Linear complex polarization propagator in a four-component Kohn-Sham framework.

International audienceAn algorithm for the solution of the linear response equation in the random phase approximation is presented. All entities including frequency arguments, matrices, and vectors, are assumed to be complex, and it represents the core equation solver needed in complex polarization propagator approaches where nonstimulated relaxation channels are taken into account. Stability and robustness of the algorithm are demonstrated in applications regarding visible, ultraviolet, and x-ray spectroscopies. An implementation of the algorithm at the level of four-component relativistic, noncollinear, density functional theory for imaginary (but not complex) frequency arguments has been achieved and is used to determine the electric dipole dispersion interaction coefficients for the rubidium and cesium dimers. Our best estimates for the C(6) coefficients of Rb(2) and Cs(2) are equal to 14.0x10(3) and 21.9x10(3) a.u., respectively

On the Importance of Clar Structures of Polybenzenoid Hydrocarbons as Revealed by the pi-Contribution to the Electron Localization Function

The degree of pi-electron (de) localization and aromaticity of a series of polybenzenoid hydrocarbons (PBHs) has been analyzed through the pi-contribution to the electron localization function (ELF pi), calculated at the B3LYP/ 6-311G(d, p) hybrid density functional theory level. The extent of. -electron delocalization in the various hexagons of a PBH was determined through analysis of the bifurcation values of the ELF. basins (BV(ELF.)), the spans in the bifurcation values in each hexagon (BV(ELF pi)), and the ring-closure bifurcation values of the ELF pi (RCBV(ELF pi)). These computed results were compared to the qualitative description of local aromaticities of the different hexagons in terms of Clar structures with pi-sextets. Benzene, [18] annulene, and thirty two PBHs were analyzed at their equilibrium geometries, and benzene and triphenylene were also analyzed at bond length distorted structures. In general, the description of PBHs in terms of Clar valence structures is supported by the ELF pi properties, although there are exceptions. For PBHs at their equilibrium geometries there is a clear sigmoidal relationship between the CC bond lengths and the amount of pi-electron (de) localization at these bonds, however, this relationship is lost for bond distorted geometries. In the latter cases, we specifically examined benzene in D3h symmetric " 1,3,5-cyclohexatriene" structures and triphenylene in eight different structures. From the distorted benzenes and triphenylenes it becomes clear that there is a distinct tendency for the pi-electron network to retain delocalization (aromaticity). The ELF. analysis thus reveals an antidistortive rather than a distortive behavior of the pi-electrons in these investigated compounds

On the Importance of Clar Structures of Polybenzenoid Hydrocarbons as Revealed by the n-Contribution to the Electron Localization Function

The degree of p-electron (de)localization and aromaticity of a series of polybenzenoid hydrocarbons (PBHs) has been analyzed through the π-contribution to the electron localization function (ELFπ), calculated at the B3LYP/6-311G(d,p) hybrid density functional theory level. The extent of p-electron delocalization in the various hexagons of a PBH was determined through analysis of the bifurcation values of the ELFp basins (BV(ELFp)), the spans in the bifurcation values in each hexagon (ΔBV(ELFπ)), and the ring-closure bifurcation values of the ELFπ (RCBV(ELFπ)). These computed results were compared to the qualitative description of local aromaticities of the different hexagons in terms of Clar structures with p-sextets. Benzene, [18]annulene, and thirty two PBHs were analyzed at their equilibrium geometries, and benzene and triphenylene were also analyzed at bond length distorted structures. In general, the description of PBHs in terms of Clar valence structures is supported by the ELFp properties, although there are exceptions. For PBHs at their equilibrium geometries there is a clear sigmoidal relationship between the CC bond lengths and the amount of p-electron (de)localization at these bonds, however, this relationship is lost for bond distorted geometries. In the latter cases, we specifically examined benzene in D3h symmetric “1,3,5-cyclohexatriene” structures and triphenylene in eight different structures. From the distorted benzenes and triphenylenes it becomes clear that there is a distinct tendency for the p-electron network to retain delocalization (aromaticity). The ELFp analysis thus reveals an antidistortive rather than a distortive behavior of the p-electrons in these investigated compounds