A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction

Revisiting Artifacts of Kohn-Sham Density Functionals for Biosimulation

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

Learning from the 4-(dimethylamino)benzonitrile twist: Two-parameter range-separated local hybrid functional with high accuracy for triplet and charge-transfer excitations

The recent ωLH22t range-separated local hybrid (RSLH) is shown to provide outstanding accuracy for the notorious benchmark problem of the two lowest excited-state potential energy curves for the amino group twist in 4-(dimethylamino)benzonitrile (DMABN). However, the design of ωLH22t as a general-purpose functional resulted in less convincing performance for triplet excitations, which is an important advantage of previous LHs. Furthermore, ωLH22t uses 8 empirical parameters to achieve broad accuracy. In this work, the RSLH ωLH23ct-sir is constructed with minimal empiricism by optimizing its local mixing function prefactor and range-separation parameter for only 8 excitation energies. ωLH23ct-sir maintains the excellent performance of ωLH22t for the DMABN twist and charge-transfer benchmarks but significantly improves the errors for triplet excitation energies (0.17 vs 0.24 eV). Additional test calculations for the AE6BH6 thermochemistry test set and large dipole moment and static polarizability test sets confirm that the focus on excitation energies in the optimization of ωLH23ct-sir has not caused any dramatic errors for ground-state properties. Although ωLH23ct-sir cannot replace ωLH22t as a general-purpose functional, it is preferable for problems requiring a universally good description of localized and charge-transfer excitations of both singlet and triplet multiplicity. Current limitations on the application of ωLH23ct-sir and other RSLHs to the study of singlet-triplet gaps of emitters for thermally activated delayed fluorescence are discussed. This work also includes the first systematic analysis of the influence of the local mixing function prefactor and the range-separation parameter in an RSLH on different types of excitations.

3D Information-Theoretic Analysis of the Simplest Hydrogen Abstraction Reaction

We investigate the course of an elementary chemical reaction from the perspective of information theory in 3D space through the hypersurface of several information-theoretic (IT) functionals such as disequilibrium (D), Shannon entropy (S), Fisher information (I), and the complexity measures of Fisher-Shannon (FS) and López-Mancini-Calbet (LMC). The probe for the study is the hydrogenic identity abstraction reaction. In order to perform the analysis, the reactivity pattern of the reaction is examined by use of the aforementioned functionals of the single-particle density, which is analyzed in position (r) and momentum (p) spaces. The 3D analyses revealed interesting reactivity patterns in the neighborhood of the intrinsic reaction coordinate (IRC) path, which allow to interpret the reaction mechanism for this reaction in a novel manner. In addition, the chemically interesting regions that have been characterized through the information functionals and their complexity measures are depicted and analyzed in the framework of the three-dimensional structure of the information-theoretical data of a chemical reaction, that is, the reactant/product (R/P) complexes, the transition state (TS), and the ones that are only revealed through IT measures such as the bond-cleavage energy region (BCER), the bond-breaking/forming (B-B/F) region, and the spin-coupling (SC) process. Furthermore, focus has been placed on the diagonal part of the hypersurface of the IT functionals, aside from the IRC path itself, with the purpose of analyzing the dissociation process of the triatomic transition-state complex that has revealed other interesting features of the bond-breaking (B-B) process. In other respects, it is shown throughout the combined analyses of the 3D structure of the IT functionals in conjugated spaces that the chemically significant regions occurring at the onset of the TS are completely characterized by information-theoretic aspects of localizability (S), uniformity (D), and disorder. Further, novel regions of low complexity seem to indicate new boundaries for chemically stable complex molecules. Finally, the study reveals that the chemical reaction occurs at low-complexity regions, where the concurrent phenomena take place: bond-breaking/forming (B-B/F), bond-cleavage energy reservoirs (BCER), spin-coupling (SC), and transition state (TS).

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

One-electron self-interaction error and its relationship to geometry and higher orbital occupation

Density Functional Theory (DFT) sees prominent use in computational chemistry and physics; however, problems due to the self-interaction error (SIE) pose additional challenges to obtaining qualitatively correct results. As an unphysical energy an electron exerts on itself, the SIE impacts most practical DFT calculations. We conduct an in-depth analysis of the one-electron SIE in which we replicate delocalization effects for simple geometries. We present a simple visualization of such effects, which may help in future qualitative analysis of the one-electron SIE. By increasing the number of nuclei in a linear arrangement, the SIE increases dramatically. We also show how molecular shape impacts the SIE. Two- and three-dimensional shapes show an even greater SIE stemming mainly from the exchange functional with some error compensation from the one-electron error, which we previously defined [D. R. Lonsdale and L. Goerigk, Phys. Chem. Chem. Phys. 22, 15805 (2020)]. Most tested geometries are affected by the functional error, while some suffer from the density error. For the latter, we establish a potential connection with electrons being unequally delocalized by the DFT methods. We also show how the SIE increases if electrons occupy higher-lying atomic orbitals; seemingly one-electron SIE free methods in a ground are no longer SIE free in excited states, which is an important insight for some popular, non-empirical density functional approximations (DFAs). We conclude that the erratic behavior of the SIE in even the simplest geometries shows that robust DFAs are needed. Our test systems can be used as a future benchmark or contribute toward DFT development.

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn-Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn-Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.

Ligand Additivity and Divergent Trends in Two Types of Delocalization Errors from Approximate Density Functional Theory

The predictive accuracy of density functional theory (DFT) is hampered by delocalization errors, especially for correlated systems such as transition-metal complexes. Two complementary strategies have been developed to reduce delocalization error: eliminating the global curvature with change in charge, and applying a linear response Hubbard U as a measure of local curvature at a metal center at fixed charge in a DFT+U framework. We investigate the relationship between the two delocalization error measures as the ligand field strength is varied with the number of strong-field ligands in a series of heteroleptic complexes or by geometrically constraining the metal-ligand bond length in homoleptic octahedral complexes. We show that across these sets of complexes an inverse relationship generally exists between global and local curvatures. We find that effects of ligand substitution on both measures of delocalization are typically additive, but the quantities seldom coincide.

Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT + U

Approximate semilocal density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT + U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT + U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT + U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT + U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT + U. We demonstrate this molecular DFT + U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO₂) and late (i.e., PtO₂) transition-metal oxides. Molecular DFT + U simultaneously corrects adsorption energies and surface formation energies of multilayer models of rutile TiO₂(110) and PtO₂(110) to resolve the paradoxical description of surface stability and surface reactivity of semilocal DFT.

Study of self-interaction-errors in barrier heights using locally scaled and Perdew-Zunger self-interaction methods

We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose, we use the well-known Perdew-Zunger self-interaction-correction (PZSIC) [J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)] as well as two variations of the recently developed, locally scaled self-interaction correction (LSIC) [Zope et al., J. Chem. Phys. 151, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation (LDA). The version of LSIC that uses the iso-orbital indicator z as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor w based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. The LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughly equal size for the non-hydrogen transfer reactions.

Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: A path toward chemical accuracy

Second-order Moller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeing problems in organic and biological chemistry. However, MP2 suffers from known limitations in the description...

Reaction pathways in the solid state and the Hubbard U correction

We investigate how the Hubbard U correction influences vacancy defect migration barriers in transition metal oxide semiconductors. We show that, depending on the occupation of the transition metal d orbitals, the Hubbard U correction can cause severe instabilities in the migration barrier energies predicted using generalized gradient approximation density functional theory (GGA DFT). For the d⁰ oxide SrTiO₃, applying a Hubbard correction to the Ti⁴⁺ 3d orbitals below 4-5 eV yields a migration barrier of ∼0.4 eV. However, above this threshold, the barrier increases suddenly to ∼2 eV. This sudden increase in the transition state barrier arises from the Hubbard U correction changing the Ti⁴⁺ t_2g/e_g orbital occupation, and hence electron density localization, along the migration pathway. Similar results are observed in the d¹⁰ oxide ZnO; however, significantly larger Hubbard U corrections must be applied to the Zn²⁺ 3d orbitals for the same instability to be observed. These results highlight important limitations to the application of the Hubbard U correction when modeling reactive pathways in solid state materials using GGA DFT.

Challenges for density functional theory: calculation of CO adsorption on electrocatalytically relevant metals

We assess four DFT functionals, RTPSS, RPBE, SCAN and B97M-rV, for surface interactions. We find that B97M-rV predicts the correct site preference for CO binding on Ag and Au while RTPSS performs well for surface relaxations and binding of CO on Pt and Cu.

Density-functional theory models of Fe(iv)O reactivity in metal-organic frameworks: self-interaction error, spin delocalisation and the role of hybrid exchange

We study the reactivity of Fe(iv)O moieties supported by a metal-organic framework (MOF-74) in the oxidation reaction of methane to methanol using all-electron, periodic density-functional theory calculations. We compare results concerning the electronic properties and reactivity obtained using two hybrid (B3LYP and sc-BLYP) and two standard generalised gradient corrected (PBE and BLYP) semi-local density functional approximations. The semi-local functionals are unable to reproduce the expected reaction profiles and yield a qualitatively incorrect representation of the reactivity. Non-local hybrid functionals provide a substantially more reliable description and predict relatively modest (ca. 60 kJ mol^-1) reaction energy barriers for the H-atom abstraction reaction from CH₄ molecules. We examine the origin of these differences and we highlight potential means to overcome the limitations of standard semi-local functionals in reactivity calculations in solid-state systems.

Multicomponent Orbital-Optimized Perturbation Theory Methods: Approaching Coupled Cluster Accuracy at Lower Cost

Multicomponent quantum chemistry methods such as the nuclear-electronic orbital (NEO) method allow the consistent quantum mechanical treatment of electrons and nuclei. The development of computationally practical, accurate, and robust multicomponent wave function methods is challenging because of the importance of orbital relaxation effects. Herein the variational orbital-optimized coupled cluster with doubles (NEO-OOCCD) method and the orbital-optimized second-order Møller-Plesset perturbation theory (NEO-OOMP2) method with scaled-opposite-spin (SOS) versions are developed and applied to molecular systems in which a proton and all electrons are treated quantum mechanically. The results highlight the importance of orbital relaxation in multicomponent wave function methods. The NEO-SOS'-OOMP2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electronic correlation energy, is found to achieve nearly the same level of accuracy as the NEO-OOCCD method for proton densities, proton affinities, and optimized geometries. An advantage of the NEO-SOS'-OOMP2 method is that it can be implemented with N⁴ scaling, where N is a measure of the system size. This method will enable future multicomponent wave function calculations of structures, energies, reaction paths, and dynamics for substantially larger chemical systems.

The one-electron self-interaction error in 74 density functional approximations: a case study on hydrogenic mono- and dinuclear systems

The self-interaction error (SIE), i.e. unphysical interactions of electrons with themselves, has plagued developers and users of Density Functional Approximations (DFAs) since the inception of Density Functional Theory (DFT). Formally, it can be separated into the one-electron and many-electron SIE; herein we present one of the most comprehensive studies of the first. While we focus mostly on the total SIE, we also make use of two different decompositions. The first is a separation into functional and density-driven errors as championed by Sim, Burke and co-workers [J. Phys. Chem. Lett., 2018, 9, 6385-6392]; the second separates the error into exchange, correlation, and one-electron components, with the latter being a density error that has not been discussed in this form before. After investigating the familiar hydrogen atom and dihydrogen cation, we establish a relationship between the SIE and the nuclear charge with the help of a series of heavier hydrogenic analogues. For the mononuclear systems and the diatomics at the dissociation limit, this relationship is linear in nature with prominent exceptions, mostly belonging to the Minnesota and range-separated (double-)hybrid DFAs. For the first time, we also show how the magnitude of the SIE depends on the underlying atomic-orbital basis set and how DFAs that rely on a popular van-der-Waals DFT type London-dispersion term exhibit "self-dispersion". We find that range separation is not a panacea for solving the one-electron SIE. DFAs that have been developed to be one-electron SIE free for one system, such as the hydrogen atom, show larger errors for heavier hydrogenic systems. Often, one-electron SIE-free DFAs rely on fortuitous error cancellation between their exchange and correlation components. An analysis of the most robust methods for general applications to date reveals that they suffer moderately from the one-electron SIE, while DFAs that are nearly SIE-free do not perform well in applications. Implicit in the continued existence of the one-electron SIE is that well-performing DFAs continue to suffer insufficiencies at their fundamental levels that are being compensated for by the SIE. Our analysis includes more than 250 000 datapoints, resulting in multiple insights that may drive future developments of new DFAs or SIE corrections.

Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics

The origin of distinct 3d vs. 4d transition metal complex sensitivity to exchange is explored over a large data set.

Density Functional Theory as a Data Science

The development of density functional theory (DFT) functionals and physical corrections are reviewed focusing on the physical meanings and the semiempirical parameters from the viewpoint of data science. This review shows that DFT exchange-correlation functionals have been developed under many strict physical conditions with minimizing the number of the semiempirical parameters, except for some recent functionals. Major physical corrections for exchange-correlation function- als are also shown to have clear physical meanings independent of the functionals, though they inevitably require minimum semiempirical parameters dependent on the functionals combined. We, therefore, interpret that DFT functionals with physical corrections are the most sophisticated target functions that are physically legitimated, even from the viewpoint of data science.

Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?

Approximate, semilocal density functional theory (DFT) suffers from delocalization error that can lead to a paradoxical model of catalytic surfaces that both overbind adsorbates yet are also too stable. We investigate the effect of two widely applied approaches for delocalization error correction, (i) affordable DFT+U (i.e., semilocal DFT augmented with a Hubbard U) and (ii) hybrid functionals with an admixture of Hartree-Fock (HF) exchange, on surface and adsorbate energies across a range of rutile transition metal oxides widely studied for their promise as water-splitting catalysts. We observe strongly row- and period-dependent trends with DFT+U, which increases surface formation energies only in early transition metals (e.g., Ti and V) and decreases adsorbate energies only in later transition metals (e.g., Ir and Pt). Both global and local hybrids destabilize surfaces and reduce adsorbate binding across the periodic table, in agreement with higher-level reference calculations. Density analysis reveals why hybrid functionals correct both quantities, whereas DFT+U does not. We recommend local, range-separated hybrids for the accurate modeling of catalysis in transition metal oxides at only a modest increase in computational cost over semilocal DFT.

Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT

Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.

A noncovalent interaction insight onto the concerted metallation deprotonation mechanism

The CMD/AMLA mechanisms of cyclopalladation and the parent fictitious cyclonickelation of N,N-dimethylbenzylamine have been investigated by joint DFT-D and DLPNO-CCSD(T) methods assisted by QTAIM.

Unraveling substituent effects on the glass transition temperatures of biorenewable polyesters

Converting biomass-based feedstocks into polymers not only reduces our reliance on fossil fuels, but also furnishes multiple opportunities to design biorenewable polymers with targeted properties and functionalities. Here we report a series of high glass transition temperature (Tg up to 184 °C) polyesters derived from sugar-based furan derivatives as well as a joint experimental and theoretical study of substituent effects on their thermal properties. Surprisingly, we find that polymers with moderate steric hindrance exhibit the highest Tg values. Through a detailed Ramachandran-type analysis of the rotational flexibility of the polymer backbone, we find that additional steric hindrance does not necessarily increase chain stiffness in these polyesters. We attribute this interesting structure-property relationship to a complex interplay between methyl-induced steric strain and the concerted rotations along the polymer backbone. We believe that our findings provide key insight into the relationship between structure and thermal properties across a range of synthetic polymers.

Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost

The flat-plane condition is the union of two exact constraints in electronic structure theory: (i) energetic piecewise linearity with fractional electron removal or addition and (ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree-Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane and we find this shape to be remarkably consistent across ions and molecules. We introduce the judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. We select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.

Thermal decomposition of FC(O)OCH3 and FC(O)OCH2CH3

The thermal decomposition of methyl and ethyl formates has been extensively studied due to their importance in the oxidation of several fuels, pesticidal properties and their presence in interstellar space. We hitherto present the study of the thermal decomposition of methyl and ethyl fluoroformates, which could help in the elucidation of the reaction mechanisms. The reaction mechanisms were studied using FTIR spectroscopy in the temperature range of 453-733 K in the presence of different pressures of N2 as bath gas. For FC(O)OCH3 two different channels were observed; the unimolecular decomposition which is favored at higher temperatures and has a rate constant kFC(O)OCH3 = (5.3 ± 0.5) × 1015 exp[-(246 ± 10 kJ mol-1/RT)] (in units of s-1) and a bimolecular channel with a rate constant kFC(O)OCH3 = (1.6 ± 0.5) × 1011 exp[-(148 ± 10 kJ mol-1/RT)] (in units of s-1 (mol L)-1). However for ethyl formate, only direct elimination of CO2, HF and ethylene operates. The rate constants of the homogeneous first-order process fit the Arrhenius equation kFC(O)OCH2CH3 = (2.06 ± 0.09) × 1013 exp[-(169 ± 6 kJ mol-1/RT)] (in units of s-1). The difference between the mechanisms of the two fluoroformates relies on the stabilization of a six-centered transition state that only exists for ethyl formate. First principles calculations for the different channels were carried out to understand the dynamics of the decomposition.

Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U

Approximate density functional theory (DFT) is widely used in chemistry and physics, despite delocalization errors that affect energetic and density properties. DFT+U (i.e., semilocal DFT augmented with a Hubbard U correction) and global hybrid functionals are two commonly employed practical methods to address delocalization error. Recent work demonstrated that in transition-metal complexes both methods localize density away from the metal and onto surrounding ligands, regardless of metal or ligand identity. In this work, we compare density localization trends with DFT+U and global hybrids on a diverse set of 34 transition-metal-containing solids with varying magnetic state, electron configuration and valence shell, and coordinating-atom orbital diffuseness (i.e., O, S, Se). We also study open-framework solids in which the metal is coordinated by molecular ligands, i.e., MCO₃, M(OH)₂, M(NCNH)₂, K₃M(CN)₆ (M = V-Ni). As in transition-metal complexes, incorporation of Hartree-Fock exchange consistently localizes density away from the metal, but DFT+U exhibits diverging behavior, localizing density (i) onto the metal in low-spin and late transition metals and (ii) away from the metal in other cases in agreement with hybrids. To isolate the effect of the crystal environment, we extract molecular analogues from open-framework transition-metal solids and observe consistent localization of the density away from the metal in all cases with both DFT+U and hybrid exchange. These observations highlight the limited applicability of trends established for functional tuning on transition-metal complexes even to equivalent coordination environments in the solid state.

Correcting density-driven errors in projection-based embedding

Projection-based embedding provides a simple and numerically robust framework for multiscale wavefunction-in-density-functional-theory (WF-in-DFT) calculations. The approach works well when the approximate DFT is sufficiently accurate to describe the energetics of the low-level subsystem and the coupling between subsystems. It is also necessary that the low-level DFT produces a qualitatively reasonable description of the total density, and in this work, we study model systems where delocalization error prevents this from being the case. We find substantial errors in embedding calculations on open-shell doublet systems in which self-interaction errors cause spurious delocalization of the singly occupied orbital. We propose a solution to this error by evaluating the DFT energy using a more accurate self-consistent density, such as that of Hartree-Fock (HF) theory. These so-called WF-in-(HF-DFT) calculations show excellent convergence towards full-system wavefunction calculations.

Radical Reaction Control in the AdoMet Radical Enzyme CDG Synthase (QueE): Consolidate, Destabilize, Accelerate

Controlling radical intermediates and thus catalysing and directing complex radical reactions is a central feature of S-adensosylmethionine (SAM)-dependent radical enzymes. We report ab initio and DFT calculations highlighting the specific influence of ion complexation, including Mg2+ , identified as a key catalytic component on radical stability and reaction control in 7-carboxy-7-deazaguanine synthase (QueE). Radical stabilisation energies (RSEs) of key intermediates and radical clock-like model systems of the enzyme-catalysed rearrangement of 6-carboxytetrahydropterin (CPH4), reveals a directing role of Mg2+ in destabilising both the substrate-derived radical and corresponding side reactions, with the effect that the experimentally-observed rearrangement becomes dominant over possible alternatives. Importantly, this is achieved with minimal disruption of the thermodynamics of the substrate itself, affording a novel mechanism for an enzyme to both maintain binding potential and accelerate the rearrangement step. Other mono and divalent ions were probed with only dicationic species achieving the necessary radical conformation to facilitate the reaction.

How Large Should the QM Region Be in QM/MM Calculations? The Case of Catechol O-Methyltransferase

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely used in studies of enzymatic catalysis. Until recently, it has been cost prohibitive to determine the asymptotic limit of key energetic and structural properties with respect to increasingly large QM regions. Leveraging recent advances in electronic structure efficiency and accuracy, we investigate catalytic properties in catechol O-methyltransferase, a prototypical methyltransferase critical to human health. Using QM regions ranging in size from reactants-only (64 atoms) to nearly one-third of the entire protein (940 atoms), we show that properties such as the activation energy approach within chemical accuracy of the large-QM asymptotic limits rather slowly, requiring approximately 500-600 atoms if the QM residues are chosen simply by distance from the substrate. This slow approach to asymptotic limit is due to charge transfer from protein residues to the reacting substrates. Our large QM/MM calculations enable identification of charge separation for fragments in the transition state as a key component of enzymatic methyl transfer rate enhancement. We introduce charge shift analysis that reveals the minimum number of protein residues (approximately 11-16 residues or 200-300 atoms for COMT) needed for quantitative agreement with large-QM simulations. The identified residues are not those that would be typically selected using criteria such as chemical intuition or proximity. These results provide a recipe for a more careful determination of QM region sizes in future QM/MM studies of enzymes.

Complex Orbitals, Multiple Local Minima, and Symmetry Breaking in Perdew-Zunger Self-Interaction Corrected Density Functional Theory Calculations

Implentation of seminumerical stability analysis for calculations using the Perdew-Zunger self-interaction correction is described. It is shown that real-valued solutions of the Perdew-Zunger equations for gas phase atoms are unstable with respect to imaginary orbital rotations, confirming that a proper implementation of the correction requires complex-valued orbitals. The orbital density dependence of the self-interaction corrected functional is found to lead to multiple local minima in the case of the acrylic acid, H6, and benzene molecules. In the case of benzene, symmetry breaking that results in incorrect ground state geometry is found to occur, erroneously leading to alternating bond lengths in the molecule.

Characterization of water dissociation on α-Al2O3(11[combining macron]02): theory and experiment

The interaction of water with α-alumina (i.e. α-Al2O3) surfaces is important in a variety of applications and a useful model for the interaction of water with environmentally abundant aluminosilicate phases. Despite its significance, studies of water interaction with α-Al2O3 surfaces other than the (0001) are extremely limited. Here we characterize the interaction of water (D2O) with a well defined α-Al2O3(11[combining macron]02) surface in UHV both experimentally, using temperature programmed desorption and surface-specific vibrational spectroscopy, and theoretically, using periodic-slab density functional theory calculations. This combined approach makes it possible to demonstrate that water adsorption occurs only at a single well defined surface site (the so-called 1-4 configuration) and that at this site the barrier between the molecularly and dissociatively adsorbed forms is very low: 0.06 eV. A subset of OD stretch vibrations are parallel to this dissociation coordinate, and thus would be expected to be shifted to low frequencies relative to an uncoupled harmonic oscillator. To quantify this effect we solve the vibrational Schrödinger equation along the dissociation coordinate and find fundamental frequencies red-shifted by more than 1500 cm(-1). Within the context of this model, at moderate temperatures, we further find that some fraction of surface deuterons are likely delocalized: dissociatively and molecularly absorbed states are no longer distinguishable.

Hydrogen Abstraction from Fluorinated Ethyl Methyl Ether Systems by OH Radicals

A systematic computational investigation of hydrogen abstraction by OH from the full series of fluorinated ethyl methyl ethers (EME) containing at least one H and one F, C2HnX5-nOCHmX3-m (n=0–5, m=0–3; and n=m=0 not allowed), including 147 reactants and 469 transition states, has been carried out, employing the MP2/6-31G(d) level of theory. Results for optimized geometries, including evidence of intramolecular hydrogen bonding in transition states, and barrier heights are presented. Trends pertaining to the number of fluorines substituted, key bond lengths, barrier heights, and key bond angles were found with good correlations and were investigated. An increase in the number of F increases the barrier height of the reaction. An increase in some parameters such as C–H length of TS, relative change in C–H from reactants to TS, ∠COC of reactants, ∠HOH in the TS, and relative change in ∠HOH between TS and free water bond angle also correlates with increased barrier height. An increase in other parameters like C–H length in the reactants and hydrogen bonding can decrease the barrier height.

Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals

The scaled mean absolute deviations (s-MADs) of the optimized geometric parameters for covalent bondings (the CCse set), nonbonded interactions (the S22G30 set) and the transition state structures (the TSG36 set), with Tot referring to the averaged s-MAD for general performances.

The Hubbard dimer: a density functional case study of a many-body problem

This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.

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

Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.

Structure and electronic properties of MoVO type mixed-metal oxides – a combined view by experiment and theory

The current state of experimental and theoretical work on structure and reactivity of MoVO type mixed-metal oxides is critically reviewed.