HeH+ under Spatial Confinement

In the present study, the influence of spatial confinement on the bond length as well as dipole moment, polarizability and (hyper)polarizabilities of HeH+ ion was analyzed. The effect of spatial confinement was modelled by cylindrically symmetric harmonic oscillator potential, that can be used to mimic high pressure conditions. Based on the conducted research it was found that the spatial confinement significantly affects the investigated properties. Increasing the confinement strength leads to a substantial decrease of their values. This work may be of particular interest for astrochemistry as HeH+ is believed to be the first compound to form in the Universe.     

Natural orbital functional approach: Calculation of dielectric properties in molecules

Recently, we proposed a new natural orbital functional for taking into account the electronic correlation in molecular systems. Calculation of dipole moments and polarizabilities of eight selected molecules are presented. By comparison with other correlated methods, it is shown that the method has predictive capabilities for these properties. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

SWKB formalism for confined quantum systems

A formalism is developed to study spatially confined one‐dimensional quantum mechanical systems in the framework of the supersymmetric Wentzel–Kramers–Brillouin (SWKB) method. The approximation technique is applied to estimate the energy eigenvalues of two confined potentials—the harmonic oscillator V(x)=x² and the screened Coulomb potential V(x)=−V₀sech²x. The results thus obtained are found to be in better agreement with the exact numerical values than are those from the ordinary WKB approach. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 267–273, 2000     

Polarized basis sets for accurate calculations of static and dynamic electric properties of molecules

We report on the development and testing of large polarized basis sets (LPolX, where X is the element symbol) for accurate calculations of linear and nonlinear electric properties of molecules. The method used to generate LPolX sets is based on our studies of the analytic dependence of Gaussian functions on external time‐independent and time‐dependent electric fields. At variance with the earlier investigations of small, highly compact (ZPolX) basis sets for moderately accurate calculations of electric properties of large molecules, the present goal is to obtain basis sets that are nearly saturated with respect to the selected class of electric properties and can be used for accurate studies of interaction‐induced properties. This saturation makes the LPolX sets also useful in calculations of optical properties for chiral molecules. In this article, the LPolX sets are generated for X = H, C, N, O, and F, and examined in calculations of linear and nonlinear electric properties of four standard test systems: HF, N₂, CO, and HCN. The study of the performance of LPolX basis sets has been carried out at different levels of approximation ranging from the SCF HF method to highly correlated CCSD(T) approach. The results obtained in this study compare favorably with accurate reference data and show a high level of saturation of LPolX basis sets with respect to the polarization effect due to external electric fields. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Degeneracy of confined D‐dimensional harmonic oscillator

Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D‐dimensional (D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius R_c. Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Expansion of potential 1/r12 of c‐spherical harmonics

The expansion coefficient C^D_|L| of Coulomb potential 1/r₁₂ of atomic system in hyper‐spherical harmonics is derived and the explicit expression is given.     

Critical parameters and spherical confinement of H atom in screened Coulomb potential

Critical parameters in three screened potentials, namely, Hulthén, Yukawa, and exponential cosine screened Coulomb potential are reported. Accurate estimates of these parameters are given for each of these potentials, for all states having . Comparison with literature results is made, wherever possible. Present values compare excellently with reference values; for higher n, ?, our results are slightly better. Some of these are presented for first time. Further, we investigate the spherical confinement of H atom embedded in a dense plasma modeled by an exponential cosine screened potential. Accurate energies along with their variation with respect to box size and screening parameter are calculated and compared with reference results in literature. Sample dipole polarizabilities are also provided in this case. The generalized pseudospectral method is used for accurate determination of eigenvalues and eigenfunctions for all calculations. © 2016 Wiley Periodicals, Inc.     

Multipole polarizabilities of spherically confined hydrogen atom and positronium in screened Coulomb potential

The static multipole polarizabilities of the hydrogen atom interacting with a screened Coulomb potential confined in an impenetrable spherical box are calculated in the sum-over-states formalism. The system eigenenergies and wave functions are produced by employing the generalized pseudospectral method. High-precision results are obtained to resolve the discrepancies between previous predictions, and used to analyze the critical behavior of the system with varying the confinement radius and screening parameter. A scaling law of the multipole polarizabilities with respect to the nuclear charge and electron reduced mass is proposed. Based on the scaling law we extend the investigation to the spatially confined positronium atom in a screened Coulomb potential by utilizing a reduced one-electron model. The results are in good agreement with previous estimates. However, it is conjectured that when the confinement radius is small the confined positronium atom should be treated more reasonably by an effective two-electron model.     

Enhanced optoelectronic properties with aromatic bridges: A computational study on N-methyl pyridinium and phenolate types of push-pull zwitterions

A series of zwitterions with varying bridges, connecting N-methyl pyridinium acceptor, with phenolate donor, are investigated using various methodologies like, HF, B3LYP, CAM-B3LYP and ωB97xD. In this systematic study effects of various mono aromatic rings as bridges, on the response properties like, the dipole moments (μ), polarizabilities (α), hyperpolarizabilities (β) and adiabatic absorptions were analyzed using CPHF and TDDFT (or TDHF) theories. Compared to many traditional bridges, as well as without a bridge, enhanced nonlinear optical (2ND order NLO) responses were observed for these aromatically bridged zwitterions (with benzene ring as bridge ~5.3 times and ~7.9 times enhanced hyperpolarizabilities were observed compared to either the ethylene bridge or without any bridge cases, respectively). Also, many significant differences and large enhancements in response properties were observed compared to our earlier works on non-zwitterionic system (~4.3 times enhanced hyperpolarizability—benzene as bridge case). For some bridge cases, 10- to 15-fold enhanced hyperpolarizabilities were observed compared to without any bridge case. This work reports a class of non-TICT chromophores, promoting bridge aromaticity control on structure–property correlation, as a suitable and efficient chromophore design strategy to create a wide range of function molecular chromophores. Also, unidirectional natures of response properties and large dipole moments can make these zwitterions suitable 1D-molecular materials for various contemporary technological applications, as poled polymer-based materials.     

Effect of crystal potential on dynamic polarizability of negative ions

Summary We combine a time-dependent approach with a crystal potential model to study environment-specific optical linear response of closed-shell ions within crystals under the influence of an external time-varying field. It is shown how the dynamic dipole polarizability of free halogen anions within the normal dispersion region is altered due to the crystal potentials felt by the anions in environments appropriate for different binary cubic ionic lattices. The pole-positions of the in-crystal anion polarizability are found to be consistent with the vacuum ultraviolet absorption edges of the corresponding alkali halides and to vary linearly with the lattice potentials at the anion sites in these salts. It is observed that the crystal potential induces quite a large enhancement in the anionic absorption oscillator strengths of these dipole transitions, thereby making these values conform well with those of the first excitonic absorptions in such crystals.     

Entropic measures of Rydberg‐like harmonic states

The Shannon entropy, the desequilibrium and their generalizations (Rényi and Tsallis entropies) of the three‐dimensional single‐particle systems in a spherically symmetric potential V(r) can be decomposed into angular and radial parts. The radial part depends on the analytical form of the potential, but the angular part does not. In this article, we first calculate the angular entropy of any central potential by means of two analytical procedures. Then, we explicitly find the dominant term of the radial entropy for the highly energetic (i.e., Rydberg) stationary states of the oscillator‐like systems. The angular and radial contributions to these entropic measures are analytically expressed in terms of the quantum numbers which characterize the corresponding quantum states and, for the radial part, the oscillator strength. In the latter case, we use some recent powerful results of the information theory of the Laguerre polynomials and spherical harmonics which control the oscillator‐like wavefunctions.     

Rovibrational spectra of bounded diatomic molecules

Spectra of a bounded diatomic molecule is studied numerically. Shifted Deng–Fan oscillator potential has been used to model the molecule. The accurate five‐point finite difference method has been used to solve the Schrödinger equation for rovibrational motion of the molecule. The energies of the bound states as well as free states of the molecule have been calculated. In addition, radial matrix elements like , n = 1, 2, and 3 have been calculated. These have been used to calculate the ‐pole static polarizabilities. The variation of bound state energies, matrix elements and ‐pole static polarizabilities with the boundary radius has also been studied. The Stark effect in case of this bounded system has also been investigated.     

Effect of dense plasma on the spectral properties of hydrogenic ions

The effect of strongly coupled plasma on the energy levels, dynamic polarizabilities, oscillator strengths, and transition probabilities of a number of hydrogenic ions is estimated, using the ion‐sphere (IS) model. The transition properties are calculated using time‐dependent variation perturbation theory. The variation of the atomic properties under different plasma densities are analyzed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Study of the molecular configuration and the dipole moment in fluorinated liquid crystals

We have investigated the relationship between the molecular configuration and dipole moment of some fluorinated liquid crystals (LCs). The geometries of the molecules were preliminarily optimized at empirical AM1 and then were further optimized at B3LYP/6‐31G(d) level. The dipole moment has been calculated. It is strongly influenced by the position and number of fluorine substituents in the benzene ring of the molecule. The polarizability, mean polarizabilities, and anisotropic polarizability of the phenylbicyclohexane (PBC) fluorine substituents are also given and discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

NLO‐X (X = I–III): New Gaussian basis sets for prediction of linear and nonlinear electric properties

New adjusted Gaussian basis sets are proposed for first and second rows elements (H, B, C, N, O, F, Si, P, S, and Cl) with the purpose of calculating linear and mainly nonlinear optical (L–NLO) properties for molecules. These basis sets are new generation of Thakkar‐DZ basis sets, which were recontracted and augmented with diffuse and polarization extrabasis functions. Atomic energy and polarizability were used as reference data for fitting the basis sets, which were further applied for prediction of L–NLO properties of diatomic, H₂, N₂, F₂, Cl₂, BH, BF, BCl, HF, HCl, CO, CS, SiO, PN, and polyatomic, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, OCS, NNO, and HCN molecules. The results are satisfactory for all electric properties tested; dipole moment (µ), polarizability (α), and first hyperpolarizability (β), with an affordable computational cost. Three new basis sets are presented and called as NLO‐I (ADZP), NLO‐II (DZP), and NLO‐III (VDZP). The NLO‐III is the best choice to predict L–NLO properties of large molecular systems, because it presents a balance between computational cost and accuracy. The average errors for β at B3LYP/NLO‐III level were of 8% for diatomic molecules and 14% for polyatomic molecules that are within the experimental uncertainty. © 2014 Wiley Periodicals, Inc.     

Enhancement of molecular polarizabilities by the push-pull mechanism; a DFT study of substituted benzene, furan, thiophene and related molecules

We report Density Functional Theory (DFT) studies of the dipole polarizabilities of benzene, furan and thiophene together with a number of substituted and related systems. All geometries were optimized (and characterized) at the B3LYP/6-311g(2d,1p) level of theory and polarizabilities then calculated with B3LYP/6-311++G(2d,1p). For the R-ring systems we find group polarizabilities in the order R = NO₂ ∼ OCH₃ ∼ CN ∼ CHO > NH₂ > OH > H = 0. For systems R-ring-R, 〈α〉 differs little from the additivity model, with small positive and negative increments. For systems D-ring-A (where D and A are deactivating and activating groups) we find a positive enhancement to 〈α〉 over and above the value expected on the basis of pure additivity for all pairs A and D studied. This enhancement can be increased greatly by extending the length of the conjugated chain to D-ring-CH=CH-ring-A and D-ring-N=N-ring-A systems. Empirical models of polarizability such as AM1 agree badly with the DFT calculations in an absolute sense but give excellent statistical correlation coefficients. Calculated 〈α〉’s also agree well in a statistical sense with the molecular volumes calculated from molecular mechanics force fields Analysis of the results in terms of the π electrons alone is not satisfactory.     

Description of high‐spin restricted open‐shell molecules with the Piris natural orbital functional

The Piris natural orbital functional (PNOF) based on a new approach for the two‐electron cumulant is considered for the case of high‐spin restricted open‐shell systems. The theory is applied to the calculation of molecular energies, dipole moments, vertical ionization potentials (IP), and electron affinities (EA) of 10 open‐shell molecules. Vertical values of IP and EA were used to evaluate the hardness. It was observed that the results obtained using the PNOF method are comparable to the corresponding results obtained using CCSD(T) in the case of energies and dipole moments. Best agreement between theory and experiment is achieved by PNOF for EA and hardness values. The calculated PNOF values for the mentioned properties are in good agreement with the available experimental data, considering the basis sets used (6–31 ++G**). © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Vibrational spectrum of a 1D oscillator: The quantum,the Wigner,and the classical ways

Infrared spectra have been used in many chemical applications, and theoretical calculations have been useful for analyzing these experimental results. While quantum mechanics is used for calculating the spectra for small molecules, classical mechanics is used for larger systems. However, a systematic understanding of the similarities and differences between the two approaches is not clear. Previous studies focused on peak position and relative intensities of the spectra obtained by various quantum and classical methods, but here, we included “absolute” intensities in the evaluation. The infrared spectrum of a one-dimensional (1D) harmonic oscillator (HO) and Morse oscillator were examined using four treatments: quantum, Wigner, truncated Wigner, and classical microcanonical treatments. For a 1D HO with a linear dipole moment function (DMF), the quantum and Wigner treatments give nearly the same spectra. On the other hand, the truncated Wigner underestimates the fundamental transition's intensity by half. In the case of cubic DMF, the truncated Wigner and classical methods fail to reproduce the relative intensity between the fundamental and second overtone transitions. Unfortunately, all the Wigner and classical methods fail to agree with the quantum results for a Morse oscillator with just 1% anharmonicity.     

Electro-optical investigations of the dipole moments of nanoparticles

In this paper, the electric properties of polar nanoparticles are examined. Special attention is paid to the terminology, classification and the physical bases of the different electric moments. A short history of the electro-optic studies of dipole moments of nanoparticles and the electro-optic Conferences is presented. The connection of the polar properties with the particle electric charge is considered. The potential of the colloid electro-optics for studying the properties of anisometric, anisotropic polar nanoparticles is discussed in details. Examples of such studies are presented. A comparative analysis is made of the potential of dielectric, electro-optic and dielectrophoretic measurements for studying the electric properties, size, shape and structure of polar nanoparticles.