Hybrid Hartree-Fock Density Functionals Research Articles

First-principles study of nitrogen doping and oxygen vacancy in cubic PbTiO3

The structural and electrical properties of the intrinsic PbTiO3, N-doped PbTiO3 and N-VO co-doping PbTiO3 have been studied by using the first-principles calculations based on the hybrid Hartree–Fock density functionals. In addition, Hall effect measurement experiment is performed, both the experimental and theoretical results are compared. In N-doped PbTiO3 system, the N impurity states occur at the top of valance band, and Fermi energy level intersects with valance bands. The band gap becomes narrowed, the N-doped PbTiO3 shows a typical p-type semiconductor characteristic. When oxygen vacancy and N impurity coexist in PbTiO3, the conduction bands move downward and the acceptors are found to be fully compensated.

Defect energetics in ZnO: A hybrid Hartree-Fock density functional study

First-principles calculations based on hybrid Hartree-Fock density functionals provide a clear picture of the defect energetics and electronic structure in ZnO. Among the donorlike defects, the oxygen vacancy and hydrogen impurity, which are deep and shallow donors, respectively, are likely to form with a substantial concentration in $n$-type ZnO. The zinc interstitial and zinc antisite, which are both shallow donors, are energetically much less favorable. A strong preference for the oxygen vacancy and hydrogen impurity over the acceptorlike zinc vacancy is found under oxygen-poor conditions, suggesting that the oxygen vacancy contributes to nonstoichiometry and that hydrogen acts as a donor, both of which are without significant compensation by the zinc vacancy. The present results show consistency with the relevant experimental observations.

CO adsorption on metal surfaces: A hybrid functional study with plane-wave basis set

We present a detailed study of the adsorption of CO on Cu, Rh, and Pt (111) surfaces in top and hollow sites. The study has been performed using the local density approximation, the gradient corrected functional PBE, and the hybrid Hartree-Fock density functionals PBE0 and HSE03 within the framework of generalized Kohn-Sham density functional theory using a plane-wave basis set. As expected, the local density approximation and generalized gradient approximation functionals show a tendency to favor the hollow sites, at variance with experimental findings that give the top site as the most stable adsorption site. The PBE0 and HSE03 functionals reduce this tendency. In fact, they predict the correct adsorption site for Cu and Rh but fail for Pt. However, even in this case, the hybrid functional destabilizes the hollow site by $50\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ compared to the PBE functional. The results of the total energy calculations are presented along with an analysis of the projected density of states.

Why does the B3LYP hybrid functional fail for metals?

The B3LYP hybrid functional has shown to successfully predict a wide range of molecular properties. For periodic systems, however, the failure to attain the exact homogeneous electron gas limit as well as the semiempirical construction turns out to be a major drawback of the functional. We rigorously assess the B3LYP functional for solids through calculations of lattice parameters, bulk moduli, and thermochemical properties (atomization energies and reaction energies). The theoretical lattice constants overestimate the experimental ones by approximately 1%, and hence behave similarly to the PBE gradient-corrected exchange-correlation functional. B3LYP atomization energies of solids are drastically worse than those of nonempirical hybrid Hartree-Fock/density functionals (HF/DFT) such as PBE0 and HSE03. These large errors can be traced back to the lack of a proper description of "free-electron-like" systems with a significant itinerant character (metals and small gap semiconductors). Similar calculations using the popular semiempirical B3PW91 hybrid functional, which fulfills the uniform electron gas limit, show a clear improvement over B3LYP regarding atomization energies. Finally, theoretical values for heats of formation for both the B3LYP as well as the B3PW91 functionals are presented. These document a most likely fortuitously good agreement with experiment for the B3LYP hybrid functional.

Adiabatic Connection for Kinetics

A new hybrid Hartree−Fock−density functional (HF-DF) model called the modified Perdew−Wang 1-parameter model for kinetics (MPW1K) is optimized against a database of 20 forward barrier heights, 20 r...

Structures, Vibrational Frequencies, and Normal Modes of Substituted Azo Dyes: Infrared, Raman, and Density Functional Calculations

The vibrational structures of 4-nitro-azobenzene (NAB), 4-(dimethylamino)-azobenzene (DAB), and 4-nitro,4‘-(dimethylamino)-azobenzene (NDAB) are of interest due to their importance in optoelectronic applications as well as the unique isomerization mechanism involving the inversion process (at the nitrogen site). In this paper, we present the Fourier transform infrared (FTIR) and Raman spectral studies of NAB, DAB, and NDAB and also report their equilibrium structures, harmonic frequencies, and normal mode assignments, employing the hybrid Hartree−Fock/density functional (HF/DF) method with the 6-31G basis set. The results of the optimized molecular structure obtained on the basis of B3LYP with 6-31G basis set suggest a greater conjugation and π-electron delocalization for the substituted azo dyes in comparison to the parent azo molecule, viz. trans-azobenzene (TAB). It is found that the B3LYP/6-31G method is very accurate in predicting harmonic vibrational frequencies and the normal modes for the substituted azo dyes and their isotopic analogues. On the basis of the B3LYP/6-31G force field, the infrared intensities for NAB, DAB, and NDAB, and their isotopomers, are calculated and then compared with those observed experimentally. Finally, the main differences in the vibrational spectra of the substituted azobenzene derivatives are discussed from an analysis of the normal modes.

In Vivo, in Vitro, and Calculated Vibrational Spectra of Plastoquinone and the Plastosemiquinone Anion Radical

Plastoquinone (PQ-9) is active as an electron/proton transfer component in photosynthetic membranes. For example, in the photosynthetic complex, photosystem II (PSII), PQ-9 acts as QA, a one-electron acceptor, and as QB, a two electron, two proton accepting species. Light-minus-dark difference Fourier transform infrared (FT-IR) spectroscopy is a technique with which mechanistic information can be obtained concerning PSII. Here, we present combined experimental and computational studies designed to identify the vibrational contributions of the electron acceptor, QA, in its oxidized and one-electron reduced states to the difference FT-IR spectrum. Infrared spectra of decyl-PQ and PQ-9 were obtained; the difference infrared spectra associated with the formation of the corresponding anion radicals were also generated in ethanol solutions. Vibrational mode assignments were made based on hybrid Hartree−Fock/density functional (HF/DF) B3LYP calculations with a 6-31G(d) basis set. Calculations were performed for ...

Oxidative Aromatic Substitutions: Hartree−Fock/Density Functional and ab Initio Molecular Orbital Studies of Benzene and Toluene Nitrosation

Aromatic nitrosations are prototypes of a recently proposed reaction mechanismoxidative aromatic substitutionsincorporating ground-state electron transfer prior to the substitution step. Ab initio MO and B3LYP hybrid Hartree−Fock/density-functional (HF/DF) calculations confirm that nitrosation proceeds through initial formation of intermediate electron donor−acceptor (EDA) π-complexes. Calculated π-complex geometries and energies agree qualitatively with experimental data and indicate the applicability of HF/DF methods for modeling EDA complexes. Subsequent transformation of (benzene−NO)+ and (toluene−NO)+ π-complexes into N-protonated nitroso-derivatives in B3LYP and MP2 calculations suggest an alternative to the currently proposed mechanism involving π-complex transformation into Wheland type σ-complexes (supported by CISD calculations). Kinetic analysis suggests the alternative mechanism is plausible and indicates that proton transfer from the N-protonated nitroso-derivatives to the medium would not be...

Density Functional Calculations of Structures, Vibrational Frequencies, and Normal Modes of trans- and cis-Azobenzene

The vibrational structures of trans- (TAB) and cis-azobenzene (CAB) are of interest due to their importance in optoelectronic applications as well as due to the unique isomerization mechanism involving the inversion process (at the nitrogen site). In this paper, we report the equilibrium structures, harmonic frequencies, and mode assignments for TAB and CAB and their isotopic analogues, using restricted Hartree-Fock (RHF), hybrid Hartree-Fock/density functional (HF/DF), and pure density functional theoretical (DFT) methods utilizing the 6-31G* basis set. The results of the optimized molecular structure obtained on the basis of RHF and all the DFT calculations are presented and then critically compared with the experimental electron diffraction results. It is observed that best structural parameters are predicted by the hybrid HF/DF method, viz. B3LYP and B3P86 followed by the pure DFT method BP86. In the case of harmonic vibrational frequencies (unsealed) and the normal modes, it is found that the BP86/6-31G* is the most accurate. The data obtained here has been used to reassign (in contrast to the previously reported MP2 results) some of the vibrational frequencies, particularly, for the main N=N and C-N vibrations of TAB. On the basis of BP86/6-31G* force field, the infrared intensities for both TAB and CAB and their isotopomers have also been calculated. Moreover, the main differences in the vibrational spectra of the two isomers of azobenzene have been discussed from normal mode analysis.

Density-Functional Studies on the Structure and Vibrational Spectra of Transient Intermediates of p-Benzoquinone

Prediction of vibrational frequencies of polyatomic molecules using density-functional theory (DFT) methods has become common because of its accuracy and therefore consistency with experimental data. However, the utility of DFT methods in predicting vibrational frequencies and normal mode descriptions of excited state intermediates has not been addressed so far. In this paper we have evaluated the performance of Hartree- Fock (HF) and various density-functional (DF) and hybrid Hartree-Fock/density-functional (HF/DF) methods in predicting the structure, vibrational frequencies, and normal mode descriptions of transient intermediates, taking p-benzoquinone (BQ) as an example. The structures, bond orders, harmonic vibrational frequencies, and isotopic shifts for BQ and its lowest triplet state, semiquinone radical, and semiquinone radical anion have been calculated using all of these methods employing 6-31G(d) and 6-31G(d,p) basis sets. Assignments of the calculated vibrational frequencies were made with the help of normal mode analysis. The calculated structural parameters and bond orders indicate that the structure of the triplet state is intermediate between those of the ground state and radical anion. The semiquinone radical shows a mixed aromatic and quinonoid structure. Geometrical changes involved in the triplet excited state and semiquinone radical anion with respect to ground state structure are explained on the basis of the calculated electronic structures. Of all the methods tested, the three parameter hybrid HF/DF methods (B3LYP, B3P86, and B3PW91) were found to give the most accurate geometries. These methods are also found to reproduce the experimental frequencies of the ground state as well as transient species within 2-4% error, whereas the isotopic shifts calculated for the deuterated species using the BP86 method are superior and show excellent agreement with experiment. Calculations using all of the methods show that both 6-31G d) and 6-31G(d,p) basis sets yield very similar results.

Trimethyl-p-benzoquinone Provides Excellent Structural, Spectroscopic, and Thermochemical Models for Plastoquinone-1 and Its Radical Anion

Trimethyl-p-benzoquinone (TMQ) has been proposed to furnish an accurate thermochemical model for plastoquinones, key electron acceptors in oxygenic photosynthetic electron transfer. Free energy perturbation/molecular dynamics simulations combined with hybrid Hartree−Fock/density functional (HF/DF) calculations confirm that TMQ and plastoquinone-1 have approximately equal aqueous one-electron reduction potentials, within the accuracy of the calculations. HF/DF calculations using the B3LYP/6-31G(d) method also show that TMQ and its radical anion have (1) structures almost identical to those of PQa model for plastoquinone-1 without the isoprenoid chain's methyl groupsand its radical anion, respectively, have (2) spin densities for TMQ•- and PQ•- which differ by 0.01 electrons at most, and have (3) key CO and CC stretching frequencies for the TMQ/PQ and TMQ•-/PQ•- pairs differing by only 1−8 cm-1. Thus, TMQ and TMQ•- are excellent models for the structures, spin densities, and vibrational frequencies of plast...

Structural and vibrational analysis of indole by density functional and hybrid Hartree–Fock/density functional methods

Accurately assigned vibrational frequencies for indole and its derivatives, particularly tryptophan, are critical for analyses of vibronic coupling, excited state fluorescence spectra and resonance Raman spectra. Examination of published, assigned, experimental vibrational frequencies for indole reveals that while most observed bands assigned to fundamentals are in agreement among the different reports, there are notable exceptions in six different spectral regions. We have calculated the structure and assigned the harmonic vibrational spectrum of indole by application of local and gradient-corrected density functional theory methods (DFT) and a hybrid Hartree–Fock/density functional (HF/DFT) method. The hybrid method B3LYP predicts the structure of indole within 0.005 A and 1.1° of a recently published CASSCF structure. Unscaled harmonic frequencies calculated with the gradient-corrected method BLYP with the 6-31G(d) basis set exhibit the best overall agreement with experiment with an RMSD of 31 cm–1 for all modes including hydrogen stretching and bending. The hybrid B3LYP method gives frequencies in closest agreement for the out-of-plane modes, except for the NH wagging mode. Our calculations, which include electron correlation effects for approximately the same computational resources as a Hartree–Fock calculation, predict two fundamentals in the 1330–1360 cm–1 region, where a Fermi resonance pair has previously been hypothesized. This report demonstrates the utility of DFT and HF/DFT methods for heteroaromatic molecules such as indole. We provide the first complete assignment of vibrational modes for indole based on unscaled calculated frequencies which have not been empirically fit to experiment.

Density-Functional-Derived Structures, Spin Properties, and Vibrations for Phenol Radical Cation

Phenol radical cation (PhOH•+) structures, proton hyperfine coupling constants, atomic spin densities, vibrational frequencies, and deuterium isotopic vibrational frequency shifts were calculated by using spin-unrestricted Hartree−Fock (UHF), second-order Møller−Plesset perturbation (UMP2), as well as density-functional (DF) and hybrid Hartree−Fock/density-functional (HF/DF) methods. Of the methods tested, the three-parameter, hybrid HF/DF method incorporating the gradient-corrected correlation functional of Lee, Yang, and Parr (B3LYP) appears to yield the most accurate overall results. Calculated CC bond distances for PhOH•+ display pronounced quinoidal features, and the CO bond distance (1.313 Å) implies significant double-bond character. Unscaled vibrational frequencies calculated by using the B3LYP method differ from experiment by an average absolute magnitude of only 15 cm-1 and are therefore more accurate than uniformly scaled UMP2-derived frequencies. Our assignment of the CO stretching mode to a calculated frequency of 1522 cm-1 and the strong mixing between the CO stretching mode 7a and a CH bending mode at lower frequency (19a) suggests that isotopic frequency shifts be measured to distinguish clearly the CO stretching and CH bending modes in radicals related to PhOH•+. PhOH•+ displays a spin density distribution reminiscent of an odd-alternant hydrocarbon, but with large spin density on its oxygen-bearing C1 atom. Of the methods tested, the gradient-corrected BP86 and BLYP and hybrid B3LYP methods yield the most accurate proton hyperfine coupling constants for PhOH•+, whereas calculated spin densities on the carbon and oxygen atoms are much less sensitive to the particular DF method used. The B3LYP method also gives an accurate proton affinity for PhO• (208.5 kcal/mol), within 2.9 kcal/mol of experiment (205.6 ± 0.3 kcal/mol).

Density-functional methods give accurate vibrational frequencies and spin densities for phenoxyl radical

The structure, electronic spin density ratios, harmonic vibrational frequencies, and deuterium isotopic vibrational frequency shifts for phenoxyl radical, C6H5Ȯ, were calculated by using spin unrestricted Hartree–Fock (UHF), second-order Mo/ller–Plesset perturbation (UMP2), and various density functional (DF) and hybrid Hartree–Fock/density functional (HF/DF) methods with a 6–31G(d) basis set. Computed results are compared with experiment and with recently published complete active space self-consistent field (CASSCF) and unrestricted natural orbital-complete active space (UNO-CAS) calculations to evaluate the accuracy of DF and HF/DF methods for the highly delocalized, strongly correlated phenoxyl radical. Bond lengths and angles calculated by using DF and HF/DF methods appear as accurate as those obtained by using the UMP2 method. The correlation functional of Vosko, Wilk, and Nusair combined with Slater’s exchange functional (SVWN) gives a structure closest to the best available CASSCF calculations, with the structures from three parameter hybrid HF/DF methods (B3P86 and B3LYP) nearly as good. Electronic spin density ratios computed by using DF methods are closest to experimentally derived spin density ratios, UHF spin densities are the worst, and the hybrid HF/DF methods give intermediate quality spin density ratios. Unscaled vibrational frequencies from the DF and HF/DF methods are closer to experimentally measured frequencies than uniformly scaled UHF or UMP2 frequencies. Unscaled frequencies calculated by using the B3LYP method, for example, differ from the nine experimentally observed frequencies by an average of only 22 cm−1. The vibrational mode of phenoxyl radical observed experimentally at 1552 cm−1 is confirmed to correspond to a C=C stretching vibration and the band observed at 1505 cm−1 is primarily a C–O stretch. Vibrational modes of phenoxyl radical shift to lower frequencies upon deuteration and the larger shift of the C=C stretch, compared to the C–O stretch, confirms their assignment. Thus density functional methods give electronic spin density ratios, vibrational frequencies, mode assignments, and isotopic frequency shifts in good agreement with experiment and with more expensive UNO-CAS//CASSCF calculations for phenoxyl radical.