Dipole-octopole Polarizability Research Articles

R-8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method.

The anisotropic and isotropic R-8 dispersion contributions (disp8) are derived and implemented within the framework of the effective fragment potential (EFP) method formulated with imaginary frequency-dependent Cartesian polarizability tensors distributed at the centroids of the localized molecular orbitals (LMOs). Two forms of damping functions, intermolecular overlap-based and Tang-Toennies, are extended for disp8. To obtain LMO polarizability tensors centered at LMO centroids, an origin-shifting transformation is derived and implemented for the dipole-octopole polarizability tensor and the quadrupole-quadrupole polarizability tensor. The analytic gradient is derived and implemented for the isotropic disp8 contribution. Relative to the previously implemented empirical EFP disp8 energy, the isotropic disp8 component of the interaction energy improves the overall agreement of the EFP dispersion energies with the symmetry-adapted perturbation theory (SAPT) benchmarks, reducing the mean absolute errors (MAEs) and mean absolute percentage errors for most of the databases examined in this work. While the anisotropic disp8 can further enhance the accuracy of the EFP dispersion energy and yield smaller MAEs, significantly overbound dispersion energies are predicted by the anisotropic disp8 when the maximum element in the intermolecular overlap matrix is greater than 0.1, possibly due to the breakdown of the approximations made in the EFP dispersion derivation at a short range. For potential energy scan databases, the newly developed EFP dispersion model with isotropic disp8 yields the overall correct curvature and good agreement with SAPT benchmarks around equilibrium and longer but overestimates the dispersion interactions at a short range. While the overlap-based dispersion-damping functions produce better MAEs than Tang-Toennies damping functions, further improvement is needed to better screen the large attractive dispersion energies at a short range (overlap >0.1).

Molecular multipoles and (hyper)polarizabilities of water by ab initio calculations

The dipole, quadrupole, octopole, hexadecapole, dipole polarizability, first hyperpolarizability, second hyperpolarizability, dipole-quadrupole polarizability, dipole–dipole-quadrupole polarizability, quadrupole–quadrupole polarizability, and dipole-octopole polarizability of water molecule are calculated by CCSD(T) level of theory and complete basis set limit (CBS) with finite field method. Comparisons with previous ab initio calculations as well as the known experimental measurements are also made. It is shown that the calculated dipole, quadrupole, and dipole polarizability are in good agreements with the experimental measurements. Considering the nuclear vibration and dispersion effect, the average first and second hyperpolarizabilities at CCSD(T)/CBS level are also in reasonable agreement with experimental measurements.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state.

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r0 in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H2 in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Θ have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, αxx and αzz show the expected functional forms, to leading order in r-1. As r increases further, Θ and Φ vanish, while α, γ, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers υ = 0-14) with rotational quantum numbers J = 0-3.

Spectral lineshapes of collision-induced absorption (CIA) and collision-induced light scattering (CILS) for molecular nitrogen using isotropic intermolecular potential. New insights and perspectives

The rototranslational collision-induced absorption (CIA) at different temperatures and collision-induced light scattering (CILS) at room temperature of nitrogen gas are analyzed in terms of new isotropic intermolecular potential, multipole-induced dipole functions and interaction-induced pair polarizability models, using quantum spectral lineshape computations. The irreducible spherical form for the induced operator of light scattering mechanisms was determined. The high frequency wings are discussed in terms of the collision-induced rotational Rayleigh effect and estimates for the dipole–octopole polarizability E4, is obtained and checked with the ab initio theoretical value. The quality of the present potential has been checked by comparing between calculated and experimental thermo-physical and transport properties over a wide temperature range, which are found to be in good agreement.

Dipole–octopole polarizability of sulfur hexafluoride from isotropic and anisotropic light scattering experiments

The higher order dipole–octopole polarizability E of sulfur hexafluoride has been determined from isotropic and anisotropic collision-induced light scattering (CILS) experiments of pure SF6 gas and from anisotropic light scattering of its mixture with inert gases. The CILS spectra are analyzed by using the new updated and different intermolecular potentials. Our final estimates for this property is |E|=96.405±12.045a.u. which is in excellent agreement with the ab initio theoretical value.

High Frequency Interaction-Induced Anisotropic Rototranslational Light Scattering Spectra of Gaseous Carbon Dioxide

The anisotropic rototranslational scattering of carbon dioxide gas is studied theoretically at 294.5 K, in the frequency range 10–470 cm−1, at a density of 1.026254 mole/litre. The anisotropic double differential cross-section for scattered light is calculated theoretically using new site–site Morse–Morse–Morse–spline–van der Waals intermolecular potentials with the parameters fitted to the different thermophysical and transport properties. Our theoretical calculations take into account multipole contributions from the firstand second-order dipole-induced dipole, first-order dipole-induced octopole and first-order dipole–dipole–quadrupole light scattering mechanisms as well as their cross contributions. The irreducible spherical form for the induced operator of these light scattering mechanisms was determined. The high frequency wings are discussed in terms of the collision-induced rotational Rayleigh effect and estimates for the dipole–octopole polarizability E4, is obtained and checked with the ab initio theoretical value. Good agreement is obtained at moderate frequencies between the theoretical and experimental spectra. When an exponential contribution exp(−ν/ν0), with ν0 = 115 cm−1 is considered to model very short-range light scattering mechanism, good agreement is found over the whole frequency range.

Higher order multipolar polarizabilities of carbon tetrafluoride from isotropic and anisotropic light scattering experiments

The higher order dipole–quadrupole and dipole–octopole polarizabilities of carbon tetrafluoride has been determined from isotropic and anisotropic collision-induced light scattering (CILS) experiments of CF 4 and from anisotropic light scattering of its mixture with argon gas. The CILS spectra are analyzed by using the new updated and different intermolecular potentials. Our final estimates for these properties are ∣ A∣ = (1.051 ± 0.073) Å 4 and ∣ E∣ = (1.235 ± 0.282) Å 5 which are in excellent agreement with the ab initio theoretical values.

Contributions of multipolar polarizabilities to the isotropic and anisotropic light scattering induced by molecular interactions in gaseous methane

The binary isotropic and anisotropic collision-induced light scattering spectra of gaseous methane at room temperature are analyzed in terms of a recent ab initio intermolecular potential and interaction-induced pair polarizability trace and anisotropy models, using quantum line-shapes computations. The translational spectra at relatively low frequencies are determined largely by the effects of bound and free transitions. At intermediate frequencies the spectra are sensitive to both the attractive part of the potential and the short-range part of the polarizability trace and anisotropy. The high frequency wings are discussed in terms of the collision-induced rotational Raman effect and estimates for the dipole-quadrupole polarizability A and the dipole-octopole polarizability E are obtained and checked with recent ab initio theoretical values.

A comparative study of the dipole–quadrupole and dipole–octopole polarizability of the CdS and CdSe tetramers

We have calculated the octopole and hexadecapole moment and the dipole–quadrupole ( A) and dipole–octopole ( E) polarizability of the tetrahedral (CdS) 4 and (CdSe) 4 clusters using all-electron ab initio and density functional theory calculations and systematic sequences of purpose-oriented basis sets. Both clusters are characterized by very large octopole and small hexadecapole moments. Our estimates for the polarizabilities are A / e 2 a 0 3 E h - 1 = −56.6 ± 5.7, E / e 2 a 0 4 E h - 1 = −1732 ± 346 for (CdS) 4 and A / e 2 a 0 3 E h - 1 = −140.7 ± 14.0, E / e 2 a 0 4 E h - 1 = −2252 ± 450 for (CdSe) 4.

Electric polarizabilities ofGe(CH3)4from collision-induced light-scattering experiments andab initiocalculations

The dipole-quadrupole and dipole-octopole polarizabilities A and E of Ge(CH{sub 3}){sub 4} have been determined from collision-induced light-scattering experiments and ab initio calculations. Our experimental results are |A|/e{sup 2}a{sub 0}{sup 3}E{sub h}{sup -1}<143 and |E|/e{sup 2}a{sub 0}{sup 4}E{sub h}{sup -1}<545. Our best theoretical values are A=45.48 and E=-389.9, respectively. The calculated value for the dipole polarizability is {alpha}/e{sup 2}a{sub 0}{sup 2}E{sub h}{sup -1}=83.26, in fine accord with our static experimental estimate of 83.2. We present a detailed discussion of the level of agreement between experiment and theory.

Dipole–quadrupole- and dipole–octopole polarizability of Sn(CH 3) 4: Experiment and bond polarizability model

We studied the collision-induced light scattering spectrum of tetramethyltin, Sn(CH 3) 4, in the gas phase. The spectra are analyzed in view of the dipole–quadrupole ( A) and dipole–octopole polarizability ( E) giving ∣ A∣ = 149(5) au and ∣ E∣ = 780(200) au. We show that these experimental results are in reasonable agreement with bond-polarizability considerations.

Experimental and theoretical determination of the dipole-quadrupole and dipole-octopole polarizabilities of the group IV tetrachlorides TiCl4, ZrCl4, and HfCl4

The dipole-quadrupole and dipole-octopole polarizabilities A and E of TiCl4, ZrCl4, and HfCl4 have been determined from collision-induced light-scattering experiments. Our respective experimental results for /A/ are (165+/-10), (110+/-30), and (140+/-20) e2a0 3Eh (-1), whereas /E/ is determined to be (675+/-125), (750+/-200), and (670+/-400) e2a0 4Eh (-1). Theory predicts values convincingly close to experiment, as A=(181.4+/-9.1), (167.6+/-8.4), and (139.8+/-7.0) e2a0 3Eh (-1), and E=(-671+/-67), (-688+/-69), and (-574+/-57) e2a0 4Eh (-1). In addition our quantum chemical ab initio calculations give reliable values for the dipole polarizability alpha, as well as for the octopole and hexadecapole moments Omega and Phi for all three substances.

High-frequency interaction-induced rototranslational wings of anisotropic nitrogen spectra

The anisotropic rototranslational scattering spectra of nitrogen gas at high frequency up to 700 cm −1 for several temperatures and from low densities are analyzed in terms of new site–site (M3SV) intermolecular potential and interaction-induced pair polarizability models, using quantum spectral shapes computations. Our theoretical calculations take into account multipole contributions from the mean value and anisotropy of the dipole–dipole polarizability tensor α, two independent components of the dipole–octopole polarizability tensor E and dipole–dipole–quadrupole hyperpolarizability tensor B. The high-frequency wings are discussed in terms of the collision-induced rotational Rayleigh effect and estimates for the dipole–octopole polarizability | E 4| are obtained and checked with recent ab initio theoretical value. Good comparison is found in the frequency range 0–400 cm −1 between the theoretical and experimental spectra. When an exponential contribution [exp(− ν/ ν 0)] with ν 0 = 425 cm −1 is considered to model very short-range light scattering mechanisms at room temperature, good agreement is found over the whole frequency range.

Dipole-quadrupole and dipole-octopole polarizability of OsO4 from depolarized collision-induced light scattering experiments, ab initio and density functional theory calculations

The dipole-quadrupole and dipole-octopole polarizability of osmium tetroxide (OsO(4)) has been determined from collision-induced light-scattering experiments. Our final estimates for these properties are |A|=(84+/-5)e(2)a(3)(0)E(-1)(h) and |E|=(214+/-25)e(2)a(4)(0)E(-1)(h). We have also analyzed previous experimental data of the relative permittivity and refractivity of OsO(4) to propose the electronic part of the static dipole polarizability of alpha=51.0e(2)a(2)(0)E(-1)(h). To support our findings we have performed high-level ab initio and density functional theory calculations to obtain theoretical static estimates alpha=(50.2+/-1.6)e(2)a(2)(0)E(-1)(h), A=(84+/-10)e(2)a(3)(0)E(-1)(h), and E=(-252+/-32)e(2)a(4)(0)E(-1)(h), in essential agreement with the proposed experimental values.

Contributions of Multipolar Polarizabilities to the Isotropic and Anisotropic Light Scattering Induced by Molecular Interactions in Gaseous Sulfur Hexafluoride

Abstract The binary isotropic and anisotropic collision-induced light scattering spectra of the gaseous sulfur hexafluoride at room temperature are analyzed in terms of recent intermolecular potential and interaction-induced pair polarizability models, using quantum line-shapes computations. The spectra at relatively low frequencies are determined largely by the effect of bound and free transitions. At intermediate frequencies the spectra are sensitive to both the attractive part of the potential and the short-range part of the polarizability trace and anisotropy. The high frequency wings are discussed in terms of the collision-induced rotational Raman effect and estimates for the dipole–octopole polarizability E, is obtained and checked with recent ab initio theoretical value. Absolute zeroth moment of both spectra have been measured and compared with theoretical calculations using different models of the intermolecular potentials. Also, the temperature dependence of the pressure second virial coefficient, viscosity and thermal conductivity are also discussed for the proposed potentials. The results show that (M3SV) is the most accurate potential yet reported for this system.

Multipolar polarizations of methane from isotropic and anisotropic collision-induced light scattering

The anisotropic and isotropic binary collision-induced spectra scattered by gaseous methane have been measured in absolute units up to 900 cm{sup -1} from the Rayleigh line. Corresponding theoretical intensities taking into account multipolar polarizabilities have been calculated using a semiclassical procedure. From the analysis of, mainly, our isotropic scattering data, values of the dipole-quadrupole and dipole-octopole polarizabilities are deduced. They are found to be in good agreement with recent ab initio calculations.

Depolarized collision-induced light scattering of gaseous CCl 4

Depolarized collision-induced light-scattering spectra of CCl 4 in the saturated vapour-phase have been measured in the ranges of temperature and density between T=501 and 561 K and ϱ=687 and 1524 mol m −3, respectively. The CILS spectra are analyzed by using an isotropic Lennard–Jones type (18.6–6) intermolecular-interaction potential. It is found that the polarizability anisotropy of the CCl 4-dimer contains a significant short-range repulsive term. Taking into account collision-induced rotational Raman scattering (CIRR) the dipole–quadrupole polarizability A, and dipole–octopole polarizability E of CCl 4 were obtained as | A|=3.8(1.0)×10 −40 m 4 and | E|<4×10 −49 m 5.

Isotropic and anisotropic collision-induced light scattering by gaseous sulfur hexafluoride at the frequency region of the ν1 vibrational Raman line

Experimental binary isotropic and anisotropic Stokes spectra of the collision-induced light scattered by gaseous sulfur hexafluoride are measured at the frequency region of the ν1 vibrational Raman line. They are compared to theoretical intensities due to dipole–multipole interactions. Taking into account the results of a previous study on the interaction-induced intensities in the Rayleigh wings of gaseous sulfur hexafluoride, an experimental value of the derivative of the dipole–octopole polarizability associated with the ν1 vibrational mode is provided and compared to the result of a recent ab initio calculation.

Polarization components of rototranslational light scattering spectra from gaseous SF6

Experimental binary anisotropic and isotropic collision-induced scattering spectra of gaseous sulphur hexafluoride at room temperature are reported on an absolute scale up to 210cm-1. On the basis of a comparison of experiment with theoretical computations of scattering intensities, the value of the independent component E of the dipole-octopole polarizability tensor is discussed for several intermolecular potentials and compared with a recent ab initio theoretical value. A recommended value of E is given.

Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2

We report accurate values of the electric moments, static polarizabilities, hyperpolarizabilities and their respective derivatives for N2. Our values have been extracted from finite-field Møller–Pleset perturbation theory and coupled cluster calculations performed with carefully designed basis sets. A large [15s12p9d7f] basis set consisting of 290 CGTF is expected to provide reference self-consistent-field values of near-Hartree–Fock quality for all properties. The Hartree–Fock limit for the mean hyperpolarizability is estimated at γ̄=715±4e4a04Eh−3 at the experimental bond length Re=2.074 32a0. Accurate estimates of the electron correlation effects were obtained with a [10s7p6d4f] basis set. Our best values are Θ=−1.1258ea02 for the quadrupole and Φ=−6.75ea04 for the hexadecapole moment, ᾱ=11.7709 and Δα=4.6074e2a02Eh−1 for the mean and the anisotropy of the dipole polarizability, C̄=41.63e2a04Eh−1 for the mean quadrupole polarizability and γ̄=927e4a04Eh−3 for the dipole hyperpolarizability. The latter value is quite close to Shelton’s experimental estimate of 917±5e4a04Eh−3 [D. P. Shelton, Phys. Rev. A 42, 2578 (1990)]. The R dependence of all properties has been calculated with a [7s5p4d2f] basis set. At the CCSD(T) level of theory the dipole polarizability varies around Re as ᾱ(R)/e2a02Eh−1=11.8483+6.1758(R−Re)+0.9191(R−Re)2−0.8212(R−Re)3−0.0006(R−Re)4, Δα(R)/e2a02Eh−1=4.6032+7.0301(R−Re)+1.9340(R−Re)2−0.5708(R−Re)3+0.1949(R−Re)4. For the Cartesian components and the mean of γαβγδ, (dγzzzz/dR)e=1398, (dγxxxx/dR)e=867, (dγxxzz/dR)e=317, and (dγ̄/dR)e=994e4a03Eh−3. For the quadrupole polarizability Cαβ,γδ, we report (dCzz,zz/dR)e=19.20, (dCxz,xz/dR)e=16.55, (dCxx,xx/dR)e=10.20, and (dC̄/dR)e=23.31e2a03Eh−1. At the MP2 level of theory the components of the dipole–octopole polarizability (Eα,βγδ) and the mean dipole–dipole–octopole hyperpolarizability B̄ we have obtained (dEz,zzz/dR)e=36.71, (dEx,xxx/dR)e=−12.94e2a03Eh−1, and (dB̄/dR)e=−108e3a03Eh−2. In comparison with some other 14-electron systems, N2 appears to be less (hyper)polarizable than most, as near the Hartree–Fock limit we observe ᾱ(N2)&amp;lt;ᾱ(CO)&amp;lt;ᾱ(HCN)&amp;lt;ᾱ(BF)&amp;lt;ᾱ(HCCH) and γ̄(N2)&amp;lt;γ̄(CO)&amp;lt;γ̄(HCN)&amp;lt;γ̄(HCCH)&amp;lt;γ̄(BF).