Damped response theory description of two-photon absorption

Damped response theory is applied to the calculation of two-photon absorption (TPA) spectra, which are determined directly, at each frequency, from a modified damped cubic response function. The TPA spectrum may therefore be evaluated for selected frequency ranges, making the damped TPA approach attractive for calculations on large molecules with a high density of states, where the calculation of TPA using standard theory is more problematic. Damped response theory can also be applied to the case of intermediate state resonances, where the standard TPA expression is divergent. Both exact damped response theory and its application within density functional theory are discussed. The latter is implemented using an atomic-orbital based density matrix formulation, which makes the approach especially suitable for studies on large systems. A test preliminary study is presented for the TPA spectrum of R-(+)-1,1'-bi(2-naphtol).     

Variational response-function formulation of vibrational circular dichroism

The atomic axial tensor (AAT) of vibrational circular dichroism is expressed as the frequency derivative at zero frequency of a linear response function for operators referencing a nuclear displacement and a magnetic field. This is used in the density matrix-based quasienergy derivative Lagrangian approach of Thorvaldsen et al. [J. Chem. Phys., 2008, 129, 214108] to express the AAT in a form where the need to solve response equations for the nuclear displacements is removed, significantly reducing the computation cost compared to existing formulations. The density matrix-based quasienergy derivative Lagrangian approach also allows us straightforwardly to use London atomic orbitals to remove the gauge-origin dependence and to account for the atomic orbitals' dependence on the nuclear coordinates. The formalism is entirely based on atomic-orbital density and integral matrices and therefore amenable to linear scaling for sufficiently sparse matrices and given a linearly scaling response solver.     

Thin noble metal films on Si (111) investigated by optical second-harmonic generation and photoemission

Thin noble metal films (Ag, Au and Cu) on Si (111) have been investigated by optical second-harmonic generation (SHG) in combination with synchrotron radiation photoemission spectroscopy. The valence band spectra of Ag films show a quantization of the sp-band in the 4-eV energy range from the Fermi level down to the onset of the d-bands. For Cu and Au the corresponding energy range is much narrower and quantization effects are less visible. Quantization effects in SHG are observed as oscillations in the signal as a function of film thickness. The oscillations are strongest for Ag and less pronounced for Cu, in agreement with valence band photoemission spectra. In the case of Au, a reacted layer floating on top of the Au film masks the observation of quantum well levels by photoemission. However, SHG shows a well-developed quantization of levels in the Au film below the reacted layer. For Ag films, the relation between film thickness and photon energy of the SHG resonances indicates different types of resonances, some of which involve both quantum well and substrate states. Received: 16 October 2001 / Revised version: 14 March 2002 / Published online: 29 May 2002     

Dynamical approach to complex regional economic growth based on Keynesian model for China

The paper addresses the problem of complex regional economic growth by using nonlinear Keynesian model with focusing on direct foreign investments effects. We investigate the dynamics of the model for the broad range of parameters which, in particular, contains the parameter values obtained recently by econometric analysis of the data for economic growth in China. For the single-region model we give conditions for which the dynamics of the model will be chaotic or regular. The parameters which prevent the economic stagnation are indicated. Further, we consider the model for two regions with a common trade as a coupling factor. The conditions are given for the two trading systems to exhibit chaotic synchronization, in-phase and out-of-phase behavior.     

Novel retinylidene iminium salts for defining opsin shifts: synthesis and intrinsic chromophoric properties

Retinal Schiff bases serve as chromophores in many photoactive proteins that carry out functions such as signalling and light-induced ion translocation. The retinal Schiff base can be found as neutral or protonated, as all-trans, 11-cis or 13-cis isomers and can adopt different conformations in the protein binding pocket. Here we present the synthesis and characterisation of isomeric retinylidene iminium salts as mimics blocked towards isomerisation at the C11 position and conformationally restrained. The intrinsic chromophoric properties are elucidated by gas phase absorption studies. These studies reveal a small blue-shift in the S0-->S1 absorption for the 11-locked derivative as compared to the unlocked one. The gas phase absorption spectra of all the cationic mimics so far investigated show almost no absorption in the blue region. This observation stresses the importance of protein interactions for colour tuning, which allows the human eye to perceive blue light.     

Toward superlensing with metal–dielectric composites and multilayers

We report on the fabrication of two types of adjustable, near-field superlens designs: metal–dielectric composites and metal–dielectric multilayer films. We fabricated a variety of films with different materials, thicknesses and compositions. These samples were characterized physically and optically to determine their film composition, quality, and optical responses. Our results on metal–dielectric composites indicate that although the real part of the effective permittivity generally follows effective medium theory predictions, the imaginary part does not and substantially higher losses are observed. Going forward, it appears that multilayer metal–dielectric designs are more suitable for sub-diffraction imaging applications because they could provide both tunability and low loss.     

Relaxation of signed integral functionals in BV

For integral functionals initially defined for ${u \in {\rm W}^{1,1}(\Omega; \mathbb{R}^m)}$ by $$\int_{\Omega} f(\nabla u) \, {\rm d}x$$ we establish strict continuity and relaxation results in ${{\rm BV}(\Omega; \mathbb{R}^m)}$ . The results cover the case of signed continuous integrands ${f : \mathbb{R}^{m \times d} \to \mathbb{R}}$ of linear growth at infinity. In particular, it is not excluded that the integrands are unbounded below.     

BMO and uniform estimates for multi-well problems

We establish optimal local regularity results for vector-valued extremals and minimizers of variational integrals whose integrand is the squared distance function to a compact set K in matrix space ${{{\mathbb M}^{N \times n}}}$ . The optimality is illustrated by explicit examples showing that, in the nonconvex case, minimizers need not be locally Lipschitz. This is in contrast to the case when the set K is suitably convex, where we show that extremals are locally Lipschitz continuous. The results rely on the special structure of the integrand and elementary Cordes–Nirenberg type estimates for elliptic systems.     

Benchmark density functional theory calculations for nanoscale conductance

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code in combination with maximally localized Wannier functions and the norm-conserving pseudopotential code SIESTA which applies an atomic orbital basis set. All calculations have been converged with respect to the supercell size and the number of k|| points in the surface plane. For all systems we find that the SIESTA transmission functions converge toward the plane-wave result as the SIESTA basis is enlarged. Overall, we find that an atomic basis with double zeta and polarization is sufficient (and in some cases, even necessary) to ensure quantitative agreement with the plane-wave calculation. We observe a systematic downshift of the SIESTA transmission functions relative to the plane-wave results. The effect diminishes as the atomic orbital basis is enlarged; however, the convergence can be rather slow.