Partial projective representations and partial actions

The concept of a partial projective representation of a group is introduced and studied. The interaction with partial actions is explored. It is shown that the factor sets of partial projective representations over a field K are exactly the K-valued twistings of crossed products by partial actions. (C) 2009 Elsevier B.V. All rights reserved.

New insights on surface-enhanced Raman scattering based on controlled aggregation and spectroscopic studies, DFT calculations and symmetry analysis for 3,6-bi-2-pyridyl-1,2,4,5-tetrazine adsorbed onto citrate-stabilized gold nanoparticles

Asystematic study on the surface-enhanced Raman scattering (SERS) for 3,6-bi-2-pyridyl-1,2,4,5-tetrazine (bptz) adsorbed onto citrate-modified gold nanoparticles (cit-AuNps) was carried out based on electronic and vibrational spectroscopy and density functional methods. The citrate/bptz exchange was carefully controlled by the stepwise addition of bptz to the cit-AuNps, inducing flocculation and leading to the rise of a characteristic plasmon coupling band in the visible region. Such stepwise procedure led to a uniform decrease of the citrate SERS signals and to the rise of characteristic peaks of bptz, consistent with surface binding via the N heterocyclic atoms. In contrast, single addition of a large amount of bptz promoted complete aggregation of the nanoparticles, leading to a strong enhancement of the SERS signals. In this case, from the distinct Raman profiles involved, the formation of a new SERS environment became apparent, conjugating the influence of the local hot spots and charge-transfer (CT) effects. The most strongly enhanced vibrations belong to a(1) and b(2) representations, and were interpreted in terms of the electromagnetic and the CT mechanisms: the latter involving significant contribution of vibronic coupling in the system. Copyright (C) 2010 John Wiley & Sons, Ltd.