Dynamic Electric Dipole Polarizabilities Research Articles

Origin-Independent Dynamic Polarizability Density from Coupled Cluster Response Theory.

The calculation of the origin-independent density of the dynamic electric dipole polarizability, previously presented for uncorrelated and density functional theory (DFT)-based methods, has been developed and implemented at the coupled cluster singles and doubles (CCSD) level of theory. A pointwise analysis of polarizability densities calculated for a number of molecules at Hartree-Fock (HF) and CCSD clearly shows that the electron correlation effect is much larger than one would argue considering the integrated dipole electric polarizability alone. Large error compensations occur during the integration process, which hide fairly large deviations mainly located in the internuclear regions. The same is observed when calculated CCSD and B3LYP polarizability densities are compared, with the remarkable feature that positive/negative deviations between CCSD and HF reverse sign, becoming negative/positive when comparing CCSD to B3LYP.

Magic wavelengths for 6s1/2 → 5d3/2,5/2 transitions of Yb+ ions

The wave functions, energy levels and matrix elements of Yb+ ions are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined. Then, the magic wavelengths of the magnetic sublevel 6s1/2,m = 1/2 → 5d3/2,m = ±3/2,±1/2 and 6s1/2,m = 1/2 → 5d5/2,m = ±5/2,±3/2,±1/2 transitions in the linearly, right-handed, and left-handed polarized light are further determined. The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.

Tune-out wavelengths of the hyperfine components of the ground level of Cs133 atoms

The static and dynamic electric-dipole polarizabilities and tune-out wavelengths for the ground state of Cs atoms are calculated by using a semiempirical relativistic configuration interaction plus core polarization approach. By considering the hyperfine splittings, the static and dynamic polarizabilities, hyperfine Stark shifts, and tune-out wavelengths of the hyperfine components of the ground level of $^{133}$Cs atoms are determined. It is found that the hyperfine shifts of the first primary tune-out wavelengths are about $-$0.0135 nm and 0.0106 nm, which are very close to the hyperfine interaction energies. Additionally, the contribution of the tensor polarizability to the tune-out wavelengths is determined to be about $10^{-5} \sim 10^{-6}$ nm.

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.

Polarizabilities and tune-out wavelengths of the hyperfine ground states of 133Cs atom

SynopsisThe static and dynamic electric dipole polarizabilities of the ground state and hyperfine ground states of the 133Cs have been calculated by using relativistic configuration interaction plus core polarization (RCICP) approach. The tune-out wavelengths of ground and hyperfine ground states are also determined.

Magic wavelengths for the transition in ytterbium atom

The static and dynamic electric dipole polarizabilities of the and states of Yb are calculated by using the relativistic ab initio method. Focusing on the red detuning region to the transition, we find two magic wavelengths at 1035.7(2) and 612.9(2) nm for the transition and three magic wavelengths at 1517.68(6), 1036.0(3) and 858(12) nm for the transitions. Such magic wavelengths are of particular interest for attaining the state-insensitive cooling, trapping, and quantum manipulation of neutral Yb atom.

Empirically constructed dynamic electric dipole polarizability function of magnesium and its applications

The dynamic electric dipole polarizability function for the magnesium atom is formed by assembling the atomic electric dipole oscillator strength distribution from combinations of theoretical and experimental data for resonance oscillator strengths and for photoionization cross sections of valence and inner shell electrons. Consistency with the oscillator strength (Thomas-Reiche-Kuhn) sum rule requires the adopted principal resonance line oscillator strength to be several percent lower than the values given in two critical tabulations, though the value adopted is consistent with a number of theoretical determinations. The static polarizability is evaluated. Comparing the resulting dynamic polarizability as a function of the photon energy with more elaborate calculations reveals the contributions of inner shell electron excitations. The present results are applied to calculate the long-range interactions between two and three magnesium atoms and the interaction between a magnesium atom and a perfectly conducting metallic plate. Extensive comparisons of prior results for the principal resonance line oscillator strength, for the static polarizability, and for the van der Waals coefficient are given in the Appendix.

On the determination of the diagonal components of the optical activity tensor in chiral molecules

It is shown that the diagonal components of the mixed electric-magnetic dipole polarizability tensor, used to rationalize the optical rotatory power of chiral molecules, are origin independent, if they are referred to the coordinate system defined by the eigenvectors of the dynamic electric dipole polarizability, for a given value ω of the frequency of a monochromatic wave impinging on an ordered sample. Within this reference frame, the individual diagonal components of the mixed electric-magnetic dipole polarizability are separately measurable properties. The theoretical method is applied via a test calculation to the cyclic 1,2-M enantiomer of the dioxin molecule, using a large Gaussian basis set to estimate near Hartree-Fock values within a series of dipole length, velocity, and acceleration representations.

Scattering of nitrogen molecules by silver atoms

We present a quantal study of the rotationally elastic and inelastic scattering of Ag and N(2), with the nitrogen molecule treated as a rigid rotor. The two-dimensional potential energy surface of the AgN(2) complex is obtained ab initio by means of the spin unrestricted coupled-cluster method with single, double, and perturbative triple excitations. The global minimum is found to be located at an internuclear distance of 8.13 a(0) and an angle of 127.2°. The long-range part of the potential is constructed from the dynamic electric dipole polarizabilities of Ag and N(2). Elastic, excitation, and relaxation cross sections and rates are calculated for energies between 0.1 and 5000 cm(-1). The momentum transfer cross sections and rates are also computed. Finally, we compare the cross sections for Ag-N(2) and Na-N(2) to explore the possibility of using silver instead of sodium in experimental tests.

A new implementation of dynamic polarizability evaluation using a multi-resolution multi-wavelet basis set

An algorithm to evaluate the response function on the space spanned by Multi-resolution Multi-wavelet (MRMW) basis functions is implemented in a new efficient quantum chemical program system. Dynamic electric dipole polarizability of a molecule is evaluated for a range of applied optical frequencies as a preliminary application of the implementation. The results obtained by the MRMW provide the one in near completeness limit. We also compare a few examples of the dynamic polarizabilities evaluated using conventional Gaussian basis set functions with the one evaluated by the MMMW basis functions. For small frequencies, there is no significant difference among them and large Gaussian results are close to the MRMW value, but they diverge from the MRMW value when the applied frequency approaches to the resonance region.

Elastic scattering and rotational excitation of nitrogen molecules by sodium atoms

A quantal study of the rotational excitation of nitrogen molecules by sodium atoms is carried out. We present the two-dimensional potential energy surface of the NaN(2) complex, with the N(2) molecule treated as a rigid rotor. The interaction potential is computed using the spin unrestricted coupled-cluster method with single, double, and perturbative triple excitations (UCCSD(T)). The long-range part of the potential is constructed from the dynamic electric dipole polarizabilities of Na and N(2). The total, differential, and momentum transfer cross sections for rotationally elastic and inelastic transitions are calculated using the close-coupling approach for energies between 5 cm(-1) and 1500 cm(-1). The collisional and momentum transfer rate coefficients are calculated for temperatures between 100 K and 300 K, corresponding to the conditions under which Na-N(2) collisions occur in the mesosphere.

David Bishop's approach to vibrational dynamic contributions to molecular properties: Application to Jones and magnetoelectric birefringences in diatomic molecules

AbstractThe expressions derived by D. M. Bishop for the pure vibrational contributions to the dynamic electric dipole polarizabilities and hyperpolarizabilities of polyatomic molecules (see Bishop, D. M. Rev Mod Phys, 1990, 62, 343) are generalized to arbitrary linear, quadratic and cubic response functions, and then applied to determine the effect of nuclear motion on two diatomic molecules (N2 and CO) on Jones (and Magnetoelectric) linear birefringences. The influence of nuclear motion on the anisotropy of the refractive index appears to be quite contained: the observable differs from the equilibrium electronic estimate by ≈4% for N2, and by ≈8–9% in CO. As a case study, also the effect of vibrations on the temperature independent contribution to Buckingham birefringence of H2 and D2 is analyzed and discussed. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Time-independent coupled cluster theory of the polarization propagator. Implementation and application of the singles and doubles model to dynamic polarizabilities and van der Waals constants†

Recently proposed time-independent coupled cluster theory of the polarization propagator [R. Moszynski, P. S. Żuchowski, and B. Jeziorski, Collect. Czech. Chem. Commun. 70, 1109, 2005] has been implemented at the single and double excitations (CCSD) level. The performance of the new approach was investigated by carrying out calculations of static and dynamic electric dipole polarizabilities for various molecules and by making a comparison with values obtained from other ab initio methods, including the full configuration interaction (FCI) technique. Our results show that the polarizabilities computed with the new approach are in a good agreement with the time-dependent CCSD and (when available) FCI values. The isotropic C 6 dispersion coefficients for several benchmark van der Waals complexes, e.g. dimers of helium, argon, water, and benzene, are also reported. They compare very well with existing experimental and best theoretical data. The new propagator, implemented already in the MOLPRO package, is computationally somewhat less demanding than the propagator of the time-dependent coupled cluster theory, and can be considered as an alternative to the latter in applications to large molecules and in studies of their interactions.

Relativistic effects on the electric polarizabilities and their geometric derivatives for hydrogen halides and dihalogens – a Dirac–Hartree–Fock study

The geometric derivatives of the static and dynamic electric dipole polarizability have been calculated at the all-electron Dirac–Hartree–Fock level for the dihalogen molecules F 2, Cl 2, Br 2, and I 2 and for the hydrogen halides HF, HCl, HBr, and HI. A comparison with the non-relativistic Hartree–Fock values shows that the relativistic corrections tend to be larger for the geometric derivatives of the polarizabilities than for the polarizabilities. The frequency dispersion of the corrections due to relativity is significant for the molecules containing bromine and iodine. As expected, for the same molecules relativistic effects are sizable, and they improve the agreement between theory and experiment for the electric dipole polarizabilities. In the case of the Raman scattering cross sections, only a few experimental data are available. In general the relativistic effects are in this case within the range of the experimental error.

Electric-dipole polarizabilities of molecules of CFxCl4−x (x=1–4) Freons. Coefficients of dispersion interaction between different freons and between freons and noble gases

Average values of dynamic electric-dipole polarizabilities of molecules of CFCl3, CF2Cl2, CF3Cl, and CF4 Freons in a wide frequency range (from near-infrared to far-ultraviolet regions of the spectrum) were calculated on the basis of the latest data on the distributions of oscillator strengths in the absorption spectra of these Freons. An accurate analytical approximation of the polarizability dispersion is suggested for these Freons. Values of polarizabilities at imaginary frequencies were calculated. Coefficients of dispersion interaction of different Freon molecules with each other and with noble-gas atoms were determined for the first time. The high accuracy of the geometric mean combination rule used to estimate interaction constants for pairs of unlike particles is demonstrated.

The singlet oxygen absorption to the upper state of the Schumann–Runge system: the B 3Σu-←a 1Δg and B 3Σu-←b 1Σg+ transitions intensity calculation

The singlet–triplet transition dipole moments were calculated by quadratic response (QR) multi-configuration self-consistent field (MCSCF) method from the two metastable singlet states of molecular oxygen, a1Δg and b1Σg+, to the upper triplet excited states. The most intense transitions in the near UV region (200–250 nm) are connected with the upper state of the Schumann–Runge (SR) system, B3Σu-, and with the 13Πu dissociative state. Calculations of the transition dipole moments for the spin allowed bands, SR, n1Σu+â†�b1Σg+ and n1Δuâ†�a1Δg, by linear response (LR) MCSCF method were compared with previous studies and found to be quite reliable. A similar analysis was performed for the spin–orbit coupling matrix elements, calculated with the full Breit–Pauli operator. Spin–orbit coupling between the b1Σg+ and X3Σg- (MS=0) states provides their effective mixing at all internuclear distances (r) and produces a strong contribution to the parallel component of the B3Σu-â†�b1Σg+ transition dipole moment (Dz) by intensity borrowing from the Schumann–Runge band in a wide range of the r values. The Dz(B–b) integral has an averaged value 0.08 ea0† in the most important range, r=1.18 to 1.45 A, but exhibits some irregular behaviour at longer distances. The perpendicular component of the B–b transition is negligible. The B3Σu-â†�a1Δg transition has only perpendicular dipole moment which is relatively non-intense, D(B–a)∽0.0004 ea0, in order to compete with the absorption in the Herzberg I continuum (D∽0.001 ea0). The transition dipole moments as functions of r have some oscillations at very short and long distances, connected with level crossings and avoided crossings. The singlet–triplet transitions 13Πuâ†�a1Δg and 13Πuâ†�b1Σg+ are 30–20 times weaker than the B–b absorption. Static and dynamic electric dipole polarizabilities for the ground triplet and both singlet excited states are also calculated and briefly discussed.

Long-range coefficients for the low-lying electronic states of LiB

Dynamic electric dipole polarizabilities of Li ( 2S; 2P) and B ( 2P) are obtained by a time dependent gauge invariant method. C 6 coefficients are deduced from the fit of sum-over-states functions to the dynamic polarizabilities at imaginary frequencies, in taking the first oscillator strength and transition energy values calculated at the configuration interaction level as starting points. The dispersion coefficients for the low-lying electronic states of LiB that dissociate into Li 2S(2s 1)+ B 2P(2p 1) and Li 2 P(2p 1) + B 2 P(2p 1) are reported.

Calculation of dynamic electric dipole polarizability, nuclear electric shieldings, and their Cauchy moments in benzene

Theoretical methods based on the random-phase approximation have been applied to evaluate near Hartree–Fock dynamic electric polarizability and shielding tensors of carbon and hydrogen nuclei in the benzene molecule. Cauchy moments of the various properties have been determined. The results obtained in different gauges (dipole length, velocity, and acceleration) are reported.

Evaluation of retardation energy shifts in a Rydberg helium atom.

The microscopic system best suited to the high-precision confirmation of a retardation (or Casimir) effect: originating in the finiteness of the speed of light: would seem to be the Rydberg helium atom (a helium atom with one electron in its ground state and the other in a high-n state, preferably with lapprox. =n). For the helium atom, calculation of the retardation energy shift ..delta..E/sub ret/(n,l) that arises from the retardation effective potential V/sub ret/(r) seen by the outer electron, where r is the separation of the nucleus and the outer electron, is not limited to the case of a Rydberg outer electron. We evaluate ..delta..E/sub ret/(n,l) numerically in the dipole approximation for a range of values of n and l. The dynamic electric dipole polarizability of the He/sup +/ core is approximated using pseudostates (a finite number of effective excitation energies and oscillator strengths for the core). We also show how the evaluation can be performed analytically, again using pseudostates. Finally, we give V/sub ret/(r) as an expansion in powers of 1/r; this often provides an easy means of estimating ..delta..E/sub ret/(n,l) quickly and relatively accurately, and we present various results of use for the Rydberg helium atom, in tabularmore » and graphical form. The effects of exchange, higher multipoles, and of the finite nuclear mass have not been included. As experimental capabilities improve, other systems, such as an ion composed of a nucleus with Z>2, a single core electron, and a Rydberg electron, may someday prove as useful as helium. The formalism for helium can readily be adapted to this case.« less