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.     

Solving the self-interaction problem in Kohn–Sham density functional theory: Application to atoms

In previous work, we proposed a computational methodology that addresses the elimination of the self-interaction error from the Kohn–Sham formulation of the density functional theory. We demonstrated how the exchange potential can be obtained, and presented results of calculations for atomic systems up to Kr carried out within a Cartesian coordinate system. In this paper, we provide complete details of this self-interaction free method formulated in spherical coordinates based on the explicit equidensity basis ansatz. We prove analytically that derivatives obtained using this method satisfy the Virial theorem for spherical orbitals, where the problem can be reduced to one dimension. We present the results of calculations of ground-state energies of atomic systems throughout the periodic table carried out within the exchange-only mode.     

Electrostatic potential of several small molecules from density functional theory

A number of density functional theory (DFT) methods were used to calculate the electrostatic potential for the series of molecules N2, F2, NH3, H2O, CHF3, CHCl3, C6H6, TiF4, CO(NH2)2 and C4H5N3O compared with QCISD (quadratic configuration interaction method including single and double substitutions) results. Comparisons were made between the DFT computed results and the QCISD ab initio ones and MP2 ab initio ones, compared with the root-mean-square deviation and electrostatic potential difference contours figures. It was found that the hybrid DFT method B3LYP, yields electrostatic potential in good agreement with the QCISD results. It is suggest this is a useful approach, especially for large molecules that are difficult to study by ab initio methods.     

Surface rumpling of cubic CaTiO3 from density functional theory

In this paper, the structure of cubic CaTiO3 （001） surfaces with CaO and TiO2 terminations has been studied from density functional calculations. It has been found that the Ca atom has the largest relaxation for both kinds of terminations, and the rumpling of the CaO-terminated surface is much larger than that of TiO2-terminated surface. Also we have found that the metal atom relaxes much more prominently than the O atom does in each layer. The CaO-terminated surface is slightly more energetically favourahle than the TiO2-terminated surface from the analysis of the calculated surface energy.     

On a solution of the self-interaction problem in Kohn–Sham density functional theory

We report on a methodology for the treatment of the Coulomb energy and potential in Kohn–Sham density functional theory that is free from self-interaction effects. Specifically, we determine the Coulomb potential given as the functional derivative of the Coulomb energy with respect to the density, where the Coulomb energy is calculated explicitly in terms of the pair density of the Kohn–Sham orbitals. This is accomplished by taking advantage of an orthonormal and complete basis that is an explicit functional of the density that then allows for the functional differentiation of the pair density with respect to the density to be performed explicitly. This approach leads to a new formalism that provides an analytic, closed-form determination of the exchange potential. This method is applied to one-dimensional model systems and to the atoms Helium through Krypton based on an exchange only implementation. Comparison of our total energies (denoted SIF) to those obtained using the usual Hartree–Fock (HF) and optimized effective potential (OEP) methods reveals the hierarchy $E_{\mathrm{HF}}\le E_{\mathrm{OEP}}\le E_{\mathrm{SIF}}$ that is indicative of the greater variation freedom implicit in the former two methods.     

Structural and magnetic properties of bimetallic Co n − 1Cr clusters with density functional theory

We have investigated the structural and magnetic properties of small bimetallic Co _{n ? 1}Cr (n = 2 ? 9) clusters by means of spin-polarized density functional theory approach. We found the ground state structures of Co _{n ? 1}Cr were very similar to those of pure Co _n except n = 3,6. The clusters were of high stability at n = 6. Magnetic moments showed an interesting size-dependent variation: the magnetic moments of Co _{n ? 1}Cr can be obtained by minus 7µB for n = 2, 4, 6–9 or by plus 1µB for n = 5 from those of the Co _n counterparts. The different magnetic behavior stems from ferromagnetic alignment or ferrimagnetic alignment of Co and Cr atoms in Co _{n ? 1}Cr, associated with their longer or shorter interatomic distances.     

Optimized local basis set for Kohn–Sham density functional theory

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton–GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.     

Demixing of amphiphile–polymer mixtures investigated using density functional theory

We construct a functional for amphiphile–polymer mixtures and investigate the demixing transition by using a proposed version of density functional theory. It is found that increase of the amphiphilic size ratio and polymer length can effectively promote phase separation of the systems. Phase diagrams are plotted to clarify these influences. The results provide an effective way of controlling the stability of the fluid–fluid phase equilibrium of the mixtures.     

Prediction of vicinal proton–proton coupling constants 3 J HH from density functional theory calculations

Vicinal coupling constants ³ J _HH have been calculated at the optimized geometries for a series of selected molecules with the aim of developing a practical procedure for predicting this kind of coupling. Calculations of couplings and optimizations of molecular geometries have been carried out at the DFT/B3LYP level using a moderate sized basis set. When the Fermi contact contributions to ³ J _HH calculated for 25 mono- and 23 1,1-di-substituted ethanes are multiplied by a factor of 0.904, the corresponding predicted couplings J ^pre are in good agreement with the experimental J ^exp couplings, with standard deviation σ of 0.10?Hz. When such a comparison is carried out for the remaining sets of molecules the σ deviation increases to 0.26?Hz for a dataset of 21 couplings from 11 monosubstituted cyclohexanes, to 0.19?Hz for a dataset of 40 couplings from 6 norbornane type molecules and to 0.25?Hz for a dataset of 54 couplings from 14 three-membered rings. For the complete dataset of 163 couplings the?σ?deviation amounts to 0.20?Hz. This figure is further reduced to 0.17?Hz by adding to the J ^pre coupling a small correction given by the term ?0.15cos?, depending on the dihedral angle ? between the coupled protons. A larger σ deviation of 0.31?Hz was reported for the best empirically parameterized extended Karplus equation. DFT J ^pre values could be further improved by more accurate calculations for the pertinent substituted ethane constituents of the molecule in question by applying a substituent effect model.     

A mesh-free convex approximation scheme for Kohn–Sham density functional theory

Density functional theory developed by Hohenberg, Kohn and Sham is a widely accepted, reliable ab initio method. We present a non-periodic, real space, mesh-free convex approximation scheme for Kohn–Sham density functional theory. We rewrite the original variational problem as a saddle point problem and discretize it using basis functions which form the Pareto optimum between competing objectives of maximizing entropy and minimizing the total width of the approximation scheme. We show the utility of the approximation scheme in performing both all-electron and pseudopotential calculations, the results of which are in good agreement with literature.     

Energy–density functional plus quasiparticle–phonon model theory as a powerful tool for nuclear structure and astrophysics

During the last decade, a theoretical method based on the energy–density functional theory and quasiparticle–phonon model, including up to three-phonon configurations was developed. The main advantages of themethod are that it incorporates a self-consistentmean-field and multi-configuration mixing which are found of crucial importance for systematic investigations of nuclear low-energy excitations, pygmy and giant resonances in an unified way. In particular, the theoretical approach has been proven to be very successful in predictions of new modes of excitations, namely pygmy quadrupole resonance which is also lately experimentally observed. Recently, our microscopically obtained dipole strength functions are implemented in predictions of nucleon-capture reaction rates of astrophysical importance. A comparison to available experimental data is discussed.     

Structural and magnetic properties of bimetallic Con ? 1Cr clusters with density functional theory

We have investigated the structural and magnetic properties of small bimetallic Co _{n − 1}Cr (n = 2 − 9) clusters by means of spin-polarized density functional theory approach. We found the ground state structures of Co _{n − 1}Cr were very similar to those of pure Co _n except n = 3,6. The clusters were of high stability at n = 6. Magnetic moments showed an interesting size-dependent variation: the magnetic moments of Co _{n − 1}Cr can be obtained by minus 7μB for n = 2, 4, 6–9 or by plus 1μB for n = 5 from those of the Co _n counterparts. The different magnetic behavior stems from ferromagnetic alignment or ferrimagnetic alignment of Co and Cr atoms in Co _{n − 1}Cr, associated with their longer or shorter interatomic distances.      

Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation

Kohn–Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn–Sham Hamiltonian generally results in a large number of basis functions per atom in order to resolve the rapid oscillations of the Kohn–Sham orbitals around the nuclei. Previous attempts to reduce the number of basis functions per atom include the usage of atomic orbitals and similar objects, but the atomic orbitals generally require fine tuning in order to reach high accuracy. We present a novel discretization scheme that adaptively and systematically builds the rapid oscillations of the Kohn–Sham orbitals around the nuclei as well as environmental effects into the basis functions. The resulting basis functions are localized in the real space, and are discontinuous in the global domain. The continuous Kohn–Sham orbitals and the electron density are evaluated from the discontinuous basis functions using the discontinuous Galerkin (DG) framework. Our method is implemented in parallel and the current implementation is able to handle systems with at least thousands of atoms. Numerical examples indicate that our method can reach very high accuracy (less than 1 meV) with a very small number (4–40) of basis functions per atom.     

Energy of hydrogen dissolution in FCC hydrides of disordered Ti–V–Cr alloys according to density functional theory data

Ti–V–Cr alloys are hydrogen storage materials, but their characteristics, which are important for practical applications, depend strongly on composition. The search for an optimal composition with given characteristics requires the support of theoretical calculations of the electronic structure of alloys and their hydrides. In this paper, the interstitial energy and energy of hydrogen dissolution in the hydride of a ternary disordered Ti_0.33V_0.27Cr_0.4H_1.75 alloy with a face-centered cubic lattice were calculated within the framework of the density functional theory using the pseudopotential method. The deviation of the dissolution energy distribution from the Gaussian distribution is shown. Based on the data obtained for a particular hydride, the energy distributions of hydrogen dissolution in a number of hydrides of alloys (Ti_0.8Cr)_1–xV_x with x = 0.9, 0.8, 0.7, and 0.6 have been derived. A correlation was found between the theoretically calculated width of the energy distribution of hydrogen dissolution and the experimental slope of the pressure “plateau.”     

Structure and stability of β-Mo2C bulk and surfaces: A density functional theory study

Density functional theory calculations have been performed on the structure and stability of β-Mo₂C bulk and the corresponding low-index surfaces. The eclipse configuration with a Mo-C-Mo-C stacking is the most stable, followed by the structure with a Mo-C-Mo-Mo-C stacking where there is an empty carbon layer every fourth layer. For (0 0 1) and (1 0 0) surfaces, the pure C terminations are more stable than the pure Mo terminations. For (0 1 0) and (1 1 1) surfaces, the Mo terminations are more stable than the C terminations. For the (0 1 1) surface, the mixed Mo/C termination is a little more stable than the Mo termination. Relaxation of these surfaces is moderate with no relaxation degree exceeding 12.8%. Among these surfaces, the mixed Mo/C termination of the (0 1 1) surface is the most stable with the lowest surface free energy, followed by the (1 0 1) surface and the T_Mo-2 termination of the (0 1 0) surface.     

Friedmann cosmology with decaying vacuum density in Brans–Dicke theory

The European Physical Journal C - We study numerical solutions corresponding to spherically symmetric gravitating electroweak monopole and magnetically charged black holes of the...     

Electronic structure and optical properties of In-doped SrTiO3 by density function theory

The effect of In doping on the electronic structure and optical properties of SrTiO3 is investigated by the first-principles calculation of plane wave ultra-soft pseudo-potential based on the density function theory （DFT）. The calculated results reveal that due to the hole doping, the Fermi level shifts into valence bands （VBs） for SrTi1-x InxO3 with x = 0.125 and the system exhibits p-type degenerate semiconductor features. It is suggested according to the density of states （DOS） of SrTi0.875In0.125O3 that the band structure of p-type SrTIO3 can be described by a rigid band model. At the same time, the DOS shifts towards high energies and the optical band gap is broadened. The wide band gap, small transition probability and weak absorption due to the low partial density of states （PDOS） of impurity in the Fermi level result in the optical transparency of the film. The optical transmittance of In doped SrTiO3 is higher than 85% in a visible region, and the transmittance improves greatly. And the cut-off wavelength shifts into a blue-light region with the increase of In doping concentration.     

Calculation of the Kirkwood–Frohlich correlation factor and dielectric constant of methanol using a statistical model and density functional theory

The geometries of methanol monomer and methanol clusters, (CH₃OH) _m , m = 2–10, were optimized using the DFT/B3LYP/6-31++G(d,p) method. For each m > 2, a number of conformers were found to satisfy the optimization condition, showing no imaginary frequency in their calculated IR spectra. With increasing m, five- and six-membered rings begin to appear with open chain branches and the calculated IR spectra approach the experimentally observed IR spectrum of liquid methanol. Using the average energy of formation of one hydrogen bond and a statistical model, the Kirkwood–Frohlich (K–F) correlation factor (g) and dielectric constant (ε) were calculated for each methanol cluster. From a plot of ε versus cluster size (m), the bulk dielectric constant was obtained by extrapolation to m→∞. The value of g averaged over all conformers is in almost complete agreement with the g value obtained in an earlier molecular dynamics simulation study by Fonseca and Ladanyi [J. Chem. Phys. 93, 8148 (1990)]. Using this value of g in the K–F equation, the dielectric constant (ε) of methanol was calculated and found to be in fair agreement with (～17% lower than) the experimental value and also with an earlier molecular dynamics simulation [Mol. Phys. 94, 435 (1998)]. The calculated ε follows the same trend in variation with temperature as the experimental ε in the range 288–318 K.