme. While all methods provide a systematic reduction of errors upon extension of the grid sizes, significant differences are observed in the accuracies for similar grid sizes with various approaches. For the tests in this work, the SG-x fixed grids are less suitable to achieve high accuracies in the DFT integration, while our new adaptive grid performed best among the schemes studied in this work. The extra computational time to generate the adaptive grid scales linearly with molecular size and is negligible compared with the time needed for the self-consistent field iterations for large molecules. A comparison of the grid accuracies using various density functionals shows that meta-GGA functionals need larger integration grids than GGA functionals to reach the same degree of accuracy, confirming previous investigations of the numerical stability of meta-GGA functionals. On the other hand, the grid integration errors are almost independent of the basis set, and the basis set errors are mostly much larger than the errors caused by the numerical integrations, even when using the smallest grids tested in this work. [ABSTRACT FROM AUTHOR]

Revealing the effect of external applied potential on the reaction mechanism and product selectivity is of great significance in electrochemical studies. In this work, the grand canonical density functional theory method was applied to simulate the explicit electrocatalytic process of oxygen evolution reaction and electrochemical ozone production due to the O3 product sensitivity toward the applied potential. Over the Pt/Pd single atom embedded on B/N co-doped graphene (Pt/Pd-BNC) surface, crossover points of O2/O3 selectivity inversion were predicted to be 1.33 and 0.89 V vs standard hydrogen electrode, which were also consistent with the previous experimental results. An in-depth analysis of the energetic terms in the reaction free energies also found the considerable impact of the applied potential on the Helmholtz free energy term, with optimal potential predicted for the key elementary steps, and linear correlations between electrode potential (U) and reaction free energy were found for each elementary step. This study offers extensive knowledge on the potential effect on the O2/O3 selective formation on two-dimensional anode surfaces and provides new insights for investigating the reactivity/selectivity on electrode surfaces in real reaction conditions. [ABSTRACT FROM AUTHOR]

Most computational studies in chemistry and materials science are based on the use of density functional theory. Although the exact density functional is unknown, several density functional approximations (DFAs) offer a good balance of affordable computational cost and semi-quantitative accuracy for applications. The development of DFAs still continues on many fronts, and several new DFAs aiming for improved accuracy are published every year. However, the numerical behavior of these DFAs is an often-overlooked problem. In this work, we look at all 592 DFAs for three-dimensional systems available in Libxc 5.2.2 and examine the convergence of the density functional total energy based on tabulated atomic Hartree–Fock wave functions. We show that several recent DFAs, including the celebrated SCAN family of functionals, show impractically slow convergence with typically used numerical quadrature schemes, making these functionals unsuitable both for routine applications and high-precision studies, as thousands of radial quadrature points may be required to achieve sub-μEh accurate total energies for these functionals, while standard quadrature grids like the SG-3 grid only contain O (100) radial quadrature points. These results are both a warning to users to always check the sufficiency of the quadrature grid when adopting novel functionals, as well as a guideline to the theory community to develop better-behaved density functionals. [ABSTRACT FROM AUTHOR]

The core excitation energies and related principal ionization energies are obtained for selected molecules using several density functionals and compared with benchmark equation-of-motion coupled cluster (EOM-CC) results. Both time-dependent and time-independent formulations of excitation spectra in the time-dependent density functional theory and the EOM-CC are employed to obtain excited states that are not always easily accessible with the time-independent method. Among those functionals, we find that the QTP(00) functional, which is only parameterized to reproduce the five IPs of water, provides excellent core IPs and core excitation energies, consistently yielding better excitation and ionization energies. We show that orbital eigenvalues of KS density functional theory play an important role in determining the accuracy of the excitation and photoelectron spectra. [ABSTRACT FROM AUTHOR]

Electrons in zero external magnetic field can be studied with the Kohn–Sham (KS) scheme of either density functional theory (DFT) or spin-DFT (SDFT). The latter is normally used for open-shell systems because its approximations appear to model better the exchange and correlation (xc) functional, but also because, so far the application of DFT implied a closed-shell-like approximation. In the first part of this Communication, we show that correcting this error for open shells allows the approximate DFT xc functionals to become as accurate as those in SDFT. In the second part, we consider the behavior of SDFT for zero magnetic field. We show that the KS equations of SDFT emerge as the generalized KS equations of DFT in this limit, thus establishing a so far unknown link between the two theories. [ABSTRACT FROM AUTHOR]

The structure of the double-layer formed at the surface of carbon electrodes is governed by the interactions between the electrode and the electrolyte species. However, carbon is notoriously difficult to simulate accurately, even with well-established methods such as electronic density functional theory and molecular dynamics. Here, we focus on the important case of a lithium ion in contact with the surface of graphite, and we perform a series of reference quantum Monte Carlo calculations that allow us to benchmark various electronic density functional theory functionals. We then fit an accurate carbon–lithium pair potential, which is used in molecular density functional theory calculations to determine the free energy of the adsorption of the ion on the surface in the presence of water. The adsorption profile in aqueous solution differs markedly from the gas phase results, which emphasize the role of the solvent on the properties of the double-layer. [ABSTRACT FROM AUTHOR]

Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw–Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficient and viscosity of aluminum at 116 045 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods. [ABSTRACT FROM AUTHOR]

The absence of a reliable formulation of the kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions, which have been proposed in the literature, and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals—a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H2, LiH, LiF, and a one-dimensional chain of eight hydrogens using data from Kohn–Sham density functional theory calculations for only a few structures. [ABSTRACT FROM AUTHOR]

The multi-configurational short-range (sr) density functional theory has been extended to the calculation of indirect spin–spin coupling constants (SSCCs) for nuclear magnetic resonance spectroscopy. The performance of the new method is compared to Kohn–Sham density functional theory and the ab initio complete active space self-consistent field for a selected set of molecules with good reference values. Two density functionals have been considered, the local density approximation srLDA and srPBE from the GGA class of functionals. All srDFT calculations are of Hartree–Fock-type HF-srDFT or complete active space-type CAS-srDFT. In all cases, the calculated SSCC values are of the same quality for srLDA and srPBE functionals, suggesting that one should use the computationally cost-effective srLDA functionals in applications. For all the calculated SSCCs in organic compounds, the best choice is HF-srDFT; the more expensive CAS-srDFT does not provide better values for these single-reference molecules. Fluorine is a challenge; in particular, the FF, FC, and FO couplings have much higher statistical errors than the rest. For SSCCs involving fluorine and a metal atom CAS-srDFT with singlet, generalized Tamm–Dancoff approximation is needed to get good SSCC values although the reference ground state is not a multi-reference case. For V F 6 − 1 , all other considered models fail blatantly. [ABSTRACT FROM AUTHOR]

Electrostatic properties are important for understanding and modeling many phenomena, such as the adsorption of a catalytic metal upon an oxide support. The charge transfer between the metal and the support can lead to positive or negative charges on the metal. Here, the static dipole polarizability is computed for atomic platinum in charge states 0, +1, and −1 in several low-lying electronic terms and levels. Core pseudopotentials are used along with coupled-cluster theory. The best results are estimates for the coupled-cluster CCSDTQ/q-aug-cc-pwCV∞Z-PP values for atomic terms, combined with compositional data from spin–orbit configuration interaction. The polarizability of the anion Pt− is especially challenging for the theory with wildly varying results from different coupled-cluster perturbative approximations such as CCSD(T). For atomic mercury (Hg), selected as a nearby experimental value, our polarizability volume is larger than experiment by 0.8 bohrs3 (or 0.12 × 10−30 m3). For the ground level of neutral platinum, Pt(3D3), we find α0 = (41.2 ± 1.1) bohrs3 or (6.10 ± 0.16) × 10−30 m3. A handful of density functional theory methods are tested and found generally within 10% of our best values. [ABSTRACT FROM AUTHOR]

We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24 × 5 dataset. The dataset consists of high-spin dimers up to 11 atoms selected to assure diversity with respect to interaction types: dispersion, electrostatics, and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation (from aug-cc-pVQZ to aug-cc-pV5Z). We have analyzed the performance of selected wave function methods MP2, CCSD, and CCSD(T) as well as the F12a and F12b variants of coupled-cluster theory. In addition, we have tested dispersion-corrected density functional theory methods based on the PBE exchange-correlation model. The O24 × 5 dataset is a challenge to approximate methods due to the wide range of interaction energy strengths it spans. For the dispersion-dominated and mixed-type subsets, any tested method that does not include the triples contribution yields errors on the order of tens of percent. The electrostatic subset is less demanding with errors that are typically an order of magnitude smaller than the mixed and dispersion-dominated subsets. [ABSTRACT FROM AUTHOR]

The accurate description of biradical systems, and in particular the resolution of their singlet–triplet gaps, has long posed a major challenge to the development of electronic structure theories. Biradicaloid singlet ground states are often marked by strong correlation and, hence, may not be accurately treated by mainstream, single-reference methods such as density functional theory or coupled cluster theory. The anti-Hermitian contracted Schrödinger equation (ACSE), whose fundamental quantity is the two-electron reduced density matrix rather than the N-electron wave function, has previously been shown to account for both dynamic and strong correlations when seeded with a strongly correlated guess from a complete active space (CAS) calculation. Here, we develop a spin-averaged implementation of the ACSE, allowing it to treat higher multiplicity states from the CAS input without additional state preparation. We apply the spin-averaged ACSE to calculate the singlet–triplet gaps in a set of small main group biradicaloids, as well as the organic four-electron biradicals trimethylenemethane and cyclobutadiene, and naphthalene, benchmarking the results against other state-of-the-art methods reported in the literature. [ABSTRACT FROM AUTHOR]

Exchange–correlation (XC) functionals from Density Functional Theory (DFT) developed under the rigorous arguments of Correlated Orbital Theory (COT) address the Devil's Triangle of prominent errors in Kohn–Sham (KS) DFT. At the foundation of this triangle lie the incorrect one-particle spectrum, the lack of integer discontinuity, and the self-interaction error. At the top level, these failures manifest themselves in incorrect charge transfer and Rydberg excitation energies, along with poor activation barriers. Accordingly, the Quantum Theory Project (QTP) XC functionals have been created to address several of the long-term issues encountered in KS theory and its Time Dependent DFT (TDDFT) variant for electronic excitations. Recognizing that COT starts with a correct one-particle spectrum, a condition imposed on the QTP functionals by means of minimum parameterization, the question that arises is how does this affect the electronically excited states? Among up to 28 XC functionals considered, the QTP family provides one of the smallest mean absolute deviations for charge-transfer excitations while also showing excellent results for Rydberg states. However, there is some room for improvement in the case of excitation energies to valence states, which are systematically underestimated by all functionals investigated. An alternative path for better treatment of excitation energies, mainly for valence states, is offered by using orbital energies from QTP functionals, especially by CAM-QTP-02 and LC-QTP. In this case, the deviations from the reference data can be reduced approximately by half. [ABSTRACT FROM AUTHOR]

Reactions of molecules on metal surfaces are notoriously difficult to simulate accurately. Density functional theory can be utilized to generate a potential energy surface, but with presently available functionals, the results are not yet accurate enough. To provide benchmark barrier heights with a high-quality method, diffusion Monte Carlo (DMC) is applied to H2 + Al(110). Barrier heights have been computed for six geometries. Our present goal is twofold: first, to provide accurate barrier heights for the two lowest lying transition states of the system, and second, to assess whether density functionals are capable of describing the variation of barrier height with molecular orientation and impact site through a comparison with DMC barriers. To this end, barrier heights computed with selected functionals at the generalized gradient approximation (GGA) and meta-GGA levels are compared to the DMC results. The comparison shows that all selected functionals yield a rather accurate description of the variation of barrier heights with impact site and orientation, although their absolute values may not be accurate. RPBE-vdW-DF and BEEF-vdW were found to perform quite well even in terms of absolute numbers. Both functionals provided barrier heights for the energetically lowest lying transition state that are within 1 kcal/mol of the DMC value. [ABSTRACT FROM AUTHOR]

A seminumerical algorithm capable of performing large-scale (time-dependent) density functional theory (TD-DFT) calculations to extract excitation energies and other ground-state and excited-state properties is outlined. The algorithm uses seminumerical integral techniques for evaluating Coulomb and exchange parts for a set of density matrices as occurring in standard TD-DFT or similar methods for the evaluation of vibrational frequencies. A suitable optimized de-aliasing procedure is introduced. The latter does not depend on further auxiliary quantities and retains the symmetry of a given density matrix. The algorithm is self-contained and applicable to any orbital basis set available without the need for further auxiliary basis sets or optimized de-aliasing grids. Relativistic two-component excited-state TD-DFT calculations are reported for the first time using the developed seminumerical algorithm for standard and local hybrid density functional approximations. Errors are compared with the widely used "resolution of the identity" (RI) approximations for Coulomb (RI-J) and exchange integrals (RI-K). The fully seminumerical algorithm does not exhibit an enlarged error for standard DFT functionals compared to the RI approximation. For the more involved local hybrid functionals and within strong external fields, accuracy is even considerably improved. [ABSTRACT FROM AUTHOR]

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted due to the risk of "variational collapse" down to the ground state. We employ the recently developed square gradient minimization [D. Hait and M. Head-Gordon, J. Chem. Theory Comput. 16, 1699 (2020)] algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP, and ωB97X-D3) are found to predict excitation energies from the core to singly occupied levels with high accuracy (≤0.3 eV RMS error) against available experimental data. Higher excited states are, however, more challenging by virtue of being intrinsically multiconfigurational. We thus present a configuration interaction inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO+, and the N K-edge of NO2 with high accuracy relative to experiment, indicating substantial promise in using this approach for the computation of core-level spectra for doublet species [vs more traditional time dependent DFT, equation of motion coupled cluster singles and doubles (EOM-CCSD), or using unrecoupled mixed configurations]. We also present general guidelines for computing core-excited states from orbital optimized DFT. [ABSTRACT FROM AUTHOR]

Spin crossover materials are bi-stable systems with potential applications as molecular scale electronic switches, actuators, thermometers, barometers, and displays. However, calculating the enthalpy difference, ΔH, between the high spin and low spin states has been plagued with difficulties. For example, many common density functional theory (DFT) methods fail to even predict the correct sign of ΔH, which determines the low temperature state. Here, we study a collection of Fe(II) and Fe(III) materials, where ΔH has been measured, which has previously been used to benchmark density functionals. The best performing hybrid functional, TPSSh, achieves a mean absolute error compared to experiment of 11 kJ mol−1 for this set of materials. However, hybrid functionals scale badly in the solid state; therefore, local functionals are preferable for studying crystalline materials, where the most interesting spin crossover phenomena occur. We show that both the Liechtenstein and Dudarev DFT+U methods are a little more accurate than TPSSh. The Dudarev method yields a mean absolute error of 8 kJ mol−1 for Ueff = 1.6 eV. However, the mean absolute error for both TPSSh and DFT+U is dominated by a single material, for which the two theoretical methods predict similar enthalpy differences—if this is excluded from the set, then DFT+U achieves chemical accuracy. Thus, DFT+U is an attractive option for calculating the properties of spin crossover crystals, as its accuracy is comparable to that of meta-hybrid functionals, but at a much lower computational cost. [ABSTRACT FROM AUTHOR]

We continue our work on the long-range corrected double-hybrid density functionals (LC-DHDFs) ωB2PLYP and ωB2GP-PLYP that we developed in the context of time-dependent (TD) Density Functional Theory (DFT) to enable the robust description of singlet–singlet excitations [M. Casanova-Páez, M. B. Dardis, and L. Goerigk, J. Chem. Theory Comput. 15, 4735 (2019)]. In our initial study, we only assessed the impact of a LC on BLYP-based DHDFs, and herein, we extend our understanding by providing the first test of PBE-based LC-DHDFs within the established TD-DHDF scheme. Moreover, this study is one of few that provides a direct comparison between TD-DHDFs and their faster Tamm–Dancoff-approximation variants (TDA-DHDFs). Most importantly, this is the first TDA-DHDF study since Grimme and Neese's TDA-B2PLYP [J. Chem. Phys. 127, 154116 (2007)] and the first work on TD-DHDFs that addresses singlet–triplet excitations. We show how the difference between TD-DHDFs and TDA-DHDFs is often negligible for singlet–singlet excitations, but how one has to apply TDA-DHDFs for triplet excitations. For both excitation types, the LC is beneficial to the BLYP-based DHDFs, but detrimental to the PBE-based ones. For local-valence and Rydberg excitations, ωB2PLYP and ωB2GP-PLYP as well as the global DHDF PBE-QIDH can be recommended. If a transition exhibits charge-transfer character, ωB2PLYP and ωB2GP-PLYP should be applied. An analysis of the gaps between the first singlet and triplet excited states of our systems revealed that there is room for further improvements to reach better robustness. Until that goal has been achieved, we recommend ωB2PLYP and ωB2GP-PLYP as some of the currently best TDA-DFT methods. [ABSTRACT FROM AUTHOR]

An efficient implementation for calculations of the electronic g-tensor at the level of second-order Møller–Plesset perturbation theory (MP2) is presented. The resolution of identity (RI) approximation is applied for the efficient treatment of two-electron integrals, and gauge including atomic orbitals are used to circumvent the gauge problem present in all magnetic property calculations. Furthermore, given that MP2 is an ingredient in double-hybrid density functional theory (DHDFT), the latter is also featured in the implementation. Calculated g-shifts with RI-MP2 and DHDFT using the double-hybrid density functionals B2PLYP and DSD-PBEP86 are compared to experimental data and published data from other methods including coupled cluster singles doubles. Additionally, the computational performance for medium to large size molecular systems was studied using the RIJK and RIJCOSX approximations for the two-electron integral treatment in the formation of Fock and Fock-like matrices necessary for the calculation of analytic second derivatives. [ABSTRACT FROM AUTHOR]

Molecular multibond dissociation displays a variety of electron correlation effects posing a challenge for theoretical description. We propose a CASΠ(M)DFT approach, which includes these effects in an efficient way by combining the complete active space self-consistent field method with density functional theory (DFT). Within CASΠ(M)DFT, a small complete active space (CAS) accounts for the long-range intrabond and middle-range interbond nondynamic correlation in the stretched bonds. The common short-range dynamic correlation is calculated with the Lee–Yang–Parr (LYP) correlation DFT functional corrected for the suppression of dynamic correlation with nondynamic correlation. The remaining middle-range interbond dynamic correlation is evaluated with the modified LYP functional of the bond densities. As a result, CASΠ(M)DFT potential energy curves (PECs) calculated in the relatively small triple-zeta basis closely reproduce the benchmark complete basis set PECs for the following prototype multibonded molecules: N2, CO, H2O, and C2. [ABSTRACT FROM AUTHOR]

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives. [ABSTRACT FROM AUTHOR]

We performed a combination of quantum chemical calculations and molecular dynamics simulations to assess the stability of various size N H 3 n − ammonia cluster anions up to n = 32 monomers. In the n = 3–8 size range, cluster anions are optimized and the vertical detachment energy of the excess electron (VDE) from increasing size clusters is computed using various level methods including density functional theory, MP2, and coupled-cluster singles doubles with perturbative triples. These clusters bind the electrons in nonbranched hydrogen bonding chains in dipole bound states. The VDE increases with size from a few millielectron volt up to ∼200 meV. The electron binding energy is weaker than that in water clusters but comparable to small methanol cluster VDEs. We located the first branched hydrogen bonding cluster that binds the excess electron at n = 7. For larger (n = 8–32) clusters, we generated cold, neutral clusters by semiempirical and ab initio molecular dynamics simulations and added an extra electron to selected neutral configurations. VDE calculations on the adiabatic and the relaxed anionic structures suggest that the n = 12–32 neutral clusters weakly bind the excess electron. Electron binding energies for these clusters (∼100 meV) appear to be significantly weaker than those extrapolated from experimental data. The observed excess electron states are diffuse and localized outside the molecular frame (surface states) with minor (∼1%) penetration to the nitrogen frontier orbitals. Stable minima with excess electron states surrounded by solvent molecules (cavity states) were not found in this size regime. [ABSTRACT FROM AUTHOR]

Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT. [ABSTRACT FROM AUTHOR]

A series of basis sets optimized for the calculation of the hyperfine coupling constant is proposed. The pcH-n basis sets are defined in qualities from double-ζ to pentuple-ζ for the elements H to Ar. They are derived from the polarization consistent basis sets by addition of two tight s-functions and one tight p-, d-, and f-function and are shown to provide an exponential convergence toward the complete basis set limit, and they have significantly lower basis set errors than other commonly used basis sets for a given ζ quality. The pcH basis sets display very similar basis set convergence with a range of density functional theory methods and may also be suitable for wave function based methods. [ABSTRACT FROM AUTHOR]

Organic molecular crystals contain long-range dispersion interactions that can be challenging for solid-state methods such as density functional theory (DFT) to capture, and in some industrial sectors are overlooked in favor of classical methods to calculate atomistic properties. Hence, this publication addresses the critical question of whether dispersion corrected DFT calculations for organic crystals can reproduce the structural and energetic trends seen from experiment, i.e., whether the calculations can now be said to be truly "on-trend." In this work, we assess the performance of three of the latest dispersion-corrected DFT methods, in calculating the long-range, dispersion energy: the pairwise methods of D3(0) and D3(BJ) and the many-body dispersion method, MBD@rsSCS. We calculate the energetics and optimized structures of two homologous series of organic molecular crystals, namely, carboxylic acids and amino acids. We also use a classical force field method (using COMPASS II) and compare all results to experimental data where possible. The mean absolute error in lattice energies is 9.59 and 343.85 kJ/mol (COMPASS II), 10.17 and 16.23 kJ/mol (MBD@rsSCS), 10.57 and 18.76 kJ/mol [D3(0)], and 8.52 and 14.66 kJ/mol [D3(BJ)] for the carboxylic acids and amino acids, respectively. MBD@rsSCS produces structural and energetic trends that most closely match experimental trends, performing the most consistently across the two series and competing favorably with COMPASS II. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT) including van der Waals (vdW) interactions and accounting for zero-point energy (ZPE) is believed to provide a good description of crystalline ice phases [B. Pamuk et al., Phys. Rev. Lett. 108, 193003 (2012)]. Given the computational cost of DFT, it is not surprising that extensive phonon calculations, which yield the ZPE, have only been done for a limited amount of ice structures. Computationally convenient force fields on the other hand are the method of choice for large systems and/or dynamical simulations, e.g., of supercooled water. Here, we present a systematic comparison for seven hydrogen-ordered crystalline ice phases (Ih, IX, II, XIII, XIV, XV, and VIII) between many commonly used nonpolarizable force fields and density functionals, including some recently developed meta-GGA functionals and accounting for vdW interactions. Starting from the experimentally determined crystal structures, we perform space-group-constrained structural relaxations. These provide the starting point for highly accurate phonon calculations that yield effectively volume-dependent ZPEs within the quasiharmonic approximation. In particular, when including ZPE, the force fields show a remarkably good performance for equilibrium volumes and cohesive energies superior to many density functionals. A decomposition of the cohesive energies into intramolecular deformation, electrostatic, and vdW contributions quantifies the differences between force fields and DFT. Results for the equilibrium volumes and phase transition pressures for all studied force fields are much more strongly affected by ZPE than all studied density functionals. We track this down to significantly smaller shifts of the O–H-stretch modes and compare with experimental data from Raman spectroscopy. [ABSTRACT FROM AUTHOR]

We present a purely numerical approach in a Cartesian grid, for efficient computation of the Hartree-Fock (HF) exchange contribution in the HF and density functional theory models. This takes inspiration from a recently developed algorithm by Liu et al., in 2017, where the rate-determining step is the accurate evaluation of electrostatic potential. This introduces the Fourier convolution theorem in conjunction with a range-separated Coulomb interaction kernel. The latter is efficiently mapped into a real grid through a simple optimization procedure, giving rise to a constraint in the range-separated parameter. The overall process offers logarithmic scaling with respect to the molecular size. It is then extended toward global hybrid functionals such as B3LYP, PBE0, and BHLYP within pseudopotential Kohn-Sham theory, through an LCAO-MO ansatz in a Cartesian grid, developed earlier in our laboratory. For the sake of comparison, a parallel semi-numerical approach has also been worked out that exploits the familiar Obara-Saika recursion algorithm without any additional techniques. An excellent agreement between these two routes is demonstrated through total energy and orbital energy in a series of atoms and molecules (including 10 π-electron molecules), employing an LANL2DZ-type basis function. A critical analysis of these two algorithms reveals that the proposed numerical scheme could lead to very attractive and competitive scaling. The success of our approach also enables us for further development of optimally tuned range-separated hybrid and hyper functionals. [ABSTRACT FROM AUTHOR]

A meta-generalized gradient approximation (meta-GGA) level screened hybrid functional is developed for the solid-state electronic structure calculations. Assessment of the proposed functional for the solid-state lattice constants and bandgaps indicates that it is quite efficient in describing those properties. Specifically, the improvement in the bandgap performance of the presently proposed meta-GGA level screened hybrid functional is noticeable. From the construction point of view, the present screened hybrid functional is one step forward to the density functional screened hybrid functional rung by adding extra ingredients in its functional form. The most appealing feature of the present screened functional is that it is constructed upon an accurate semilocal functional by adopting a simple modification on the top of that functional. [ABSTRACT FROM AUTHOR]

The recently developed multiconfiguration pair-density functional theory (MC-PDFT) combines multiconfiguration wave function theory with a density functional that depends on the on-top pair density of an electronic system. In an MC-PDFT calculation, there are two steps: a conventional multiconfiguration self-consistent-field (MCSCF) calculation and a post-MCSCF evaluation of the energy with an on-top density functional. In this work, we present the details of the MC-PDFT algorithm that avoids steeply scaling steps that are present in other post-self-consistent-field multireference calculations of dynamic correlation energy. We demonstrate the favorable scaling by considering systems of H2 molecules with active spaces of several different sizes. We then apply the MC-PDFT method to calculate the heterolytic dissociation enthalpy of ferrocene. We find that MC-PDFT yields results that are at least as accurate as complete active space second-order perturbation theory and are more stable with respect to basis set, but at a fraction of the cost in both time and memory. [ABSTRACT FROM AUTHOR]

The structural properties of a-HfO2/Ge(2 × 1)-(001) and a-ZrO2/Ge(2 × 1)-(001) interfaces were investigated with and without a GeOx interface interlayer using density-functional theory (DFT) molecular dynamics (MD) simulations. Realistic a-HfO2 and a-ZrO2 samples were generated using a hybrid classical-DFT MD "melt-and-quench" approach and tested against experimental properties. The oxide/Ge stacks were annealed at 700 K, cooled to 0 K, and relaxed providing the system withenough freedom toform realistic interfaces. For each high-K/Ge stack type, two systems with single and double interfaces were investigated. All stacks were free of midgap states; however, stacks with a GeOx interlayer had band-edge states which decreased the band gaps by 0%-30%. These band-edge states were mainly produced by under-coordinated Ge atoms in GeOx layer or its vicinity due to deformation, intermixing, and bond-breaking. The DFT-MD simulations show that electronically passive interfaces can be formed either directly between high-K dielectrics and Ge or with a monolayer of GeO2 if the processing does not create or properly passivate under-coordinated Ge atoms and Ge's with significantly distorted bonding angles. Comparison to the charge states of the interfacial atoms from DFT to experimental x-ray photoelectron spectroscopy results shows that while most studies of gate oxide on Ge(001) have a GeOx interfacial layer, it is possible toform an oxide/Ge interface without a GeOx interfacial layer. Comparison to experiments is consistent with the dangling bonds in the suboxide being responsible for midgap state formation. [ABSTRACT FROM AUTHOR]

In energy decomposition analysis (EDA) of intermolecular interactions calculated via density functional theory, the initial supersystem wavefunction defines the so-called "frozen energy" including contributions such as permanent electrostatics, steric repulsions, and dispersion. This work explores the consequences of the choices that must be made to define the frozen energy. The critical choice is whether the energy should be minimized subject to the constraint of fixed density. Numerical results for Ne2, (H2O)2, BH3 -NH3, and ethane dissociation show that there can be a large energy lowering associated with constant density orbital relaxation. By far the most important contribution is constant density inter-fragment relaxation, corresponding to charge transfer (CT). This is unwanted in an EDA that attempts to separate CT effects, but it may be useful in other contexts such as force field development. An algorithm is presented for minimizing single determinant energies at constant density both with and without CT by employing a penalty function that approximately enforces the density constraint. [ABSTRACT FROM AUTHOR]

We propose a new form of orbital-free (OF) kinetic energy density functional (KEDF) for semiconductors that is based on the Wang-Govind-Carter (WGC99) nonlocal KEDF. We enhance within the latter the semi-local von Weizsäcker KEDF term, which is exact for a single orbital. The enhancement factor we introduce is related to the extent to which the electron density is localized. The accuracy of the new KEDF is benchmarked against Kohn-Sham density functional theory (KSDFT) by comparing predicted energy differences between phases, equilibrium volumes, and bulk moduli for various semiconductors, along with metal-insulator phase transition pressures. We also compare point defect and (100) surface energies in silicon for a broad test of its applicability. This new KEDF accurately reproduces the exact non-interacting kinetic energy of KSDFT with only one additional adjustable parameter beyond the three parameters in the WGC99 KEDF; it exhibits good transferability between semiconducting to metallic silicon phases and between various III-V semiconductors without parameter adjustment. Overall, this KEDF is more accurate than previously proposed OF KEDFs (e.g., the Huang-Carter (HC) KEDF) for semiconductors, while the computational efficiency remains at the level of theWGC99 KEDF (several hundred times faster than the HC KEDF). This accurate, fast, and transferable new KEDF holds considerable promise for large-scale OFDFT simulations of metallic through semiconducting materials. [ABSTRACT FROM AUTHOR]

In this work, the adiabatic connection (AC) formalism, coordinate scaling relations, and the second order Görling-Levy perturbation theory (GL2) are first reviewed. Emphasis is laid upon the construction of the AC integrand (Wxcλ), with suitable input data {Wxc0,Wxcr0,Wxc1} and the proper asymptotic behavior on λ−1/2 as λ→∞. This leads to a non-empirical DH functional, namely, PBE-ACDH. The PBE-ACDH functional is unique in that it explicitly considers contributions from density scaling and singles, and it utilizes density and orbital information from the PBE functional, which has a local multiplicative potential, being most compatible with the GL2 theory. Systematical tests on heats of formation, bond dissociation enthalpies, reaction barrier heights, and nonbonded interactions, using some well-established benchmarking sets, suggest that PBE-ACDH is a significant improvement over its parent functional PBE, as well as PBE0, Becke's Half-and-Half (PBE-HH), and GL2. The physical insight gained in the present work should prove useful for the further development of new functionals. [ABSTRACT FROM AUTHOR]