We use the corresponding distances method (CDM) to computationally assess the quality of 10 experimentally tested carbon nanotube (CNT) solvents. The CDM produces accurate and high-resolution potential of mean force curves from a single simulation per solvent. The method's very high efficiency allows us to investigate an unprecedented number of solvents in one study. The simulation results indicate that none of the tested molecules are solvents in the thermodynamic sense; instead, they are dispersants preventing reaggregation of already dispersed CNTs. We find that the dispersion free energy barrier correlates very well with the experimentally measured performance of the dispersants; i.e., the simulations place the solvents in the correct performance order. Our analysis of the structure-function relationship rationalizes this order.