Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the two-electron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources

Kohn-Sham density functional theory calculations of non-resonant and resonant X-ray emission spectroscopy

The accuracy of non-resonant and resonant (resonant inelastic X-ray scattering) X-ray emission spectra simulated based upon Kohn-Sham density functional theory is assessed. Accurate non-resonant X-ray emission spectra with the correct energy scale are obtained when short-range corrected exchange-correlation functionals designed for the calculation of X-ray absorption spectroscopy are used. It is shown that this approach can be extended to simulate resonant inelastic X-ray scattering by using a reference determinant that describes a core-excited state. For this spectroscopy, it is found that a standard hybrid functional, B3LYP, gives accurate spectra that reproduce the features observed in experiment. However, the ability to correctly describe subtle changes in the spectra arising from different intermediate states is more challenging and requires averaging over conformations from a molecular dynamics simulation. Overall, it is demonstrated that accurate non-resonant and resonant X ray emission spectra can be simulated directly from Kohn-Sham density functional theory

Calculating excited state properties using Kohn-Sham density functional theory

The accuracy of excited states calculated with Kohn-Sham density functional theory using the maximum overlap method has been assessed for the calculation of adiabatic excitation energies, excited state structures, and excited state harmonic and anharmonic vibrational frequencies for open-shell singlet excited states. The computed Kohn-Sham adiabatic excitation energies are improved significantly by post self-consistent-field spin-purification, but remain too low compared with experiment with a larger error than time-dependent density functional theory. Excited state structures and vibrational frequencies are also improved by spin-purification. The structures show a comparable accuracy to time-dependent density functional theory, while the harmonic vibrational frequencies are found to be more accurate for the majority of vibrational modes. The computed harmonic vibrational frequencies are also further improved by perturbative anharmonic corrections, suggesting a good description of the potential energy surface. Overall, excited state Kohn-Sham density functional theory is shown to provide an efficient method for the calculation of excited state structures and vibrational frequencies in open-shell singlet systems, and provides a promising technique that can be applied to study large systems

Density functional theory calculations of the non-resonant and resonant X-ray emission spectroscopy of carbon fullerenes and nanotubes

The non-resonant X-ray emission spectroscopy of fullerenes and carbon nanotubes is studied with density functional theory in conjunction with short-range corrected functionals. For C60 and C70 the X-ray emission spectra are insensitive to modest structural changes, and absorption onto the fullerene cage has the greatest effect with a broader less structured band observed with the high energy ⇡ band reduced in intensity. For carbon nanotubes the X-ray emission spectra are shown to be weakly dependent on the length and chirality of the nanotube. However, some variation with the diameter of the tube is observed in both resonant and non-resonant spectra

Cosmological Magnetic Fields from Primordial Helicity

Primordial magnetic fields may account for all or part of the fields observed in galaxies. We consider the evolution of the magnetic fields created by pseudoscalar effects in the early universe. Such processes can create force-free fields of maximal helicity; we show that for such a field magnetic energy inverse cascades to larger scales than it would have solely by flux freezing and cosmic expansion. For fields generated at the electroweak phase transition, we find that the predicted wavelength today can in principle be as large as 10 kpc, and the field strength can be as large as 10^{-10} G.Comment: 13 page

Photoaquation mechanism of hexacyanoferrate(II) ions: ultrafast 2D UV and transient visible and IR spectroscopies

Ferrous iron(II) hexacyanide in aqueous solutions is known to undergo photoionization and photoaquation reactions depending on the excitation wavelength. To investigate this wavelength dependence, we implemented ultrafast two-dimensional UV transient absorption spectroscopy, covering a range from 280 to 370 nm in both excitation and probing, along with UV pump/visible probe or time-resolved infrared (TRIR) transient absorption spectroscopy and density functional theory (DFT) calculations. As far as photoaquation is concerned, we find that excitation of the molecule leads to ultrafast intramolecular relaxation to the lowest triplet state of the [Fe(CN)6]4– complex, followed by its dissociation into CN– and [Fe(CN)5]3– fragments and partial geminate recombination, all within <0.5 ps. The subsequent time evolution is associated with the [Fe(CN)5]3– fragment going from a triplet square pyramidal geometry, to the lowest triplet trigonal bipyramidal state in 3–4 ps. This is the precursor to aquation, which occurs in ∼20 ps in H2O and D2O solutions, forming the [Fe(CN)5(H2O/D2O)]3– species, although some aquation also occurs during the 3–4 ps time scale. The aquated complex is observed to be stable up to the microsecond time scale. For excitation below 310 nm, the dominant channel is photooxidation with a minor aquation channel. The photoaquation reaction shows no excitation wavelength dependence up to 310 nm, that is, it reflects a Kasha Rule behavior. In contrast, the photooxidation yield increases with decreasing excitation wavelength. The various intermediates that appear in the TRIR experiments are identified with the help of DFT calculations. These results provide a clear example of the energy dependence of various reactive pathways and of the role of spin-states in the reactivity of metal complexes

Equidistribution of zeros of holomorphic sections in the non compact setting

We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL2(Z) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.Comment: 25 pages; v.2 is a final update to agree with the published pape

A longitudinal investigation of repressive coping and ageing

This is an Accepted Manuscript of an article published by Taylor & Francis in Aging & Mental Health on October 2016, available online: http://www.tandfonline.com/doi/full/10.1080/13607863.2015.1060941.Two studies investigated the possibility that repressive coping is more prevalent in older adults and that this represents a developmental progression rather than a cohort effect. Study 1 examined repressive coping and mental health cross-sectionally in young and old adults. Study 2 examined whether there was a developmental progression of repressive coping prevalence rates in a longitudinal sample of older adults.Peer reviewedFinal Accepted Versio

Competing Pathways in the Photochemistry of Ru(H)2(CO)(PPh3)3

The photochemistry of Ru(H)2(CO)(PPh3)3 (1) has been reinvestigated employing laser and conventional light sources in conjunction with NMR spectroscopy and IR spectroscopy. The sensitivity of NMR experiments was enhanced by use of p-H2-induced polarization (PHIP), and a series of unexpected reactions were observed. The photoinduced reductive elimination of H2 was demonstrated (a) via NMR spectroscopy by the observation of hyperpolarized 1 on pulsed laser photolysis in the presence of p-H2 and (b) via nanosecond time-resolved infrared (TRIR) spectroscopy studies of the transient [Ru(CO)(PPh3)3]. Elimination of H2 competes with photoinduced loss of PPh3, as demonstrated by formation of dihydrogen, triphenylarsine, and pyridine substitution products which are detected by NMR spectroscopy. The corresponding coordinatively unsaturated 16-electron intermediate [Ru(H)2(CO)(PPh3)2] exists in two isomeric forms according to TRIR spectroscopy that react with H2 and with pyridine on a nanosecond time scale. These two pathways, reductive elimination of H2 and PPh3 loss, are shown to occur with approximately equal quantum yields upon 355 nm irradiation. Low-temperature photolysis in the presence of H2 reveals the formation of the dihydrogen complex Ru(H)2(η2-H2)(CO)(PPh3)2, which is detected by NMR and IR spectroscopy. This complex reacts further within seconds at room temperature, and its behavior provides a rationale to explain the PHIP results. Furthermore, photolysis in the presence of AsPh3 and H2 generates Ru(H)2(AsPh3)(CO)(PPh3)2. Two isomers of Ru(H)2(CO)(PPh3)2(pyridine) are formed according to NMR spectroscopy on initial photolysis of 1 in the presence of pyridine under H2. Two further isomers are formed as minor products; the configuration of each isomer was identified by NMR spectroscopy. Laser pump-NMR probe spectroscopy was used to observe coherent oscillations in the magnetization of one of the isomers of the pyridine complex; the oscillation frequency corresponds to the difference in chemical shift between the hydride resonances. Pyridine substitution products were also detected by TRIR spectroscopy