A new single-time two-point closure is proposed, in which the equation for the two-point correlation between the displacement of a fluid particle and the velocity allows one to estimate a Lagrangian timescale. This timescale is used to specify the nonlinear damping of triple correlations in the closure. A closed set of equations is obtained without ad hoc constants. Taking advantage of the analogy between particle displacements and scalar fluctuations in isotropic turbulence subjected to a mean scalar gradient, the model is numerically integrated. Results for the energy spectrum are in agreement with classical scaling predictions. An estimate for the Kolmogorov constant is obtained.