Orbital energy analysis with respect to LDA and self-interaction corrected exchange-only potentials

Computational tools to study non-covalent interactions and confinement effects in chemical systems

Confinement is a very common phenomenon in chemistry, for example, when molecules are located inside cavities. In these conditions, the electronic structure of atoms and molecules is modified. These changes could be mapped through the interaction with other molecules since non-covalent interactions between molecules are also influenced by confinement. In this work we address both topics, non-covalent interactions, and confined systems, using quantum chemistry tools with new software, emphasizing the importance of analyzing both fields simultaneously.

The Exchange-Correlation Effects on the Electronic Bands of Hybrid Armchair Single-Walled Carbon Boron Nitride Nanostructure

This study investigates the effect of exchange-correlation on the electronic properties of hybridized hetero-structured nanomaterials, called single-walled carbon boron nitride nanotubes (SWCBNNT). A first principles (ab initio) method implemented in Quantum ESPRESSO codes, together with different parametrizations (local density approximation (LDA) formulated by Perdew Zunga (PZ) and the generalized gradient approximation (GGA) proposed by Perdew–Burke–Ernzerhof (PBE) and Perdew–Wang 91 (PW91)), were used in this study. It has been observed that the disappearance of interface states in the band gap was due to the discontinuity of the π–π bonds in some segments of SWCNT, which resulted in the asymmetric distribution in the two segments. This work has successfully created a band gap in SWCBNNT, where the PBE exchange-correlation functional provides a well-agreed band gap value of 1.8713 eV. Effects of orbitals on electronic properties have also been studied elaborately. It has been identified that the Py orbital gives the largest contribution to the electrical properties of our new hybrid SWCBNNT nanostructures. This study may open a new avenue for tailoring bandgap in the hybrid heterostructured nanomaterials towards practical applications with next-generation optoelectronic devices, especially in LED nanoscience and nanotechnology.

How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations?

We examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys., 2018, 20, 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew-Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi-Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys., 2019, 151, 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.

Local self-interaction correction method with a simple scaling factor

The local self-interaction correction method with a simple scaling factor performs better than the Perdew-Zunger self-interaction correction method and also provides a good description of the binding energies of weakly bonded water clusters. 

NWChem: Past, present, and future

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.

Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional

Despite the success of density functional approximations (DFAs) in describing the electronic properties of many-electron systems, the most widely used approximations suffer from self-interaction errors (SIEs) that limit their predictive power. Here, we describe the effects of removing SIE from the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation using the Fermi-Löwdin Orbital Self-Interaction Correction (FLOSIC) method. FLOSIC is a size-extensive implementation of the Perdew-Zunger self-interaction correction (PZ-SIC) formalism. We find that FLOSIC-SCAN calculations require careful treatment of numerical details and an integration grid that yields reliable accuracy with this approach. We investigate the performance of FLOSIC-SCAN for predicting a wide array of properties and find that it provides better results than FLOSIC-LDA and FLOSIC-PBE in nearly all cases. It also gives better predictions than SCAN for orbital energies and dissociation energies where self-interaction effects are known to be important, but total energies and atomization energies are made worse. For these properties, we also investigate the use of the self-consistent FLOSIC-SCAN density in the SCAN functional and find that this DFA@FLOSIC-DFA approach yields improved results compared to pure, self-consistent SCAN calculations. Thus, FLOSIC-SCAN provides improved results over the parent SCAN functional in cases where SIEs are dominant, and even when they are not, if the SCAN@FLOSIC-SCAN method is used.

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.

Using Wannier functions to improve solid band gap predictions in density functional theory

Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional electrons on Wannier functions constructed within the occupied/unoccupied subspaces. It removes the self-interaction energies of those Wannier functions, and yields accurate band gaps for solids compared to experiments. It does not have any adjustable parameters and the computational cost is at the DFT level. This method can also work for molecules, providing eigen energies in good agreement with experimental ionization potentials and electron affinities. Our approach can be viewed as an alternative approach of the standard LDA+U procedure.

Local-density approximation for orbital densities applied to the self-interaction correction

A simple approximation to the functional derivative of Perdew-Zunger-type self-interaction-corrected local-spin density functional is suggested. In this approach, the orbital density |phi(isigma)(r)|(2) is regarded as a functional of the local electron density |phi(isigma)(r)|(2)=n(isigma)(n(sigma)(r)) so as to enable a functional derivative of n(isigma)(n(sigma)(r)) with respect to n(sigma)(r). Our computational results show that this approximation gives fairly good estimates of the total energy, the ionization potential, and the electron affinity for atoms. Comparative studies of this method with the averaged-density approximation and the global averaging method for the self-interaction correction are made.

Core ionization potentials from self-interaction corrected Kohn-Sham orbital energies

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the "DeltaKohn-Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter alpha is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique alpha=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.

Substituent effect on a family of quinones in aprotic solvents: an experimental and theoretical approach

In this work a comparison between redox potentials, obtained by constructing current-potential plots from chronoamperometric measurements, and the parameter sigma(x), as proposed by Zuman in terms of the Hammett substituent parameters, was performed for several quinone compounds. This study shows the limitations of this approach and proves that methods based on quantum chemistry can be used to study the substituent effect in quinone systems. By using the Density Functional Theory, in the Kohn-Sham context with three exchange-correlation functionals, BLYP, B3LYP, and BHLYP, it was found that the electron affinity is good enough to give a useful relationship with experimental redox potentials of quinone systems. This conclusion is reached when the basis set functions involve diffuse functions, and also when the Hartree-Fock exchange energy is included in the exchange-correlation functional. The Fukui function, to describe preferential sites involved at initial stages of a system that bind an electron, is analyzed when electron donor and electron acceptor groups are present as substituents in quinone systems. The methods applied in this work are valid for any kind of quinone compound and will be used in further analysis of the electron reorganization in semiquinone species.

Accurate Calculation of Absolute One-Electron Redox Potentials of Somepara-Quinone Derivatives in Acetonitrile

Standard ab initio molecular orbital theory and density functional theory calculations have been used to calculate absolute one-electron reduction potentials of several para-quinones in acetonitrile. The high-level composite method of G3(MP2)-RAD is used for the gas-phase calculations and a continuum model of solvation, CPCM, has been employed to calculate solvation energies. To compare the theoretical reduction potentials with experiment, the reduction potentials relative to a standard calomel electrode (SCE) have also been calculated and compared to experimental values. The average error of the calculated reduction potentials using the proposed method is 0.07 V without any additional approximation. An ONIOM method in which the core is studied at G3(MP2)-RAD and the substituent effect of the rest of the molecule is studied at R(O)MP2/6-311+G(3df,2p) provides an accurate low-cost alternative to G3(MP2)-RAD for larger molecules.

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.

Bulky alkylphosphines with neopentyl substituents as ligands in the amination of aryl bromides and chlorides

Di(tert-butyl)neopentylphosphine (DTBNpP) in combination with palladium sources provided catalysts with comparable or better activity for the Hartwig-Buchwald amination of aryl bromides than tri(tert-butyl)phosphine (TTBP) under mild conditions. DTBNpP also provided effective catalysts for amination reactions of aryl chlorides at elevated temperatures. Further replacement of tert-butyl groups with neopentyl substituents resulted in less effective ligands for amination reactions. Computationally derived cone angles showed that replacement of a tert-butyl group with a neopentyl group significantly increased the cone angle of the phosphine. The larger cone angle of DTBNpP than TTBP appears to correlate with the higher activity of catalysts derived from DTBNpP in the amination of aryl bromides. TTBP is a stronger electron donor than DTBNpP, which may explain the higher activity for TTBP-derived catalysts toward aryl chlorides.

Spectroscopy and Rectification of Three Donor−Sigma−Acceptor Compounds, Consisting of a One-Electron Donor (Pyrene or Ferrocene), a One-Electron Acceptor (Perylenebisimide), and a C19 Swallowtail

We report spectroscopic characterization and unimolecular rectification (asymmetric electrical conduction) measurements of three donor-sigma-acceptor (D-sigma-A) compounds N-(10-nonadecyl)-N-(1-pyrenylmethyl)perylene-3,4,9,10-bis(dicarboximide) (1), N-(10-nonadecyl)-N-(4-[1-pyrenyl]butyl)perylene-3,4,9,10-bis(dicarboximide) (2), and N-(10-nonadecyl)-N-(2-ferrocenylethyl)perylene-3,4,9,10-bis(dicarboximide) (3). These molecules were arranged as one-molecule thick Langmuir-Blodgett monolayers between Au electrodes. In such an "Au | D-sigma-A | Au" sandwich, molecule 1 is a unimolecular rectifier, with rather small rectification ratios (between 2 and 3 at +/-1 V) that decrease upon cycling. Molecule 2 does not rectify. Molecule 3 rectifies, with a rectification ratio of between 14 and 28 at +/-1 V; the through-film rectification and currents persist, even with scans of +/-2 V, for up to 40 cycles of measurement. Qualitative arguments, based on a two-level rectification mechanism, are consistent with the current asymmetries observed in the monolayers of 1 and 3.

Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

Calculation including the electron correlation effects is reported for the ground 1 1S and lowest triplet 1 3S state energies of the confined helium atom placed at the center of an impenetrable spherical box. While the adopted wave-functional treatment involves optimization of three nonlinear parameters and 10, 20, and 40 linear coefficients contained in wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r12, via a Slater-type exponent and through polynomial terms entering the expansion, the Kohn-Sham model employed here uses the Perdew and Wang exchange-correlation functional in its spin-polarized version within the local-density approximation (LDA) with and without the self-interaction correction. All these calculations predict a systematic increase in the singlet-triplet energy splitting toward the high confinement regime, i.e., when the box radius is reduced. By using the variational results as benchmark, it is found that the LDA underestimates the singlet-triplet energy splitting, whereas the self-interaction correction overestimates such a quantity.

Electronic Structure of the Hydroxo and Methoxo Oxometalate Anions MO3(OH)- and MO3(OCH3)- (M = Cr, Mo, and W)

The electronic structure of the mononuclear hydroxo MO3(OH)- and methoxo MO3(OCH3)- Group 6 oxometalate anions (M = Cr, Mo, and W) were examined by photodetachment photoelectron spectroscopy and electronic structure calculations at the density functional and CCSD(T) levels of theory. All of the anions exhibited high electron binding energies (>4.9 eV), with the lowest-energy detachment features arising from oxygen 2p-based orbitals. The combined experimental and theoretical results allowed the change in molecular orbital energy levels to be investigated as a function of metal (Cr, Mo, or W) and ligand (-OH, -OCH3). A number of fundamental thermodynamic properties of the anions and corresponding neutrals were predicted on the basis of the theoretical calculations. The calculations indicate high O-H bond dissociation energies for MO2(OR)(O-H) (R = H, CH3) and MO3(O-H), consistent with their high Brønsted acidities (just below that of H2SO4 in the gas phase) and the high ionization energies of their conjugate base anions. This suggests that the corresponding radicals should readily abstract H atoms from organic molecules.

Ionization potentials and electron affinities in the Perdew–Zunger self-interaction corrected density-functional theory

Using a self-consistent implementation of the Perdew-Zunger self-interaction corrected (PZ-SIC) density-functional theory, we have calculated ionization potentials (IP) and electron affinities (EA) of first- and second-row atoms and a set of small molecules. Several exchange-correlation functionals were tested. IPs and EAs were obtained by two methods: as the difference in self-consistent field (SCF) energies of neutrals and ions (deltaSCF) and as negatives of highest-occupied orbital energies. We found that, except for local spin-density approximation, PZ-SIC worsens DeltaSCF IPs and EAs. On the other hand, PZ-SIC brings orbital eigenvalues into much better agreement with electron removal energies. The Perdew-Zunger SIC seems to over-correct many-electron systems; for molecules it performs worse than for atoms. We also discuss several common approximations to PZ-SIC such as spherical averaging of orbital densities in atoms.

Basis set effects on frontier molecular orbital energies and energy gaps: A comparative study between plane waves and localized basis functions in molecular systems

In order to study the Kohn-Sham frontier molecular orbital energies in the complete basis limit, a comparative study between localized functions and plane waves, obtained with the local density approximation exchange-correlation functional is made. The analyzed systems are ethylene and butadiene, since they are theoretical and experimentally well characterized. The localized basis sets used are those developed by Dunning. For the plane-waves method, the pseudopotential approximation is employed. The results obtained by the localized basis sets suggest that it is possible to get an estimation of the orbital energies in the limit of the complete basis set, when the basis set size is large. It is shown that the frontier molecular orbital energies and the energy gaps obtained with plane waves are similar to those obtained with a large localized basis set, when the size of the supercell and the plane-wave expansion have been appropriately calibrated.

The impact of the self-interaction error on the density functional theory description of dissociating radical cations: Ionic and covalent dissociation limits

Self-interaction corrected density functional theory was used to determine the self-interaction error for dissociating one-electron bonds. The self-interaction error of the unpaired electron mimics nondynamic correlation effects that have no physical basis where these effects increase for increasing separation distance. For short distances the magnitude of the self-interaction error takes a minimum and increases then again for decreasing R. The position of the minimum of the magnitude of the self-interaction error influences the equilibrium properties of the one-electron bond in the radical cations H2+ (1), B2H4+ (2), and C2H6+ (3), which differ significantly. These differences are explained by hyperconjugative interactions in 2 and 3 that are directly reflected by the self-interaction error and its orbital contributions. The density functional theory description of the dissociating radical cations suffers not only from the self-interaction error but also from the simplified description of interelectronic exchange. The calculated differences between ionic and covalent dissociation for 1, 2, and 3 provide an excellent criterion for determining the basic failures of density functional theory, self-interaction corrected density functional theory, and other methods. Pure electronic, orbital relaxation, and geometric relaxation contributions to the self-interaction error are discussed. The relevance of these effects for the description of transition states and charge transfer complexes is shown. Suggestions for the construction of new exchange-correlation functionals are given. In this connection, the disadvantages of recently suggested self-interaction error-free density functional theory methods are emphasized.

Effect of the Perdew–Zunger self-interaction correction on the thermochemical performance of approximate density functionals

The Perdew-Zunger self-interaction-corrected density functional theory (SIC-DFT) was implemented self-consistently using a quasi-Newton direct minimization method. We calculated SIC-DFT energies for a number of atoms and molecules using various approximate density functionals, including hybrids. Self-interaction errors (SIE) of these functionals were compared and analyzed in terms of contributions from valence and core orbitals. We also calculated enthalpies of formation of the standard G2-1 set of 55 molecules and found that self-interaction-correction (SIC) improves agreement with experiment only for the LSDA functional, while all other functionals show worse performance upon introducing SIC. This is the first systematic study of the effect of SIC on thermochemical properties. We found no direct connection between the magnitude of the SIE contained in a functional and its performance for thermochemistry. Approximate functionals with large self-interaction errors can accurately reproduce enthalpies of formation. Our results do not support the popular belief that a smaller SIE of hybrid functionals is the main reason for their higher accuracy.