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Discovering new materials with excellent nonlinear optical responses has recently become a very interesting research topic in the different domains of materials science. Currently, density functional theory (DFT) has been shown to be a powerful tool in the explanation and prediction of the performance of novel nonlinear optical (NLO) materials. Quantum chemical calculations using DFT/TD-DFT with the B3LYP exchange–correlation functional are reported to study the NLO properties of 26 bivalent transition-metal (TM) complexed by six acyclic hexadentate ligands providing pyridyl/pyrazine–amide-thioether/ether coordination and differing by the nature of the methylene dichalcogenate spacer between the rings. However, the geometry parameters and the theoretically predicted UV–vis absorption spectra of the optimized compounds M­(II)­L i are in excellent agreement with the experiment, when available, the trends among the nature of the TM, the importance of the ligand spacer, and of the substituents of the pyridine/pyrazine amide ligand are discussed. To the best of our knowledge, our work evidences for the first time that the hyper-polarizability, second harmonic generation, and hyper-Rayleigh scattering response of TM coordination complexes can be correlated to the second ionization potential of metal and spin state of complexes.

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The radiative corrections of order α 3 rydbergs are evaluated for the ionization energy of the metastable states 2 1 , 3 S, of the helium atom. In the calculation of the average excitation energy k 0 , the main contribution comes from the transition to and ( ms, np ) and ( ms, ∊p ) states. The oscillator strengths for transitions to (1 s, ∊p ), (2 s, ∊p ) and (3 s, ∊p ) states are evaluated by using six-parameter wavefunction for the metastable states and a product of a hydrogenic wavefunction with Z = 2 for the s electron and a wavefunction analogous to the Hartree wavefunction for the excited p electron. Making use of these oscillator strengths and a method used by Pekeris, the values of the average excitation energies for the singlet and triplet states are found to be 77.09 ± 1.6 and 79.84 ± 1.0 rydbergs respectively. With these values of the average excitation energies, the Lamb shift corrections, including the estimate of a α 4 Ry order corrections, to the ionization energies of the singlet and triplet states become – 0.106 ± 0.018 cm -1 and –0.129 ± 0.013 cm –1 respectively. When they are added to the theoretical values of the ionization energies obtained by Pekeris, the values of the ionization energies become 32033.212 ± 0.018 an d 38454.698 ± 0.013 cm -1 compared with Herzberg’s experimental values of 32033.24 ± 0.05 an d 38454.73 ± 0.05 cm -1 for the singlet and triplet states respectively.