DFT and DFT-D studies on molecular structure of double-decker phthalocyaninato-terbium(III) complex

A molecular structure of a double-decker phthalocyaninato-terbium(III) anion (TbPc₂^?) is optimised by density functional theory (DFT) and DFT with a dispersion interaction (DFT-D) method. The DFT-D method such as B3LYP-D and B97-D functional sets estimates phthalocyaninato (Pc) ions to be planar although B3LYP and PBE1PBE make them concave. In addition, the planar structure corresponds to an experimental X-ray crystallographic result. On the other hand, an optimised geometry of Pc^2? dimer by B3LYP-D estimates the convex Pc^2? structure due to the dispersion interaction between outer aromatic rings. These results suggest the importance of the dispersion interaction for the structure of TbPc₂^?.     

FeP(Im)−AB bonding energies evaluated with a large number of density functionals (P = porphine,Im = imidazole,AB = CO,NO, and O2)

Sixty-four density functionals, ranging from GGA, meta-GGA, hybrid GGA to hybrid meta-GGA, were tested to evaluate the FeP(Im)–AB bonding energies (E _bond) in the heme model complexes FeP(Im)(AB) (P?=?porphine, Im?=?imidazole, AB?=?CO, NO, and O₂). The results indicate that an accurate prediction of E _bond for the various ligands to heme is difficult with the DFT methods; usually, a functional successful for one system does not perform equally well for other system(s). Relatively satisfactory results for the various FeP(Im)–AB bonding energies are obtained with the meta-GGA functionals BLAP3 and Bmτ1; they yield E _bond values of ca. 1.1, 1.2, and 0.4?eV for AB?=?CO, NO, and O₂, respectively, which are in reasonable agreement with experimental data (0.78–0.85?eV for CO, 0.99?eV for NO, and 0.44???0.53?eV for O₂). The other functionals show more or less deficiency for one or two of the systems. The performances of the various functionals in describing the spin-state energetics of the five-coordinate FeP(Im) complex were also examined.     

K-shell core-electron binding energies for phosphorus- and sulfur-containing molecules calculated by density functional theory

In this paper, 1s ionization energies for P- and S-containing molecules were calculated using energy-difference method by DFT. Using observed core-electron binding energies (CEBEs) as reference, we found that the Becke00x(xc) exchange-correlation functional (E_xc) is the best choice for CEBEs(P1s), with an average absolute deviation (AAD) of 0.20 eV, and that the best choice for CEBEs(S1s) is E_xc = BmTau1, with an average absolute deviation (AAD) of 0.22 eV. However, the best single functional for calculation of both P and S is E_xc = VS98, resulting in the weighted AAD of 0.43 eV. Our results are also showing that the quality of AAD changes slightly with the apparent orbital hybridization of the atom.     

Methane adsorption on graphene from first principles including dispersion interaction

The methane–graphene interaction is studied using density functional theory complemented with a semiempirical dispersion correction scheme (DFT-D), an ab initio van der Waals density functional (vdW-DF) ansatz as well as using Møller Plesset perturbation theory (MP2). The adsorption energy of 0.17 eV and the molecular distance of 3.28 Å obtained from the MP2 calculations are close to the experimental data, while the vdW-DF scheme results either in a realistic adsorption energy or a realistic adsorption geometry, depending on the underlying exchange-correlation functional. The present implementation of DFT-D overbinds about as much as bare DFT calculations underbind, but yields a meaningful adsorption height.     

Density functional theory calculation of 2p core-electron binding energies of Si,P, S,Cl, and Ar in gas-phase molecules

Density functional theory (DFT) calculations have been performed on the gas-phase 2p core-electron binding energies (CEBEs) of Si, P, S, Cl, and Ar in 145 cases using the following procedure: ΔE_KS (scalar-ZORA + E_xc)/TZP//HF/6-31G(d). ΔE_KS is the difference in the total Kohn–Sham energies of the 2p-ionized cation and the neutral parent molecule calculated by DFT using different exchange-correlation functionals E_xc with triple-zeta polarized basis set, at molecular geometry optimized by HF/6-31G(d), and relativistic effects have been estimated by scalar zeroth-order regular approximation. Among the 26 functionals tested, the form of E_xc giving the best overall performance was found to be the combination of OPTX exchange and LYP correlation functionals. For that functional, the average absolute deviation (AAD) of the 145 calculated CEBEs from experiment is 0.26 eV. There are seven other exchange-correlation functionals that led to AADs of less than 0.30 eV. Some functionals give lower AADs than E_xc = OPTX-LYP for some individual elements. In the case of Si, for example, the combination of either mPW91-PBE or Becke88-Perdew86 led to an AAD of only 0.10 eV for 56 silicon-containing molecules. Another example is the case of the argon atom, for which the choice of E_xc = OPTX-Perdew86 yields a value for CEBE equal to the experimental value.     

On double magicity of the <Stack><Subscript>28</Subscript><Superscript>68</Superscript></Stack>Ni<Subscript>40</Subscript> nucleus

Single-particle energies E _nlj of neutron states in the ₂₈ ⁶⁸ Ni₄₀ nucleus are estimated on the basis of extrapolation of the experimental values of E _nlj in the ^58,60,62,64Ni isotopes. The data obtained are compared with the results of calculation within the dispersion optical model.     

First-order Raman scattering in germanium resonant with the E0 gap

We have measured the absolute Raman efficiency as well as the dispersion for first order scattering by the optical zone center phonon in germanium with the incident photon energies in the range of the E₀ gap energy. At 77 K a Raman polarizability of 68±14 Ų is found for an incident photon energy of 0.826 eV. The deformation potential d is determined to be 40 eV assuming C^″₀ ? 1 for the strength parameter of the E₀ gap.     

Calculations of vacancy formation energies and divacancy binding energies for noble metals using pseudopotential formalism

Vacancy formation energies (E^f_1v) and divacancy binding energies (E^B_2v) for noble metals have been calculated using the Moriarty's pseudopotential. While the calculated E^f_1v are coincident with the experimental values except Cu, E^B_2v agree with them for all the metals tolerably.     

Lifetimes of some excited states in 64Ni, 66Zn and 68Zn

Mean lives and excitation energies of the lowest levels in⁶⁴Ni,⁶⁶Zn and⁶⁸Zn were measured with the aid of the (α, α′γ) and (α, pγ) reactions. The γ-rays were detected in coincidence with the outgoing particles. The following mean lives were determined from DSA measurements: 400 ± 150 fs for the level at E_x = 1.35 MeV in ⁶⁴Ni; 270 ± 100, 210 ± 110, 330 ± 200, 80 ± 70 fs for the levels at E_x = 1.87, 2.45, 2.83, 2.94 MeV in ⁶⁶Zn, and 1300 ± 300, > 160, 600 ± 200 fs for the levels at E_x = 1.08, 1.89 and 2.76 MeV in ⁶⁸Zn, respectively.     

Theoretical studies of the structures and optical properties of the bifluorene and its derivatives

The ground and excited structures of the molecules are compared basis on the calculated by HF and CIS, respectively. The ionization potentials (IPs), electron affinities (EAs) and HOMO–LUMO gaps (ΔE_HOMO–LUMO) of the oligomers are studied by the density functional theory (DFT) with B3LYP functional while the vertical excitation energies (E_gs) and the maximal absorption wavelength λ_abs of oligomers of bifluorene and its derivatives DFE, DFA, DFBT, FDBO, and FSCHD are studied employing the time dependent density functional theory (TD‐DFT) and ZINDO. Compared with BF, the derivatives DFE, DFA, and DFBT are better conjugated, easier to give an electron or a hole, as well as get an electron or a hole. Their HOMO–LUMO gaps are narrower and they have lower vertical excitation energies. The absorption and emission spectra of them are red shifting. However, FDBO and FSCHD are in the other way round. It is important that FDBO and FSCHD are good blue emitters. Copyright © 2007 John Wiley & Sons, Ltd.     

In search of the dark state of 5-methyl-2-hydroxypyrimidine using a numerical DFT/MRCI gradient

In a recent publication, Lobsiger et al. [Phys. Chem. Chem. Phys. 12, 5032 (2010)] presented infrared and electronic absorption spectra of supersonic jet-cooled 5-methyl-2-hydroxypyrimidine (5M2HP), the enol form of deoxythymine. In addition, they reported on the fast nonradiative decay of the S₁ population to a dark state. In the present paper, we have investigated the mechanism and rate constants of this nonradiative decay by means of quantum chemical multi-configuration methods. To this end, minima of the lowest excited singlet and triplet states as well as the minimum-energy crossing point of singlet and triplet potential energy hypersurfaces (PEHs) have been determined employing a numerical DFT/MRCI gradient where DFT/MRCI stands for a combination of density functional theory (DFT) and a semi-empirical multi-reference configuration interaction (MRCI) approach. Rate constants have been calculated in the Condon approximation using a time-dependent approach based on harmonic oscillator functions and electronic spin–orbit coupling matrix elements evaluated at the DFT/MRCI level. It is shown that the first excited triplet state possesses ³(n?→?π*) character in the gas phase. Fast intersystem crossing is mediated by the low-lying ³(π?→?π*) state whose PEH crosses both, the S₁ ¹(n?→?π*) and T₁ ³(n?→?π*) PEHs.     

Many-body effects in the binding energies of image states at surfaces

A study of the influence of many-body effects on binding energies and effective masses of image potential induced surface states is presented. The binding energies calculated using experimentally measured ε(ω) response functions show a dependence on the electron density different from that obtained using a plasmon model, and are in agreement with recent experimental data of diesen et al. [Phys. Rev. B33 (1986) 5241]. The effects of plasmon dispersion and single particle excitations on binding energies are evaluated with a simple model, and it is shown that they result in a strong cancellation in the range of r_s values where most experimental data have been obtained (r_s ≈ 3), if realistic values of the surface plasmon dispersion relation are used. Corrections to the effective masses due to many-body effects are shown to be of the order of 1%.     

The binding energy of an adsorbed atom

Summary We discuss the effect of substrate vibrations on the binding of an adsorbed atom. At zero temperature, we compute the binding energyD ₀-E, whereD ₀ is the surface well depth (classical binding energy) andE is the quantum correction. For several simple models, we find thatE is surprisingly model independent. We compareD ₀-E with the binding energies to a rigid substrate,D ₀-E _rs, and to a vibrationally averaged substrate,D ₀-E _va. We prove thatE _va≥E≥E _rs and that similar relations hold at finite temperature for the free energy of binding. We find that in most casesE _rs is better thanE _va as an approximation toE. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Reexamine structures and relative stability of medium-sized silicon clusters: Low-lying endohedral fullerene-like clusters Si30-Si38

We report improved results of lowest-lying silicon clusters Si₃₀-Si₃₈. A large population of low-energy clusters are collected from previous searches by several research groups and the binding energies of these clusters are computed using density-functional theory (DFT) methods. Best candidates (isomers with high binding energies) are identified from the screening calculations. Additional constrained search is then performed for the best candidates using the basin-hopping method combined with DFT geometry optimization. The obtained low-lying clusters are classified according to binding energies computed using either the Perdew-Burke-Ernzerhof (PBE) functional or the Becke exchange and Lee-Yang-Parr correlation (BLYP) functional. We propose to rank low-lying clusters according to the mean PBE/BLYP binding energies in view that the PBE functional tends to give greater binding energies for more compact clusters whereas the BLYP functional tends to give greater binding energies for less compact clusters or clusters composed of small-sized magic-number clusters. Except for Si₃₀, the new search confirms again that medium-size silicon clusters Si₃₁-Si₃₈ constructed with proper fullerene cage motifs are most promising to be the lowest-energy structures.     

Vibrational and thermodynamic properties of orthorhombic CaSnO3 from DFT and DFPT calculations

Density functional theory (DFT) and density functional perturbation theory (DFPT) calculations were used to investigate the vibrational and thermodynamic properties of orthorhombic stannate CaSnO₃ compound. Our approach was based on the generalized gradient approximation with dispersion correction (GGA+D), considering the norm-conserved pseudopotentials. The phonon dispersion relation as well as theoretical peaks of the infrared (IR) and Raman spectrum in the frequency range of 100–800 cm⁻¹ was analyzed and assigned. The thermodynamic potentials and the specific heat at constant volume of the CaSnO₃ compound are also calculated, whose dependence with the temperature are discussed.     

Dynamic correlation

From a knowledge of the Hartree-Fock and exact non-relativistic energies of atoms, the correlation energy E_c, as defined by Lowdin, may be calculated. For atoms this correlation is defined as dynamic correlation. The separate like-spin and unlike-spin contributions, E_cσσ, E_cαβ, may be calculated as a sum of pair energies from quantum chemistry; we have used the unrestricted M?ller-Plesset second-order algorithm, and then scaled them to give E_c. These three values may also be computed using dynamic correlation functionals, with the Stoll partitioning. The VWN, LYP and P91 functionals were studied for the atoms from H to Ar. Although the total correlation energies of LYP and P91 are similar, only P91 gives a semi-sensible breakdown into the E_cσσ, and E_cαβ components. It is immediately apparent that a new functional, OPTC, derived from the P91 components as 0.6625 x E_cσσ, + 1. 1015 x E_cαβ is an improvement (its mean absolute error is only 0.006 E_h). Using the recently introduced improved exchange functional OPTX (obtained through a fit to the HF energies of atoms), Kohn-Sham calculations were performed on the atoms using the OPT(=OPTX + OPTC) functional. The total energies have a mean absolute error of 0.006 E_h. The study then moves to molecules. First it is shown that the dynamic correlation energy contribution to the dissociation energies is very similar (within 2kcalmol^?1 in most cases), whether it is calculated with LYP, P91 or OPTC. A calculation is then made of the HF contribution, the dynamic contribution through OPTC and the left-right contribution through OPTX, to molecular binding. In many cases the sum agrees with the observed value, but in some cases the prediction is significantly in error, e.g. O₂ is overbound by 10 kcal mol^?1. Thus either OPTX or OPTC or both are inadequate. An attempt was made to determine improved local exchange and correlation functionals by fitting to both atomic and molecular data, but this was unsuccessful. The conclusion is that the method is close to the limit of accuracy achievable from separately optimized local exchange and correlation functionals. Finally, a new hybrid functional O3LYP, which is a substantial improvement on B3LYP, is presented.     

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr ₀. It is observed from the behaviour ofr ₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr ₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E _exp−E _cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.     

Comments on chemisorption at a metal surface

The effect of the gradient correction to the exchange and correlation energies on chemisorption properties is examined using the evaluation of B_χc arrived at by Rasolt and Geldart. Quantities common to the study of hydrogen and alkali chemisorption on a high density metal are calculated for various forms of the energy functional within the linear response approach. It is found that the gradient correction is a quantitatively significant term, lowering binding energies by ≈ 10% and increasing the dipole sizably.     

Chemisorption energetics and surface reactivity: UBI-QEP versus DFT projections

The wealth of information accumulated recently by ab initio/DFT calculations of adsorption energetics and reactivity on metal surfaces makes it possible to systematically compare projections of the DFT and UBI-QEP approaches. We make such comparisons covering both qualitative regularities in and the quantitative accuracy of binding energies and activation barriers. We focus on the following areas: (1) DFT verification of the UBI-QEP assumptions and rigorous projections concerning atomic and molecular binding energies at low coverage; (2) coverage effects revealing in the M-A bond energy competition (metal sharing A-M-A) under atomic co-adsorption; (3) reactivity patterns including both qualitative (periodic dependence of the activation barriers, barrier vs. reaction enthalpy relationships, geometry of the transition state, etc.) and quantitative aspects. We demonstrate the broad agreement between the DFT and UBI-QEP projections and point out the areas where further testing by the ab initio/DFT techniques might be necessary and illuminating. In particular, while discussing the ab initio/DFT absolute values of the atomic binding energies Q _A and their periodic trends, we revised our previous assumptions about monotonic changes of the Q _A values with the changing atom A valence and along the VIII and IB group metals, where the periodic trends appear to be complicated. Accordingly, we make corrections to the original UBI-QEP parameters, summarizing the current recommended values of Q _A.     

Shell-model calculations on Ni and Cu isotopes

Binding energies, excitation energies and spectroscopic factors have been calculated for^57–67Ni and^58–68Cu in an unrestricted (2p_3/2, lf _5/2,2p_1/2) shell-model space. The effective two-body matrix elements are obtained from the modified surface delta interaction (MSDI) and from a least-squares fit to experimental binding and excitation energies (ASDI). The average deviation between about 100 experimental and calculated energies is 0.14MeV for MSDI and 0.08 MeV for ASDI. Excitation energies of high-spin states are given also. Spectroscopic factors have been calculated for all single-nucleon transfer reactions on stable Ni or Cu targets leading to Ni or Cu isotopes. For spectroscopic factors larger than 0.4 the average deviation between theory and experiment is about 30%. The experimentally observed and calculated spectroscopic strengths are compared by using sum rules and are found to be consistent. An extensive compilation has been made of experimental data on energies,J ^π assignments and spectroscopic factors.