(Hyper)polarizability dependence on the interatomic distance of N4 (Td): Fourth order polynomials and third order derivatives

We present a high level ab initio study of the electric (hyper)polarizabilities of N4 tetrahedron. Reliable estimates have been obtained at the CCSD(T)/[7s5p4d1f] level of theory, that is α=24.96e2a02Eh−1,βxyz=−15.12e3a03Eh−2andγ¯=2276e4a04Eh−3 at the equilibrium distance Re=1.4516 Å. In addition, we investigated the ΔR≡R−Re dependence of the above properties and we found that it is best described by fourth order polynomials as: α(ΔR)=24.96+16.17ΔR+2.39ΔR2−2.96ΔR3+1.06ΔR4, βxyz(ΔR)=−15.12−5.45ΔR−8.39ΔR2−6.07ΔR3+4.83ΔR4, and γ¯(ΔR)=2293+2449ΔR+1941ΔR2−628ΔR3−2512ΔR4, respectively.