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Charge mobility in molecules: Charge fluxes from second derivatives of the molecular dipole
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Image of FIG. 1.
FIG. 1.

Principal and non-principal charge fluxes calculated with Eqs. (6) and (7) for CHO: (a) CO and (b) CH (2–3) stretching fluxes.

Image of FIG. 2.
FIG. 2.

CH (1–3) stretching fluxes for the ethylene.

Image of FIG. 3.
FIG. 3.

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).

Image of FIG. 4.
FIG. 4.

CH (1–2) stretching fluxes for ethylene, butadiene, and hexatriene. Atoms are numbered by increasing distance (number of bonds in between) from H(1).

Image of FIG. 5.
FIG. 5.

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 atom. The last value reported in the plot corresponds to the value of the APT element directly obtained by DFT calculations. The charge contribution has been subtracted in the diagonal values reported ( = 0).


Generic image for table
Table I.

Stretching ∂ /∂ and bending ( and ) charge fluxes obtained through Eqs. (6) and (7) for CH, CHO, CH, HCN. For comparison, we also report the values () predicted in the past from APTs parametrization, by models neglecting some non-principal fluxes (see text). 20

Generic image for table
Table II.

IR intensity of formaldehyde predicted from DFT calculations and from the APTs reconstructed by means of Eq. (12) .

Generic image for table
Table III.

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 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 (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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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Charge mobility in molecules: Charge fluxes from second derivatives of the molecular dipole