**4.1 Quantum chemical calculations**

The semi-empirical PM3 method (Stewart, 1989) was used to perform a systematic preliminary conformational search on the arbutin potential energies surface (PES), which were later on taken into account in the subsequent, more reliable analysis performed at higher level of theory. This preliminary conformational search was carried out using the HyperChem Conformational Search module (Howard & Kollman, 1988; HyperChem, Inc. © 2002; Saunders, 1987, 1990).

The eight dihedral angles defining the conformational isomers of arbutin (Fig. 9) were considered in the random search: C2C1O23C24, C1O23C24C25, O6C5C7O11, C5C7O11H15, C3C4O10H14, C2C3O9H13, C1C2O8H12 and C26C27O34H35. Conformations with energies lower than 50 kJ mol-1 were stored while higher-energy conformations or duplicate structures were discarded. The structures obtained from this conformational search were used as start points for the construction of the input files later used in the higher level quantum chemical calculations. These latter were performed with Gaussian 03 (Gaussian, 2003) at the DFT level of theory, using the 6-311++G(d,p) basis set (Frisch et al, 1990) and the three-parameter density hybrid functional abbreviated as B3LYP, which includes Becke's gradient exchange correction (Becke, 1988) and the Lee, Yang and Parr (Lee et al, 1988) and Vosko, Wilk and Nusair correlation functionals (Vosko et al., 1980). Conformations were optimized using the Geometry Direct Inversion of the Invariant Subspace (GDIIS) method (Csaszar & Pulay,

Application of Principal Component Analysis

to Elucidate Experimental and Theoretical Information 39

glucopyranoside ring. On the contrary, in all conformers belonging to groups B and C, the phenol ring is pointing out of the glucopyranoside moiety, and oriented to the side of the oxygen atom from the glucopyranoside ring. PC2 allows a specific discrimination among the three groups of conformers. This specificity factor is given by the values of C1O23C24C25.

> **-0.45 -0.36 -0.27 -0.18 -0.09 0.00 0.00 0.09 0.18 0.27 0.36 0.45 0.00 0.09 0.18 0.27 0.36 0.45**

**Z**

**Y**

**PC1-loadings**

**X**

**C1**

**C1**

**C1**

**C3**

**(c)** 

**C3**

**C3**

**C5**

**C5**

**C7**

**C5**

**C7**

**C7**

**O9**

**O9**

**O9**

**(a) (b)** 

**O11**

**O11**

**O11**

**H13**

**H13**

**H13**

**H15**

**H15**

**H17**

**H15**

**H17**

**H17**

**H19**

**H19**

**H19**

**H21**

**H21**

**H21**

**O23**

**O23**

**O23**

**C25**

**C25**

**C25**

**C27**

**C27**

**C27**

**C29**

**C29**

**C29**

**H31**

**H31**

**H31**

**H33**

**H33**

**H33**

**H35**

**H35**

**H35**

Fig. 10. (a) PCA-scores and, (b, c) the corresponding loadings grouping arbutin conformers in terms of structural similarity. (d) total average values and standard deviations of the 8 conformationally relevant dihedral angles of arbutin in the 3 groups of conformers.

**(d)** 

**PC2-loadings**

**Y**

**Z**

**X**

**-0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4**

**C1**

**C1**

**C1**

**C3**

**C3**

**C3**

**C5**

**C5**

**C5**

**C7**

**C7**

**C7**

**O9**

**O9**

**O9**

**O11**

**O11**

**O11**

**H13**

**H13**

**H13**

**H15**

**H15**

**H15**

**H17**

**H17**

**H17**

**H19**

**H19**

**H19**

**H21**

**H21**

**H21**

**O23**

**O23**

**O23**

**C25**

**C25**

**C25**

**C27**

**C27**

**C27**

**C29**

**C29**

**C29**

**H31**

**H31**

**H31**

**H33**

**H33**

**H33**

**H35**

**H35**

**H35**

The relationship between the energetic and conformational parameters related with each of the three groups identified in the scores plot, was also investigated. Fig. 11 depicts the relative energy values (taken as reference the energy of the conformational ground state) for each conformer according to the group they belong. From an energetic point of view, groups B and C are equivalent. However, no conformer with relative energy below 15 kJ mol-1 belonging to Group A. This trend can be correlated with the orientations adopted by the

phenol ring relatively to the glucopyranoside ring, as was described before.

(copyrighted from Araujo-Andrade et al., 2010)

**-15 -10 -5 0 5 10**

**PC1 (77%)**

**-6**

**-4**

**-2**

**0**

**PC2 (7%)**

**2**

**4**

**6**

**GROUP A GROUP B GROUP C**

1984). The optimized structures of all conformers were confirmed to correspond to true minimum energy conformations on the PES by inspection of the corresponding Hessian matrix. Vibrational frequencies were calculated at the same level of theory. PCA were performed using The Unscrambler® software (v9.8).
