A TDDFT study on Keggin-type organosilicone derivative

Supporting Information

Table S1 The selected bond distances (in Å) and angles (deg) for system 1 and system 10.

1 / 10
Si-O1 / 1.662 / 1.662
Si-O2 / 1.632 / 1.628
Si-O3 / 1.640 / 1.640
W-O2 / 1.941 / 1.949
W-O3 / 1.949 / 1.950
Si-O1-Si / 124.6 / 125.0

To shed further light on the origin of the second-order NLO properties, the elucidation of a structure-property relationship is prerequisite. How does it bring the fluctuations in the computed β0 values? From the complex sum-over-states (SOS) expression [S1, S2], the two-state paradigm model that links β and a low-lying CT transition was formulated. For static case, the expression is:

(3)

where ƒgm, Egm, and Δµgm are the oscillator strength, the transition energy, and the difference of the dipole moment between the ground state (g) and the mth excited state (m), respectively. In the two-level expression, the second-order polarizability caused by CT is proportional to the optical intensity and inversely proportional to the cube of transition energy. Hence, the transition energy is a decisive factor in the β value. TDDFT calculations were carried out to study the transition nature of systems 1-18. The systems with the same length of organic chain possess the same conjugation bridge and the Δµgm values are similar. It can be found from Table 1, the β0 values are related to the transition energies. For instance, the transition energies decrease from system 1 to 3, and the computed β0 values increase from 1 to 3. This behavior can be observed in systems 4-18. Thus, the low transition energy is a decisive factor to determine the NLO response. In addition, when CT is from the heteropolyanion to the conjugated organically chain, transition energy decreased bythe elongated chain and the ledshift in the absorption band as follows: 369, and 121518. Thus, the β0 values of system9 and 18 arelarger ones among the studied systems. Therefore, the long length of organic chains and the suitableend-capped-substituted group lead to the lowest transition energy, and the highest NLO response among our studied systems.

S1. J. L. Qudar, and D. S. Chemla (1977). J. Chem. Phys.66, 2664.

S2. J. L. Qudar (1977). J. Chem. Phys.67, 446.