Determining the Waveguide Profile using the Overlap Integral

Bound states degenerated in energy (and differing in parity) may form in one-dimensional quantum mechanics if the potential is unbounded from below. We focus on symmetric potential and present quasi-exactly solvable (QES) model based on WKB method. The application of this method is limited on slow-changing potentials. We consider the overlap integral of WKB wave functions [Formula: see text] and [Formula: see text] which correspond to energies [Formula: see text] and [Formula: see text], and by setting [Formula: see text], we determine the type of spectrum depending on parameter [Formula: see text] which arises from this method. For finite value [Formula: see text], we show that the entire spectrum will consist of degenerated bound states.

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Molecular structure, optical and magnetic properties of the {SnIVPc(3-)Cl2}•- radical anions containing negatively charged Pc ligands

Journal of Porphyrins and Phthalocyanines ◽

10.1142/s1088424614501077 ◽

2014 ◽

Vol 18 (12) ◽

pp. 1157-1163 ◽

Cited By ~ 19

Author(s):

Dmitri V. Konarev ◽

Sergey I. Troyanov ◽

Maxim A. Faraonov ◽

Manabu Ishikawa ◽

Akihiro Otsuka ◽

...

Keyword(s):

Effective Magnetic Moment ◽

Room Temperature ◽

Blue Shift ◽

Ammonium Cation ◽

Antiferromagnetic Coupling ◽

Radical Anions ◽

Weiss Temperature ◽

Overlap Integral ◽

One Dimensional ◽

Epr Signal

Radical anion salt ( PPN +){ Sn IV Pc (3-) Cl 2}•- (1) was obtained by the reduction of tin(IV) phthalocyanine dichloride { Sn IV Pc (2-) Cl 2} with ( PPN +)( C 60•-) ( PPN + is bis(triphenylphosphoranylidene)-ammonium cation). It was shown that the reduction is centered mainly on the Pc ligand providing the appearance of a new band in the spectrum of 1 in the NIR range at 1006 nm and blue-shift of Soret and Q-bands of Sn IV Pc (2-) Cl 2. The alternation of short and long C – N imine bonds for two oppositely located isoindole units in 1 indicates possible disruption of aromaticity of the Pc ligand under reduction. Salt 1 has effective magnetic moment of 1.69 μB at 300 K corresponding to the contribution of one non-interacting S = 1/2 spin per formula unit and manifests antiferromagnetic coupling of spins with Weiss temperature of -7.3 K in the 400–30 K range. The salt shows a broad EPR signal with g = 1.9957 and linewidth of 19.3 mT at room temperature. The signal splits into two components below 120 K. Strong broadening of the EPR signal and shift of g-factors to smaller values in comparison with the EPR signal from radical anions of metal-free phthalocyanine { H 2 Pc (3-)}•- were attributed to the contribution of the { Sn III Pc (2-) Cl 2}- admixture with paramagnetic Sn III . There are π–π stacking one-dimensional chains composed of { Sn IV Pc (3-) Cl 2}•- in 1 along the a axis with weak overlapping between phenylene groups of phthalocyanine radical anions. The calculated HOMO–HOMO overlap integral is 0.0033 and the SOMO–SOMO overlap integral is only 0.0004. Metallic conductivity is not realized in 1 most probably due to weak SOMO–SOMO overlapping.

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