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Static excited-state polarisabilities and hyperpolarisabilities of three RuII ammine complexes are computed at the density functional theory (DFT) and several correlated ab initio levels. Most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals B3LYP, B3P86 or M06 for the complex [RuII(NH3)5(MeQ+)]3+ (MeQ+= N-methyl-4,4′-bipyridinium, 3) in acetonitrile. The match with experimental data is less good for [RuII(NH3)5L]3+ (L= N-methylpyrazinium, 2; N-methyl-4-{ E, E-4-(4-pyridyl)buta-1,3-dienyl}pyridinium, 4). These calculations confirm that the first dipole- allowed excited state (FDAES) has metal-to-ligand charge-transfer (MLCT) character. Both the solution and gas-phase results obtained for 3 by using B3LYP, B3P86 or M06 are very similar to those from restricted active-space SCF second-order perturbation theory (RASPT2) with a very large basis set and large active space. However, the time-dependent DFT λmax predictions from the long-range corrected functionals CAM-B3LYP, LC-ωPBE and wB97XB and also the fully ab initio resolution of identity approximate coupled-cluster method (gas-phase only) are less accurate for all three complexes. The ground state (GS) two-state approximation first hyperpolarisability β2SA for 3 from RASPT2 is very close to that derived experimentally via hyper-Rayleigh scattering, whereas the corresponding DFT-based values are considerably larger. The β responses calculated by using B3LYP, B3P86 or M06 increase markedly as the π-conjugation extends on moving along the series 2→ 4, for both the GS and FDAES species. All three functionals predict substantial FDAES β enhancements for each complex, increasing with the π-conjugation, up to about sevenfold for 4. Also, the computed second hyperpolarisabilities γ generally increase in the FDAES, but the results vary between the different functionals. [ABSTRACT FROM AUTHOR]