Static Electric Dipole Polarizabilities Research Articles

Dipole-dipole dispersion interactions between neutrons

We investigate the long-range interactions between two neutrons utilizing recent data on the neutron static and dynamic electric and magnetic dipole polarizabilities. The resulting long-range potentials are used to make quantitative comparisons between the collisions of a neutron with a neutron and a neutron with a proton. We also assess the importance of the first pion production threshold and first excited state of the nucleon, the $\Delta$-resonance ($J^{\pi}$ = + 3/2, I = 3/2). We found both dynamical effects to be quite relevant for distances r between ~ 50 fm up to ~$10^3$ fm in the nn system, the neutron-wall system and in the wall-neutron-wall system, reaching the expected asymptotic limit beyond that. Relevance of our findings to the confinement of ultra cold neutrons inside bottles is discussed.

All-electron Gaussian basis sets of double zeta quality for the actinides.

For the actinides, two segmented all-electron basis sets of valence double zeta quality plus polarization functions (DZP) are developed. One of them must be used along with the non-relativistic Hamiltonian, whereas the other with the Douglas-Kroll-Hess (DKH) one. Adding diffuse functions of s, p, d, f, and g symmetries to the non-relativistic and relativistic sets, augmented basis sets are developed. These functions are essential to describe correctly electrons far away from the nuclei. For some compounds, geometric parameters, atomic charges and valence orbital populations of the actinides, and bond dissociation energies are calculated using the Becke 3-parameter (exchange) and the Lee, Yang, and Parr (correlation) functional in conjunction with the DZP-DKH basis set. For Am and No, the static electric mean dipole polarizabilities are also reported. Comparison with benchmark theoretical and experimental values found in the literature is carried out. It is verified that the performances of the relativistic compact size basis sets generated in this work are regular, efficient, and reliable. They will be extremely helpful in molecular property calculations that need explicitly to consider the core electrons.

Analysis of Polarizability Measurements Made with Atom Interferometry

We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then, we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths fik, Einstein coefficients Aik, state lifetimes τk, transition dipole matrix elements Dik, line strengths Sik, and van der Waals C6 coefficients. Finally, we combine atom interferometer measurements of polarizabilities with independent measurements of lifetimes and C6 values in order to quantify the residual contribution to polarizability due to all atomic transitions other than the principal ns-npJ transitions for alkali metal atoms.

Ultracold magnetically tunable interactions without radiative-charge-transfer losses betweenCa+, Sr+, Ba+, andYb+ions and Cr atoms

The Ca$^+$, Sr$^+$, Ba$^+$, and Yb$^+$ ions immersed in an ultracold gas of the Cr atoms are proposed as experimentally feasible heteronuclear systems in which ion-atom interactions at ultralow temperatures can be controlled with magnetically tunable Feshbach resonances without charge transfer and radiative losses. \textit{Ab initio} techniques are applied to investigate electronic-ground-state properties of the (CaCr)$^+$, (SrCr)$^+$, (BaCr)$^+$, and (YbCr)$^+$ molecular ions. The potential energy curves, permanent electric dipole moments, and static electric dipole polarizabilities are computed. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), and the multireference configuration interaction method restricted to single and double excitations, MRCISD, are employed. The scalar relativistic effects are included within the small-core energy-consistent pseudopotentials. The leading long-range induction and dispersion interaction coefficients are also reported. Finally, magnetic Feshbach resonances between the Ca$^+$, Sr$^+$, Ba$^+$, and Yb$^+$ ions interacting with the Cr atoms are analyzed. The present proposal opens the way towards robust quantum simulations and computations with ultracold ion-atom systems free of radiative charge transfer losses.

Static electric dipole polarizabilities of An(5+/6+) and AnO2 (+/2+) (An = U, Np, and Pu) ions.

The parallel components of static electric dipole polarizabilities have been calculated for the lowest lying spin-orbit states of the penta- and hexavalent oxidation states of the actinides (An) U, Np, and Pu, in both their atomic and molecular diyl ion forms (An(5+/6+) and AnO2 (+/2+)) using the numerical finite-field technique within a four-component relativistic framework. The four-component Dirac-Hartree-Fock method formed the reference for MP2 and CCSD(T) calculations, while multireference Fock space coupled-cluster (FSCC), intermediate Hamiltonian Fock space coupled-cluster (IH-FSCC) and Kramers restricted configuration interaction (KRCI) methods were used to incorporate additional electron correlation. It is observed that electron correlation has significant (∼5 a.u.(3)) impact upon the parallel component of the polarizabilities of the diyls. To the best of our knowledge, these quantities have not been previously reported and they can serve as reference values in the determination of various electronic and response properties (for example intermolecular forces, optical properties, etc.) relevant to the nuclear fuel cycle and material science applications. The highest quality numbers for the parallel components (αzz) of the polarizability for the lowest Ω levels corresponding to the ground electronic states are (in a.u.(3)) 44.15 and 41.17 for UO2 (+) and UO2 (2+), respectively, 45.64 and 41.42 for NpO2 (+) and NpO2 (2+), respectively, and 47.15 for the PuO2 (+) ion.

Four-component relativistic calculations in solution with the polarizable continuum model of solvation: theory, implementation, and application to the group 16 dihydrides H2X (X = O, S, Se, Te, Po).

We present a formulation of four-component relativistic self-consistent field (SCF) theory for a molecular solute described within the framework of the polarizable continuum model (PCM) for solvation. The linear response function for a four-component PCM-SCF state is also derived, as well as the explicit form of the additional contributions to the first-order response equations. The implementation of such a four-component PCM-SCF model, as carried out in a development version of the DIRAC program package, is documented. In particular, we present the newly developed application programming interface PCMSolver used in the actual implementation with DIRAC. To demonstrate the applicability of the approach, we present and analyze calculations of solvation effects on the geometries, electric dipole moments, and static electric dipole polarizabilities for the group 16 dihydrides H2X (X = O, S, Se, Te, Po).

Ab initioproperties of the ground-state polar and paramagnetic europium–alkali-metal-atom and europium–alkaline-earth-metal-atom molecules

The properties of the electronic ground state of the polar and paramagnetic europium-$S$-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium-alkali-metal-atom, Eu$X$ ($X$=Li, Na, K, Rb, Cs), europium-alkaline-earth-metal-atom, Eu$Y$ ($Y$=Be, Mg, Ca, Sr, Ba), and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the small-core energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large internuclear distances $C_6$ are also reported. The EuK, EuRb, and EuCs molecules are examples of species possessing both large electric and magnetic dipole moments making them potentially interesting candidates for ultracold many-body quantum simulations when confined in an optical lattice in combined electric and magnetic fields.

Dynamic processes and polarizability of sodium atom in Debye plasmas

Dynamic processes including excitation and ionization, and spectrum parameters including the oscillator strengths, dipole polarizabilities from the orbital 3s,3p of sodium atom embedded in weakly coupled plasma are investigated in the entire energy range of a non-relativistic regime. The interaction between the valence electron and the atomic core is simulated by a model potential, and the plasma screening of the Coulomb interaction between charged particles is described by the Debye-Hückel model. The screening of Coulomb interactions reduces the number of bound states, decreases their binding energies, broadens their radial distribution of electron wave functions, and significantly changes the continuum wave functions including the amplitudes and phase-shift. These changes strongly affect the dipole matrix elements between the bound-bound and bound-continuum states, and even the oscillator strengths, the photo-ionization cross sections and the dipole polarizabilities. The plasma screening effect changes the interaction between the valence electron and the atomic core into a short-range potential. The energy behaviors of photo-ionization cross sections are unfolded, for instance, its low-energy behavior (obeying Wigner threshold law), and the appearance of multiple shape and virtual-state resonances when the upper bound states emerge into the continuum. The Combet-Farnoux and Cooper minima in the photo-ionization cross sections are also investigated, and here, the Cooper minima appear not only for the l→l+1 channel but also for l→l−1 one, different from that of hydrogen-like ions in a Debye plasma, which appear only in the l→l+1 channel. The total static electric dipole polarizabilities monotonously and dramatically increase with the plasma screening effect increasing, which are similar to those of hydrogen-like ions and lithium atom. Comparison of calculated results for the oscillator strength, the photo-ionization cross section and polarizability with the results of other authors, when available, is made.

Dirac‐exact relativistic methods: the normalized elimination of the small component method

Dirac‐exact relativistic methods, i.e., 2‐ or 1‐component methods which exactly reproduce the one‐electron energies of the original 4‐component Dirac method, have established a standard for reliable relativistic quantum chemical calculations targeting medium‐ and large‐sized molecules. Their development was initiated and facilitated in the late 1990s by Dyall's development of the normalized elimination of the small component (NESC). Dyall's work has fostered the conversion ofNESCand related (later developed) methods into routinely used, multipurpose Dirac‐exact methods by which energies, first‐order, and second‐order properties can be calculated at computational costs, which are only slightly higher than those of nonrelativistic methods. This review summarizes the development of a generally applicable 1‐componentNESCalgorithm leading to the calculation of reliable energies, geometries, electron density distributions, electric moments, electric field gradients, hyperfine structure constants, contact densities and Mössbauer isomer shifts, nuclear quadrupole coupling constants, vibrational frequencies, infrared intensities, and static electric dipole polarizabilities. In addition, the derivation and computational possibilities of 2‐componentNESCmethods are discussed and their use for the calculation of spin‐orbit coupling (SOC) effects in connection with spin‐orbit splittings andSOC‐corrected energies are demonstrated. The impact of scalar relativistic and spin‐orbit effects on molecular properties is presented.WIREs Comput Mol Sci2014, 4:436–467.This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure Methods

Correlation trends in the ground-state static electric dipole polarizabilities of closed-shell atoms and ions

We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A 77, 062516 (2008)] to evaluate the ground-state static electric dipole polarizabilities ($\ensuremath{\alpha}$s) of several atomic systems. In this work, we have incorporated a class of higher-order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracies of $\ensuremath{\alpha}$s. We also calculate the ground state $\ensuremath{\alpha}$s of the inert gas atoms and several isoelectronic singly and doubly charged ions in order to make a comparative study of the trends of the correlation effects. Furthermore, we have developed a method to construct intermediate diagrams that are required for the computations of the unperturbed single and doubl coupled-cluster amplitudes. Our RCC results are compared with those of many-body perturbation theory at different orders to demonstrate the importance of higher-order correlation effects for the accurate determination of ($\ensuremath{\alpha}$s) of the systems that we have considered.

Prospects for ultracold polar and magnetic chromium–closed-shell-atom molecules

The properties of the electronic ground state of the polar and paramagnetic chromium--closed-shell-atom molecules have been investigated. State-of-the-art \textit{ab initio} techniques have been applied to compute the potential energy curves for the chromium--alkaline-earth-metal-atom, CrX (X = Be, Mg, Ca, Sr, Ba), and chromium--ytterbium, CrYb, molecules in the Born-Oppenheimer approximation for the $X^7\Sigma^+$ high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within Douglas-Kroll-Hess Hamiltonian or energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large interatomic distances, $C_6$, are also reported. Molecules under investigation are an example of species possessing both large magnetic and electric dipole moments making them potentially interesting candidates for ultracold many-body physics studies.

Static electric dipole polarizabilities for isoelectronic sequences. II. Open-shell S states

We present static electric dipole polarizabilities αd(Z,N) from numerical nonrelativistic restricted Hartree-Fock (RHF) finite-field calculations for high-spin open-shell S states (L = 0) of atoms and isoelectronic ions with N ≤ 55 electrons. All these S states result from one or more half-filled shells. For eight isoelectronic sequences, those with N = 3, 7, 11, 15, 23, 29, 33 or 41 electrons where the electronic ground state of the neutral or nearly neutral members is conserved upon increase of the nuclear charge number Z, polarizability data are given for ions with charge number Q = Z − N up to Q = 90. In addition, these data are represented in terms of rational functions of Q (with absolute value of the relative error of the fit always below 4%). The rational functions are comparable to the classical nonrelativistic result αd(Z,1) = 4.5 / Z4 = 4.5 / (Q + 1)4 for the polarizability of the 2S ground state of a hydrogen-like system. Our results also contribute to constitute a reference database (i) for algebraic approaches relying on basis functions, and (ii) for the discussion of relativistic and correlation effects on polarizabilities along isoelectronic sequences.

Static Electric Dipole Polarizabilities of Tri- and Tetravalent U, Np, and Pu Ions

High-quality static electric dipole polarizabilities have been determined for the ground states of the hard-sphere cations of U, Np, and Pu in the III and IV oxidation states. The polarizabilities have been calculated using the numerical finite field technique in a four-component relativistic framework. Methods including Fock-space coupled cluster (FSCC) and Kramers-restricted configuration interaction (KRCI) have been performed in order to account for electron correlation effects. Comparisons between polarizabilities calculated using Dirac-Hartree-Fock (DHF), FSCC, and KRCI methods have been made using both triple- and quadruple-ζ basis sets for U(4+). In addition to the ground state, this study also reports the polarizability data for the first two excited states of U(3+/4+), Np(3+/4+), and Pu(3+/4+) ions at different levels of theory. The values reported in this work are the most accurate to date calculations for the dipole polarizabilities of the hard-sphere tri- and tetravalent actinide ions and may serve as reference values, aiding in the calculation of various electronic and response properties (for example, intermolecular forces, optical properties, etc.) relevant to the nuclear fuel cycle and material science applications.

Electric dipole polarizabilities of alkali-metal ions from perturbed relativistic coupled-cluster theory

We use the perturbed relativistic coupled-cluster theory to compute the static electric dipole polarizabilities of the singly ionized alkali-metal atoms, namely, Na${}^{+}$, K${}^{+}$, Rb${}^{+}$, Cs${}^{+}$, and Fr${}^{+}$. The computations use the Dirac-Coulomb-Breit Hamiltonian with the no-virtual-pair approximation and we also estimate the correction to the static electric dipole polarizability arising from the Breit interaction.

Benchmark theoretical study of the electric polarizabilities of naphthalene, anthracene, and tetracene

By applying the principles of a focal point analysis to finite field calculations, the static electric dipole polarizabilities of naphthalene, anthracene, and tetracene have been estimated up to the level of coupled cluster theory including single, double, and perturbative triple excitations in the limit of an asymptotically complete basis set. Thermal corrections to polarizabilities have been empirically estimated according to Born-Oppenheimer molecular dynamical simulations at 298 K employing density functional theory. Confrontation with the latest experimental values for isotropic polarizabilities ultimately indicates relative accuracies of the order of 1.2% (for naphthalene) to 3.5% (for anthracene), provided diffuse functions are incorporated in the focal point analysis.

On the performance of long‐range‐corrected density functional theory and reduced‐size polarized LPol‐n basis sets in computations of electric dipole (hyper)polarizabilities of π‐conjugated molecules

Static longitudinal electric dipole (hyper)polarizabilities are calculated for six medium-sized π-conjugated organic molecules using recently developed LPol-n basis set family to assess their performance. Dunning's correlation-consistent basis sets of triple-ζ quality combined with MP2 method and supported by CCSD(T)/aug-cc-pVDZ results are used to obtain the reference values of analyzed properties. The same reference is used to analyze (hyper)polarizabilities predicted by selected exchange-correlation functionals, particularly those asymptotically corrected.

Static electric dipole polarizability of lithium atoms in Debye plasmas

The static electric dipole polarizabilities of the ground state and n ≤ 3 excited states of a lithium atom embedded in a weekly coupled plasma environment are investigated as a function of the plasma screening radium. The plasma screening of the Coulomb interaction is described by the Debye—Hückel potential and the interaction between the valence electron and the atomic core is described by a model potential. The electron energies and wave functions for both the bound and continuum states are calculated by solving the Schrödinger equation numerically using the symplectic integrator. The oscillator strengths, partial-wave, and total static dipole polarizabilities of the ground state and n ≤ 3 excited states of the lithium atom are calculated. Comparison of present results with those of other authors, when available, is made. The results for the 2s ground state demonstrated that the oscillator strengths and the static dipole polarizabilities from np orbitals do not always increase or decrease with the plasma screening effect increasing, unlike that for hydrogen-like ions, especially for 2s→3p transition there is a zero value for both the oscillator strength and the static dipole polarizability for screening length D = 10.3106a0, which is associated with the Cooper minima.

Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments: Test calculations for Au, AuF, and Snn cluster (n ⩽ 20)

The response of the electronic wavefunction to an external electric or magnetic field is widely considered to be a typical valence property and should, therefore, be adequately described by accurately adjusted pseudopotentials, especially if a small-core definition is used within this approximation. In this paper we show for atomic Au and Au(+), as well as for the molecule AuF and tin clusters, that in contrast to the case of the static electric dipole polarizability or the electric dipole moment, core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation. This error increases with increasing size of the core chosen. For tin clusters, which are of interest in ongoing molecular beam experiments currently carried out by the Darmstadt group, the diamagnetic and paramagnetic isotropic components of the magnetizability tensor almost cancel out and large-core pseudopotentials do not even predict the correct sign for this property due to erroneous results in both the diamagnetic and (more importantly) the paramagnetic terms. Hence, all-electron calculations or pseudopotentials with very small cores are required to adequately predict magnetizabilities for atoms, molecules and the solid state, making it computationally more difficult to obtain this quantity for future investigations in heavy atom containing molecules or clusters. We also demonstrate for this property that all-electron density functional calculations are quite robust and give results close to wavefunction based methods for the atoms and molecules studied here.

Many-body interactions and the electric response of hydrogen-bonded molecular chains

Quantitative analysis of the impact of intermolecular interactions on the nonlinear electric response of hydrogen-bonded molecular chains has been performed. In particular, the theoretical description of cooperative effects (nonadditivity) based on the many-body calculations is provided. Nonlinear optical response of H-bonded chains (linear and zigzag HF⋯(HF) n , linear H 2CO⋯(H 2CO) n and H 3N⋯(HF) n , where n = 1–4) has also been studied. Values of the static electric dipole moment, polarizability and first-order hyperpolarizability have been calculated and analyzed at the MP2 level of theory using Dunning’s correlation-consistent basis set. The site–site function counterpoise (SSFC) method has been applied in order to avoid basis set superposition error (BSSE). Particularly interesting observations have been drawn in the case of first-order hyperpolarizability.

The Electronic Structure of Gold−Platinum Nanoparticles: Collecting Clues for Why They Are Special

We present a density functional study of the electronic and geometric structure of Au−Pt nanoparticles with up to 40 atoms. Our first-principles calculations consistently show a core−shell growth pattern, qualitatively confirming the findings of previous semiempirical calculations. The average bond lengths of small alloy clusters show a “Vegard’s law” type behavior independent of their specific geometry. We investigate the static electric dipole polarizability, the Kohn−Sham density of states, and the spatial orbital structure as possible indicators for the special, catalysis-relevant electronic properties of Au−Pt particles. Our results show that small changes in the atomic structure may considerably influence the surface properties of nanoalloy particles.