*3.4. Computational Methods*

A random conformational search of starting geometries in Discovery studio 4.0 was used to produce low-energy conformers within a 10 kcal/mol energy, which were subsequently optimized using the DFT method at mPW1PW91/6-31g(2d,p) level with GAUS-SIAN 09 [30]. The optimized conformers were further checked by frequency calculation at the same level of theory, and resulted in no imaginary frequencies. The time-dependent density functional theory (TDDFT) calculations of their low-energy conformations within 0–2.5 kcal/mol were performed to simulate their UV–vis spectra at the same level. Similarly, their 13C NMR calculations were also carried out by GIAO method at the same level [31]. Solvent effect of dimethylsulfoxide was taken into account in the above calculations by using the polarizable continuum model (PCM).

Their theoretical UV–vis spectra based on Boltzmann statistics were generated in the program SpecDis 1.63 [32] by applying Gaussian band shape with a 0.40 eV exponential half-width from dipole-length rotational strengths. Statistical parameters were used to quantify the agreemen<sup>t</sup> between experimental and calculated data, including the correlation coefficient ( *R*2) between experimental and calculated 13C NMR spectroscopic data with a linear regression, the mean absolute error (MAE), and the maximum error (MaxErr) [33]. The correlation coefficient (*R*2) was determined from a plot of *δ*calc (*x* axis) against *<sup>δ</sup>*exp (*y* axis) for each particular compound. The mean absolute error (MAE) was defined as 1 *n* --−i--Thedefined−

*n* ∑ *i*=1 -*<sup>δ</sup>*calc, i *<sup>δ</sup>*exp, --. maximum error (MaxErr) was as max|*δ*calc *<sup>δ</sup>*exp|.
