Ground-state properties and static dipole polarizabilities of the alkali dimers from K2 n to Fr2 n(n=0,+1) from scalar relativistic pseudopotential coupled cluster and density functional studies

The newly adjusted energy-consistent nine-valence-electron pseudopotentials for K to Fr are used to calculate spectroscopic properties for the neutral and positively charged alkali dimers using coupled cluster and density functional theory. For the neutral dimers the static dipole polarizability was calculated. The coupled cluster results are all in excellent agreement with experimental values. The density functionals used can give quite different spectroscopic properties especially for the dipole polarizability, with the Perdew-Wang PW91 functional performing best.     

Dynamic dipole polarizabilities of the ground and excited states of confined hydrogen atom computed by means of a mapped Fourier grid method

Accurate theoretical estimates of static and dynamic dipole polarizabilities are reported for the ground and excited states of hydrogen atom confined at the center of a spherical “box” with impenetrable walls using a novel theoretical algorithm that combines the variational–perturbation approach with an appropriately adapted mapped Fourier grid method and uniformly maintains the numerical accuracy. A variation of computed polarizabilities is observed as a function of the number of grid points. However, rapid convergence to their correct values, even far into the anomalous dispersion region, is achieved by an extrapolation procedure to the limit of an infinitely large number of grid points using a small number of the lowest‐order Padé approximants. It is shown that dipole polarizabilities strongly depend upon the electronic state and the radius of confinement. In particular, the static polarizability of 2s state changes sign under strong confinement. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Calculation of accurate permanent dipole moments of the lowest 1,3Sigma+ states of heteronuclear alkali dimers using extended basis sets

Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of core-core interaction.     

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.     

Molecule‐specific determination of atomic polarizabilities with the polarizable atomic multipole model

Recently, many polarizable force fields have been devised to describe induction effects between molecules. In popular polarizable models based on induced dipole moments, atomic polarizabilities are the essential parameters and should be derived carefully. Here, we present a parameterization scheme for atomic polarizabilities using a minimization target function containing both molecular and atomic information. The main idea is to adopt reference data only from quantum chemical calculations, to perform atomic polarizability parameterizations even when relevant experimental data are scarce as in the case of electronically excited molecules. Specifically, our scheme assigns the atomic polarizabilities of any given molecule in such a way that its molecular polarizability tensor is well reproduced. We show that our scheme successfully works for various molecules in mimicking dipole responses not only in ground states but also in valence excited states. The electrostatic potential around a molecule with an externally perturbing nearby charge also exhibits a near‐quantitative agreement with the reference data from quantum chemical calculations. The limitation of the model with isotropic atoms is also discussed to examine the scope of its applicability. © 2012 Wiley Periodicals, Inc.     

Structure, energetics, and reactions of alkali tetramers

Electronic structure calculations have been carried out for all possible alkali tetramers that can be formed from X(2) + X(2) → X(2)X(2), X(2) + Y(2) → X(2)Y(2), and XY + XY → X(2)Y(2) alkali dimer association reactions. Vibrationally stable rhombic (D(2h)) and planar (C(s)) structures are found for all possible tetramers formed from the alkali metals, Li to Cs. All tetramer formation reactions (from ground state singlet homonuclear or heteronuclear dimers) are found to be exothermic with binding energies ranging from 6282 cm(-1) for Li(2)Li(2) to 1985 cm(-1) for Cs(2)Cs(2). Extensive calculations, carried out at long-range for several reactant pairs, indicate that there are barrier-less pathways for the formation of tetramers from dimer association reactions. At low temperatures, direct formation of tetramers is unlikely, owing to the large exothermicity associated with these association reactions, but atom exchange reactions (X(2) + Y(2) ? XY + XY) are possible for some species.     

Size- and shape-dependent polarizabilities of sandwich and rice-ball Co(n)Bz(m) clusters from density functional theory

The dipole polarizabilities of Co(n)Bz(m), (n, m = 1-4, m = n, n + 1) clusters are studied by means of an all-electron gradient-corrected density functional theory and finite field method. The dipole moments are relatively large for most of the clusters, implying their asymmetric structures. The total polarizability increases rapidly as cluster size, whereas the average polarizability shows "odd-even" oscillation with relatively large values at (n, n + 1). The polarizabilities exhibit clear shape-dependent variation, and the sandwich structures have systematically larger polarizability and anisotropy than the rice-ball isomers. The dipole polarizabilities are further analyzed in terms of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, ionization potential, and electron delocalization volume. We conclude that the polarizability variations are determined by the interplay between the geometrical and electronic properties of the clusters.     

Static dipole polarizability of ytterbium

The static dipole polarizability of the ground state ytterbium atom is calculated using full and approximate relativistic ab initio methods. Our recommended polarizability of 143 au is consistent with experimental atomic spectral data. The corresponding van der Waals coefficient C6 of Yb2, derived using Padé approximants, is 2062 (200) au.     

Static electric dipole polarizability of small sodium aggregates

We present pseudopotential local-spin-density calculations of the static electric polarizability of sodium dimers and trimers and their respective cations. The electronic polarizabilities are obtained from self-consistent calculations in the presence of an external electric field, which is kept sufficiently small to avoid non-linear effects. The calculated polarizability tensor has a strong anisotropy directly related to the geometric and electronic structures of the molecules, the anisotropy being larger for the neutral clusters. The polarizabilities are averaged over the vibrational motion and rotations of the aggregates in order to be compared with the experimental measurements. The obtained values show an improvement in the agreement with experiment with respect to the values calculated in the spherical approximation.     

Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study

Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (alpha), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C(4)H(4)XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, M?ller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper)polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values (alpha(e)) by 4-12% and the (hyper)polarizability values (and gamma(e)) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper)polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

Calculation of the electric susceptibilities of the helium atom

We calculated the static and the dynamic dipole polarizabilities and the static quadrupole polarizability of the helium atom. The results are α = 0.2070 × 10^?24 cm³ for the static dipole polarizability and γ₄ = 0.1038 × 10^?40 cm⁵ for the static quadrupole polarizability.     

Excited state dipole moments and polarizabilities of centrosymmetric and dimeric molecules. II. Polyenes, polyynes and cumulenes

Electro-optical absorption spectra are measured for a series of polyenes, polyynes and cumulenes with centrosymmetric π-chromophores in cyclohexane solution at 298 K. For all molecules the long-axis component of the polarizability tensor is considerably larger in the first dipole-allowed singlet state compared to the ground state. The transition moments are found to be parallel to the long molecular axis. All polyenes and one cumulene show a linear Stark component indicating a long-axis excited state dipole moment. Both the dipole moments and the polarizabilities are corrected within the extended Onsager model for solvent cavity and reaction field effects. It is suggested that symmetry lowering solvent perturbations are the reason for the apparent excited state dipole moments.     

Universal ultracold collision rates for polar molecules of two alkali-metal atoms

Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vibrational state v = 0 and for vibrational quenching of non-reactive dimers with v ≥ 1. Using the known dipole moments and estimated van der Waals coefficients of each species, we calculate electric field dependent loss rate constants for collisions of molecules tightly confined to quasi-two-dimensional geometry by a one-dimensional optical lattice. A simple scaling relation of the quasi-two-dimensional loss rate constants with dipole strength, trap frequency and collision energy is given for like bosons or like fermions. It should be possible to stabilize ultracold dimers of any of these species against destructive collisions by confining them in a lattice and orienting them with an electric field of less than 20 kV cm(-1).     

Static and Frequency‐Dependent Dipole–Dipole Polarizabilities of All Closed‐Shell Atoms up to Radium: A Four‐Component Relativistic DFT Study

We test the performance of four‐component relativistic density functional theory by calculating the static and frequency‐dependent electric dipole–dipole polarizabilities of all (ground‐state) closed‐shell atoms up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically shape‐corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient‐regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple‐zeta quality are used. The results are compared to experimental data or to accurate ab initio results. The reference static electric dipole polarizability of palladium has been obtained by finite‐field calculations using the coupled‐cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape‐corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare‐gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptotic correction is switched on in the core region.     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

Structure and photoabsorption properties of cationic alkali dimers solvated in neon clusters

We present a theoretical investigation of the structure and optical absorption of M(2)(+) alkali dimers (M=Li,Na,K) solvated in Ne(n) clusters for n=1 to a few tens Ne atoms. For all these alkali, the lowest-energy isomers are obtained by aggregation of the first Ne atoms at the extremity of the alkali molecule. This particular geometry, common to other M(2)(+)-rare gas clusters, is intimately related to the shape of the electronic density of the X (2)Σ(g)(+) ground state of the bare M(2)(+) molecules. The structure of the first solvation shell presents equilateral Ne(3) and capped pentagonal Ne(6) motifs, which are characteristic of pure rare gas clusters. The size and geometry of the complete solvation shell depend on the alkali and were obtained at n=22 with a D(4h) symmetry for Li and at n=27 with a D(5h) symmetry for Na. For K, our study suggests that the closure of the first solvation shell occurs well beyond n=36. We show that the atomic arrangement of these clusters has a profound influence on their optical absorption spectrum. In particular, the XΣ transition from the X (2)Σ(g)(+) ground state to the first excited (2)Σ(u)(+) state is strongly blueshifted in the Frank-Condon area.     

Calculation of static and dynamic linear magnetic response in approximate time-dependent density functional theory

We report implementations and results of time-dependent density functional calculations (i) of the frequency-dependent magnetic dipole-magnetic dipole polarizability, (ii) of the (observable) translationally invariant linear magnetic response, and (iii) of a linear intensity differential (LID) which includes the dynamic dipole magnetizability. The density functional calculations utilized density fitting. For achieving gauge-origin independence we have employed time-periodic magnetic-field-dependent basis functions as well as the dipole velocity gauge, and have included explicit density-fit related derivatives of the Coulomb potential. We present the results of calculations of static and dynamic magnetic dipole-magnetic dipole polarizabilities for a set of small molecules, the LID for the SF6 molecule, and dispersion curves for M-hexahelicene of the origin invariant linear magnetic response as well as of three dynamic polarizabilities: magnetic dipole-magnetic dipole, electric dipole-electric dipole, and electric dipole-magnetic dipole. We have also performed comparison of the linear magnetic response and magnetic dipole-magnetic dipole polarizability over a wide range of frequencies for H2O and SF6.