  Recent advancements in thermogalvanic batteries offer a promising route to
efficient harvesting of low-grade heat with temperatures below 100 {\deg}C. The
thermogalvanic temperature coefficient {\alpha}, usually referred to as
effective thermopower, is the key parameter determining the power density and
efficiency of thermogalvanic batteries. However, the current understanding of
improving {\alpha} of redox pairs remains at the phenomenological level without
microscopic insights, and the development of electrolytes with high {\alpha}
largely relies on experimental trial and error. This work applies the free
energy perturbation method based on molecular dynamics simulations to predict
the {\alpha} of the {Fe^{3+}/Fe^{2+}} redox pair in aqueous and acetone
solutions. We showed that {\alpha} of the {Fe^{3+}/Fe^{2+}} redox pair can be
increased from 1.5{\pm}0.3 mV/K to 4.1{\pm}0.4 mV/K with the increased acetone
to water fraction. The predicted {\alpha} of {Fe^{3+}/Fe^{2+}} both in pure
water and acetone show excellent agreement with experimental values. By
monitoring the fluctuation of dipole orientations in the first solvation shell,
we discovered a significant change in the variance of solvent dipole
orientation between Fe^{3+} and Fe^{2+}, which can be a microscopic indicator
for large magnitudes of {\alpha}. The effect of acetone weight fraction in the
mixed acetone-water solvent on the {\alpha} of {Fe^{3+}/Fe^{2+}} is also
studied. Acetone molecules are found to intercalate into the first solvation
shell of the {Fe^{2+}} ion at high acetone fractions, while this phenomenon is
not observed in the solvation shell of the Fe^{3+} ion. Such solvation shell
structure change of {Fe^{2+}} ions contributes to the enhanced {\alpha} at high
acetone fractions. Our discovery provides atomistic insights into how solvation
shell order can be leveraged to develop electrolytes with high thermopower.
