The use of the hybrid density functional theory (DFT) approach for calculation of vibrational spectra: nitromethane

The molecular geometry of nitromethane was optimized and its force field and vibrational spectrum were calculated by the BECKE3LYP method. The accuracy of optimization of the geometry of MeNO₂ obtained by this method using the 6–311G(d,p) and 6–311++G(d,p) basis sets is not poorer than that obtained at the second-order Møller-Plesset level of perturbation theory (MP2). The vibrational frequencies of nitromethane and its d₁, d₂, and d₃ isotopomers obtained by the BECKE3LYP method are in much better agreement with the experimental data than those calculated at the MP2 level using the same basis set. The average absolute error of calculations performed without the use of any scaling factors is ～2% for frequencies; the maximum deviation is ～4%.     

Nuclear dynamics and spectator effects in resonant inelastic soft x-ray scattering of gas-phase water molecules

The electronic structure of gas-phase H(2)O and D(2)O molecules has been investigated using resonant inelastic soft x-ray scattering (RIXS). We observe spectator shifts for all valence orbitals when exciting into the lowest three absorption resonances. Strong changes of the relative valence orbital emission intensities are found when exciting into the different absorption resonances, which can be related to the angular anisotropy of the RIXS process. Furthermore, excitation into the 4a(1) resonance leads to nuclear dynamics on the time scale of the RIXS process; we find evidence for vibrational coupling and molecular dissociation in both, the spectator and the participant emission.     

Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

In this paper we employ all-electron ab initio time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) C(6) of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation [Phys. Rev. 3, 360 (1948)]. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation [Can. J. Phys. 58, 1200 (1980)] of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C(6) and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient, and find that to a very high degree of correlation C(6) scales as the square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N(2) molecule interactions.     

Time-dependent density functional theory benchmarking for the calculations of atomic spectra: efficiency of exc-ETDZ basis set

We present a time-dependent density functional theory (TD-DFT) benchmarking of recently constructed basis set, namely exc-ETDZ (Guevara et al. in J Chem Phys 131: 064104, 2009) for predicting the atomic spectra of the first-row atoms. A systematic testing with 31 density functional methods has been performed to see whether convincing performance of this basis set carries over the TD-DFT formalism. The efficiency of exc-ETDZ basis set for reproducing atomic spectra has been compared with Pople- and Dunning-style basis sets. We focused on the atomic low-lying valence excited states with single excitation character for our benchmarking, and the calculated excitation energies were compared to experimental data. On average, the functionals providing the best match with exc-ETDZ basis are BMK, BH&HLYP and ωB97. Moreover, on the basis of comparison between the results of these superior functionals with CIS(D) estimates, it turned out that TD-DFT and CIS(D) errors are of the same order of magnitude, once the exc-ETDZ basis set is used. Finally, the results of present study indicate that different functionals show results that are highly dependent on the atomic configuration as well as the basis set.     

An analytical method for the calculation of the relative intensities of bending and stretching modes in inelastic neutron scattering spectra

An approximate analytical method is presented for calculating the relative intensities of the bands due to the stretching (ν) and doubly degenerate b     

Resonant inelastic x-ray scattering at the limit of subfemtosecond natural lifetime

We present measurements of the resonant inelastic x-ray scattering (RIXS) spectra of the CH(3)I molecule in the hard-x-ray region near the iodine L(2) and L(3) absorption edges. We show that dispersive RIXS spectral features that were recognized as a fingerprint of dissociative molecular states can be interpreted in terms of ultrashort natural lifetime of ～200 attoseconds in the case of the iodine L-shell core-hole. Our results demonstrate the capacity of the RIXS technique to reveal subtle dynamical effects in molecules with sensitivity to nuclear rearrangement on a subfemtosecond time scale.     

Simulation of x-ray absorption near-edge spectra and x-ray fluorescence spectra of optically excited molecules

The x-ray absorption near-edge spectra (XANES) and fluorescence spectra of molecules in the ground state and optically excited states are computed using time-dependent density functional theory and time-dependent Hartree-Fock theory. The calculated XANES spectra of optically excited methanol, benzonitrile, hydrogen sulphide, and titanium tetrachloride and the fluorescence spectra of optically excited methanol can be used to simulate ultrafast optical pump/x-ray probe experiments.     

Universal density functional approach to the calculation of correlation energies of atoms

A new local density functional approach for the calculation of correlation energies of many-electron atomic systems is proposed by using the exact results for the correlation energy of a two-electron system bound by a harmonic oscillator external potential. This is motivated by the fact that the correlation energy is a universal functional of the electron density, and the form of this functional is independent of the external potential. The calculated numerical results for the correlation energies show very good agreement with the standard values reported in the literature. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 461–465, 1997     

Angular distributions for vibrationally inelastic nonresonant scattering of electrons by molecules

Polar graphs for differential cross section (dcs) called spatial dcs maps are presented as graphical representation of the angular distribution of vibrationally inelastic electron scattering by polyatomic molecules. The objective of this paper is to show that an intuitive understanding of the principal features of these graphs can be obtained from a simple analysis of the normal modes of vibration of the target molecule and plane-wave functions representing the scattering electron. The procedure is illustrated on the H2 and CH4 molecules.     

Excitations of lithium ammonia complexes studied by inelastic x-ray scattering

We have carried out high-resolution inelastic x-ray scattering measurements of the excitations of lithium dissolved in ammonia. The incident x-ray energy was 21.6 keV and the resolution was about 2 meV. Several different excitations are observed in the energy range of 0-60 meV (0-500 cm(-1)). In addition to acoustic phonons at low energies, we see excitations that are associated with vibrations of Li(NH3)4+ complexes. We examined these excitations as a function of momentum transfer, lithium concentration, temperature, and state of the system (solid versus liquid). Data are compared with Hartree-Fock and density-functional theory calculations of the excitations of this complex, which agree well with the measured excitation energies.     

Time-dependent four-component relativistic density functional theory for excitation energies

Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.     

Time-dependent density functional theory investigation of the absorption, fluorescence, and phosphorescence spectra of solvated coumarins

Using time-dependent density functional theory (TD-DFT) and the polarizable continuum model, we have computed the electronic transitions of a large panel of coumarin dyes in their enol, keto, cationic, and anionic forms. Several processes have been studied: absorption, fluorescence, 0-0 phosphorescence, and triplet-triplet excitations. For each process, detailed comparison with experimental data has been carried out. Using the PBE06-31+G(d) scheme, it turns out that for a given electronic transition the experimental shifts resulting from the substitution of the coumarin core are nicely reproduced. Indeed, once a simple statistical correction is applied, the mean absolute errors on the absorption and fluorescence wavelengths are limited to 8 nm (0.09 eV) and 9 nm (0.07 eV), respectively. A valuable correlation between the experimental and theoretical phosphorescence auxochromic displacements has also been unravelled. The differences between the wavelengths of the various electronic processes of a given dye tend to be fairly predicted, especially for the fluorescence-phosphoresence shifts that are strongly overestimated by TD-DFT.     

Time-dependent density functional theory investigation of the electronic spectra of hexanuclear chalcohalide rhenium(III) clusters

The UV-vis spectra of the hexanuclear chalcohalide rhenium(III) clusters of formula [Re(6)S(8)X(6)](4-) (X(-) = Cl(-), Br(-), I(-)) were investigated at the time-dependent density functional theory (TD-DFT) level employing B3LYP, PBE1PBE, and the double-hybrid B2PLYP functional in combination with the LANL2DZ basis set. We were able to reproduce the red shift experimentally observed when the halide changes from chloride to iodide. However, some discrepancies between experimental results and theory were found. First, we did not observe a remarkable dependence of the experimental ill-resolved bands on the solvent. Indeed, similar spectra were obtained taken CH(2)Cl(2) or CH(3)CN as solvents into account. Second, all calculations explained the origin of the band peaked at the low-energy region in contraposition with the one experimentally assumed by R. Long et al. (J. Am. Chem. Soc. 1996, 118, 4603), and theoretically made available by Arratia-Pe?rez et al. (J. Chem. Phys. 1999, 110, 2529). These authors have proposed a ligand-to-cluster charge transfer (LCCT) for all title complexes. Our findings undoubtedly allow such origin to be discarded. While the HGGA functionals lead to a cluster-to-halide ligand charge transfer (CLCT), an intracluster charge transfer (ICCT) has been considered by employing B2PLYP. This contribution showed B2PLYP in the presence of the solvent to be the best performer in studying the UV-vis spectra of large complexes of rhenium(III) containing the Re-S bond. We strongly recommended the use of the double-hybrid B2PLYP in studying UV-vis spectrum of rhenium complexes of size making the computational cost affordable. We expect that our work stimulates new experimental and theoretical investigations of the title complexes to confirm our assignment.     

Time-dependent density functional theory based Ehrenfest dynamics

Time-dependent density functional theory based Ehrenfest dynamics with atom-centered basis functions is developed in present work. The equation of motion for electrons is formulated in terms of first-order reduced density matrix and an additional term arises due to the time-dependence of basis functions through their dependence on nuclear coordinates. This time-dependence of basis functions together with the imaginary part of density matrix leads to an additional term for nuclear force. The effects of the two additional terms are examined by studying the dynamics of H(2) and C(2)H(4), and it is concluded that the inclusion of these two terms is essential for correct electronic and nuclear dynamics.     

Time-dependent density functional theory for nonlinear properties of open-shell systems

This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.     

Resonant inelastic x-ray scattering of methyl chloride at the chlorine K edge

We present a combined experimental and theoretical study of isolated CH(3)Cl molecules using resonant inelastic x-ray scattering (RIXS). The high-resolution spectra allow extraction of information about nuclear dynamics in the core-excited molecule. Polarization-resolved RIXS spectra exhibit linear dichroism in the spin-orbit intensities, a result interpreted as due to chemical environment and singlet-triplet exchange in the molecular core levels. From analysis of the polarization-resolved data, Cl 2p(x, y) and 2p(z) electronic populations can be determined.     

Toward panchromatic organic functional molecules: density functional theory study on the electronic absorption spectra of substituted tetraanthracenylporphyrins

To achieve full solar spectrum absorption of organic dyes for organic solar cells and organic solar antenna collectors, a series of tetraanthracenylporphyrin derivatives including H(2)(TAnP), H(2)(α-F(4)TAnP), H(2)(β,β'-F(8)TAnP), H(2)(γ,γ'-F(8)TAnP), H(2)(δ,δ'-F(8)TAnP), H(2)[α-(NH(2))(4)TAnP], H(2)[β,β'-(NH(2))(8)TAnP], H(2)[γ,γ'-(NH(2))(8)TAnP], and H(2)[δ,δ'-(NH(2))(8)TAnP] was designed and their electronic absorption spectra were systematically studied on the basis of TDDFT calculations. The nature of the broad and intense electronic absorptions of H(2)(TAnP) in the range of 500-1700 nm is clearly revealed, and different types of π → π* electronic transitions associated with different absorption bands are revealed to correspond to different electron density moving direction between peripherally fused 14-electron-π-conjugated anthracene units and the central 18-electron-π-conjugated porphyrin core. Introduction of electron-donating groups onto the periphery of the H(2)(TAnP) macrocycle is revealed to be able to lead to novel NIR dyes such as H(2)[α-(NH(2))(4)TAnP] and H(2)[δ,δ'-(NH(2))(8)TAnP] with regulated UV-vis-NIR absorption bands covering the full solar spectrum in the range of 300-2400 nm.     

Collective dynamics in molten potassium: an inelastic x-ray scattering study

The high-frequency collective dynamics of molten potassium has been investigated by inelastic x-ray scattering, disclosing an energy/momentum transfer region unreachable by previous inelastic neutron scattering (INS) experiments. We find that a two-step relaxation scenario, similar to that found in other liquid metals, applies to liquid potassium. In particular, we show how the sound velocity determined by INS experiments, exceeding the hydrodynamic value by approximately 30%, is the higher limit of a speedup, located in the momentum region 1 < Q < 3 nm(-1), which marks the departure from the isothermal value. We point out how this phenomenology is the consequence of a microscopic relaxation process that, in turn, can be traced back to the presence of "instantaneous" disorder, rather than to the crossover from a liquid to solidlike response.