Context : The theoretical apsidal motion constants are key tools to investigate the stellar interiors in close eccentric binary systems .
In addition , these constants and the moment of inertia are also important to investigate the tidal evolution of close binary stars as well as of exo-planetary systems .

Aims : The aim of the paper is to present new evolutionary models , based on the MESA package , that include the internal structure constants ( k _ { 2 } , k _ { 3 } , and k _ { 4 } ) , the radius of gyration , and the gravitational potential energy for configurations computed from the pre-main-sequence ( PMS ) up to the first ascent giant branch or beyond .
The calculations are available for the three metallicities [ Fe/H ] = 0.00 , -0.50 , and -1.00 , which take the recent investigations in less metallic environments into account .
This new set of models replaces the old ones , published about 15 years ago , using the code GRANADA .

Methods : Core overshooting was taken into account using the mass-f _ { ov } relationship , which was derived semi-empirically for models more massive than 1.2 M _ { \odot } .
The differential equations governing the apsidal motion constants , moment of inertia , and the gravitational potential energy were integrated simultaneously through a fifth-order Runge-Kutta method with a tolerance level of 10 ^ { -7 } .

Results : The resulting models ( from 0.8 up to 35.0 M _ { \odot } ) are presented in 54 tables for the three metallicities , containing the usual characteristics of an evolutionary model ( age , initial masses , log T _ { eff } , log g , and log L ) , the constants of internal structure ( k _ { 2 } , k _ { 3 } , and k _ { 4 } ) , the radius of gyration \beta, and the factor \alpha that is related with the gravitational potential energy .

Conclusions :