Static Electric Dipole Polarizabilities Research Articles

Static electric dipole polarizability and hyperpolarizability of fluorodiacetylene ☆

We report finite-field Møller–Plesset perturbation theory and coupled cluster calculations of the dipole moment and static (hyper)polarizability of fluorodiacetylene (F–CC–CC–H). A large basis set of [5s3p3d2f/5s3p3d2f/3s3p2d] type, consisting of 237 contracted gaussian-type functions, yields SCF values of μ z =0.3312 e a 0 for the dipole moment, α ̄ =49.37 and Δ α=55.29 e 2 a 0 2 E h −1 for the mean and the anisotropy of the dipole polarizability, β ̄ =−182.06 e 3 a 0 3 E h −2 and γ ̄ =9626 e 4 a 0 4 E h −3 for the mean of the first and second dipole hyperpolarizability, respectively. Electron correlation has a very small effect on the dipole polarizability but affects strongly the hyperpolarizability. The [5s3p3d2f/5s3p3d2f/3s3p2d] basis yields for the second dipole hyperpolarizability MP2 values (SCF results in parentheses), γ ̄ =12,489 (9626), Δ 1 γ=59,147 (31,532) and Δ 2 γ=7461 (1735) e 4 a 0 4 E h −3. Fluorodiacetylene is less (hyper)polarizable than diacetylene at the SCF level of theory.

Assessing the performance of ab initio methods on static (hyper)polarizability predictions for silicon clusters. Si4 as a test case

We have calculated static electric dipole (hyper)polarizabilities for a small silicon cluster, Si4. The molecular properties have been obtained from finite-field restricted-Hartree–Fock, Møller–Plesset perturbation theory, coupled-cluster and density functional theory calculations performed with carefully designed basis sets of gaussian-type functions. A large [8s6p5d2f] basis set is thought to provide near-Hartree–Fock quality results: = 142.77 and Δα = 77.93 e2a20E−1h for the mean and the anisotropy of the dipole polarizability and = 87.5 × 103e4a40E−3h for the mean hyperpolarizability. Electron correlation has a rather small effect on but a relatively strong one on Δα and . Our best values were obtained at the CCSD(T) level of theory with a [5s4p3d1f] basis set: = 140.35, Δα = 83.78 e2a20E−1h and = 106.3 × 103e4a40E−3h. At the same level of theory the differential (hyper)polarizability is (Si4) − 4Si = −9.21 e2a20E−1h and is (Si4) − 4Si = −65.3 × 103e4a40E−3h. To our knowledge, this is the first complete calculation of the dipole (hyper)polarizability of this cluster to be reported in the literature.

A measurement of the polarizability of sodium clusters

The static electric dipole polarizabilities of sodium clusters ${\mathrm{Na}}_{n}$ for a series of sizes in the range $7<~n<~93$ were measured by electric field deflection of a supersonic cluster beam. Results for the smaller clusters are in overall good agreement with previous experiments. Polarizabilities of the larger clusters continue the downward trend with increasing size, but remain considerably above the bulk limit. There is a degree of correlation between the polarizability values and electronic shell structure. Furthermore, there is an indication that the polarizability is sensitive to the source conditions, possibly reflecting the influence of internal cluster temperature.

Electric polarizability of isolatedC70molecules

We present the gas phase measurement of the static electric dipole polarizability of ${\mathrm{C}}_{70}$ fullerenes. The value is $102\ifmmode\pm\else\textpm\fi{}14{\AA{}}^{3}.$ The increase in polarizability from ${\mathrm{C}}_{60}$ to ${\mathrm{C}}_{70}$ is discussed and compared to different theoretical predictions.

An improved ab initio relativistic zeroth-order regular approximation correct to order 1/c2

The equations of the original ab initio scalar-relativistic zeroth-order regular approximation (ZORA) and the infinite-order regular approximation (IORA) are expanded in orders of 1/c2. It is shown that previous ZORA/IORA implementations in ab initio quantum chemistry programs were not correct to order 1/c2, but contained imperfections leading to fictitious self-interactions. These errors can be avoided by adding exchange-type terms (coupling the large and small components) to the relativistic ZORA correction to the Hamiltonian, yielding improved ab initio relativistic zeroth- and infinite-order regular approximations that are correct to order 1/c2. The new methods have been tested numerically by computing the total energies, orbital energies, and static electric dipole polarizabilities of the rare gas atoms He through Xe.

Polarizabilities of Carbon Dioxide and Carbodiimide. Assessment of Theoretical Model Dependencies on Dipole Polarizabilities and Dipole Polarizability Anisotropies

The atomic polarizabilities of carbon dioxide and carbodiimide, HNdCdNH, have been studied with ab initio theoretical methods. Structures were optimized and properties were determined using RHF, MP2, and QCISD theories and a variety of basis sets up to quadruple-œ quality. The static electric dipole polarizability tensor components were determined using the finite field method. The isotropic polarizability 〈R〉 and the anisotropic polarizabilities ¢R and were calculated for both heterocumulenes from the respective tensor components. The experimental tensor components and polarizabilities 〈R〉, ¢R, and are known for carbon dioxide, and these values are used to assess the accuracy of the theoretical methods. This knowledge about the achievable accuracy is then employed in the prediction of the polarizability values of carbodiimide. The only measurable polarizability values for carbodiimide are 〈R〉 and . The best level of theory employed in this study is QCISD(fc)/6-311++G(3df,2pd) and this level gives 〈R〉 and values of 16.722 and 0.289 au 3 for carbon dioxide. These values deviate somewhat from the experimental values of 17.762 and 0.267 au 3 and we rationalize these differences based on the calculated polarizability tensor components. The calculated 〈R〉 and values of carbodiimide are 28.963 and 0.310 au 3 . Taking into account the deviations from experiment for the carbon dioxide values, we predict 〈R〉 and values of 30.764 and 0.286 au 3 for carbodiimide. The discussion emphasizes the important role of the inclusion of three sets of d-polarization functions. The third, diffuse set of d-functions is essential to polarize the electron density described by the diffuse functions and also by the outer valence p-functions.

Static electric dipole polarizabilities of Na clusters

The static electric dipole polarizability of $\mathrm{Na_N}$ clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for $2\le N \le 20$, including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments.

Thermal expansion in small metal clusters and its impact on the electric polarizability

The thermal expansion coefficients of Na(N) clusters with 8</=N</=40, and Al7, Al-13, and Al-14 clusters are obtained from ab initio Born-Oppenheimer local-density-approximation molecular dynamics. Thermal expansion of small metal clusters is considerably larger than that in the bulk and is size dependent. We demonstrate that the average static electric dipole polarizability of Na clusters depends linearly on the mean interatomic distance and only to a minor extent on the detailed ionic configuration when the overall shape of the electron density is enforced by electronic shell effects. Taking thermal expansion into account brings theoretical and experimental polarizabilities into quantitative agreement.

DFT calculations of static dipole polarizabilities and hyperpolarizabilities for the boron clusters Bn (n=3–8,10)

The static electric dipole polarizabilities and second-order hyperpolarizabilities of several bare boron clusters have been calculated with density functional theory. The average second-order hyperpolarizability γav reaches a saturation limit of about 50,000 a.u. already with B5 for a given type of structure. The average polarizability per atom shows overall a decrease with increasing cluster size, while the average second hyperpolarizability per atom first increases from B3 to B6, and then starts to decrease. For the noncentrosymmetric clusters dipole moments and first-order hyperpolarizabilities are reported. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 131–135, 2000

DFT calculations of static dipole polarizabilities and hyperpolarizabilities for the boron clusters Bn (n=3-8,10)

The static electric dipole polarizabilities and second-order hyperpolarizabilities of several bare boron clusters have been calculated with density functional theory. The average second-order hyperpolarizability γav reaches a saturation limit of about 50,000 a.u. already with B5 for a given type of structure. The average polarizability per atom shows overall a decrease with increasing cluster size, while the average second hyperpolarizability per atom first increases from B3 to B6, and then starts to decrease. For the noncentrosymmetric clusters dipole moments and first-order hyperpolarizabilities are reported. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 131–135, 2000

Static electric dipole polarizabilities of alkali clusters

We have measured the static dipole polarizability of lithium and sodium clusters (n = 1 − 22). Values measured for sodium are in agreement with previous experiments. While the polarizability per atom for sodium clusters decreases slowly as a function of the cluster size, a sharp decrease between sizes 1 and 4 is observed for lithium clusters. Experimental values are compared to Density Functional Theory (DFT/PW91) calculations. The size evolutions for sodium and lithium cluster polarizabilities are well reproduced by our calculations. The sharp decrease observed for small lithium clusters is discussed in terms of electronic density.

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.

Measurement of static electric dipole polarizabilities of lithium clusters: Consistency with measured dynamic polarizabilities

Static electric dipole polarizabilities of lithium clusters made of n $(n=2--22)$ atoms have been measured. The experiment consists of deflecting a collimated cluster beam through a static inhomogeneous electric field. The strong decrease per atom from Li to ${\mathrm{Li}}_{3}\ensuremath{-}{\mathrm{Li}}_{4}$ shows that electronic delocalization is reached for very small sizes. Moreover, directly measured polarizabilities are consistent with photoabsorption data. They thus confirm unambiguously the ``missing'' optical strength in lithium clusters.

Absolute oscillator strenghts for the valence-shell photoabsorption (2–200 eV) and the molecular and dissociative photoionization (11–80 eV) of nitrogen dioxide

The valence-shell photoabsorption spectrum and absolute differential oscillator strengths (cross sections) of nitrogen dioxide have been measured at 1 eV FWHM resolution from the visible up to the soft X-ray energy region (2–200 eV) using dipole ( e, e) spectroscopy. The discrete spectral structures from 1.6 to 30 eV have also been studied at higher resolution (0.05 eV FWHM), and absolute oscillator strength values have been determined for the 2 B 1 ← 2 A 1 and 2BP 2 ← 2 A 1 systems as well as for the Rydberg states at higher energies. Comparisons have been made to previously reported absolute optical measurements in those limited energy regions where such data exist. The accuracy of the absolute oscillator strengths of nitrogen dioxide have been critically evaluated by comparison of the static electric—dipole polarizability of nitrogen dioxide derived from the present data using the S(−2) sum rule with those determined from dielectric constant measurements in the literature. In addition, dipole ( e, e + ion) coincidence spectroscopy has been used to obtain the photoion branching ratios, absolute photoionization efficiencies, and absolute partial differential oscillator strengths for the molecular and dissociative photoionization channels of nitrogen dioxide from the first ionization threshold up to 80 eV. Some qualitative deductions have been made concerning the dipole-induced breakdown pathways of nitrogen dioxide under UV, VUV, and soft X-ray radiation.

The Dirac - Coulomb Sturmians and the series expansion of the Dirac - Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom

Two relativistic Sturmian basis sets are constructed by solving first-order Sturm - Liouville problems for the Dirac - Coulomb equation. The Sturmian expansions of the Dirac - Coulomb Green function and the reduced Dirac - Coulomb Green function are derived. Their utility is illustrated by calculating static electric dipole polarizabilities for hydrogen-like atoms with .

At Most, Only One Electron Can Be Added to a Free Atom in Gas Phase

A quantitative relation between static electric dipole polarizability and ionization potential of an atomic species with some amount of charge is derived semiempirically to argue that to any free neutral atom, not more than one electron can be added in the gas phase to produce a thermodynamically stable anion. Experimentally, the argument does not hold in some closed shell neutral atoms, where addition of even one electron gives rise to thermodynamically unstable species.

Electric dipole polarizabilities of isolated gallium arsenide clusters

The static electric dipole polarizabilities of isolated Ga N As M clusters with N + M = 4–30 atoms and approximatly 1:1 composition have been measured in dependence of the cluster size N + M by means of a molecular beam deflection technique. A striking size-dependent behaviour has been observed for small Ga N As M clusters with up to 15 atoms. Within this size range the polarizability oscillates strongly between low values for even and high values for odd numbers of atoms N + M. For clusters with N + M < 12 the polarizability of gallium rich clusters is significantly larger than the values obtained for arsenic rich clusters whereas the opposite effect was observed for larger clusters with N + M >12.

Electron scattering from isoelectronic, Ne=18, CH3X molecules (X=F, OH, NH2 and CH3)

Total cross sections for methanol, methylamine and ethane molecules were measured in a linear electron-transmission experiment for impact energies from nearly 1 eV up to 250 eV. Results show that for those targets and CH3F, isoelectronic with them, between impact energies close to the cross section maximum and the highest energies applied, the total cross section increases with static electric dipole polarizability of the molecule.

Calculation of static polarizabilities and hyperpolarizabilities for the atoms He through Kr with a numerical RHF method

The static electric dipole polarizabilities and hyperpolarizabilities for different states of the ground configuration of the atoms He through Kr have been calculated at the restricted Hartree-Fock level using a finite perturbation method. The required field-dependent energy and dipole moment data have been computed with a recently developed numerical MCSCP code for atoms in a static electric field.

Electron-methyl halides scattering. Total cross section measurements for methyl chloride and methyl fluoride

Electron transmission experiments have been carried out in CH3F and CH3Cl in the energy range between 0.3 and 250 eV. Absolute values for total cross sections are presented and compared with the available data of other groups. The present cross sections are found to be in good agreement with other experiments for CH3F in the overlapping range of energies but deviate significantly from prior results in the case of CH3Cl. Our present measurements, together with previous ones for CH3Br and CH3I, confirm the correlation between static electric dipole polarizability of investigated targets and total cross sections at intermediate energies.