On the possibility of interpretation of the spectra of tetrapyrrole compounds and their radical ions on the basis of quantum-chemical calculations by the density functional method

Using the time-dependent formalism of the density functional theory (time-dependent density functional theory (TDDFT)), the energies and intensities of the electronic transitions of radical anions of Mg porphyrin and Mg phthalocyanine are calculated quantum chemically. Based on these calculations, an interpretation of the electronic spectra of these compounds is proposed. It is shown that, for the neutral Mg porphin molecule, the results of the TDDFT calculations are consistent with the generally accepted notions and with the experimental data only if hybrid density functionals are applied. In this case, the best results are obtained for an exchange-correlation functional whose parameters are close to the standard parameters of the B3LYP functional. The spectra of the electronic transitions of radical anions of the considered tetrapyrrole molecules calculated by the TDDFT (B3LYP) method are consistent both with previous semiempirical calculations and with the experimental data.     

Application of density-functional perturbation theory to calculate nonlinear polarizabilities of helium-like systems

Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.     

Interpretation of the electronic spectra of phthalocyanines with transition metals from quantum-chemical calculations by the density functional method

Using the time-dependent formalism of the density functional theory (time-dependent density functional theory (TDDFT)), the energies and intensities of the electronic transitions of some metal phthalocyanines of transition metals and of their anionic forms with different electron localization are studied quantum chemically. It is shown that, in all the cases studied, calculations using the B3LYP functional with even a comparatively narrow basis set (6–31G) are quite consistent with the previous calculations of the same objects by the ZINDO/S-CI semiempirical method taking into account double excitations. For a number of particular examples, it is shown that a lack of consideration of doubly excited configurations in the calculation of excited states by the TDDFT method can be compensated by the contribution from single excitations, which proves to be more significant due to the presence of the correlation component of the exchange-correlation functional.     

Using the local density approximation and the LYP,BLYP and B3LYP functionals within reference-state one-particle density-matrix theory

For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e. its integrand contains only the coordinates of two electrons, say r ₁ and r ₂, and it has a Dirac delta function δ(r ₁ - r ₂ as a factor. Since Brueckner and Hartree–Fock orbitals are often very similar, any local exchange functional that works well with Hartree–Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle–Salvetti correlation-energy functional and the LYP variant are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: one is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.     

Interpretation of the electronic spectra of Fe and Co porphyrins based on quantum-chemical calculations by the density functional method

Using the time-dependent formalism of the density functional theory (time-dependent density functional theory (TDDFT)), the energies and intensities of the electronic transitions of some Fe and Co porphyrins and their anionic forms with different electron localization are studied quantum chemically. It is shown that, in the majority of the considered cases, the calculations performed with the B3LYP functional with a comparatively narrow basis set (6-31G) are quite consistent with previous calculations of these objects by the ZINDO/S-CI semiempirical method taking into account double excitations. Furthermore, the level of agreement of the B3LYP calculations with experiment is the same as that obtained with the ZINDO/S-CI method.     

Electronic and magnetic properties of NiS2, NiSSe and NiSe2 by a combination of theoretical methods

We present a systematic study of the performance of numerical pseudo-atomic orbital basis sets in the calculation of dielectric matrices of extended systems using the self-consistent Sternheimer approach of [F. Giustino et al., Phys. Rev. B 81, 115105 (2010)]. In order to cover a range of systems, from more insulating to more metallic character, we discuss results for the three semiconductors diamond, silicon, and germanium. Dielectric matrices of silicon and diamond calculated using our method fall within 1% of reference planewaves calculations, demonstrating that this method is promising. We find that polarization orbitals are critical for achieving good agreement with planewaves calculations, and that only a few additional ????s are required for obtaining converged results, provided the split norm is properly optimized. Our present work establishes the validity of local orbital basis sets and the self-consistent Sternheimer approach for the calculation of dielectric matrices in extended systems, and prepares the ground for future studies of electronic excitations using these methods.     

Understanding the absorption and emission spectra of borondipyrromethene dye and its substituted analogues

Borondipyrromethene (BODIPY) dye possesses a bright and long wavelength emitting fluorescent character with a wide spectral range from visible to near infrared region. In the present work, the spectral properties of BODIPY dyes were analyzed using ab intio and density functional theory methods. The ground and excited state geometries of BODIPY and its substituted analogues in chloroform medium, were optimized using the density functional theory (DFT) and singly excited configuration interaction (CIS) methods. Based on the ground and excited state geometries, the absorption and emission spectra have been calculated using time-dependent density functional theory (TDDFT) method. The TDDFT calculations have been performed using hybrid exchange correlation functionals B3LYP and M06-HF and long-range separated functionals LC-BLYP, LC-BOP, LC-PBE, LC-PBE0 and CAM-B3LYP. The solvent phase calculations were carried out using polarizable continuum model (PCM). The TDDFT investigation reveals that the substitution of acceptor, donor–donor, donor–acceptor–donor and phenyl group in BODIPY dye influence the absorption and emission spectra significantly.     

Phase shift calculation for low-energy electron scattering from mercury

Summary The relativistic formalism is used to study the scattering of electrons from mercury at low energy. A method of numerical integration is applied to calculate phase shifts by including a local exchange approximation and phenomenological polarization potential. The phase shifts are found to exhibit a resonant behaviour which is in conformity with the results of some earlier calculations. In contrast to the previous methods, this approach has a general validity over the entire energy range and is free from divergences. The author of this paper has agreed to not receive proofs for correction.     

Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory

Time-dependent density functional theory (TDDFT) in its current adiabatic implementations exhibits three remarkable failures: (a) completely wrong behavior of the excited state surface along a bond-breaking coordinate; (b) lack of doubly excited configurations; (c) much too low charge transfer excitation energies. These TDDFT failure cases are all strikingly exhibited by prototype two-electron systems such as dissociating H2 and HeH+. We find for these systems with time-dependent density matrix functional theory that: (a) Within previously formulated simple adiabatic approximations, the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (b) An adiabatic approximation is formulated in which also the double excitations are fully accounted for.     

Quantum versus Jahn-Teller orbital physics in YVO3 and LaVO3

We argue that the large Jahn-Teller (JT) distortions in YVO3 and LaVO3 should suppress the quantum orbital fluctuation. The unusual magnetic properties can be well explained based on local density approximation + Hubbard U calculations using experimental structures, in terms of the JT orbital. The observed splitting of the spin-wave dispersions for YVO3 in a C-type antiferromagnetic state is attributed to the inequivalent VO2 layers in the crystal structure, instead of the "orbital-Peierls state." Alternative stacking of ab-plane exchange couplings produces the c-axis spin-wave splitting; thus, the spin system is highly three dimensional rather than quasi-one-dimensional. Similar splitting is also predicted for LaVO3, although it is weak.     

On the computation of electronic excitations in solids

An approximation scheme is proposed for calculating electronic excitations in solids. It is described within a projection operator formalism of the Mori-Zwanzig type. The approximation consists in successively limiting the space of dynamical variables which are treated. The selection of the variables is done by making use of the local character of the correlation hole which is surrounding an electron. The method is distinct from a perturbation expansion and can be related to a variational ansatz via the Sauermann functional. The computation of the spectral density of the Green's function is reduced to the diagonalization of matrices. Their dimension depends on the required degree of accuracy of the calculations. The present method can be considered as an extension to excited states of a previously developed. Local Approach for ground state calculations.Dedicated to Prof. S. Methfessel on the occasion of his 60th birthday     

Theoretical analysis of the experimental UV-Vis absorption spectra of some phenolic Schiff bases

The time-dependent density functional theory (TDDFT) was applied in conjunction with the natural bond orbital analysis to examine the UV-Vis properties of 10 phenolic Schiff bases. The calculations were performed with different functionals, but main discussion refers to results obtained at the B3LYP/6-311+G(d,p) level of theory. The approach based on the natural localised molecular orbital clusters indicates similar behaviour for majority of examined compounds. The HOMO (“highest occupied molecular orbital”) cluster is delocalised over the ring which is electron richer, the HOMO-1 cluster is spread over the other ring, whereas the LUMO (“lowest unoccupied molecular orbital”) cluster is situated on the imino group. The two bands at long wavelengths correspond to the HOMO → LUMO and HOMO-1 → LUMO transitions, i.e. from both A and B rings to the imino group. The next band originates from a transition from the imino group to the imino group. The band at the smallest wavelengths originates from a transition from the A ring to the A ring, or from the B ring to the B ring. Our findings are in very good agreement with the existing literature data.     

A non-self-consistent range-separated time-dependent density functional approach for large-scale simulations

We propose an efficient method for carrying out time-dependent density functional theory (TDDFT) calculations using range-separated hybrid exchange-correlation functionals. Based on a non-self-consistent range-separated Hamiltonian, the method affords large-scale simulations at a fraction of the computational time of conventional hybrid TDDFT approaches. For typical benchmark molecules including N(2), CO, C(6)H(6), H(2)CO and the C(2)H(4)-C(2)F(4) dimer, the method possesses the same level of accuracy as the conventional approaches for the valence, Rydberg, and charge-transfer excitation energies when compared to the experimental results. The method is used to determine π → π* excitations in both disordered and crystalline poly(3-hexylthiophene) (P3HT) conjugated polymers with more than six hundred atoms and it yields excitation energies and charge densities that are in excellent agreement with experiments. The simulation of the crystalline P3HT reveals that the phase of the wavefunctions could have an important effect on the excitation energy; a hypothesis based on π-π stacking is proposed to explain this novel effect in conjugated polymers.     

Dynamic exchange-correlation potentials for the 2D electron gas

Recent progress in the formulation of a fully dynamical local approximation to time-dependent density functional theory (TD-DFT) appeals to the longitudinal and transverse components of the long-wavelength exchange and correlation kernel in the homogeneous electron gas, . We extend to the two-dimensional longitudinal and transverse case our work on the 3D [J. Phys.: Condens. Matter 9 (1997) 475], which accounts for two-pair excitations through an approximate decoupling of the equation of motion for the current–current response function. We present numerical results and compare with asymptotic behaviours and previous approximations.     

Single-particle energies and density of states in density functional theory

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn– Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange– correlation functional has no dependence on the superfluid density. The Kohn– Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps.     

CO adsorption on the Cu(1 1 1) surface: A density functional study

The adsorption of CO on the Cu(1 1 1) surface has been studied with ab initio density functional theory. The adsorbate-metal system was analyzed with the local density approximation, the gradient corrected functional of Perdew and Wang and the B3LYP hybrid functional, for comparison. A slab model was used for the pattern at a coverage of 1/3. The local density approximation and the gradient corrected functional give the fcc site as the favorable adsorption site. In contrast, the B3LYP functional results in the preference of the top site, in agreement with the experiment. These results confirm the suggested explanation for the failure of standard functionals, based on the position of the highest occupied and lowest unoccupied molecular orbital. The results of total energy calculations are presented, together with projected densities of states and Mulliken populations. In addition, the basis set superposition error is discussed for CO/Cu(1 1 1) and for CO/Pt(1 1 1).     

Density functional theory study on the magnetic properties of Co3O4 with normal spinel structure

The magnetic properties of Co₃O₄ with a normal spinel structure were investigated via the full potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). The exchange and correlation effects between electrons were treated with a standard generalized gradient approximation (GGA) from Perdew–Burke–Ernzerhof (PBE), as a function of the on-site Coulomb U term, the GGA−PBE+U method, and a B3PW91 hybrid functional with different Hartree–Fock exchange admixtures. Were calculated all of these exchange–correlation (XC) functionals both with and without spin–orbit coupling (SOC). The objective for these calculations was to predict the ground-state magnetic structure of Co₃O₄ crystal using different XC functionals and to investigate the influence that SOC had on these results. All of our calculations confirmed that the collinear antiferromagnetic (AFM) order was energetically more favorable than the ferromagnetic (FM) one, which agrees with experimental findings. This conclusion was not influenced by the XC functional type employed or whether the spin–orbit effect was used. Thus, the present work does not confirm the recent DFT plane wave pseudopotential results that when including spin–orbit effects, the calculations determined that the collinear FM state had lower energy than the AFM one.