Historically, narrow-gap semiconductors and semimetals have been suggested for low-temperature TE devices. This suggestion has partly stemmed from the longstanding proposition that the optimal band gap of TE materials is between 6 k B T and 10 k B T . Mahan and Sofo 100 arrived at this conclusion by parameterizing the band e↵ective mass in terms of the band gap using a linear Kane band model, where materials with narrower band gaps tend to exhibit smaller carrier e↵ective masses. Although such a direct relationship between the e↵ective mass and band gap is apparent for particular material systems e.g. binary zinc blende compounds, 102,103 we find in our calculations that this is generally not true. There is no systematic trend between carrier e↵ective masses and band gaps within the Zintl phases considered in this study, as shown in Figure . We believe that the primary reason for the absence of a trend is because the relationship between e↵ective mass and band gap used by Mahan and Sofo was constructed assuming a direct, positive band gap within the k • p theory. 100,102 These assumptions break down in real materials because band gaps can be direct or indirect, as well as positive (semiconductor) or negative (semimetals).