Numerical solution of Dalgarno-Lewis equations by a mapped Fourier grid method

Inhomogeneous radial differential equations emerging in applications of standard perturbation theory are numerically solved by a novel approach making use of Fourier grid methods in conjunction with a simple mapping scheme. The proposed algorithm is applied along the lines of the Dalgarno-Lewis method [Proc. R. Soc. London, Ser. A 223, 70 (1955)] to the calculation of the static dipole polarizabilities and hyperpolarizabilities of 1s, 2s, and 2p states of hydrogen atom and their frequency dependent dynamic dipole polarizabilities. The high efficiency and accuracy of the algorithm are demonstrated for the above test cases, where exact values are available. Then, the frequency dependent dipole polarizability of the ground state of lithium atom is computed by a variationally stable method combining an effective local potential approach with a second-order energy correction. The obtained results are in perfect agreement with other elaborate theoretical approaches.     

Calculations of static dipole polarizabilities of alkali dimers: prospects for alignment of ultracold molecules

The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.     

Polarizabilities of heteroaromatic molecules: Azines revisited

Ab initio electron-correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities are reported for benzene and 12 heteroaromatic six-membered rings obtained from it by aza-substitution. Our geometries and dipole moments agree well with available experimental microwave determinations. The polarizabilities are in reasonable agreement with the fragmentary experimental data available. Uncoupled Hartree-Fock calculations indicate that as much as half the polarizability comes from the σ-electrons. Simple empirical formulas based on atom- and bond-additive models correlate the calculated polarizabilities of 33 five- and six-membered heteroaromatic rings (10 azoles, 10 oxazoles, 13 azines) quite well. The correlation improves significantly if systematic data of uniform quality are used. © 1996 John Wiley & Sons, Inc.     

Ab initio SCRF study of solvent effect on the nonlinear polarizabilities of different intramolecular charge-transfer molecules

The macroscopic solvent effect on static nonlinear polarizabilities of a number of intramolecular charge-transfer (ICT) molecules have been studied by using the self-consistent-reaction field (SCRF) model in the framework of ab initio time-dependent-HF (TDHF) method using 3-21G basis set. The two-state model of static β and <γ> have been used to obtain their functional dependence on the ground-state hardness parameter, dipole moment and solvation energy. The methyl substituted 4-quinopyran and other zwitterionic molecules are found to exhibit strong diminution of both quadratic and cubic polarizabilities at higher solvent reaction field due to negative solvatochromic effect. However, molecules showing positive solvatochromism lead to strong enhancement of the NLO response on increase in solvent polarity. The evolution pattern of the solvent modulated static β and <γ> of 4-quinopyran (4QP) obtained for varying inter-ring torsion angle differ strikingly from that shown by p-amino p'-nitro biphenyl (ANB).     

Spectroscopic and theoretical optical properties of indoleninyl-substituted dibenzotetraaza[14]annulenes

Two new macrocyclic dibenzotetraaza[14]annulene (DBTAA) compounds with indolenine ( 5 ) and pyridoindolenine ( 6 ) moieties were synthesized and characterized by spectroscopy. Both DBTAAs exhibit strong UV-Vis absorption properties in the Soret band region. The theoretical second-order nonlinear optical property, electric dipole moment (μ), dispersion-free dipole polarizability (α) and first hyper-polarizability values were calculated by density functional theory and time dependent density functional theory. The ab-initio quantum mechanical calculation by time-dependent Hartree-Fock method was utilized to investigate the dynamic dipole polarizabilities, dynamic second-order, static, and dynamic third-order (γ) hyper-polarizabilities of the DBTAAs. The configuration interaction technique of all doubly occupied molecular orbitals possesses theoretically defined single-photon absorption (OPA) specifications for the examined structures. The computed maximum OPA wavelengths on both macrocyclic compounds coincide with the preceding measurement outcomes.     

The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods

Dipole moments and static dipole polarizabilities have been calculated for a number of small molecules using the linear combination of Gaussian-type orbitals–local spin density method. The effect of augmenting standard orbital basis sets with polarization functions has been investigated. A set of optimum ζ_d, for use in calculating polarizabilities, has been derived for the first-row atoms C, N, O, and F. The results of this optimized doubly polarized double-zeta basis set compare well with results obtained using a double-zeta basis set augmented by four even-tempered ζ_d polarization functions. The results of the optimized basis set, and a basis set augmented with only a single ζ_d polarization function derived from it, compare very favorably with those obtained from Møller–Plesset perturbation theory and with experimental data. They show a marked improvement on results obtained using standard Hartree–Fock self-consistent-field molecular orbital methods where no treatment of electron-correlation is included.     

On exact calculation of response properties of oscillators in static electric field: A Fourier grid Hamiltonian approach. I. One-dimensional systems

The Fourier grid Hamiltonian method is used to calculate the response properties of different types of 1-d (one-dimensional) quantum oscillators in a uniform static electric field. The calculations are potentially exact. Excepting the harmonic oscillator, the other model oscillators studied are seen to possess nonlinear polarizabilities. In general, the polarizabilities are not monotonic functions of appropriate vibrational quantum numbers. The exact nature of this vibrational-state dependence of polarizabilities is shown to depend on the type of mechanical anharmonicity in which the nuclei move and the nature of electrical anharmonicity characterizing the field–oscillator coupling. The large vibrational contribution to nonlinear polarizabilities often predicted for real diatomics could therefore originate from the mechanical and electrical anharmonicities of the potential in which the nuclei move when placed in a static electric field. © 1994 John Wiley & Sons, Inc.     

Electric dipole,polarizability and structure of cesium chloride clusters with one-excess electron

The measurement of the electric dipole of gas phase one-excess electron Cs_nCl_n−1 clusters is reported together with a theoretical ab initio prediction of stable structures, dipole moments and electronic polarizabilities for these species in their ground state. Results are in agreement with NaCl cubic structures.     

Stark effect of hyperfine levels of the configuration 4f 7 (8 S) 6s6p in the europium I spectrum

The quadratic Stark effect in the hyperfine structure of all levels of the configuration 4f ⁷(⁸ S)6s6p in europium I, which can be excited by electric dipole radiation from the ground state, has been investigated by laser-atomic-beam spectroscopy. From the measured shifts and splittings of the hyperfine components the scalar and tensor polarizabilities have been deduced. From the polarizabilities radial integrals for electric dipole radiation were determined by a parametric analysis. With these radial integrals theoretical values of the polarizabilities were calculated.     

Stark effect,polarizabilities and the electric dipole moment of heteronuclear diatomic molecules in 1Σ states

The theory of second-order Stark effect in ¹Σ states of heteronuclear diatomic molecules is thoroughly reviewed. The rigorous treatment given demonstrates that by introducing rotational, vibrational and electronic branch polarizabilities, the intrinsic character of the second-order Stark effect in diatomic molecules can be shown to be related more closely to polarizabilities than to dipole moments. The well-known expression for the Stark shift in ¹Σ levels which is dominated by the square of the dipole moment is only a crude, though sufficient approximation whenever large dipole moments are involved. For small dipole moments, however, this approximation is likely to fail, leading to an erroneous determination of such dipole moments. In the limiting case of negligible influence of the molecular rotation on the vibronic matrix elements, the arithmetic mean of the electronic branch polarizabilities turns out to be equal to the well-known static electronic polarizabilities α_∥ and α_⊥. The results are applied to the interpretation of the Stark splitting in the A¹Σ⁺, υ′ = 5, J′ = 1 level of ⁷LiH, recently determined by Stark quantum-beat spectroscopy.     

Large changes of static electric properties induced by hydrogen bonding: an ab initio study of linear HCN oligomers

We report the partitioning of the interaction-induced static electronic dipole (hyper)polarizabilities for linear hydrogen cyanide complexes into contributions arising from various interaction energy terms. We analyzed the nonadditivities of the studied properties and used these data to predict the electric properties of an infinite chain. The interaction-induced static electric dipole properties and their nonadditivities were analyzed using an approach based on numerical differentiation of the interaction energy components estimated in an external electric field. These were obtained using the hybrid variational-perturbational interaction energy decomposition scheme, augmented with coupled-cluster calculations, with singles, doubles, and noniterative triples. Our results indicate that the interaction-induced dipole moments and polarizabilities are primarily electrostatic in nature; however, the composition of the interaction hyperpolarizabilities is much more complex. The overlap effects substantially quench the contributions due to electrostatic interactions, and therefore, the major components are due to the induction and exchange-induction terms, as well as the intramolecular electron-correlation corrections. A particularly intriguing observation is that the interaction first hyperpolarizability in the studied systems not only is much larger than the corresponding sum of monomer properties, but also has the opposite sign. We show that this effect can be viewed as a direct consequence of hydrogen-bonding interactions that lead to a decrease of the hyperpolarizability of the proton acceptor and an increase of the hyperpolarizability of the proton donor. In the case of the first hyperpolarizability, we also observed the largest nonadditivity of interaction properties (nearly 17%) which further enhances the effects of pairwise interactions.     

Theoretical description of the electronic structure of the alkali hydride cation NaH+

A theoretical determination of the electronic structure of NaH+ is presented. Potential energy curves and dipole moments have been computed for 48(2)Lambda(+) electronic states (i.e., correlated adiabatically up to Na(6s) + H+) through a model-potential-type method over a wide range of R. Equilibrium distances, transition energies, depths of wells, and/or heights of humps predicted at short and large interatomic separations are reported and compared with available experimental and theoretical values. Variations of the static dipole polarizabilities versus internuclear distance have been determined for the two lowest states.     

Analytic calculation of second-order electric response properties with the normalized elimination of the small component (NESC) method

Analytic second derivatives of the relativistic energy for the calculation of electric response properties are derived utilizing the normalized elimination of the small component (NESC) method. Explicit formulas are given for electric static dipole polarizabilities and infrared intensities by starting at the NESC representation of electric dipole moments. The analytic derivatives are implemented in an existing NESC program and applied to calculate dipole moments, polarizabilities, and the infrared spectra of gold- and mercury-containing molecules as well as some actinide molecules. Comparison with experiment reveals the accuracy of NESC second order electric response properties.     

Additivity of atomic static polarizabilities and dispersion coefficients

A new empirical method is proposed to evaluate the average molecular polarizabilities assuming the additivity of atomic static polarizability. Atomic static polarizability for each atom in a particular valence state is obtained. Calculated molecular polarizabilities of 94 non-halogenated compounds and of the bases in nucleic acids show the excellent agreement with experimental data.To check the further validity of this method, dispersion coefficients for CH₄, C₂H₆, C₃H₈,n–C₄H₁₀,n–C₅H₁₂,n–C₆H₁₄,n–C₇H₁₆,n–C₈H₁₈, H₂, H₂O and NH₃ are obtained from a sum of atomic terms using a London-type formula, and are compared with the accurate values of dipole oscillator strength distribution (DOSD) method. The results show the excellent agreement between theory and experiment.     

Direct computation of second-order SCF properties of large molecules on workstation computers with an application to large carbon clusters

Summary The ab initio SCF computation of second-order properties of large molecules (with 50 atoms or more) on workstation computers is demonstrated for static dipole polarizabilities and nuclear magneting shieldings. The magnetic shieldings are calculated on the basis of gauge including atomic orbitals (GIAO). Algorithmic advances (semi-direct algorithms with efficient integral pre-screening, and use of a quadratically convergent functional for the polarizabilities) are presented together with an illustrative application to the fullerenes C₆₀ and C₇₀.     

State-interacting spin-orbit configuration interaction method for <Emphasis Type="Italic">J</Emphasis>-resolved anisotropic static dipole polarizabilities: Application to Al,Ga, In,and Tl atoms

The state-interacting spin-orbit (SO) configuration interaction (CI) method, which uses the non-relativistic CI wave functions as the basis of the total SO Hamiltonian matrix, is combined with the finite-field approach and applied to J-resolved anisotropic static dipole polarizabilities of the third-group atoms from Al to Tl. Comparison with available data reveals excellent performance of the method for atoms up to the fifth period (In), especially if the scalar relativitic and the high-level correlation corrections are included. The method performs worse for 6s ²6p Tl atom, most likely due to growing effect of the second-order SO coupling. Refined values of all the scalar and the tensor ground-state non-relativistic and J-resolved polarizabilities and, whenever possible, excited-state polarizabilities, are recommended based on the calculations performed and thorough analysis of the literature data.     

Static and dynamic dipole polarizabilities and electron density at origin: Ground and excited states of hydrogen atom confined in multiwalled fullerenes

We report accurate computations of static and dynamic dipole polarizabilities for the ground and excited states of hydrogen atom confined at the center of either a single and/or multiwalled fullerene cage, using the Galerkin variational method developed on a B‐spline basis set. The results obtained in the cage‐free case are in good agreement with other numerical techniques such as the mapped Fourier grid method. It is shown that the addition of new walls does not modify the polarizability of the ground state, but changes significantly those of the excited states. A condition on the ratio of the scaled second derivative of density to the scaled density evaluated at the nuclear position is tested in case of the cage confined atoms for the first time, and the significance of such numerical results are discussed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

TDDFT-SOS Studies on the Polarizabilities and Second-order Hyperpolarizabilities of Zn_3O_3 II-VI Semiconductor Clusters

1 INTRODUCTION II-VI semiconductor materials with ZnO as the representative possess wide forbidden gaps and high exciton binding energy, which have paved the way for the study of exciton characters and short wave photo-conducting devices. They present wide appli- cations, such as ultraviolet laser transmitting device, piezoelectric device, optical waveguild and high efficient quantum dot luminous apparatus[1～8]. Re- cently, II-VI semiconductor cluster materials with nano-structure ha…