Bond formation insights into the Diels-Alder reaction: A bond perception and self-interaction perspective.

The behavior of electrons during bond formation and breaking cannot commonly be accessed from experiments. Thus, bond perception is often based on chemical intuition or rule-based algorithms. Utilizing computational chemistry methods, we present intrinsic bond descriptors for the Diels-Alder reaction, allowing for an automatic bond perception. We show that these bond descriptors are available from localized orbitals and self-interaction correction calculations, e.g., from Fermi-orbital descriptors. The proposed descriptors allow a sparse, simple, and educational inspection of the Diels-Alder reaction from an electronic perspective. We demonstrate that bond descriptors deliver a simple visual representation of the concerted bond formation and bond breaking, which agrees with Lewis' theory of bonding.

How good are recent density functionals for ground and excited states of one-electron systems?

Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density-functional approximations (DFAs) should exhibit large energy errors for excited states as a necessary consequence of orbital nodality. Motivated by self-interaction corrected density-functional calculations on many-electron systems, we continue their study with the exactly solvable 1s, 2p, and 3d states of 36 hydrogenic one-electron ions (H-Kr35+) and demonstrate with self-consistent calculations that state-of-the-art DFAs indeed exhibit large errors for the 2p and 3d excited states. We consider 56 functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as meta-GGA levels, and several hybrid functionals such as the recently proposed machine-learned DM21 local hybrid functional. The best non-hybrid functional for the 1s ground state is revTPSS. As predicted by Sun et al., the 2p and 3d excited states are more difficult for DFAs, and LDA functionals turn out to yield the most systematic accuracy for these states among non-hybrid functionals. The best performance for the three states overall is observed with the BHandH global hybrid GGA functional, which contains 50% Hartree-Fock exchange and 50% LDA exchange. The performance of DM21 is found to be inconsistent, yielding good accuracy for some states and systems and poor accuracy for others. Based on these results, we recommend including a variety of one-electron cations in future training of machine-learned density functionals.

Data-driven and constrained optimization of semi-local exchange and nonlocal correlation functionals for materials and surface chemistry.

Reliable predictions of surface chemical reaction energetics require an accurate description of both chemisorption and physisorption. Here, we present an empirical approach to simultaneously optimize semi-local exchange and nonlocal correlation of a density functional approximation to improve these energetics. A combination of reference data for solid bulk, surface, and gas-phase chemistry and physical exchange-correlation model constraints leads to the VCML-rVV10 exchange-correlation functional. Owing to the variety of training data, the applicability of VCML-rVV10 extends beyond surface chemistry simulations. It provides optimized gas phase reaction energetics and an accurate description of bulk lattice constants and elastic properties.

Chemical bonding theories as guides for self-interaction corrected solutions: Multiple local minima and symmetry breaking.

Fermi-Löwdin orbitals (FLOs) are a special set of localized orbitals, which have become commonly used in combination with the Perdew-Zunger self-interaction correction (SIC) in the FLO-SIC method. The FLOs are obtained for a set of occupied orbitals by specifying a classical position for each electron. These positions are known as Fermi-orbital descriptors (FODs), and they have a clear relation to chemical bonding. In this study, we show how FLOs and FODs can be used to initialize, interpret, and justify SIC solutions in a common chemical picture, both within FLO-SIC and in traditional variational SIC, and to locate distinct local minima in either of these approaches. We demonstrate that FLOs based on Lewis theory lead to symmetry breaking for benzene-the electron density is found to break symmetry already at the symmetric molecular structure-while ones from Linnett's double-quartet theory reproduce symmetric electron densities and molecular geometries. Introducing a benchmark set of 16 planar cyclic molecules, we show that using Lewis theory as the starting point can lead to artifactual dipole moments of up to 1 D, while Linnett SIC dipole moments are in better agreement with experimental values. We suggest using the dipole moment as a diagnostic of symmetry breaking in SIC and monitoring it in all SIC calculations. We show that Linnett structures can often be seen as superpositions of Lewis structures and propose Linnett structures as a simple way to describe aromatic systems in SIC with reduced symmetry breaking. The role of hovering FODs is also briefly discussed.

MCML: Combining physical constraints with experimental data for a multi-purpose meta-generalized gradient approximation.

The predictive power of density functional theory for materials properties can be improved without increasing the overall computational complexity by extending the generalized gradient approximation (GGA) for electronic exchange and correlation to density functionals depending on the electronic kinetic energy density in addition to the charge density and its gradient, resulting in a meta-GGA. Here, we propose an empirical meta-GGA model that is based both on physical constraints and on experimental and quantum chemistry reference data. The resulting optimized meta-GGA MCML yields improved surface and gas phase reaction energetics without sacrificing the accuracy of bulk property predictions of existing meta-GGA approaches.

porE: A code for deterministic and systematic analyses of porosities.

Accurate numerical calculations of porosities and related properties are of importance when analyzing metal-organic frameworks (MOFs). We present porE, an open-source, general-purpose implementation to compute such properties and discuss all results regarding their sensitivity to numerical parameters. Our code combines the numerical efficiency of Fortran with the user-friendliness of Python. Three different approaches to calculate porosities are implemented in porE, and their advantages and drawbacks are discussed. In contrast to commonly used implementations, our approaches are entirely deterministic and do not require any stochastic averaging. In addition to the calculation of porosities, porE can calculate pore size distributions and offers the possibility to analyze pore windows. The underlying approaches are outlined, and pore windows are discussed concerning their impact on the analyzed porosities. Comparisons with reference values aim for a clear differentiation between void and accessible porosities, which we provide for a small benchmark set consisting of eight MOFs. In addition, our approaches are used for a bigger benchmark set containing 370 MOFs, where we determine linear relationships within our approaches as well as to reference values. We show how these relationships can be used to derive corrections to a give porosity approach, minimizing its mean error. As a highlight we show how complex workflows can be designed with a few lines of Python code using porE.

PyFLOSIC: Python-based Fermi-Löwdin orbital self-interaction correction.

We present pyflosic, an open-source, general-purpose python implementation of the Fermi-Löwdin orbital self-interaction correction (FLO-SIC), which is based on the python simulation of chemistry framework (pyscf) electronic structure and quantum chemistry code. Thanks to pyscf, pyflosic can be used with any kind of Gaussian-type basis set, various kinds of radial and angular quadrature grids, and all exchange-correlation functionals within the local density approximation, generalized-gradient approximation (GGA), and meta-GGA provided in the libxc and xcfun libraries. A central aspect of FLO-SIC is the Fermi-orbital descriptors, which are used to estimate the self-interaction correction. Importantly, they can be initialized automatically within pyflosic; they can also be optimized within pyflosic with an interface to the atomic simulation environment, a python library that provides a variety of powerful gradient-based algorithms for geometry optimization. Although pyflosic has already facilitated applications of FLO-SIC to chemical studies, it offers an excellent starting point for further developments in FLO-SIC approaches, thanks to its use of a high-level programming language and pronounced modularity.

Application of Self-Interaction Corrected Density Functional Theory to Early, Middle, and Late Transition States.

Density functional theory (DFT)-based methods often significantly underpredict chemical reaction barriers compared with experiments because of the tendency of DFT to overstabilize transition states with stretched bonds due to the impact of unphysical electron self-interaction. However, many reactions have early or late transition states where the transition state geometry closely resembles the reactants or products, respectively. The role of self-interaction in those cases is not known. Here we compare the performance of DFT with and without self-interaction correction (SIC) for describing the hydrogenation of CO and CO2 catalyzed by a Lewis acid-base pair incorporated onto an aromatic cluster, using CCSD(T) results for reference. The three elementary steps in these reactions consist of an early, a middle, and a late transition. Our results show that the Perdew-Zunger SIC (PZ-SIC), implemented in the Fermi-Löwdin orbital SIC (FLO-SIC) approach, qualitatively improves the description of the forward and reverse reaction barriers relative to uncorrected DFT for the middle transition but not the early or late transitions. By contrast, the local scaling SIC (LSIC) method, also implemented in the FLO-SIC framework, significantly improves the calculated barriers over DFT and PZ-SIC in all but one case. The results also show how the FLO-SIC approach can provide insight into the bonding in aromatic systems.

Interpretation and Automatic Generation of Fermi-Orbital Descriptors.

We present an interpretation of Fermi-orbital descriptors (FODs) and argue that these descriptors carry chemical bonding information. We show that a bond order derived from these FODs agrees well with reference values, and highlight that optimized FOD positions used within the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method correspond to expectations from Linnett's double-quartet theory, which is an extension of Lewis theory. This observation is independent of the underlying exchange-correlation functional, which is shown using the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA), and the strongly constrained and appropriately normed meta-GGA. To make FOD positions generally accessible, we propose and discuss four independent methods for the generation of Fermi-orbital descriptors, their implementation as well as their advantages and drawbacks. In particular, we introduce a re-implementation of the electron force field, an approach based on the centers of mass of orbital densities, a Monte Carlo-based algorithm, and a method based on Lewis-like bonding information. All results are summarized with respect to future developments of FLO-SIC and related methods. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Stretched or noded orbital densities and self-interaction correction in density functional theory.

Semilocal approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semilocal approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semilocal approximations satisfy, suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus, PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here, in particular, to the strongly constrained and appropriately normed (SCAN) meta-GGA, for which the correlation part is already self-interaction-free. This property makes SCAN a natural first candidate for a generalized SIC.

Analytic atomic gradients in the fermi-löwdin orbital self-interaction correction.

We derived, implemented, and thoroughly tested the complete analytic expression for atomic forces, consisting of the Hellmann-Feynman term and the Pulay correction, for the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method. Analytic forces are shown to be numerically accurate through an extensive comparison to forces obtained from finite differences. Using the analytic forces, equilibrium structures for a small set of molecules were obtained. This work opens the possibility of routine self-interaction free geometrical relaxations of molecules using the FLO-SIC method. © 2018 Wiley Periodicals, Inc.

Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings.

We analyze the effect of removing self-interaction error on magnetic exchange couplings using the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in the framework of density functional theory (DFT). We compare magnetic exchange couplings obtained from self-interaction-free FLOSIC calculations with the local spin density approximation (LSDA) with several widely used DFT realizations and wave function based methods. To this end, we employ the linear H-He-H model system, six organic radical molecules, and [Cu2Cl6]2- as representatives of different types of magnetic interactions. We show that the simple self-interaction-free version of LSDA improves calculated couplings with respect to LSDA in all cases, even though the nature of the exchange interaction varies across the test set, and in most cases, it yields results comparable to modern hybrids and range-separated approximate functionals.

Shrinking Self-Interaction Errors with the Fermi-Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation.

The self-interaction error (SIE) is one of the major drawbacks of practical exchange-correlation functionals for Kohn-Sham density functional theory. Despite this, the use of methods that explicitly remove SIE from approximate density functionals is scarce in the literature due to their relatively high computational cost and lack of consistent improvement over standard modern functionals. In this article we assess the performance of a novel approach recently proposed by Pederson, Ruzsinszky, and Perdew [ J. Chem. Phys. 2014, 140, 121103] for performing self-interaction free calculations in density functional theory based on Fermi orbitals. To this end, we employ test sets consisting of reaction energies that are considered particularly sensitive to SIE. We found that the parameter-free Fermi-Löwdin orbital self-interaction correction method combined with the standard local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) functionals gives a much better estimate of reaction energies compared to their parent LSDA and PBE functionals for most of the reactions in these two sets. They also perform on par with the global PBE0 and range-separated LC-ωPBE hybrids, which partially eliminate the SIE by including Hartree-Fock exchange. This shows the potential of the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for practical density functional calculations without SIE.

Fermi-Löwdin orbital self-interaction corrected density functional theory: Ionization potentials and enthalpies of formation.

The Fermi-Löwdin orbital self-interaction correction (FLO-SIC) methodology is applied to atoms and molecules from the standard G2-1 test set. For the first time FLO-SIC results for the GGA-type PBE functional are presented. In addition, examples where FLO-SIC like any proper SIC provides qualitative improvements compared to standard DFT functionals are discussed in detail: the dissociation limit for H 2 + , the step-wise linearity behavior for fractional occupation, as well as the significant reduction of the error of static polarizabilities. Further, ionization potentials and enthalpies of formation obtained by means of the FLO-SIC DFT method are compared to other SIC variants and experimental values. The self-interaction correction gives significant improvements if used with the LDA functional but shows worse performance in case of enthalpies of formation if the PBE-GGA functional is used. The errors are analyzed and the importance of the overbinding of hydrogen is discussed. © 2018 Wiley Periodicals, Inc.

Theoretical and experimental investigations of 129Xe NMR chemical shift isotherms in metal-organic frameworks.

The pressure dependence of the 129Xe chemical shift in the metal-organic frameworks (MOFs) UiO-66 and UiO-67 (UiO - University of Oslo) has been investigated using both theory and experiment. The resulting chemical shift isotherms were analyzed with a theoretical approach based on model systems (as proposed by K. Trepte, J. Schaber, S. Schwalbe, F. Drache, I. Senkovska, S. Kaskel, J. Kortus, E. Brunner and G. Seifert, Phys. Chem. Chem. Phys., 2017, 19, 10020-10027) and experimental 129Xe NMR measurements at different pressures. All investigations were carried out at T = 237 K while the pressure range was chosen according to the maximum pressure at which Xe liquifies (p0 = 1.73 MPa or 17.3 bar), thus 0 < p ≤ p0. The theoretically predicted chemical shift isotherms agree well with the experimental ones. Additionally, a comparison of the chemical shift isotherms with volumetric adsorption isotherms was carried out to determine the similarities and differences of both isotherms.

On the Question of the Total Energy in the Fermi-Löwdin Orbital Self-Interaction Correction Method.

The Fermi-Löwdin orbital self-interaction correction (FLOSIC) formalism is a novel method for implementing the Perdew-Zunger self-interaction correction (PZ-SIC) in density functional theory calculations. In this paper we consider how the use of Fermi orbitals affects total energies and other calculated properties compared to a standard approach to PZ-SIC that utilizes the localization equation conditions. We directly compare the results of the two methods using identical basis sets and numerical techniques in calculations for isolated atoms up to Kr and for a large test set of molecules. We find differences in total energies that increase with increasing atomic number and show that these differences can be traced to a less negative SIC correction for the 1s orbital in FLOSIC. Importantly, energies for highest occupied orbitals and molecular atomization energies are nearly identical in the two methods.

The origin of the measured chemical shift of 129Xe in UiO-66 and UiO-67 revealed by DFT investigations.

The NMR chemical shift of the xenon isotope 129Xe inside the metal-organic frameworks (MOFs) UiO-66 and UiO-67 (UiO - University of Oslo) has been investigated both with density functional theory (DFT) and in situ high-pressure 129Xe NMR measurements. The experiments reveal a decrease of the total chemical shift comparing the larger isoreticular MOF (UiO-67) with the smaller one (UiO-66), even though one may expect an increase due to the higher amount of adsorbed Xe atoms. We are able to calculate contributions to the chemical shift individually. This allows us to evaluate the shift inside the different pores independently. To compare the theoretical results with the experimental ones, we performed molecular dynamics simulations of Xe in the MOFs. For this purpose, the pores were completely filled with Xe to gain insight into the distribution of Xe at high pressures. The resulting trend of the total shift agrees well between the theoretical predictions and the experiments. Moreover, we are able to describe specific contributions to the total shift per pore, explaining the experimental behavior at an atomistic level.

NiII formate complexes with bi- and tridentate nitrogen-donor ligands: synthesis, characterization, and magnetic and thermal properties.

The synthesis of four NiII formate complexes of the type [Ni(N∩N)n][O2CH]2 (2, adduct with 3/4 EtOH, N∩N = en, e[combining low line]thylen[combining low line]ediamine, n = 3; 4, N∩N = dien, N,N',N''-d[combining low line]i[combining low line]e[combining low line]thylen[combining low line]etriamine, n = 2), [Ni2(O2CH)4(H2O)(tmeda)2] (3, tmeda = N,N,N',N'-t[combining low line]etram[combining low line]ethyle[combining low line]thylened[combining low line]ia[combining low line]mine) and [{Ni(O2CH)2(pmdta)}2·H2O] (5, pmdta = N,N',N',N'',N''-p[combining low line]entam[combining low line]ethyld[combining low line]iethylenet[combining low line]ria[combining low line]mine) by a reaction of [{Ni(O2CH)2}·2H2O] (1) with the respective N-donor bases is reported. The structures of 2-5 in the solid state were determined by single X-ray structure analysis, revealing a discrete dinuclear structure of 3 and the formation of polymeric networks in the case of 2, 4 and 5 due to intermolecular hydrogen bonding. SQUID and ESR measurements of 3 evidenced a weak antiferromagnetic coupling between the NiII ions and an easy plane magnetic anisotropy. Accompanying quantum chemical studies of the magnetic properties and IR characteristics of 3 were performed to strengthen the conclusions drawn from experimentally obtained data. The thermal decomposition temperatures of 2-5 were determined by TG (thermogravimetry) and obtained residues were analyzed by PXRD (powder X-ray diffraction) measurements. The decomposition processes were completed at 207 (3), 215 (5), 250 (2) and 273 °C (4) and are shown to result in the formation of pure metallic nickel.

Screening for high-spin metal organic frameworks (MOFs): density functional theory study on DUT-8(M1,M2) (with Mi = V, ,Cu).

We present a first principles study of low-spin (LS)/high-spin (HS) screening for 3d metal centers in the metal organic framework (MOF) DUT-8(Ni). Various density functional theory (DFT) codes have been used to evaluate numerical and DFT related errors. We compare highly accurate all-electron implementations with the widely used plane wave approach. We present electronically and magnetically stable DUT-8(Ni) HS secondary building units (SBUs). In this work we show how to tune the magnetic and electronic properties of the original SBU only by changing the metal centers.

Correction: Electronic and magnetic properties of DUT-8(Ni).

Correction for 'Electronic and magnetic properties of DUT-8(Ni)' by Kai Trepte et al., Phys. Chem. Chem. Phys., 2015, 17, 17122-17129.