In this work, a comprehensive study of the diffusivity of CDs in aqueous 43 solutions is reported. Such a study is largely lacking and is important for not 44 only supplementing and further guiding experiments, but also for providing performing solute (i.e. water) force field, the effect of NaCl concentration on the 56 diffusion of CDs is also investigated using two different NaCl force fields. Finally, 57 as a model system for a drug-delivery application, the diffusion coefficient of the 58 ibuprofen:β-CD inclusion complex is computed. 59 The remainder of this article is structured as follows. The following sec- 60 tion contains details about the force fields and the MD simulation scheme used. 61 In Section 3 (i.e., Results and Discussion), the effect of the system size is in- All bonded and non-bonded force field parameters of CDs were taken from 68 the q4md-CD force field [51] . This force field is shown to be very accurate in 69 reproducing the experimentally measured structure of CDs, as well as the bind- tools [68] . The equilibration scheme used is as follows: (1) energy minimization 117 of the system using the steepest descent method, (2) 50 ps MD simulation at 118 50 K at constant volume, (3) 1 ns MD simulation in which the temperature 119 is ramped up from 50 K to the production temperature in the NVT ensemble, 120 and (4) 2 ns MD simulation in the NPT ensemble at the production tempera-121 ture and pressure. This thorough equilibration scheme is based on the inclusion 122 complexation studies by Gilson 
where t is the time, N i is the number of molecules of type i, and r j,i is the CPUs, achieving a performance of 100 -160 ns/day. field is in predicting transport properties of pure water. In Table S1 of the Sup- The rims refer to the two openings in the CD molecule as can be seen in Figure   231 1. In Figure 4 , the average number of hydrogen bonds formed between the water the NaCl concentration (see Table S2 of the Supplementary Material), which 295 also contributes to the slower diffusion of the CDs. In Figure 5 , it can also be 296 observed that for NaCl molarities up to 0.4 mol L −1 , both ion force fields yield 297 the same self-diffusivities (within the statistical uncertainty) for all three CDs. diffusion coefficients (see Figure 5c ).
To obtain a better understanding of the cause for these differences, the radial Table 1 : Computed self-diffusion coefficients of the βCD:Ibuprofen inclusion complex (the two orientations can be seen in Figure 1 ) and free βCD in water at T = 298.15 K and P = 1 The authors declare that they have no known competing financial interests or 777 personal relationships that could have appeared to influence the work reported 778 in this paper. 