Van Der Waals Coefficients Research Articles

Van der Waals coefficients for interactions of dysprosium and erbium atoms with alkali-metal and alkaline-earth-metal atoms

van der Waals coefficients for interactions of dysprosium and erbium atoms with alkali-metal and alkaline-earth-metal atoms

Elastic and glancing-angle rate coefficients for heating of ultracold Li and Rb atoms by collisions with room-temperature noble gases, H2, and N2.

Trapped ultracold alkali-metal atoms can be used to measure pressure in the ultra-high-vacuum and XHV pressure regimes, those with p < 10-6 Pa. This application for ultracold atoms relies on precise knowledge of collision rate coefficients of alkali-metal atoms with residual room-temperature atoms and molecules in the ambient vacuum or with deliberately introduced gasses. Here, we determine combined elastic and inelastic rate coefficients as well as glancing-angle rate coefficients for ultracold 7Li and 87Rb with room-temperature noble gas atoms as well as H2 and 14N2 molecules. Glancing collisions are those processes where only little momentum is transferred to the alkali-metal atom and this atom is not ejected from its trap. Rate coefficients are found by performing quantum close-coupling scattering calculations using ab initio ground-state electronic Born-Oppenheimer potential energy surfaces. The potentials for Li and Rb with noble gas atoms and also for Rb(2S)-H2(XΣg +) and Rb(2S)-N2(X1Σg +) systems are based on the non-relativistic spin-restricted coupled-cluster method with single, double, and noniterative triple excitations [RCCSD(T)]. For Li(2S)-N2(X1Σg +), the potential is computed at the explicitly correlated spin-restricted RCCSD(T)-F12 level. For Rb, Kr, and Xe atoms, scalar relativistic corrections to the core electrons have been included, while second-order spin-orbit corrections from the valence electrons have been estimated. Data for Li-H2 and Li-He were taken from the existing literature. We estimate standard uncertainties of the rate coefficients by comparing rate coefficients calculated using potentials found with electronic basis sets of increasing size, including estimates of relativistic spin-orbit corrections and the uncertainty of the van der Waals coefficients. The relative uncertainties of rate coefficients are 1%-2% with the exception of 7Li or 87Rb colliding with 20Ne. Those have relative uncertainties of 9% and 8%, respectively. We also show that a commonly used semiclassical approximation for the total elastic rate coefficient agrees with the quantum calculations to 10% with the exception of 7Li and 87Rb collisions with H2, where the semiclassical value underestimates the quantum value by 20%.

Investigation of Electron Scattering from Vinyl Ether and Its Isomers

This article reports a comprehensive theoretical study of electron scattering from vinyl ether and its isomers. The electron–molecule quantum collision problem is solved through a complex optical potential approach. From the solution of the Schrödinger equation corresponding to this scattering problem, various cross sections were obtained for energies from ionization threshold of target to 5 keV. To deal with the non-spherical and complex structure, a multi-center group additivity approach is used. Furthermore, geometrical screening correction is applied to compensate for the overestimation of results due to electron charge density overlap. We found an interesting correlation between maximum ionization cross section with polarizability and ionization energy of the target molecule. The fitting of the total cross section as a function of the incident electron energy is reported in this article. The correlation between the effective diameter of the target and the projectile wavelength at maximum ionization energy is also reported for vinyl ether and its isomers. The data presented here will be useful to biomedical field, mass spectrometry, and chemical database for military range applications. The cross sections are also important to model Mars’s atmosphere due to their presence in its atmosphere. The gas-kinetic radius and the van der Waals coefficients are estimated from the electron-impact total scattering cross sections. In addition, the current study predicts the presence of isomeric effects in the cross section.

Rydberg blockade in an ultracold strontium gas revealed by two-photon excitation dynamics

We demonstrate the interaction-induced blockade effect in an ultracold $^{88}$Sr gas via studying the time dynamics of a two-photon excitation to the triplet Rydberg series $5\mathrm{s}n\mathrm{s}\, ^3\textrm{S}_1$ for five different principle quantum numbers $n$ ranging from 19 to 37. By using a multi-pulse excitation sequence to increase the detection sensitivity we could identify Rydberg-excitation-induced atom losses as low as $<1\%$. Based on an optical Bloch equation formalism, treating the Rydberg-Rydberg interaction on a mean-field level, the van der Waals coefficients are extracted from the observed dynamics, which agree fairly well with \emph{ab initio} calculations.

Electrostatically actuated double walled piezoelectric nanoshell subjected to nonlinear van der Waals effect: nonclassical vibrations and stability analysis

Abstract In this paper, nonlinear vibration and frequency response analysis of double walled piezoelectric nanoshell (DWPENS) is investigated using nonclassical approach of the Gurtin–Murdoch surface/interface (GMSIT) theory. The piezoelectric nanoshell is simultaneously subjected to visco-Pasternak medium, the nonlinear van der Waals and electrostatic forces. Hamilton’s principles, the assumed mode method combined with Lagrange–Euler’s are used for the governing equations and boundary conditions. Complex averaging method combined with Arc-length continuation is used to achieve the nonlinear frequency response and stability analysis of the DWPENS. It is found that the electrostatic and piezoelectric voltages, the length to radius ratio, the nanoshell gap width, van der Waals (vdW) coefficients and other parameters can effectively change the flexural rigidity of the system which in turn affects the nonlinear frequency response. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system’s instability, nonlinear behavior, and bandwidth.

Van der Waals coefficients of the multi-layered MoS2 with alkali metals

The van der Waals coefficients and the separation dependent retardation functions of the interactions between the atomically thin films of the multi-layered transition metal molybdenum disulfide (MoS2) dichalcogenides with the alkali atoms are investigated. First, we determine the frequency-dependent dielectric permittivity and intrinsic carrier density values for different layers of MoS2 by adopting various fitting models to the recently measured optical data reported by Yu and co-workers (2015 Sci. Rep. 5, 16 996) using spectroscopy ellipsometry. Then, dynamic electric dipole polarizabilities of the alkali atoms are evaluated very accurately by employing the relativistic coupled-cluster theory. We also demonstrate the explicit change in the above coefficients for different number of layers. These studies are highly useful for the optoelectronics, sensing and storage applications using layered MoS2.

Nonlinear vibration and stability analysis of double-walled piezoelectric nanoresonator with nonlinear van der Waals and electrostatic excitation

In this work, nonlinear vibration and frequency response analysis of a double-walled piezoelectric nanoresonator based on a cylindrical nanoshell is performed using the Gurtin–Murdoch surface/interface theory. The piezoelectric nanoresonator is simultaneously subjected to the visco-Pasternak medium and nonlinear van der Waals and electrostatic forces. It is found that the electrostatic and piezoelectric voltages, length to radius ratio, nanoresonator gap width, linear and nonlinear van der Waals coefficients and other parameters can effectively change the flexural rigidity of the system, which in turn affects the nonlinear frequency response. Also, increasing or decreasing of some parameters leads to increase or decrease in the resonance amplitude, resonant frequency, instability of the system, nonlinear behavior and bandwidth.

Anisotropic interactions in electric field polarized ultracold Rydberg gases

We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective C3 dipole–dipole and C6 van der Waals coefficients. We compare the C3 and C6 with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole–dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in states in the blockade regime. For internuclear distances close to the blockade radius, Rbl ≈ 4–6 μm, molecular calculations are in much better agreement with experimental results than those based on the properties of single atoms and independent calculations of C3 and C6 which were used to analyze the original experiment. We find that the calculated C6 coefficient is within 8% of the experimental value while the C3 coefficient is within 20% of the experimental value.

Pressure shifts in high-precision hydrogen spectroscopy: II. Impact approximation and Monte-Carlo simulations

We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.

Pressure shifts in high-precision hydrogen spectroscopy: II. Impact approximation and Monte-Carlo simulations

We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S–4P experiment (and an ongoing 2S–6P experiment) in Garching, but numerical input data are provided for other transitions (e.g. involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.

Pressure shifts in high-precision hydrogen spectroscopy. I. long-range atom–atom and atom–molecule interactions

We study the theoretical foundations for the pressure shifts in high-precision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P_1/2 and 4P_3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P-2S interaction, where the inclusion of quasi-degenerate 4S-2P_1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasi-degenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R^6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom-atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atom-molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.

Pressure shifts in high-precision hydrogen spectroscopy. I. Long-range atom–atom and atom–molecule interactions

We study the theoretical foundations for the pressure shifts in high-precision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P1/2 and 4P3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P–2S interaction, where the inclusion of quasi-degenerate 4S–2P1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasi-degenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom–atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atom–molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.

Thermodynamics of Natural Pigment-Doped Ethanol under Monochromatic Laser Irradiation

Abstract A laser beam heats a mixture of ethanol and anthocyanins producing the effect of a reciprocating machine. This behaviour is analyzed in terms of the stable, metastable and unstable states of Landau and Lifschitz. Trying first with the van der Waals equation of state, with negative results because the system state is normally far from the critical state, a modified version, with van der Waals coefficients depending linearly on the temperature is proposed, based in the thermodynamic properties of ethanol at room and critical temperatures. The resulting theory allows us to understand the discontinuous results concerning the absorption of the laser beam in terms of a thermodynamic cycle and its frequency dependence on the laser light focus position. Slight changes in the experimental setup may enable the measurement of thermodynamic properties in metastable states.

First-principles study of the binding energy between nanostructures and its scaling with system size

The equilibrium binding energy is an important factor in the design of materials and devices. However, it presents great computational challenges for materials built up from nanostructures. Here we investigate the binding-energy scaling law from first-principles calculations. We show that the equilibrium binding energy per atom between identical nanostructures can scale up or down with nanostructure size. From the energy scaling law, we predict finite large-size limits of binding energy per atom. We find that there are two competing factors in the determination of the binding energy: Nonadditivities of van der Waals coefficients and center-to-center distance between nanostructures. To uncode the detail, the nonadditivity of the static multipole polarizability is investigated. We find that the higher-order multipole polarizability displays ultra-strong intrinsic nonadditivity, no matter if the dipole polarizability is additive or not.

Primary vacuometer based on an ultracold gas in a shallow optical dipole trap

A calibration-free primary vacuometer based on an ultracold atomic gas in a shallow far-off-resonance optical dipole trap is proposed and demonstrated. The pressure is obtained by measuring the loss of trapped atoms which is caused by collisions with the ambient gas of the vacuum chamber. The loss is related to the ambient-gas pressure via a theoretical model based on first principles. The model is applicable owing to elimination of a number of systematic effects which otherwise preclude or complicate construction of a first-principle model. These systematics include loss unrelated to collisions with the ambient gas as well as loss dependance on the number and energy of trapped atoms. In the demonstrated vacuometer, the atom-number decay is exponential with the rate proportional to the pressure, where the proportionality coefficient is expressed via the gas composition and van der Waals coefficients C6. Whenever the gas composition is unknown, the systematic error is typically well below that of the hot-cathode ionization gauge. The vacuometer is implemented using a gas of ultracold lithium-6, which is the optimal working body for such a vacuometer. The lowest measured pressure, Pa, is limited by the vacuum in the apparatus, while the dominant error source of 4% is due to uncertainty in the C6 value and may be improved. Comparison with reading of a hot-cathode ionization gauge is also shown.

Accurate van der Waals coefficients between fullerenes and fullerene-alkali atoms and clusters: Modified single-frequency approximation

Long-range van der Waals (vdW) interaction is critically important for intermolecular interactions in molecular complexes and solids. However, accurate modeling of vdW coefficients presents a great challenge for nanostructures, in particular for fullerene clusters, which have huge vdW coefficients but also display very strong nonadditivity. In this work, we calculate the coefficients between fullerenes, fullerene and sodium clusters, and fullerene and alkali atoms with the hollow-sphere model within the modified single-frequency approximation (MSFA). In the MSFA, we assume that the electron density is uniform in a molecule and that only valence electrons in the outmost subshell of atoms contribute. The input to the model is the static multipole polarizability, which provides a sharp cutoff for the plasmon contribution outside the effective vdW radius. We find that the model can generate ${C}_{6}$ in excellent agreement with expensive wave-function-based ab initio calculations, with a mean absolute relative error of only $3%$, without suffering size-dependent error. We show that the nonadditivities of the coefficients ${C}_{6}$ between fullerenes and ${\mathrm{C}}_{60}$ and sodium clusters ${\mathrm{Na}}_{n}$ revealed by the model agree remarkably well with those based on the accurate reference values. The great flexibility, simplicity, and high accuracy make the model particularly suitable for the study of the nonadditivity of vdW coefficients between nanostructures, advancing the development of better vdW corrections to conventional density functional theory.

Communication: Accurate higher-order van der Waals coefficients between molecules from a model dynamic multipole polarizability.

Due to the absence of the long-range van der Waals (vdW) interaction, conventional density functional theory (DFT) often fails in the description of molecular complexes and solids. In recent years, considerable progress has been made in the development of the vdW correction. However, the vdW correction based on the leading-order coefficient C6 alone can only achieve limited accuracy, while accurate modeling of higher-order coefficients remains a formidable task, due to the strong non-additivity effect. Here, we apply a model dynamic multipole polarizability within a modified single-frequency approximation to calculate C8 and C10 between small molecules. We find that the higher-order vdW coefficients from this model can achieve remarkable accuracy, with mean absolute relative deviations of 5% for C8 and 7% for C10. Inclusion of accurate higher-order contributions in the vdW correction will effectively enhance the predictive power of DFT in condensed matter physics and quantum chemistry.

Long-range states of the NaRb molecule near theNa(3 2S1/2)+Rb(5 2P3/2)asymptote

We report a high-resolution spectroscopic investigation of the long-range states of the $^{23}$Na$^{87}$Rb molecule near its Na($3^2S_{1/2}$)+Rb($5^2P_{3/2}$) asymptote. This study was performed with weakly bound ultracold molecules produced via magneto-association with an inter-species Feshbach resonance. We observed several regular vibrational series, which are assigned to the 5 attractive long-range states correlated with this asymptote. The vibrational levels of two of these states have sharp but complex structures due to hyperfine and Zeeman interactions. For the other states, we observed significant linewidth broadenings due to strong predissociation caused by spin-orbit couplings with states correlated to the lower Na($3^2S_{1/2}$)+Rb($5^2P_{1/2}$) asymptote. The long-range $C_6$ van der Waals coefficients extracted from our spectrum are in good agreement with theoretical values.

Casimir and van der Waals energy of anisotropic atomically thin metallic films

We discuss the van der Waals (Casimir) free energies and pressures of thin metallic films, consisting from one to fifteen atomic layers, with regard to the anisotropy in their dielectric properties. Both free-standing films and films deposited on a dielectric substrate are considered. The computations are performed for a Au film and a sapphire substrate. According to our results, for free-standing Au films consisting of one and three atomic layers the respective relative error arising from the use of an isotropic (bulk) dielectric permittivity is equal to 73% and 37% for the van der Waals energy, and 70% and 35% for the pressure. We tabulate the energy and pressure van der Waals coefficients of thin Au films computed with account of their anisotropy. It is shown that the bulk permittivity of Au can be used for the films consisting of more than 30 atomic layers, i.e., more than approximately 7 nm thickness. The role of relativistic effects is also investigated and shown to be important even for the films consisting of two or three layers. The obtained results can find applications in the investigation of stability of thin films and development of novel nanoscale devices.

The ground-state potential energy curve of the radium dimer from relativistic coupled cluster calculations.

The potential energy curve for the ground-state of radium dimer (Ra2) is provided by means of atomic and molecular relativistic coupled cluster calculations. The short-range part of this curve is defined by an equilibrium bond length of 5.324 Å, a dissociation energy of 897 cm(-1), and a harmonic vibrational frequency of 20.5 cm(-1). The asymptotic behavior at large interatomic distances is characterized by the van der Waals coefficients C6 = 5.090 × 10(3), C8 = 6.978 × 10(5), and C10 = 8.786 × 10(7) atomic units. The two regions are matched in an analytical potential to provide a convenient representation for use in further calculations, for instance, to model cold collisions between radium atoms. This might become relevant in future experiments on ultracold, optically trapped, radioactive radium atoms that are used to search for a permanent electric dipole moment.