An accurate description of the electrical properties of atoms and molecules is critical for quantitative predictions of the nonlinear properties of molecules and of long‐range atomic and molecular interactions between both neutral and charged species. We report a systematic study of the basis sets required to obtain accurate correlated values for the static dipole (α1), quadrupole (α2), and octopole (α3) polarizabilities and the hyperpolarizability (γ) of the rare gas atoms He, Ne, and Ar. Several methods of correlation treatment were examined, including various orders of Moller–Plesset perturbation theory (MP2, MP3, MP4), coupled‐cluster theory with and without perturbative treatment of triple excitations [CCSD, CCSD(T)], and singles and doubles configuration interaction (CISD). All of the basis sets considered here were constructed by adding even‐tempered sets of diffuse functions to the correlation consistent basis sets of Dunning and co‐workers. With multiply‐augmented sets we find that the electrical properties of the rare gas atoms converge smoothly to values that are in excellent agreement with the available experimental data and/or previously computed results. As a further test of the basis sets presented here, the dipole polarizabilities of the F− and Cl− anions and of the HCl and N2 molecules are also reported.

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Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties

The non-linear optical polarization of an isolated atom or molecule is treated, giving careful consideration to secular and resonant terms in the perturbation expansion. The Method of Averages introduced by Bogoliubov and Mitropolsky is used. The case where resonance-induced excited state populations are negligible, which is relevant to a wide range of non-linear optical experiments, is examined in detail for polarizations through third order in the perturbing fields. This yields concise expressions which are valid for any combination of applied field frequencies, including static fields.

Perturbation theory of the non-linear optical polarization of an isolated system

Soot particle measurements in diffusion flames

Third-order optical susceptibilities of liquids and solids

https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=912608

Laser-induced incandescence measurements of soot production in steady and flickering methane, propane, and ethylene diffusion flames

The depolarization ratio for Rayleigh scattering by 39 molecular species are reported for λ= 488.0, 514.5 and 632.8 nm. The literature has been critically surveyed for refractivities which are used in conjunction with the observed depolarization ratios to yield the anisotropy of the molecular polarizability of the molecules. Results are given for CO2, OCS, CS2, C2H6, C3H8, isobutane, cyclopropane, C2H4, allene, C2H2, methylacetylene, dimethylacetylene, spiropentane, cyclohexane, C6H6, C6H5F, 1,3,5-C6H3F3, C6F6, CH3CN, (CH3)2CO, CH3F, CH2F2, CHF3, CH3Cl, CH2Cl2, CHCl3, CF2Cl2, CH3Br, CH3I, t-butylchloride, t-butylbromide, ethylene oxide, (CH3)2O, (CH3)2S, H2S, SO2, N2, N2O and CO.

Rayleigh scattering depolarization ratio and molecular polarizability anisotropy for gases

Measurements of the Kerr effect in nitrogen, carbon dioxide, ethane, ethylene, acetylene and cyclopropane are reported at a series of temperatures and pressures. Values for the second molecular hyperpolarizabilities of these molecules have been derived from the results, together with values for their polarizability anisotropies. The contribution of interacting pairs of molecules to the Kerr effect has been determined for these gases.

Kerr effect in some simple non-dipolar gases

A detailed theory of the frequency dependence of the electro-optical Kerr effect of an atom in the region of absorption lines is presented and applied to the particular case of 2 P←2 S doublets of sodium and lithium vapours. Doppler broadening is taken into account. With electric dipole matrix elements derived from the Coulomb approximation for both discrete and continuum states, the molar Kerr constant, m K(32 P←32 S), of atomic sodium vapour in the D-line absorption region is calculated to ±30 per cent; the calculations indicate that m K in the vicinity of the D2 line (32 P 3/2←32 S 1/2) should be very much greater than near the D1 line (32 P 1/2←32 S 1/2) in qualitative agreement with the experiments of Kopfermann and Ladenburg Qualitative consideration is also given to dispersion of magnetic birefringence; in contrast with electric birefringence strong dispersion is expected near both lines of alkali metal 2 P←2 S doublets.

Kerr dispersion of atomic sodium and lithium

Measurements of the Kerr effect (electric birefringence) are reported for the four chloromethanes (CH3CI, CH2CI2, CHCI3, CCI4) in the vapour phase over a range of temperature (260–370 K). For CCI4, the second hyperpolarisability γK is found to be (1.23 ± 0.04)× 10–60 C4 m4 J–3, in reasonable agreement with other nonlinear optical measurements. For CH2CI2, a polarisability anisotropy parameter (α33–α) is determined to be (–0.68 ± 0.08)× 10–40 C2 m2 J–1, demonstrating the inadequacy of the bond additivity approximation. The first hyperpolarisabilities βK of CH3Cl, CH2Cl2 and CHCl3 are relatively small and therefore poorly determined, indicating that hyperpolarisability contributions to the Kerr effect of dipolar molecules may in general be less significant than has previously been suggested.

Temperature-dependence of the Kerr effect of chloromethanes

A method is proposed for measuring electric quadrupole moments of atoms and molecules in excited states by observing electric field gradient induced birefringence (quadrupolar birefringence) in regions of absorption. The theory is based on the general treatment of quadrupolar birefringence of Buckingham and Longuet-Higgins [4]. For electric dipole allowed transitions the effect is proportional to the transition probability and to the difference between the quadrupole moment of the excited state and of the ground state. For electric quadrupole allowed transitions the effect is more complicated and involves the transition quadrupole. Using Coulomb approximation and SCF matrix elements, quantitative estimates of quadrupolar birefringence for 2 P ← 2 S and 2 D ← 2 S transitions in vapours of atomic lithium and sodium are obtained. The magnitude of the effect in these cases is such that a measurement of quadrupole moments of low-lying 2 P states in sodium and lithium is feasible.

Martin P. Bogaard

Papers

Rayleigh scattering depolarization ratio and molecular polarizability anisotropy for gases

Kerr effect in some simple non-dipolar gases

Kerr dispersion of atomic sodium and lithium

Temperature-dependence of the Kerr effect of chloromethanes

A method of measuring electric quadrupole moments of molecules in excited states