Instability of a system and its estimation in terms of the hybrid density functional theory method: a magnetic effective density functional (MEDF) approach

Potential curves and high and low spin energy gaps for radical clusters were calculated by spin polarized molecular orbital methods. Through-space effective exchange integrals (J _ab) and relative energies of spin projected low spin states by post-Hartree-Fock (HF) calculation were reproduced by the hybrid density functional theory (DFT) method. The hybrid parameters that could reproduce post-HF values such as UCCSD(T)'s for each model had close relations with the instabilities of those systems. Information entropy and related chemical indices were used to estimate the magnitude of the instabilities. A magnetic effective density functional (MEDF) scheme for spin clusters was proposed for practical computation of J _ab values in molecular magnetic materials.     

The electronic structure and magnetic property of μ-hydroxo bridged manganese porphyrin dimer

The electronic structure and effective exchange integrals (J _ab) between two manganese (III) ions of porphyrin dimer (PPMn(III)–OH–Mn(III)PP) were examined by using unrestricted hybrid DFT (UHDFT) methods. The dependence of J_ab on bond angle between two manganese ( Mn–OH–Mn) is also calculated to elucidate orbital overlap effect for J_ab value in the system. Natural orbital analysis is performed to explain the overlap effect in terms of the instability of the π, σ and δ orbitals by using diradical character.     

The NMR indirect nuclear spin–spin coupling constant of the HD molecule

We present new calculated and experimental values of the NMR indirect nuclear spin–spin coupling constant in HD. In the quantum-chemical ab initio calculations, the full configuration-interaction (FCI) method is used, yielding an equilibrium value of 41.22?Hz in the basis-set limit. Adding a calculated zero-point vibrational correction of 1.89?Hz and a temperature correction of 0.20?Hz at 300?K, we obtain a total calculated spin–spin coupling constant of J _FCI(HD)?=?43.31(5)?Hz at 300?K. This result is within the error bars of the experimental gas-phase NMR value, J _exp(HD)?=?43.26(6)?Hz, obtained by extrapolating values measured in HD–He mixtures to zero density.     

Photoinduced dynamics to photoluminescence in Ln3+ (Ln = Ce,Pr) doped β-NaYF4 nanocrystals computed in basis of non-collinear spin DFT with spin-orbit coupling

ABSTRACT

In this work, non-collinear spin DFT + U approaches with spin-orbit coupling (SOC) are applied to Ln³⁺ doped β-NaYF₄ (Ln = Ce, Pr) nanocrystals in Vienna ab initio Simulation Package taking into account unpaired spin configurations using the Perdew–Burke–Ernzerhof functional in a plane wave basis set. The calculated absorption spectra from non-collinear spin DFT + U approaches are compared with that from spin-polarised DFT + U approaches. The spectral difference indicates the importance of spin–flip transitions of Ln³⁺ ions. Suite of codes for nonadiabatic dynamics has been developed for 2-component spinor orbitals. On-the-fly nonadiabatic coupling calculations provide transition probabilities facilitated by nuclear motion. Relaxation rates of electrons and holes are calculated using Redfield theory in the reduced density matrix formalism cast in the basis of non-collinear spin DFT + U with SOC. The emission spectra are calculated using the time-integrated method along the excited state trajectories based on nonadiabatic couplings.     

Raman spectrum of vanadium pentoxide from density‐functional perturbation theory

We present ab initio calculation within the framework of the density‐functional theory (DFT) on band structure and vibrational properties of bulk V₂O₅. The structure of V₂O₅ comes from optimization of the experimental data with lattice parameters fixed. The band structure of the optimized structure has been calculated, and the result fits the experimental data very well and also gives similar results as those calculated by other methods. The phonon eigenwavenumbers of the Γ‐ point of V₂O₅ bulk have been calculated ab initio in density‐functional perturbation theory (DFPT). The calculated vibrational wavenumbers are in good agreement with observed infrared and Raman wavenumbers, and the predictive full phonon dispersion of bulk V₂O₅ has also been obtained. Further we calculated the Raman spectrum of vanadium pentoxide (V₂O₅) powder sample using the obtained Raman susceptibility. Calculated and measured intensities show overall good agreement. Copyright © 2008 John Wiley & Sons, Ltd.     

Assessment of DFT functionals with fluorine–fluorine coupling constants†

Density functional theory (DFT) calculations of nuclear magnetic resonance (NMR) spin–spin coupling constants (SSCCs) provide an important contribution for understanding experimentally observed values. It is known that calculated SSCCs using DFT methods correlate well with those experimentally measured. Unlike most of SSCCs, in fluorine compounds, fluorine–fluorine SSCC J_FF shows that the Fermi contact (FC) term is not dominant, particularly for J_FF in polyfluorinated organic molecules. In order to devise a DFT approach that would correctly reproduce the variation of SSCCs within a series of fluorine compounds, we test several DFT-based approaches, using different exchange and correlation functionals. Isotropic contributions to NMR fluorine–fluorine coupling constants (FC, spin-dipolar, SD, paramagnetic spin-orbit, PSO, and diamagnetic spin-orbit, DSO) have been calculated. Results show that DFT methods give appropriate values for ⁿJ_FF (n = 4 to 7), while for geminal and vicinal J_FF present large deviations from experimental values. For the latter SSCCs (²J_FF and ³J_FF), the four contributions (FC, SD, PSO and DSO) are analysed as a function of the local and nonlocal exchange in 1,1- and 1,2-difluoroethylene. Although FC term is not dominant for these SSCCs, the variation of this contribution with exchange is remarkable. On the other hand, SD and PSO contributions can be suitably computed without and with exact exchange, respectively.     

Theoretical spin density in nitroxides

The influence of alkyl substitution on the spin density distribution in nitroxide radicals is studied by performing ab initio UHF calculations on a series of radicals from H₂NO to C₅H₁₀NO. Comparison of spin populations and spin density maps in the series shows a net spin migration from oxygen to nitrogen when hydrogens are replaced by methyl groups. This result does not depend on the size of the alkyl substituents. The substitution effect explains in part the discrepancy between the theoretical spin density in H₂NO and the experimental result obtained by polarized neutron diffraction on tanol suberate biradical C₈H₁₂O₄((CH₃)₄C₅H₅NO)₂.     

Nuclear spin–spin constants,rotational g factor and susceptibility of sulphur hexafluoride

Following our previous study on spin–rotation and shielding constants of the SF₆ molecule, the rotational g factor and the magnetic susceptibility are calculated here, using ab initio methods to evaluate the electronic contribution to the nuclear hyperfine constants, and compared with experimental results. It is shown, for the first time, that the electronic component of the rotational g factor is proportional to a constant, which is given by a sum over electronic states. We also evaluate for the SF₆ molecule the indirect, or electron-coupled spin–spin interaction, theoretically described by Ramsey, and show that it gives non-negligible corrections to direct coupling constants d ₁ and d ₂. The contributions of the terms included in this interaction (DSO, PSO, SD and FC) are also analysed.     

Electric dipole moments of acrylonitrile and of propionitrile measured in supersonic expansion

New determinations of the ground-state electric dipole moments of acrylonitrile and propionitrile have been made from Stark effect measurements at conditions of supersonic expansion. The measurements were made on selected Stark lobes of fully resolved hyperfine components of several lowest-J rotational transitions. The results are μ_a = 3.821(3) D, μ_b = 0.687(8) D, μ_tot = 3.882(3) D for acrylonitrile, and μ_a = 3.816(3) D, μ_b = 1.235(1) D, μ_tot = 4.011(3) D for propionitrile. The new value of μ_b for acrylonitrile is appreciably different from those reported previously and it has been substantiated by both ab initio calculations and relative intensity measurements. The new dipole moment implies a considerable revision in the calculated intensities of the strongest THz-region rotational transitions of acrylonitrile, to 59% of previous values.     

Calculation of vibrational spectra for dioxouranium monochloride monomer and dimers

Structural models were built and spectral characteristics were calculated based on ab initio calculations for the monomer and dimers of dioxouranium monochoride UO₂Cl. The calculations were carried out in the effective core potential LANL2DZ approximation for the uranium atom and all-electron basis sets using DFT methods for oxygen and chlorine atoms (B3LYP/cc-pVDZ). The monomer UO₂Cl was found to possess an equilibrium planar (close to T-shaped) configuration with C_2v symmetry. The obtained spectral characteristics were analyzed and compared with experimental data. The adequacy of the proposed models and the qualitative agreement between calculation and experiment were demonstrated.     

Singlet–triplet transitions in three-atomic molecules studied by time-dependent MCSCF and density functional theory

Singlet–triplet transition moments and phosphorescence lifetimes have been calculated for the three-atomic molecules HCN, O₃, H₂O, H₂S, GeF₂, GeCl₂ and GeBr₂ by time-dependent density functional theory (DFT) utilizing quadratic response functions in order to qualify DFT which recently has become available for studies of this kind [TUNELL, I., Rinkevivius, Z., VAHTRAS, O., SALEK, P., HELGAKER, T., and ÅGREN, H., 2003, J. chem. phys., 119, 11024]. Comparison with ab initio and experimental data indicates that DFT exhibit results of similar quality as explicitly correlated methods which indicates that it indeed is a viable approach for singlet–triplet transitions. O₃ provides an intriguing example in that a systematic investigation of the singlet–triplet transition moment of its Wulf band indicates a clear advantage of the DFT technique despite the multiconfigurational character of the electronic structure of this molecule. The electronic spin–spin coupling and the hyperfine nuclear coupling constants have also been calculated in order to further characterize the triplet state in the spectra of the investigated systems.     

Ab initio determination of the torsional spectra of acetic acid

The torsional potential energy surface and the favourite geometries of acetic acid are determined with MP4/cc-p VTZ ab initio calculations. The molecule shows two planar trans and cis conformers whose energy difference is 1882.7 cm^?1. Both minimum energy geometries are separated by a barrier of 4432.1 cm^?1. The most stable trans-conformer shows a quite low methyl torsion barrier of 169.8 cm^?1. The roto-torsional energy levels have been calculated up to J = 10. The two torsional fundamental frequencies of the trans-conformer, the methyl and the OH torsion are 82.857 (A²) and 77.050cm^?1 (E) and 568.532 (A²) and 568.418cm^?1 (E). The V₃ barrier causes a splitting of 0.315cm^?1 in the ground vibrational state where the quartic centrifugal distortion constants have been predicted to be D_J = 90.4kHz, D_JK = ?301.5kHz and D_K = 165.4kHz. Finally, the far-infrared spectra of two isotopomers have been simulated from ab initio calculations.     

Ab initio determination of an extended Heisenberg Hamiltonian in CuO 2 layers

Accurate ab initio calculations on embedded Cu₄O₁₂ square clusters, fragments of the La₂CuO₄ lattice, confirm a value of the nearest neighbor antiferromagnetic coupling (J = 124 meV) previously obtained from ab initio calculations on bicentric clusters and in good agreement with experiment. These calculations predict non negligible antiferromagnetic second-neighbor interaction (J' = 6.5 meV) and four-spin cyclic exchange (K = 14 meV), which may affect the thermodynamic and spectroscopic properties of these materials. The dependence of the magnetic coupling on local lattice distortions has also been investigated. Among them the best candidate to induce a spin-phonon effect seems to be the movement of the Cu atoms, changing the Cu-Cu distance, for which the variation of the nearest neighbor magnetic coupling with the Cu-O distance is Δ J /Δ d _{Cu - O} ∼ 1700 cm^-1?^-1. Received 20 November 2000     

Non-singular descriptions of dislocation cores: a hybrid ab initio continuum approach

The core structure of straight and curved dislocations is studied by developing a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The approach is an extension of the Peierls–Nabarro (PN) model, with the following features: (1) all three components of the displacement vector for atoms within the dislocation core are included; (2) the entire generalized stacking fault energy surface (GSFS) obtained from ab initio calculations is utilized; and (3) the method is generalized to treat curved dislocations. We combine the parametric dislocation dynamics (DD) approach for the interaction and motion of dislocations with ab initio calculations of lattice restoring forces. These forces, which are extracted from the GSFS (γ-surface), are calculated from both first-principles density functional theory (DFT) and the embedded-atom method (EAM). Dislocation core structures in aluminium and silver are determined. For straight dislocations, the results from the model are shown to be in excellent agreement with experiments for both Al and Ag. In contrast to undissociated dislocation loops in Al, it is found that the core width and the separations between partials in Ag vary along the angular direction measured with respect to the Burgers vector. It is also shown that the core-cutoff radius, which is usually employed in DD calculations to avoid singularities, must be adjusted as a function of loop size to account for the correct dislocation core energy.     

Mixed spin- and spin- Ising models with random nearest-neighbour interactions

Using the effective field theory with correlations, we study mixed spin?3/2 and spin?1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings J_ij are taken as random variables with distribution P(J_ij) = pδ(J_ij ? J)+(1 ? p)δ(J_ij ? αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = ?1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features.     

Hartree-Fock and density functional theory studies on ionization and fragmentation of halomethane molecules by positron impact

The fragmentation patterns of halomethane molecules CF₄, CCl₂F₂, CClF₃ and CHF₃ due to positron impact have been studied by using ab initio and density functional theory (DFT) methods. The geometries of parent molecules and fragments are optimized at HF, MP2 and B3LYP levels of theory using the 6–31+G(d, p) basis set. The calculated reaction energies agree with the experimental values. The condensed Fukui functions have been calculated using the atomic charges of the Mulliken population analysis (MPA) scheme for the halomethane molecules. The calculated condensed Fukui functions successfully predict the reactive site of the halomethane molecules for the positron, electron and radical attacks. The chemical hardness and chemical potential for the above molecules and its fragments are calculated.     

The keto-enol equilibrium in substituted acetaldehydes: focal-point analysis and ab initio limit

High-level ab initio electronic structure calculations up to the CCSD(T) theory level, including extrapolations to the complete basis set (CBS) limit, resulted in high precision energetics of the tautomeric equilibrium in 2-substituted acetaldehydes (XH₂C-CHO). The CCSD(T)/CBS relative energies of the tautomers were estimated using CCSD(T)/aug-cc-pVTZ, MP3/aug-cc-pVQZ, and MP2/aug-cc-pV5Z calculations with MP2/aug-cc-pVTZ geometries. The relative enol (XHC?=?CHOH) stabilities (ΔE _{e,CCSD(T)/CBS}) were found to be 5.98?±?0.17, ?1.67?±?0.82, 7.64?±?0.21, 8.39?±?0.31, 2.82?±?0.52, 10.27?±?0.39, 9.12?±?0.18, 5.47?±?0.53, 7.50?±?0.43, 10.12?±?0.51, 8.49?±?0.33, and 6.19?±?0.18?kcal?mol^?1 for X?=?BeH, BH₂, CH₃, Cl, CN, F, H, NC, NH₂, OCH₃, OH, and SH, respectively. Inconsistencies between the results of complex/composite energy computations methods Gn/CBS (G2, G3, CBS-4M, and CBS-QB3) and high-level ab initio methods (CCSD(T)/CBS and MP2/CBS) were found. DFT/aug-cc-pVTZ results with B3LYP, PBE0 (PBE1PBE), TPSS, and BMK density functionals were close to the CCSD(T)/CBS levels (MAD?=?1.04?kcal?mol^?1).     

Calculated spin-spin coupling surfaces in the water molecule; prediction and analysis of J (O,H), J (O,D) and J (H,D) in water isotopomers

Ab initio symmetry and internal valence coordinate oxygen–proton and proton–proton spin–spin coupling surfaces for the water molecule have been computed for the first time. Calculations have been performed at the SOPPA (CCSD) level using a large basis set and a grid of forty-nine geometries on the two surfaces. Equilibrium values differ significantly from some other calculated values especially for the Fermi contact terms. The bond length dependence of J(O, H) is ‘normal’ i.e. J(O, H₁) is much more sensitive to stretching the O–H₁ bond than the O–H₂ bond. This contrasts greatly with the corresponding situation in methane.

The surfaces have been averaged over the nuclear motion using a recent highly accurate force field to give values of J (O, H) and J (O, D) for H₂ ¹⁷O, HD¹⁷O and D₂ ¹⁷O and J(H, D) for HD¹⁶O, HD¹⁷O and HD¹⁸O over a range of temperatures. For J (O, H) and J (O, D) bond stretching at first order is the dominant part of the nuclear motion correction with second order bending making an important contribution. For J (H, D) the second order bending is by far the largest contribution to the nuclear motion corrections although the other terms partially cancel this contribution. Non-additivity can be largely attributed to the bending term for J (O, H). As expected, the bending terms also contribute relatively more to the temperature dependence of the couplings for J (O, H), J (O, D) and J (H, D). Our calculated J (O, H) in H₂ ¹⁷O of -77.22Hz at 293K is in very good agreement with Wasylishen and Friedrich's observed value of -78.70 (±0.02) Hz in cyclohexane at this temperature. Our calculated J(H, D) in HD ¹⁶O at 323K of -1.233Hz is close to a recent experimental value of -1.114 (±0.003) Hz in nitromethane-d ₃ observed by Sergeyev et al. at that temperature.     

Theoretical study of the fine-structure coupling constants in the 2p 3Π u state of H2

The one and two-electron fine-structure constants for the 2p ³Π _u state of the H₂ molecule have been calculated using all-integral, ab initio methods for a variety of molecular wavefunctions. The results have been averaged over the first three vibrational states and are compared with previous calculations and with experiment.     

Ab Initio Calculation of Hyperfine Interaction Parameters: Recent Evolutions, Recent Examples

For some years already, ab initio calculations based on Density Functional Theory (DFT) belong to the toolbox of the field of hyperfine interaction studies. In this paper, the standard ab initio approach is schematically sketched. New features, methods and possibilities that broke through during the past few years are listed, and their relation to the standard approach is explained. All this is illustrated by some highlights of recent ab initio work done by the Nuclear Condensed Matter Group at the K.U.Leuven.