Molecular electrical properties theory

This chapter deals with a number of applications of group theory to molecular properties and structure, all connected by the idea of symmetrized powers of representations. The GT calculator has a general facility for calculation of these powers, and specialised routines for their application to angular momentum, molecular electric properties and isomer counting. 

Molecular orbital theory explains the electrical properties of solids by treating them as one huge molecule and supposing that their valence electrons occupy molecular orbitals that spread throughout the solid. 

We then turn to the question of how to eliminate the spin-orbit interaction in four-component relativistic calculations. This allows the assessment of spin-orbit effects on molecular properties within the framework of a single theory. In a previous publication [13], we have shown how the spin-orbit interaction can be eliminated in four-component relativistic calculations of spectroscopic properties by deleting the quaternion imaginary parts of matrix representations of the quaternion modified Dirac equation. We show in this chapter how the application of the same procedure to second-order electric properties takes out spin-forbidden transitions in the spectrum of the mercury atom. Second-order magnetic properties require more care since the straightforward application of the above procedure will extinguish all spin interactions. After careful analysis on how to proceed we... 

While the study of the conventional semiconducting materials has progressed rapidly, the study of organic materials has received much less attention until the past few years. In particular the electrical properties of polymers have been much neglected and little authoritative work exists in the literature. In view of current developments in theories of the electrical properties of organic molecular crystals, it seems profitable to take stock of the situation as far as charge transfer in polymers is concerned. 

The electrical properties of any material are a result of the material s electronic structure. The presumption that CPs form bands through extensive molecular obital overlap leads to the assumption that their electronic properties can be explained by band theory. With such an approach, the bands and their electronic population are the chief determinants of whether or not a material is conductive. Here, materials are classified as one of three types shown in Scheme 2, being metals, semiconductors, or insulators. Metals are materials that possess partially-filled bands, and this characteristic is the key factor leading to the conductive nature of this class of materials. Semiconductors, on the other hand, have filled (valence bands) and unfilled (conduction bands) bands that are separated by a range of forbidden energies (known as the band gap ). The conduction band can be populated, at the expense of the valence band, by exciting electrons (thermally and/or photochemically) across this band gap. Insulators possess a band structure similar to semiconductors except here the band gap is much larger and inaccessible under the environmental conditions employed. 

Metals form a class of solids with characteristic macroscopic properties. They are ductile, have a silver-white luster, and they conduct electricity and heat remarkably well. An early, but still relevant microscopic model aimed at explaining the electrical conductivity, heat conductivity, and optical properties was proposed by Drude [10]. His model incorporates two important successes of modem science the discovery of the electron in 1887 by J. J. Thomson, and the molecular kinetic gas theory put forward by Boltzmann and Maxwell in the second half of the 19th century. 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

In the present review article 1985 s results obtained in applications of the concept of vibronic interactions to the investigation of electric properties of molecules (dipole and multipole moments and polarizabilities) are presented. Molecular aspects of these topics are almost untouched in the publications listed in the preceding paragraph. The idea of dipole instability was used first as a basis of the so-called vibronic theory of ferroelectricity (Bersuker, 1966 Bersuker and Vekhter, 1978). Meanwhile, the manifestation of the electronic or vibronic degeneracy in the electric responses of molecules, being no less essential than other vibronic effects, has some special features. 

In the theory of electric properties of molecular systems in degenerate electronic states some unsolved problems remain. First, the problem of intermolecular interactions considering the degeneracy of the electronic states of the interacting molecules has not been solved completely. In this case, besides the lowering of the multipolarity of the interaction described in this paper, one can expect an essential contribution of anisotropic induction and dispersion interactions to different virial correction to the equations of state, refraction, and other electric characteristics of matter. 

Electric properties were obtained for the ground state using finite perturbation theory. An electric field, E, along the molecular axis was varied in steps of 0.005 a.u. and the resulting energies were fitted to a fourth-order polynomial in E. The first and second derivative then gave the dipole moment and polarizability along file molecular axis. 

First, quantum mechanics methods and the formalism of the theoretical calculation of electrical properties for finite and infinite systems, level of theory implemented such as methods and basis sets, and single molecule conductance of molecular junctions are described. 

At present, two quantum mechanical theories are used to describe covalent bond formation and the electronic structure of molecules. Valence bond (VB) theory assumes that the electrous in a molecule occupy atomic orbitals of the individual atoms. It enables us to retain a picture of individual atoms taking part in the bond formation. The second theory, called molecular orbital MO) theory, assumes the formation of molecular orbitals from the atomic orbitals. Neither theory perfectly explains all aspects of bonding, but each has contributed something to our understanding of many observed molecular properties. 

The electrical properties of an infinite polyene have intrigued theoretical chemists for more than fifty years. Shortly after Hiickel introduced his 7i-electron theory for unsaturated systems in 1931, speculations began to appear about the carbon-carbon bond lengths to be expected in an infinite polyene. The question was interesting because, if the bonds were of equal length, 7i-electron theory predicted that the 7i-molecular orbitals would form a continuous band which would be half-filled, whereas alternating carbon-... 

J. Autschbach, T. Ziegler. Calculating molecular electric and magnetic properties from time-dependent density functional response theory. /. Chem. Phys., 116(3) (2002) 891-896. 

The earliest semiempirical methods were well in advance of ab initio methods partly because of the limits on computing power. The first of these is the ir-molecular orbital (MO) theory of conjugated and aromatic molecules proposed by Hiickel " in 1931. Most succeeding semiempirical theories are direct descendants of Hiickel s original approach wherein one or more of the approximations has been improved. It is interesting to note that Hiickel theory in its original form still sees infrequent application to properties such as electric susceptibilities, soliton dynamics, and others. 

The description of dipole moments of molecular complexes is significantly sophisticated as the number of atoms in the interacting molecules increases. The electrical properties of molecular van der Waals complexes are now studied not fully enough. Below, we concentrate our attention only on two relatively large molecular complexes CH4-N2 and C2H2-C2H2 (Sect. 3.2.4) which have, on the one hand, the astrophysical interest and on the other hand, they illustrate effectively the theory discussed above. 

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