Which characteristics of the compound affect the number of theoretical plates in a GC experiment?
The number of theoretical plates can be calculated as:  


  $\mathrm{N_t = \frac {H}{HETP}}$  
  
  $\mathrm{N_t =}$ number of theoretical plates
  $\mathrm{H =}$ total height (or usually length) of the column [$\mathrm{m}$]
  $\mathrm{HETP =}$ Height Equivalent to a Theoretical Plate [$\mathrm{m}$] 


Where $\mathrm{HETP =}$ can be calculated from the Van Deemter equation: 


  $\mathrm{HETP = A + \frac {B}{u} + (C_s + C_m) * u}$  
  
  $\mathrm{A =}$ Eddy-diffusion parameter, related to channeling through a non-ideal packing [$\mathrm{m}$]
  $\mathrm{B =}$ diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [$\mathrm{m^2 s^{−1}}$]
  $\mathrm{C =}$ Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [$\mathrm{s}$]
  $\mathrm{u =}$ Linear Velocity [$\mathrm{m s^{−1}}$]


So, the characteristics specific to the analyte molecule that determine the number of theoretical plates are B and, unfortunately from the standpoint of developing an ab initio model, C.  

Various models have been developed, however.  Below is a list of references to some articles of interest in this field.  

[ 1 (abstract)]"The problem of plate modeling: Theoretical and computational results", Computer Methods in Applied Mechanics and Engineering, Volume 100, Issue 2, October 1992, Pages 249–273  

[ 2 ]"Plate Models in Chromatography: Analysis and Implication for Scale Up", Chromatograpy,Springer-Verlag 

[ 3 (abstract)]"Neural Network Modeling of Structured Packing Height Equivalent to a Theoretical Plate", Ind. Eng. Chem. Res., 2000, 39 (5), pp 1520–1525