Hartree-Fock Density Functional Theory Research Articles

Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights.

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree-Fock electron densities, which has been known for ∼30 years. The conventional explanation is that the Hartree-Fock theory yields the more accurate density. This work presents a benchmark Kohn-Sham inversion of accurate coupled-cluster densities for the reaction H2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree-Fock density functional theory. This confirms earlier conclusions (Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532-543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.

Corrected density functional theory and the random phase approximation: Improved accuracy at little extra cost.

We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory [DC(HF)-DFT] calculations and an extension to it we called "corrected" HF DFT [C(HF)-DFT] [Graf and Thom, J. Chem. Theory Comput. 19 5427-5438 (2023)]. In this work, we take a further step and combine C(HF)-DFT, augmented with a straightforward orbital energy correction, with the random phase approximation (RPA). We refer to the resulting methodology as corrected HF RPA [C(HF)-RPA]. We evaluate the proposed methodology across various RPA methods: direct RPA (dRPA), RPA with an approximate exchange kernel, and RPA with second-order screened exchange. C(HF)-dRPA demonstrates very promising performance; for RPA with exchange methods, on the other hand, we often find over-corrections.

Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory.

The crucial step in density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) is to decide whether the density produced by the density functional for a specific calculation is erroneous and, hence, should be replaced by, in this case, the HF density. We introduce an indicator, based on the difference in noninteracting kinetic energies between DFT and HF calculations, to determine when the HF density is the better option. Our kinetic energy indicator directly compares the self-consistent density of the analyzed functional with the HF density, is size-intensive, reliable, and most importantly highly efficient. Moreover, we present a procedure that makes best use of the computed quantities necessary for DC(HF)-DFT by additionally evaluating a related hybrid functional and, in that way, not only "corrects" the density but also the functional itself; we call that procedure corrected Hartree-Fock density functional theory (C(HF)-DFT).

Polyaniline grafted pullulan: Optical, thermal, structural, and electrical characterization studies in combination withdensity functional theorycalculations

AbstractPolyaniline (PANI), a conducting polymer, has great interest for a large number of applications. However, poor processability and mechanical properties limits its usage and many methods like blending, grafting etc. are used to overcome this disadvantage. We have carried out grafting of PANI onto pullulan (PULL) via chemical oxidative polymerization technique. The percentage of grafting is favored by increasing concentration of aniline monomer. The formation of PANI is confirmed through UV–Vis spectroscopic studies. The possible grafting mechanism is studied using Fourier transform infrared spectroscopy and validated by Hartree‐Fock density functional theory (HF‐DFT) calculations. Further, thermal properties of grafted polymers are studied using differential scanning calorimetry and thermo gravimetric analysis. Using FESEM and x‐ray diffraction, structural properties of graft polymer were studied. DC electrical conductivity of grafted polymer is measured from I‐V characteristics, shows a significant conductivity which is the highlight of this work.

The role of symmetry-breaking strains on quartz inclusions in anisotropic hosts: Implications for Raman elastic geobarometry

Raman elastic geobarometry for mineral host-inclusion systems is used to determine the strains acting on an inclusion still entrapped in its host by measuring its Raman wavenumber shifts which are interpreted through the phonon-mode Grüneisen tensors of the inclusion phase. The calculated inclusion strains can then be used in an elastic model to calculate the pressure and temperature conditions of entrapment. This method is applied frequently to host inclusion systems where the host is almost elastically isotropic (e.g. garnet) and the inclusion is elastically anisotropic (e.g. quartz and zircon). In this case, when the entrapment occurs under hydrostatic conditions the host will impose isotropic strains on the inclusion which in turn will develop non-hydrostatic stress. In this scenario the symmetry of the inclusion mineral is preserved and the strains in the inclusion can be measured via Raman spectroscopy using the phonon-mode Grüneisen tensor approach. However, a more complex situation arises when the host-inclusion system is fully anisotropic, such as when a quartz inclusion is entrapped within a zircon host, because the symmetry of the inclusion can be broken due to the external anisotropic strain field imposed on the inclusion by the host, which in turn will modify the phonon modes. We therefore calculated the strain states of quartz inclusions entrapped in zircon hosts in multiple orientations and at various geologically relevant pressure and temperature conditions. We then performed ab initio Hartree-Fock/Density Functional Theory (HF/DFT) simulations on α-quartz in these strain states. These HF/DFT simulations show that the changes in the positions of the Raman modes produced by strains that are expected for symmetry broken quartz inclusions in zircon are generally similar to those that would be seen if the quartz inclusions remained truly trigonal in symmetry. Therefore, the use of the trigonal phonon-mode Grüneisen tensor to determine the inclusion strains does not lead to geologically significant errors in calculated quartz inclusion entrapment pressures in zircon. • Mineral inclusions in anisotropic hosts can be subject to symmetry-breaking strains. • Symmetry-breaking strains modify the Raman spectrum of quartz. • Applicability of the trigonal Grüneisen tensor to symmetry-broken quartz is tested. • Entrapment pressures from the isotropic elastic model are in error by <0.185 GPa. • Entrapment pressures from the anisotropic elastic model are in error by <0.034 GPa.

Topochemical Synthesis of LiCoF3 with a High-Temperature LiNbO3-Type Structure.

A novel perovskite fluoride, LixCoF3, which has an exceptionally low tolerance factor (0.81), has been synthesized via low-temperature lithium intercalation into a distorted ReO3-type fluoride CoF3 using organolithium reagents. Interestingly, this reaction is completed within 15 min at room temperature. Synchrotron X-ray diffractometry and optical second harmonic generation at room temperature have revealed that this compound shows a high-temperature LiNbO3-type structure (space group: R3̅c) involving Li-Co antisite defects and A-site splitting along the c direction. A-site splitting is consistent with the prediction based on hybrid Hartree-Fock density functional theory calculations. Co-L2,3 edge X-ray absorption spectroscopy, as well as bond valence sum analysis, has verified the divalent oxidation state of Co ions in the lithiated phase, suggesting that its composition is close to LiCoF3 (x ≈ 1). This compound exhibits a paramagnetic-to-antiferromagnetic transition at 36 K on cooling, accompanied by weak ferromagnetic ordering. The synthetic route based on low-temperature lithiation of metal fluorides host paves the way for obtaining a new LiNbO3-type fluoride family.

Measuring Density-Driven Errors Using Kohn-Sham Inversion.

Kohn-Sham (KS) inversion, that is, the finding of the exact KS potential for a given density, is difficult in localized basis sets. We study the precision and reliability of several inversion schemes, finding estimates of density-driven errors at a useful level of accuracy. In typical cases of substantial density-driven errors, Hartree-Fock density functional theory (HF-DFT) is almost as accurate as DFT evaluated on CCSD(T) densities. A simple approximation in practical HF-DFT also makes errors much smaller than the density-driven errors being calculated. Two paradigm examples, stretched NaCl and the HO·Cl- radical, illustrate just how accurate HF-DFT is.

Treatment of pharmaceutical wastewater by heterogeneous Fenton process: an innovative approach

With indiscriminate use and disposal, antibiotics enter the water bodies and thus are categorized as emerging pollutants. We report the studies on the degradation of norfloxacin, a well-known antibiotic, using hydrogen peroxide (H2O2) and zinc oxide nanoparticles (ZnO) by heterogeneous Fenton process in the presence of sunlight. We fabricated ZnO nanoparticles by hydrothermal method. The geometry of norfloxacin was optimized using Hartree–Fock density functional theory. We used UV–Vis spectroscopy, X-ray diffraction, scanning electron microscopy and transmission electron microscopy techniques to determine various crystal properties, i.e., structure, morphology, size and shape of the ZnO nanoparticles. However, we evaluated the crystal size, particle size and their distribution employing Debye–Scherrer equation and ImageJ processing. The catalytic efficacy of ZnO nanoparticles was assessed by the abatement of norfloxacin at pH 10. The activity and stability of used ZnO catalyst for norfloxacin degradation were established. The recovered catalyst is reusable up to six times without activity loss. Liquid chromatography–mass spectrometry analysis confirmed the presence of various intermediates. A probable reaction mechanism for degradation of norfloxacin is proposed. The ZnO-catalyzed heterogeneous Fenton process proves to be the ideal approach for the degradation of antibiotics in wastewater. Herein, we report that generation of hydroxyl radical by the action of sunlight along with ZnO nanoparticles from hydrogen peroxide effectively degrades norfloxacin. Its structure has been optimized by density functional theory using Gauss view computational software. ZnO nanoparticles have been characterized by various techniques, e.g., XRD, SEM, TEM, etc. Various intermediate products have been recognized by LCMS analysis.

Hypernuclear stars from relativistic Hartree-Fock density functional theory

The hypernuclear matter is studied within the relativistic Hartree-Fock theory employing several parametrizations of the hypernuclear density functional with density-dependent couplings. The equations of state and compositions of hypernuclear matter are determined for each parametrization and compact stars are constructed by solving their structure equations in spherical symmetry. We quantify the softening effect of Fock terms on the equation of state, as well as discuss the impact of tensor interactions, which are absent in the Hartree theories. Starting from models of density functionals which are fixed in the nuclear sector to the nuclear phenomenology, we vary the couplings in the hyperonic sector around the central values which are fitted to the hyperon potentials in nuclear matter. We use the SU(6) spin-flavor and SU(3) flavor symmetric quark models to relate the hyperonic couplings to the nucleonic ones. We find, consistent with previous Hartree studies, that for the SU(6) model the maximal masses of compact stars are below the two-solar mass limit. In the SU(3) model we find sufficiently massive compact stars with cores composed predominantly of $\Lambda$ and $\Xi$ hyperons and a low fraction of leptons (mostly electrons). The parameter space of the SU(3) model is identified where simultaneously hypernuclear compact stars obey the astrophysical limits on pulsar masses and the empirical hypernuclear potentials in nuclear matter are reproduced.

Pressure stability field of Mg-perovskite under deep mantle conditions: A topological approach based on Bader's analysis coupled with catastrophe theory

The pressure stability field of the Mg-perovskite phase was investigated by characterizing the evolution of the electron arrangement in the crystal. Ab initio calculations of the perovskite structures in the range 0–185 GPa were performed at the HF/DFT (Hartree-Fock/Density Functional Theory) exchange–correlation terms level. The electron densities, calculated throughout the ab-initio wave functions, were analysed by means of the Bader's theory, coupled with Thom's catastrophe theory. To the best of our knowledge the approach is used for the first time. The topological results show the occurrence of two topological anomalies at P~20 GPa and P~110 GPa which delineate the pressure range where Mg-perovskite is stable.The paper accomplishes the twofold objectives of providing a contribution in shading light into the behaviour of the dominant component of the Earth's lower mantle across the D’’ layer and of proposing a novel approach in predicting the stability of a compound at extreme conditions.

Experimental and Theoretical Insights into Influence of Hydrogen and Nitrogen Plasma on the Water Splitting Performance of ALD Grown TiO2 Thin Films

Specific effects of hydrogen and nitrogen plasma treatment on anatase TiO2 photoanodes, grown via atomic layer deposition (ALD), and their respective impact on water splitting properties are reported. ALD grown TiO2 samples were exposed to reactive hydrogen and nitrogen plasmas and the photoelectrochemical efficiency of the modified samples were comparatively analyzed. Both H2 and N2 plasma treatment enhanced the photocurrent values compared to pristine TiO2. Electron density at oxygen vacancy sites was decreased upon nitrogen incorporation, reflected in band gap modulation and decreased recombination probability as confirmed by spectral data. Surface modification via H2 plasma induce more midgap states to augment the photoinduced charge carriers concentration that was supported by theoretical investigation performed on the electronic properties of both H- and N-doped TiO2 (anatase). First-principles calculations based on Hartree–Fock–Density Functional Theory (HF–DFT) hybrid models showed good agreement ...

Unusual Metallic Multiferroic Transitions in Electron‐Doped PbTiO3

The coexistence of some materials which are normally in mutually exclusive states is attracting considerable attention as an intriguing means of obtaining nontrivial physical phenomena and unconventional multifunctional substances. Although single‐phase materials endowed with integrated ferroelectric, magnetic, and optical multifunctions hold promise for new technological paradigms, the mutually exclusive mechanisms within ferroelectricity, conductivity, and magnetism hinder the discovery of conducting multiferroics. Here, a new path toward metallic multiferroics is provided by theoretically demonstrating the possible compatible nature of ferroelectric distortion, free carriers, and magnetism in electron‐doped PbTiO3 using the hybrid Hartree–Fock density functional theories. Doping with electrons is found to induce metallic conductivity that coexists with and even enhances the ferroelectric distortion in PbTiO3, due to the unique lone‐pair ferroelectricity in this material. The injected excess electrons, in spin‐polarized states, interact with one another in the plane perpendicular to the polar direction, resulting in layer‐arranged ferromagnetism and multiferroics with nonlinear magnetoelectric coupling. These results indicate a means of circumventing conventional restrictions, leading to new types of multifunctional materials in which unusual multiferroic and conductive characteristics are simultaneously present.

Multiferroic nature of intrinsic point defects inBiFeO3: A hybrid Hartree-Fock density functional study

To achieve a fundamental understanding of the multiferroic behavior and electronic properties of intrinsic vacancies in $\mathrm{BiFe}{\mathrm{O}}_{3}$, here we performed first-principles calculations based on hybrid Hartree-Fock density functional theories, which can accurately describe defect electronic structures. Oxygen vacancies, which behave as deep donors with high concentrations under oxygen-poor conditions, reduce the magnetic moments at neighboring Fe ions in the neutral state, while charged oxygen vacancies induce additional ferroelectric polarizations. Cation vacancies, on the other hand, are likely to form under oxygen-rich conditions and result in multiferroic properties distinct from those induced by oxygen vacancies. Bi vacancies act as triple-shallow acceptors and strongly suppress spontaneous polarization regardless of charge states, while Fe vacancies locally interfere with both electric and spin polarization and are thus regarded as multiferroic singular points in $\mathrm{BiFe}{\mathrm{O}}_{3}$. A rich variety of the multiferroic behavior of vacancies can be systematically understood from the localized/delocalized features of defect states, and the different formation conditions for vacancies provide a strategy to tailor the multiferroic properties of $\mathrm{BiFe}{\mathrm{O}}_{3}$ through control of the concentration and charge states of vacancies.

Mixed pentele-chalcogen cationic chains from aluminum and gallium halide melts.

The reactions of tellurium or selenium with bismuth or antimony in chloridogallate and iodidoaluminate melts in the presence of group 15 trihalides as weak oxidants yielded the compounds (Sb2Te2)[GaCl4] (1), (Sb2Te2)I[AlI4] (2), (Bi2Te2)Cl[GaCl4] (3a), (Bi2Se2)Cl[GaCl4] (3b), (Sb3Te4)[GaCl4] (4), and (SbTe4)[Ga2Cl7] (5). In the crystal structures one-dimensional polymeric cations (Sb2Te2(+))n (1), (Sb2Te2(2+))n (2), (Bi2Te2(2+))n (3a), (Bi2Se2(2+))n (3b), (Sb3Te4(+))n (4), and (SbTe4(+))n (5) are present. The polymeric cationic strands in 2, 3a, 3b, and 4 consist of pentele/chalcogen dumbbells, which are connected to ladder-shaped bands. The strands in 1 and 5 consist of condensed rings that involve four-membered Sb2Te2 rings for 1, and five-membered SbTe4 rings for 5. The counteranions are the weakly coordinating [GaCl4](-), [AlI4](-), and [Ga2Cl7](-) in addition to Cl(-) and I(-) anions, which are coordinated to the atoms of the cations. The crystal structures of 1-4 are characterized by a statistical disorder in the anions with alternatively occupied positions for the Al and Ga atoms. For 4 superstructure reflections appear in the diffractions patterns, indicating a partial order. A correct assignment of the Sb and Te positions in the cation of 5 was achieved by periodic quantum-chemical calculations, which were performed via a Hartree-Fock density functional theory hybrid method. A clear preference of the 4-fold coordinated site was obtained for Sb.

Vibrational analysis using FT-IR, FT-Raman spectra and HF–DFT methods and NBO, NLO, NMR, HOMO–LUMO, UV and electronic transitions studies on 2,2,4-trimethyl pentane

In this work, the vibrational spectral analysis was carried out by using Raman and infrared spectroscopy in the range 100–4000cm−1and 50–4000cm−1, respectively, for 2,2,4-Trimethyl Pentane, TMP (C8H18) molecule. The molecular structure, fundamental vibrational frequencies and intensity of the vibrational bands are interpreted with the aid of structure optimizations and geometrical parameter calculations based on Hartree Fock (HF) and density functional theory (DFT) method with 6-311++G(d,p) basis set. The scaled B3LYP/6-311++G(d,p) results shows the best agreement with the experimental values over the other method. The calculated HOMO and LUMO energies shows that charge transfer within the molecule. The physical reactions of single bond hydrocarbon TMP were investigated. The results of the calculations were applied to simulate spectra of the title compound, which shows the excellent agreement with observed spectra. Besides, Mulliken atomic charges, UV, frontier molecular orbital (FMO), MEP, NLO activity, Natural Bond-Orbital (NBO) analysis, NMR and thermodynamic properties of title molecule were also performed.

Complex of heavy magnetic ions and luminescent silicon nanoparticles

We study the optical properties of luminescent silicon nanoparticles in the presence of magnetic ions of iron or erbium under wet conditions and electric biasing. Upon the introduction of the ions under zero biasing, the brightness is enhanced with some spectral change. Under biasing including breakdown field conditions, the enhancement remains stable and is maintained after recovery of the particles into nanosolid films using electric spray. The ion-nanoparticle interaction is analyzed using first principle atomistic calculations employing unrestricted Hartree-Fock density functional theory. The calculations yield configurations, which show strong binding and stability. The complexes promise diverse applications in magnetic/optical imaging, spatially programmable deposition, spin-based memories and transistors, infrared communications, filtration, as well as interplanetary and interstellar observation and modeling.

The Importance of Electron Correlation on Stacking Interaction of Adenine-Thymine Base-Pair Step in B-DNA: A Quantum Monte Carlo Study.

We report fixed-node diffusion Monte Carlo (DMC) calculations of stacking interaction energy between two adenine(A)-thymine(T) base pairs in B-DNA (AA:TT), for which reference data are available, obtained from a complete basis set estimate of CCSD(T) (coupled-cluster with singles, doubles, and perturbative triples). We consider four sets of nodal surfaces obtained from self-consistent field calculations and examine how the different nodal surfaces affect the DMC potential energy curves of the AA:TT molecule and the resulting stacking energies. We find that the DMC potential energy curves using the different nodes look similar to each other as a whole. We also benchmark the performance of various quantum chemistry methods, including Hartree-Fock (HF) theory, second-order Møller-Plesset perturbation theory (MP2), and density functional theory (DFT). The DMC and recently developed DFT results of the stacking energy reasonably agree with the reference, while the HF, MP2, and conventional DFT methods give unsatisfactory results.

Ionization potentials of (112) and (112¯) facet surfaces of CuInSe2and CuGaSe2

The ionization potentials of the faceted and nonfaceted (110) surfaces of CuInSe${}_{2}$ (CIS) and CuGaSe${}_{2}$ (CGS), which are key components of CuIn${}_{1\ensuremath{-}x}$Ga${}_{x}$Se${}_{2}$ (CIGS) thin-film solar cells, are investigated using first-principles calculations based on a hybrid Hartree-Fock density functional theory approach. Slab models of the chalcopyrite (110) surface with both (112) and (11$\overline{2}$) facets on each surface of the slab are employed. Surface energy evaluations point out that two types of faceted surfaces with point defects, namely a combination of Cu${}_{\mathrm{In}}$ (Cu${}_{\mathrm{Ga}}$) and In${}_{\mathrm{Cu}}$ (Ga${}_{\mathrm{Cu}}$) antisites and a combination of Cu vacancies and In${}_{\mathrm{Cu}}$ (Ga${}_{\mathrm{Cu}}$) antisites, are the most stable depending on the chemical potentials. The ionization potentials are evaluated with two definitions: One highly sensitive to and the other less sensitive to localized surface states. The latter varies by 0.4 eV in CIS and 0.5 eV in CGS with the surface structure. The ionization potentials are reduced by 0.2 eV for faceted surfaces with Cu${}_{\mathrm{In}}$ (Cu${}_{\mathrm{Ga}}$) and In${}_{\mathrm{Cu}}$ (Ga${}_{\mathrm{Cu}}$) antisites when the effects of the localized surface states are considered. The values of both ionization potentials are similar between CIS and CGS with a difference of about 0.1 eV for the most stable surface structures.

Insufficient Hartree-Fock Exchange in Hybrid DFT Functionals Produces Bent Alkynyl Radical Structures.

Density functional theory (DFT) is often used to determine the electronic and geometric structures of molecules. While studying alkynyl radicals, we discovered that DFT exchange-correlation (XC) functionals containing less than ∼22% Hartree-Fock (HF) exchange led to qualitatively different structures than those predicted from ab initio HF and post-HF calculations or DFT XCs containing 25% or more HF exchange. We attribute this discrepancy to rehybridization at the radical center due to electron delocalization across the triple bonds of the alkynyl groups, which itself is an artifact of self-interaction and delocalization errors. Inclusion of sufficient exact exchange reduces these errors and suppresses this erroneous delocalization; we find that a threshold amount is needed for accurate structure determinations. Below this threshold, significant errors in predicted alkyne thermochemistry emerge as a consequence.

Multideterminant assessment of mean-field methods for the description of electron transfer in the weak-coupling regime

Multideterminant calculations have been performed on model systems to emphasize the role of many-body effects in the general description of charge quantization experiments. We show numerically and derive analytically that a closed-shell ansatz, the usual ingredient of mean-field methods, does not properly describe the steplike electron-transfer characteristic in weakly coupled systems. With the multideterminant results as a benchmark, we have evaluated the performance of common ab initio mean-field techniques, such as Hartree-Fock (HF) and density-functional theory (DFT) with local and hybrid exchange-correlation functionals, with a special focus on spin-polarization effects. For HF and hybrid DFT, a qualitatively correct open-shell solution with distinct steps in the electron-transfer behavior can be obtained with a spin-unrestricted (i.e., spin-polarized) ansatz although this solution differs quantitatively from the multideterminant reference. We also discuss the relationship between the electronic eigenvalue gap and the onset of charge transfer for both HF and DFT and relate our findings to recently proposed practical schemes for calculating the addition energies in the Coulomb blockade regime for single-molecule junctions from closed-shell DFT within the local-density approximation.