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

We have measured the dispersion of the gas phase depolarization ratio of Rayleigh scattered light for 12 linear and symmetric top molecules Combining these data with known refractive index data we obtain the frequency dependence of the polarizability anisotropy For all molecules studied we find that the polarizability anisotropy increases more rapidly with increasing frequency than the bulk polarizability We have correlated this behavior with the oscillator strength and direction of the first electronic transition We have also compared our zero frequency extrapolated anisotropies with the anisotropies determined from static fields with the Kerr effect and the Stark effect in microwave spectroscopy

Measurement of the dispersion in polarizability anisotropies

Due to formal and computational advances in coupled-cluster theory over the past few years, it is now possible to obtain very accurate molecular geometries, vibrational frequencies, heats of formation, binding energies, and vertical electronic excitation energies. For example, based on statistical analyses of a large number of calculations, it is shown that the CCSD(T)/spdfg level of theory gives rXH,rXY (double bonds), and rXY (triple bonds) with an average error of 0.0010, 0.0020, and 0.0026 A, respectively, with the theoretical bond distances usually too long relative to experiment. This level of theory yields bond angle predictions that are too small by 0.21 degrees on average. Fundamental vibrational frequencies predicted at the CCSD(T)/spdfg level of theory are accurate to better than 8.0 cm-1 on average, but the remaining errors are less systematic than those found for the geometrical parameters, except for X–Y stretches which are usually underestimated relative to experiment. For molecules described reasonably well by a single determinant reference function, single- and multiple-bond energies are given to within 1.0 and 2.0 kcal/mol, respectively, at the CCSD(T)/spdfg level of theory. The present monograph reviews the advances that have lead to the current state-of-the art, and also summarizes selected examples from the published literature.

Achieving Chemical Accuracy with Coupled-Cluster Theory

The polarizability and second hyperpolarizability of polyacetylene oligomer chains of increasing size up to C24H26 were investigated by means of the Coulomb-attenuating method (CAM-B3LYP) using response theory. It was found that this long-range corrected density functional removes to large parts the overestimation observed for standard methods and in many cases provides results close to those of coupled cluster calculations. A direct comparison to experimentally observed dynamic hyperpolarizabilities is made to estimate the accuracy of the method. A basis set study revealed a noticeable contribution of diffuse orbitals to the hyperpolarizability also for larger oligomers. Furthermore, CAM-B3LYP is also confirmed to provide molecular geometries close to experimentally observed structures, especially for longer chain lengths.

On the accurate calculation of polarizabilities and second hyperpolarizabilities of polyacetylene oligomer chains using the CAM-B3LYP density functional.

In this paper we present time-dependent density functional calculations on frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules, N2, CO2, CS2, C2H4, NH3, CO, HF, H2O, and CH4, and compare them to Hartree–Fock and correlated ab initio calculations, as well as to experimental results. Both the static hyperpolarizabilities and the frequency dispersion are studied. Three approximations to the exchange-correlation (xc) potential are used: the widely used Local Density Approximation (LDA), the Becke–Lee–Yang–Parr (BLYP) Generalized Gradient Approximation (GGA), as well as the asymptotically correct Van Leeuwen–Baerends (LB94) potential. For the functional derivatives of the xc potential the Adiabatic Local Density Approximation (ALDA) is used. We have attempted to estimate the intrinsic quality of these methods by using large basis sets, augmented with several diffuse functions, yielding good agreement with recent numerical static LDA results. Contrary to claims which have appeared in the literature on the basis of smaller studies involving basis sets of lesser quality, we find that the static LDA results for β and γ are severely overestimated, and do not improve upon the (underestimated) Hartree–Fock results. No improvement is provided by the BLYP potential which suffers from the same incorrect asymptotic behavior as the LDA potential. The results are however clearly improved upon by the LB94 potential, which leads to underestimated results, slightly improving the Hartree–Fock results. The LDA and BLYP potentials overestimate the frequency dependence as well, which is once again improved by the LB94 potential. Future improvements are expected to come from improved models for asymptotically correct exchange-correlation potentials. Apart from the LB94 potential used in this work, several other asymptotically correct potentials have recently been suggested in the literature and can also be expected to improve considerably upon the relatively poor LDA and GGA results, for both the static properties and their frequency dependence.

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Accurate density functional calculations on frequency-dependent hyperpolarizabilities of small molecules

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.

C. P. Hobbs

Papers

Kerr effect in some simple non-dipolar gases