The thermal scattering law (TSL) of 1H in H2O describes the interaction of the neutron with the hydrogen bound to light water. No recommended procedure exists for computing covariances of TSLs available in the international evaluated nuclear data libraries. This work presents an analytic methodology to produce such a covariance matrix-associated to the water model developed at the Atomic Center of Bariloche (Centro Atomico Bariloche, CAB, Argentina). This model is called as CAB model, it calculates the TSL of hydrogen bound to light water from molecular dynamic simulations. The performance of the obtained covariance matrix has been quantified on integral calculations at “cold” reactor conditions between 20 and 80∘ C. For UOX fuel, the uncertainty on the calculated reactivity ranges from ±71 to ±155 pcm. For MOX fuel, it ranges from ±110 to ±203 pcm.