The ��j(1)(r) is defined as derivative of the charge density function ��(r, F) with respect to the applied fields F (r is the position vector). Baricitinib LY3009104 The ��(r, F) is commonly expanded in powers of F +12!��j��jkl(3)(r)FjFkFl+?,��j(1)(r)=?��(r,F)?Fj|Fj=0,��ij=?��ri??��j(1)(r)dr.(2)For?as��(r,F)=��(0)(r)+��j��j(1)(r)Fj+12!��j��jk(2)(r)FjFk a certain positive-negative ��j(1)(r) pair, the sign is positive when the direction of the positive to negative densities coincides with the positive direction of the chosen coordinate system, whereas the magnitude is proportional to the distance between the two densities. In the present study, we determined the ��j(1)(r) densities at the CAM-B3LYP/6-31+G* level for the longitudinal component (j = x).
As representative cases of the ��,��-DMN and ��,��-DMN isomers, we investigated the ��x(1)(r) densities for 1,4-DMN and 2,3-DMN. The ��x(1)(r) distributions are displayed in Figure 3. From the CAM-B3LYP/6-31+G* computations, the ��xx(2,3-DMN) value is higher than the corresponding datum of the 1,4-DMN isomer by about 4?3 (Table 2). For both the isomers, the largest positive to negative ��x(1)(r) contributions are mainly placed over the N moiety. However, as can be appreciated from the plots in Figure 3, the 2,3-DMN isomer exhibits additional relevant ��x(1)(r) densities localized on both the CH3 groups. These methylic ��x(1)(r) amplitudes are much more conspicuous than those found for the 1,4-DMN isomer, contributing to the increase of the ��xx component by ca. 17%.Figure 3Calculated ��x(1)(r) density distributions for the 1,4-DMN (top) and 2,3-DMN (bottom) isomers.
Positive and negative are represented by yellow and blue isosurfaces (0.001a.u.), respectively. CAM-B3LYP/6-31+G* results.3.3. Static and Dynamic First-Order Hyperpolarizabilities of the DMN IsomersThe calculated static ��xxx and ��vec values of the DMN isomers obtained in vacuum at the CAM-B3LYP/6-31+G* level are collected in Table 3. As for the computed dipole moments [14], due to the mutual disposition of the methyl substituents, the 1,5-DMN and 2,6-DMN isomers are nonpolar compounds. In the present study, besides to the static first-order hyperpolarizabilities we also determined the frequency-dependent properties for the SHG and EOPE NLO phenomena since observed data are nearly always obtained at incident optical fields.
In order to minimize resonance enhancements, the dynamic hyperpolarizabilities were evaluated at the �� value of 1064nm (�� = 0.04282a.u.), which is sufficiently apart from Carfilzomib the observed lowest-energy absorption of DMNs (the experimental ��max values are in the range 274�C289nm) [73]. The dynamic ��vec (?�ئ�; ��1, ��2) data are included in Table 3. As should be expected, ��vec (?2��; ��, ��)>��vec (?��; ��, 0) for all the isomers.