Principal and non-principal charge fluxes calculated with Eqs. (6) and (7) for CH2O: (a) CO and (b) CH (2–3) stretching fluxes.
CH (1–3) stretching fluxes for the ethylene.
CH stretching principal fluxes on H belonging to many different molecules. Comparison between fluxes obtained from the second derivatives of the molecular dipole (Eq. (9) ) and those calculated from APTs completely neglecting the non-principal charge fluxes (0 order approximation, see text).
CH (1–2) stretching fluxes for ethylene, butadiene, and hexatriene. Atoms are numbered by increasing distance (number of bonds in between) from H(1).
APTs elements for H(1) and H(3) of butadiene, reconstructed using Eq. (12) , with decreasing degree of approximation: namely, method A (panel (a)) and method B (panel (b)) with n = 1, 2, 3, or 4 bonds from the β atom. The last value reported in the plot corresponds to the true value of the APT element directly obtained by DFT calculations. The charge contribution has been subtracted in the diagonal values reported (P′ ii = P ii − q 0).
IR intensity of formaldehyde predicted from DFT calculations and from the APTs reconstructed by means of Eq. (12) .
Comparison between IR intensities of butadiene directly obtained by DFT calculations and those obtained by the approximated APT (method B) with n = 1, 2, 3, or 4 bonds from the β atom. The IR active modes absent in the list, show negligible intensity in any approximations. Values relative to out of plane modes are written in boldface. The vertical lines allows to identify the approximation step where the difference between the true (from GAUSSIAN 09 output) and the approximated IR intensity become less than 1 km/mol (for modes with low intensity) and 5 km/mol (for mode with high intensity).
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