Low-energy unphysical saddle in polynomial molecular potentials

Vibrational spectra of polyatomic molecules are often obtained from a polynomial expansion of the adiabatic potential around a minimum. For several molecules, we show that such an approximation displays an unphysical saddle point of comparatively small energy, leading to a region where the potential is negative and unbounded. This poses an upper limit for a reliable evaluation of vibrational levels. We argue that the presence of such saddle points is general.Comment: The preprint version of the published Mol. Phys. paper, 19 pages, 3 figure

Novel Chiral Pyromellitdiimide (1,2,4,5-Benzenetetracarboxydiimide) Dimers and Trimers: Exploring Their Structure, Electronic Transitions and Exciton Coupling

The chiral but highly symmetrical acyclic and cyclic pyromellitic diimide dimers and trimers 2-5 have been obtained and characterized for the first time. The pyromellitdiimide chromophores in these molecules are linked by a rigid diequatorially 1,2-disubstituted cyclohexane skeleton. The structures of the compounds have been determined in detail by molecular modeling and, in the case of cyclic dimer 4 and trimer 5, by means of X-ray diffraction analysis. The electronically excited states of the pyromellitdiimide chromophore (1a) have been studied in these and other model compounds by means of linear dichroism (LD), magnetic circular dichroism (MCD), and circular dichroism (CD) spectroscopy. CD spectra of the rigid cyclic trimer 5 have provided the most detailed information on the excited states of the pyromellitdiimide chromophore. The low-energy tail (340-360 nm) of the absorption envelope can be assigned to out-of-plane polarized n-pi* transitions (I, II). The higher energy bands are due to contributions from up to six pi-pi* transitions, these being polarized either along the long (IV-VI, VIII) or short axis (III, VII). The results of ab initio CIS/cc-pVDZ and semiempirical INDO/S-CI calculations have been compared with the experimental data. CD Cotton effects in the region 200260 nm, which result from exciton interactions between electric dipole allowed transitions of two pyromellitdiimide chromophores in compounds 2-5, provide reliable and useful information concerning the conformation and absolute configuration of these molecules, which may be extrapolated to other oligoimide systems

Novel Chiral Pyromellitdiimide (1,2,4,5-Benzenetetracarboxydiimide) Dimers and Trimers: Exploring Their Structure, Electronic Transitions and Exciton Coupling

The chiral but highly symmetrical acyclic and cyclic pyromellitic diimide dimers and trimers 2-5 have been obtained and characterized for the first time. The pyromellitdiimide chromophores in these molecules are linked by a rigid diequatorially 1,2-disubstituted cyclohexane skeleton. The structures of the compounds have been determined in detail by molecular modeling and, in the case of cyclic dimer 4 and trimer 5, by means of X-ray diffraction analysis. The electronically excited states of the pyromellitdiimide chromophore (1a) have been studied in these and other model compounds by means of linear dichroism (LD), magnetic circular dichroism (MCD), and circular dichroism (CD) spectroscopy. CD spectra of the rigid cyclic trimer 5 have provided the most detailed information on the excited states of the pyromellitdiimide chromophore. The low-energy tail (340-360 nm) of the absorption envelope can be assigned to out-of-plane polarized n-pi* transitions (I, II). The higher energy bands are due to contributions from up to six pi-pi* transitions, these being polarized either along the long (IV-VI, VIII) or short axis (III, VII). The results of ab initio CIS/cc-pVDZ and semiempirical INDO/S-CI calculations have been compared with the experimental data. CD Cotton effects in the region 200260 nm, which result from exciton interactions between electric dipole allowed transitions of two pyromellitdiimide chromophores in compounds 2-5, provide reliable and useful information concerning the conformation and absolute configuration of these molecules, which may be extrapolated to other oligoimide systems

HellRank: a Hellinger-based centrality measure for bipartite social networks

Measuring centrality in a social network, especially in bipartite mode, poses many challenges, for example, the requirement of full knowledge of the network topology, and the lack of properly detecting top-k behavioral representative users. To overcome the above mentioned challenges, we propose HellRank, an accurate centrality measure for identifying central nodes in bipartite social networks. HellRank is based on the Hellinger distance between two nodes on the same side of a bipartite network. We theoretically analyze the impact of this distance on a bipartite network and find upper and lower bounds for it. The computation of the HellRank centrality measure can be distributed, by letting each node uses local information only on its immediate neighbors. Consequently, one does not need a central entity that has full knowledge of the network topological structure. We experimentally evaluate the performance of the HellRank measure in correlation with other centrality measures on real-world networks. The results show partial ranking similarity between the HellRank and the other conventional metrics according to the Kendall and Spearman rank correlation coefficient