Vibrational analysis of Ni(II) complex with 4,12-ditolyl-16,24-diphenyl-3-thiaporphyrin (SDTDPPNi(II)Cl) and its isotopic labeled (61Ni(II), −d6, and −d10) derivatives

This work presents complete vibrational analysis of a chloride complex of Ni (II) 4,12-ditolyl-16,24-diphenyl-3-thiaporphyrin ( SDTDPPNi (II) Cl ) and its isotopic derivatives (61 Ni (II), − d 6, and −d 10). Five-coordinate SDTDPPNi (II) Cl , SDTDPP 61 Ni (II) Cl , ( SDTDPP - d 6) Ni (II) Cl , and ( SDTDPP - d 10) Ni (II) Cl were investigated by Fourier-Transform infrared (FT-IR), resonance Raman (RR), and electronic absorption (UV-vis) methods. Because the methyl groups of tolyl rings at the para-position have negligible influence on geometry and vibrational spectra of SDTDPPNi (II) Cl , they can be treated as point groups. Thus, geometry optimization and vibrational frequencies were calculated for the 4,12,16,24-tetraphenyl-3-thiaporphyrin ( STPPNi (II) Cl ) model molecule and its isotopically labeled analogs using Gaussian'03. Moreover, charge distributions (General Atomic Polar Tensor – GAPT) and geometrical aromaticity indexes (Bird's I 5 and Harmonic Oscillator Model of Aromaticity – HOMA) were calculated. All theoretical calculations were performed at the B3LYP level with the LANL2DZ basis set. As is shown, the experimental FT-IR and RR spectra for each compound are reproduced well by the corresponding theoretical spectra.

Pyroelectricity

As the name implies, pyroelectricity is a first rank tensor property relating a change polarization P to a change in temperature δT. The defining relation can also be written in terms of the electric displacement D since no field is applied: . . . Pi = Di = piδT [C/m2]. . . Pyroelectricity is a first rank polar tensor because of the way it transforms. Being polar vectors, Pi and Di transform as . . . D'i = aijDj . . . whereas the temperature change transforms as a zero rank tensor, or a scalar: . . . δT' = δT. . . . Transforming the defining relation for pyroelectricity we get . . . D'i = aijDj = aijpjδT = aijpjδT' = p'iδT'. . . . Both the independent variable δT and the dependent variable Di have now been transformed to the new coordinate system. The property relating D'i to δT' is the transformed pyroelectric coefficient p'i = aijpj. Thus the pyroelectric coefficient is a polar first rank tensor property. In Sections 6.1 and 7.3 it was shown that the electrocaloric effect and the pyroelectric effect are governed by the same set of coefficients pi. The change in entropy per unit volume caused by an electric field is . . . δS = piEi [J/m3]. The pyroelectric (=electrocaloric coefficient) coefficient is usually expressed in units of μC/m2 K and can be either positive or negative in sign depending on whether the spontaneous (built-in) polarization is increasing or decreasing with temperature. Pyroelectricity disappears in all centrosymmetric materials. The proof follows. For a first rank tensor there are, in general, three nonzero coefficients p1, p2, and p3 representing the values of the pyroelectric coefficient along property axes Z1, Z2, and Z3, respectively. The principal axes are perpendicular to each other and are chosen in accordance with the IEEE convention (Section 4.3).

Electrical resistivity

The next six chapters describe the transport phenomena associated with the flow of charge, heat, and matter. In each case there is a vector flux that is governed by a vector field. Linear relationships between flux and field include electrical resistivity (Chapter 17), thermal conductivity (Chapter 18), diffusion (Chapter 19), and thermoelectricity (Chapter 21). All are represented by second rank tensors similar to electric permittivity (Chapter 9), but the underlying physics is somewhat different. Transport properties are nonequilibrium phenomena governed by statistical mechanics and the concept of microscopic reversibility, rather than the second law of thermodynamics that applies to equilibrium properties such as specific heat, permittivity, and elasticity. Higher order tensors appear when the transport experiments are carried out in the presence of magnetic fields or mechanical stresses. Galvanomagnetic, thermomagnetic (Chapter 20), and piezoresistance effects (Chapter 22) require third- and fourth-rank tensors. When an electric field is applied to a conductor, an electric current flows through the sample. The field Ei (in V/m) is related to the current density Jj (in A/m2) through Ohm’s Law, where ρij is the electrical resistivity (in Ω m). In tensor form, . . . Ei = ρijJj . . . Ei and Jj are polar vectors (first rank polar tensors) and ρij is a second rank polar tensor property which follows Neumann’s law in the usual way. Sometimes it is more convenient to use the reciprocal relation involving the electrical conductivity σij : . . . Ji = σijEj . . . .