Atomic Dipole Polarizabilities Research Articles

Van der Waals Radii of Free and Bonded Atoms from Hydrogen (Z = 1) to Oganesson (Z = 118).

Reliable numerical values of van der Waals (vdW) radii are required for constructing empirical force fields, vdW-inclusive density functional, and quantum-chemical methods, as well as for implicit solvent models. However, multiple definitions exist for vdW radii, involving either equilibrium or the closest contact distances between free or bonded atoms within molecules or crystals. For the paradigmatic case of the hydrogen atom, its reported vdW radius fluctuates between 2.15 and 3.70 Bohr depending on the definition, leading to a high uncertainty in calculations and different conceptual interpretations of noncovalent interactions. In this work, we systematically review different definitions and methodologies to establish the free and bonded vdW radii for hydrogen, based on equilibrium vdW distances in noncovalently bonded molecules, enveloping electron density cutoffs, noncovalent positron bonds in hydrogen anion dimer, vacuum virtual photon cloud caused by the hydrogen atom, and atomic dipole polarizability. By doing so, we show that the vdW radius of the free hydrogen atom is 3.16 ± 0.06 Bohr. By employing the most general and elegant definition of atomic vdW radius as a function of the atomic polarizability, we tabulate consistent values of vdW radii for all atoms in the periodic table up to Z = 118.

Polarization characteristics and structural modifications of Cu nanoparticles under high electric fields

High electric fields affect the diffusion dynamics of atoms on a metal surface, causing biased surface diffusion that possibly leads to the growth of intensively field emitting protrusions and consequent vacuum breakdown (VBD). The scientific understanding of this process, as well as other fundamental VBD initiation mechanisms, is far from complete. Here we investigate the exact atomic behaviour of metal surfaces exposed to extremely high electric fields using density functional theory (DFT). Previous theories describe the field-surface dynamics in terms of the effective dipole moments and polarizability of surface atoms, disregarding higher-order (hyperpolarizability) terms. The validity of this approximation has been evaluated only for electric fields up to 3 GV/m, due to computational limitations of the plane-wave DFT basis used in previous works. In this work, we test the validity of this approximation for a much wider field range, relevant for VBD and field emission (FE), using Cu nanoparticles as our test structures. We find that although such high fields can change the entire structure of Cu nanoparticles, their energetics are described very precisely by the permanent dipole moment and polarizability terms. Thus, we show that neglecting the hyperpolarizability terms is valid even for field values that exceeds the range that is relevant for intense FE and VBD. This work lays a solid foundation for further developing atomic-level simulation models for electric field-induced surface diffusion on metal surfaces and its effects on protrusion growth and VBD initiation.

Fock-space perturbed relativistic coupled-cluster theory for electric dipole polarizability of one-valence atomic systems: Application to Al and In

We have developed a Fock-space relativistic coupled-cluster theory based method for the calculation of electric dipole polarizability of one-valence atoms and ions. We employ this method to compute the ground-state and spin-orbit coupled excited state electric dipole polarizability of Al and In. To check the quality of many-electron wavefunctions, we also compute the excitation energies of some low-lying states of Al and In. The effects of Breit interaction and QED corrections from the Uehling potential and the self-energy are included to improve the accuracy of $\alpha$ further. Our recommended value of ground-state $\alpha$ for both atoms are in good agreement with the previous theoretical results. From our computations, we find that more than 65\% of contributions come from the dipolar mixing of $3p$($5p$) with $3d$($5d$) and $4s$($6s$)-electrons for Al(In). The largest Breit and QED contributions are found to be 1.3\% and 0.6\%, respectively.

Static dipole polarizabilities of atoms and ions from Z = 1 to 20 calculated within a single theoretical scheme

Static dipole polarizabilities for the first 20 atoms and ions of the Periodic Table are calculated within a single theoretical scheme: the coupled-cluster method with a Hartree–Fock reference wavefunction using an augmented-polarization-consistent and polarization-consistent basis set. The values of the atomic polarizabilities of neutral atoms obtained here agree extremely well with the experimentally measured values. For the ions, all the calculations are consistent with experimental values with the highest resolution so far, except for the monovalent calcium ion, probably due to strong relativistic effects. To the best of our knowledge, this is the first time, applying a single theoretical scheme successfully predicts static polarizabilities of all 20 consecutive elements across 8 columns and more than 3 full periods being consistent with the experimentally measured values both for neutrals and ions. The results clearly signal the universality of this theoretical scheme for the atomic polarizability calculation, and should be easy to extend to other elements with weak relativistic effects. We adopt the CCSD(T) method with an augmented polarization-consistent and polarization-consistent basis set to calculate the atomic and ionic polarizabilities for the first 20 atoms and ions of the Periodic Table. Our calculation results are in good agreement with the experimental data with the highest accuracy so far and the reported high accuracy calculation results. Semi-logarithm plot of calculated static polarizabilities of neutral atoms (filled circles, black line) and ions (open circles). The colored lines join isoelectronic species.

Magic Wavelengths for Optical-Lattice Based Cs and Rb Active Clocks

Active clocks could provide better stabilities during initial stages of measurements over passive clocks, in which stabilities become saturated only after long-term measurements. This unique feature of an active clock has led to search for suitable candidates to construct such clocks. The other challenging task of an atomic clock is to reduce its possible systematics. A major part of the optical lattice atomic clocks based on neutral atoms are reduced by trapping atoms at the magic wavelengths of the optical lattice lasers. Keeping this in mind, we find the magic wavelengths between all possible hyperfine levels of the transitions in Rb and Cs atoms that were earlier considered to be suitable for making optical active clocks. To validate the results, we give the static dipole polarizabilities of Rb and Cs atoms using the electric dipole transition amplitudes that are used to evaluate the dynamic dipole polarizabilities and compare them with the available literature values.

Accurate calculation of multipole polarizabilities for one-electron atom in Debye plasmas

The electric multipole polarizabilities of one-electron atoms embedded in weakly coupled Debye plasmas are calculated in the non-relativistic framework. The static dipole, quadrupole, octopole, and hexadecapole polarizabilities for hydrogen atoms in both ground and excited states at a variety of Debye screening parameters are calculated in high precision based on the sum-over-states method, where the system bound and continuum states are produced by employing the generalized pseudospectral method. It is shown that the contribution of bound states to the polarizability decreases with increasing the plasma screening strength, whereas the contribution of continuum states is enhanced. At very small screening parameters where the plasma environment starts to take effect, it is found that the 2l-pole polarizability for s-wave states with principle quantum number n≥l+1 has an abrupt change from its non-screening value to infinity. We attribute such a phenomenon to the sudden non-degeneracy of different angular momentum states in the n shell. With continuously increasing the screening strength, the polarizabilities for n≥l+1 states decrease to certain values and, eventually, they approach to infinity at the critical screening parameter. For states with n≤l, the 2l-pole polarizabilities show regular enhancement from the non-screening value to infinity. The present results are compared with other theoretical calculations available in the literature and it is shown that our work has established by now the most accurate predictions of multipole oscillator strengths and polarizabilities for one-electron atoms in Debye plasmas.

High pressure effects on the excitation spectra and dipole properties of Li, Be+, and B2+ atoms under confinement

Properties of atoms and molecules undergo significant changes when subjected to spatial confinement. We study the excitation spectra of lithium-like atoms in the initial 1s22s electronic configuration when confined by an impenetrable spherical cavity. We implement Slater’s X-α method in Hartree–Fock theory to obtain the excitation spectrum. We verify that as the cavity size decreases, the total, 2s, 2p, and higher excited energy levels increase. Furthermore, we confirm the existence of crossing points between ns–np states for low values of the confinement radius such that the ns → np dipole transition becomes zero at that critical pressure. The crossing points of the s–p states imply that instead of photon absorption, one observes photon emission for cavities with radius smaller than the critical radius. Hence, the dipole oscillator strength associated with the 2s → 2p transition becomes negative, and for higher pressures, the 2s → 3p dipole oscillator strength transition becomes larger than unity. We validate the completeness of the spectrum by calculating the Thomas–Reiche–Kuhn sum rule, as well as the static dipole polarizability and mean excitation energy of lithium-like atoms. We find that the static dipole polarizability decreases and exhibits a sudden change at the critical pressure for the absorption-to-emission transition. The mean excitation energy increases as the pressure rises. However, as a consequence of the critical transition from absorption to emission, the mean excitation energy becomes undetermined for higher pressures, with implications for material damage under extreme conditions. For unconfined systems, our results show good to excellent agreement with data found in the literature.

Relativistic configuration interaction with core polarization method for the divalent systems

SynopsisThe relativistic configuration interaction with core polarization method and program for the divalent systems have been developed. Based on this new program, the energy levels, transition matrix elements, static and dynamic dipole polarizabilities of He, Be, and Mg atoms have been calculated systematically.

Long-range potentials and dipole moments of the CO electronic states converging to the ground dissociation limit.

The asymptotic, R → ∞, behavior of the potential-energy and dipole-moment functions (PEFs and DMFs) for all six (1,2)Σ+, (1,2)Π, Σ-, and Δ electronic states converging to the ground C(3P) + O(3P) dissociation limit of the CO molecule are studied in the framework of long-range (LR) perturbation theory. The analytical expressions for the leading coefficients of the LR expansion, C5/R5 for PEF and d4/R4 for DMF, in terms of the atomic quadrupole constants and static dipole polarizabilities are derived. The exact relationships between the LR coefficients for the states of different spatial symmetry are established as well. The analytical results are complemented with the first-principles calculation of the PEFs and DMFs for all the above states at large distances (R = 5-20 Å). The electronic structure calculation is conducted by means of the multi-reference configuration interaction and the averaged-coupled-pair functional methods, which both implemented the aug-cc-pwCVXZ (X = T, Q, and 5) basis sets and finite-field approach. The dispersion coefficients, C5 and C6, extracted from the ab initio PEFs, are found to be very close to their present and previous theoretical counterparts. The analytically estimated d4 = -5 DÅ4 obtained for the ground X1Σ+ state perfectly agrees with the present ab initio DMF but diverges significantly from the literature data.

Interferometric measurements of static and dynamic dipole polarizability of titanium atoms using fast electrical explosion of fine metal wires in vacuum

The rapid electrical explosion of fine metal wires in vacuum generates gas cylinders of metal atoms surrounded by low-density and fast-expanding plasma corona. For fully vaporized wires, we utilize the integrated-phase technique, based on laser interferometry, to measure the dynamic dipole polarizability of metal atoms. Titanium wire with a diameter of 20 μm and a length of 1 cm was rapidly vaporized by a fast-rising current at ∼10 ns. We find that the dynamic dipole polarizability of titanium atoms equals 20.5 ± 2 Å3 for 532 nm and 10.6 ± 1 Å3 for 1064 nm. The wire reaches a totally vaporized state when the expansion velocity in a vacuum is ∼5.5 km/s. To vaporize Ti wire, the deposited Joule energy exceeded tabulated enthalpy of atomization by ∼2.8 times. Two-wavelength diagnostic allows reconstruction of the static dipole polarizability 9.13 ± 1.7 Å3 and electron transition energy 3.13 ± 0.2 eV with the corresponding transition wavelength of 396.6 ± 26 nm. This reconstructed wavelength matches to the group of strong dipole-allowed atomic spectral lines for Ti between 394.87 and 402.46 nm for ground-state transitions 3d24s2.

A new scale of atomic static dipole polarizability invoking other periodic descriptors

Knowledge of the nature of a chemical reactivity descriptor holds immense value to theoretical scientists. An appreciable number of works have been carried out in this realm. Polarizability (α) is one amongst such constructs. Fundamentally, it is a linear response of a systems electron cloud to an external applied electric field. The concept of polarizability is being widely adopted in the contemporary world of chemistry; however a suitable scale of measurement of atomic polarizability is still to be designed. In this work, an ansatz to compute atomic static dipole polarizability is proposed considering the conjoint action of absolute radius (r) and electronegativity (χ) for 103 elements of periodic table. We have evaluated the data invoking regression analysis. The computed data mirrors the periodicity remarkably satisfying all the sine qua non of a standard scale of polarizability. It presents an excellent quantitative correlation with ionization energy. Further, molecular polarizability (αm) is determined conceptualizing the property of additivity. A superior correlation between theoretical vis-a-vis existing molecular polarizabilities is observed.

Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi-Löwdin self-interaction correction

The static electric dipole polarizability of a system is a measure of the binding of its electrons. In density functional theory calculations, this binding is weakened by the presence of unphysical self-interaction in the density functional approximation (DFA), leading to overestimates of polarizabilities. To investigate this systematically we compare polarizabilities for the atoms from H to Ar and their anions and cations calculated in several DFAs and the corresponding self-interaction-corrected (SIC) DFAs with experiment and with high-level quantum chemistry reference values. The SIC results are obtained using the Fermi-L\"owdin orbital self-interaction correction (FLO-SIC) method. Removing self-interaction generally leads to smaller polarizabilities that agree significantly better with reference values. We find that FLO-SIC improves the performance of the local spin density approximation and the generalized gradient approximation (GGA) for polarizabilities to a quality that is comparable to so-called rung 4 functionals, but slightly degrades the performance of the strongly constrained and appropriately normed meta-GGA functional.

A generally applicable atomic-charge dependent London dispersion correction.

The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.

Dynamic dipole polarizability of gold and copper atoms for 532- and 1064-nm wavelengths

The fast electrical explosion of fine metal wires in a vacuum will produce calibrated gas cylinders of metal atoms surrounded by a low-density corona. For fully vaporized wires, the integrated-phase technique, based on laser interferometry, provides the dynamic dipole polarizability of metal atoms. A fast-rising current of $\ensuremath{\sim}1\phantom{\rule{0.16em}{0ex}}\mathrm{kA}/\mathrm{ns}$ will vaporize thin 12.7-\textmu{}m-diameter Au and Cu wires in a vacuum and generate a radial-expanding gas cylinder surrounded by low-density plasma corona. Employing the integrated-phase technique on fast-exploding Au and Cu wires, we find that the dynamic dipole polarizability of Au atoms is $8.3\ifmmode\pm\else\textpm\fi{}0.8\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$ for 532 nm and $7.0\ifmmode\pm\else\textpm\fi{}0.7\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$ for 1064 nm. Measurements collected from exploding Cu wire provide dynamic dipole polarizability of $10.2\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$ for 532 nm and $6.5\ifmmode\pm\else\textpm\fi{}0.7\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$ for 1064 nm. All experimental values correspond to theoretical predictions based on quantum-mechanical calculations.

Quantum-Mechanical Relation between Atomic Dipole Polarizability and the van der Waals Radius.

The atomic dipole polarizability α and the van der Waals (vdW) radius R_{vdW} are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently and separately from each other. Here, we derive the quantum-mechanical relation R_{vdW}=const×α^{1/7}, which is markedly different from the common assumption R_{vdW}∝α^{1/3} based on a classical picture of hard-sphere atoms. As shown for 72 chemical elements between hydrogen and uranium, the obtained formula can be used as a unified definition of the vdW radius solely in terms of the atomic polarizability. For vdW-bonded heteronuclear dimers consisting of atoms A and B, the combination rule α=(α_{A}+α_{B})/2 provides a remarkably accurate way to calculate their equilibrium interatomic distance. The revealed scaling law allows us to reduce the empiricism and improve the accuracy of interatomic vdW potentials, at the same time suggesting the existence of a nontrivial relation between length and volume in quantum systems.

Rayleigh scattering in dense fluid helium

Iglesias et al. (2002) showed that the Rayleigh scattering from helium atoms decreases by collective effects in the atmospheres of cool white dwarf stars. Their study is here extended to consider an accurate evaluation of the atomic polarizability and the density effects involved in the Rayleigh cross section over a wide density-temperature region. The dynamic dipole polarizability of helium atoms in the ground state is determinated with the oscillator-strength distribution approach. The spectral density of oscillator strength considered includes most significant single and doubly excited transitions to discrete and continuum energies. Static and dynamic polarizability results are confronted with experiments and other theoretical evaluations shown a very good agreement. In addition, the refractive index of helium is evaluated with the Lorentz-Lorenz equation and shows a satisfactory agreement with the most recent experiments. The effect of spatial correlation of atoms on the Rayleigh scattering is calculated with Monte Carlo simulations and effective energy potentials that represent the particle interactions, covering fluid densities between 0.005 and a few g/cm$^3$ and temperatures between $1000$ K and $15000$ K. We provide analytical fits from which the Rayleigh cross section of fluid helium can be easily calculated at wavelength $\lambda>505.35$ \AA. Collision-induced light scattering was estimated to be the dominant scattering process at densities greater than 1-2 g/cm$^3$ depending on the temperature.

Anisotropic optical trapping as a manifestation of the complex electronic structure of ultracold lanthanide atoms: The example of holmium

The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula only comprises transitions involving electrons in the valence orbitals like $6s$, $5d$, $6p$ or $7s$, while transitions involving $4f$ core electrons are neglected. Applying this formalism to the ground level of configuration $4f^q6s^2$, we restrict the sum to transitions implying the $4f^q6s6p$ configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between $4f^q6s6p$ and other configurations, we demonstrate that the imaginary part of the scalar, vector and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate is thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of energy levels, Land\'e $g$-factors, transition probabilities, polarizabilities and van der Waals $C_6$ coefficients, previously performed on erbium and dysprosium, and presently performed on holmium. Our results show that, although the density of states decreases with increasing $q$, the configuration interaction between $4f^q6s6p$, $4f^{q-1}5d6s^2$ and $4f^{q-1}5d^26s$ is surprisingly stronger in erbium ($q=12$), than in holmium ($q=11$), itself stronger than in dysprosium ($q=10$).

Optical trapping of ultracold dysprosium atoms: transition probabilities, dynamic dipole polarizabilities and van der Waals C6 coefficients

The efficiency of the optical trapping of ultracold atoms depends on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited levels. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the C6 coefficients characterizing the van der Waals interaction between two dysprosium atoms in the two lowest levels. We have computed the energies of excited states and the transition probabilities appearing in the sums, using a combination of ab initio and least-square-fitting techniques provided by the Cowan codes and extended in our group. Regarding the real part of the polarizability, for field frequencies far from atomic resonances, the vector and tensor contributions are two-orders-of-magnitude smaller than the scalar contribution, whereas for the imaginary part, the vector and tensor contributions represent a noticeable fraction of the scalar contribution. Finally, our anisotropic C6 coefficients are much smaller than those published in the literature.

Dynamic polarizability of tungsten atoms reconstructed from fast electrical explosion of fine wires in vacuum

For nanosecond electrical explosion of fine metal wires in vacuum generates calibrated, radially expanded gas cylinders of metal atoms are surrounded by low-density fast expanding plasma corona. Here, a novel integrated-phase technique, based on laser interferometry, provides the dynamic dipole polarizability of metal atoms. This data was previously unavailable for tungsten atoms. Furthermore, an extremely high melting temperature and significant pre-melt electronic emission make these measurements particularly complicated for this refractory metal.

Van der Waals coefficients for positronium interactions with atoms

The random-phase approximation with exchange (RPAE) is used with a $B$-spline basis to compute dynamic dipole polarizabilities of noble-gas atoms and several other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values of the van der Waals ${C}_{6}$ constants for positronium interactions with these atoms are determined and compared with existing data. After correcting the RPAE polarizabilities to fit the most accurate static polarizability data, our best predictions of ${C}_{6}$ for Ps--noble-gas pairs are expected to be accurate to within 1%, and to within a few percent for the alkaline-earth metals. We also used accurate dynamic dipole polarizabilities from the literature to compute the ${C}_{6}$ coefficients for the alkali-metal atoms. Implications of increased ${C}_{6}$ values for Ps scattering from more polarizable atoms are discussed.