Dipole Polarizability of C28 and its Counterparts Nb4B18 and Ta4B18. Insights from a Density Functional Theory (DFT) Endeavour

We report on a preliminary investigation of the non linear optical (NLO) properties and in particular dipole polarizability. The target species are two perfect tetrahedral nanoclusters Nb4B18 and Ta4B18, along with their nanofullerene counterpart that is C28. Our study based on density functionals (DFs) that have gained popularity among the scientific community. In addition we performed Hartree-Fock calculations known for not including dynamic electron correlation. The DF obtained values are characterized by some dispersion, with maximal differences to be around 5 %, in all three cases. Given that the DFT introduces a fuzzy percentage of electron correlation sets the observed convergence of HF values to DFT ones is at least surprising. Furthermore, it should be said that though the values can be characterized as accurate their reliability should not be taken for granted. Last, we note the smooth convergence of LC-BLYP, LC-BP86, LC-BPW91 to LC-whPBE.

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules

The electric dipole–magnetic dipole polarizability tensor κ′, introduced to interpret the optical activity of chiral molecules, has been expressed in terms of a series of density functions kαβ′, which can be integrated all over the three-dimensional space to evaluate components καβ′ and trace καα′. A computational approach to kαβ′, based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of kαβ′ on the origin of the coordinate system has been investigated in connection with the corresponding change of καβ′. It is shown that only the trace kαα′ of the density function defined via dynamic current density evaluated using the continuous translation of the origin of the coordinate system is invariant of the origin. Accordingly, this function is recommended as a tool that is quite useful for determining the molecular domains that determine optical activity to a major extent. A series of computations on the hydrogen peroxide molecule, for a number of different HO–OH dihedral angles, is shown to provide a pictorial documentation of the proposed method.

Quantum-Chemical Study of the Biogenic Amino Acids

Ten amino acids have been subjected to the quantum chemical calculations using the ab initio MO-LCAO-SCF calculations and semiempirical PM3 method. When the geometry optimization started form the X-ray structure confirming the zwitterionic form, the ab initio calculations in vacuo result in the amino acid (canonical) form with the hydrogen atom attached not to the amine but to the carboxylate group. At the optimum geometry a number of properties were evaluated: dipole moment, dipole polarizability, molecular surface, molecular volume, HOMO, LUMO, ionization energy and electron affinity using the ΔSCF approach and their values corrected for electron correlation by the 2 nd –order perturbation theory (MP2). In addition, the molecular electrostatic potential and the charge density have been drawn. These properties have been mutually correlated by employing the statistical multivariate methods: the cluster analysis, the probabilistic neural network classifier, the principal component analysis and the Pearson pair correlation.

Nuclear Equation of State in the Relativistic Point-Coupling Model Constrained by Excitations in Finite Nuclei

Nuclear equation of state is often described in the framework of energy density functional. However, the isovector channel in most functionals has been poorly constrained, mainly due to rather limited available experimental data to probe it. Only recently, the relativistic nuclear energy density functional with an effective point-coupling interaction was constrained by supplementing the ground-state properties of nuclei with the experimental data on dipole polarizability and isoscalar monopole resonance energy in 208Pb, resulting in DD-PCX parameterization. In this work, we pursue a complementary approach by introducing a family of 8 relativistic point-coupling functionals that reproduce the same nuclear ground-state properties, including binding energies and charge radii, but in addition have a constrained value of symmetry energy at saturation density in the range J = 29, 30, …, 36 MeV. In the next step, this family of functionals is employed in studies of excitation properties such as dipole polarizability and magnetic dipole transitions, and the respective experimental data are used to validate the optimal choice of functional as well as to assess reliable values of the symmetry energy and slope of the symmetry energy at saturation.

Ramsauer–Townsend minimum in electron scattering from CF$$_4$$: modified effective range analysis

Elastic cross sections for electron scattering on tetrafluoromethane (CF$$_4$$ 4 ) from 0 up to 5 eV energy are analyzed using semi-analytical approach to the modified effective range theory (MERT). It is shown that energy and angular variations of differential, integral and momentum transfer cross sections can be parameterized accurately by six MERT coefficients up to the energy region of the resonant scattering. In particular, the model is used to determine the depth and the position of the Ramsauer–Townsend minimum as well as the s-wave scattering length. Moreover, we investigate the influence of the dipole polarizability value on the predictions of present model. To further validate our approach, the elastic data are combined with the Born-dipole cross sections for vibrational excitations as the input data for Monte Carlo simulation of electron swarm coefficients. Graphic Abstract