The static first hyperpolarizability of the van der Waals CH4N2 complex was calculated. The calculations were carried out in the approximation of the rigid interacting molecules for a broad range of intermolecular separations (R = 6–40 a0) and for six configurations at CCSD(T) level of theory using the correlation consistent aug-cc-pVTZ basis set with the basis set superposition error correction. It was shown that the long-range classical approximation, including the terms up to R−6, is in a good agreement with ab initio calculations for R > 11 a0. It was found out that for the family of most stable configurations of the complex, the first hyperpolarizability invariants practically do not change (the changes are less than 0.1%). Under forming the stable van der Waals CH4N2 complex, the intensity and degree of depolarization of the hyper-Rayleigh scattering are noticeable decreased (by ∼10%) to be compared with the free CH4 and N2 molecules. © 2012 Wiley Periodicals, Inc.