A study of basis set and electron correlation effects in the ab initio calculation of the electric dipole hyperpolarizability of ethene (H2C=CH2)

We report finite-field self-consistent field (SCF) and many-body perturbation theory calculations of the dipole polarizability and hyperpolarizability of ethene. Large Gaussian-type basis sets have been used to ensure the determination of reliable, near Hartree–Fock values for all the independent components of the dipole hyperpolarizability tensor γαβγδ. The calculated SCF values of γ display strong basis set dependence. Electron correlation changes drastically the SCF picture of γαβγδ. The most important effect is the increase by nearly 70% of the component parallel to the double bond, γzzzz (molecular plane xz). It is found that the contribution from the fourth-order triple substitutions T4, dominates the fourth-order correction to the SCF value for almost all components of γ. The best SCF values obtained in this work are (in atomic units), γxxxx=3466, γyyyy=11 080, γzzzz=3351, γxxyy=2390, γyyzz=2936, γzzxx=1660, and γ̄=6374e4a04Eh−3. The estimated electron correlation corrections (Δ corr) are 431±79, −870±421, 2318±87, −134±101, −67±133, 240±62, and 392±236e4a04Eh−3, respectively. Albeit electron correlation affects strongly the individual tensor components of γ, the overall effect on the mean hyperpolarizability γ̄ does not exceed a few percent. The final estimate of γ̄=(68 ± 2)×102 e4 a04 Eh−3 is in essential agreement with the experimental results of Ward and Elliott.