Selected configuration interaction (sCI) methods, when complemented with a second order perturbative correction , provide near full configuration interaction (FCI) quality energies with only a small fraction of the Slater determinants of the FCI space. The selection of the determinants is often implemented in a determinant-based formalism, and therefore does not provide spin adapted wave functions. In other words, sCI wave functions are not eigenfunctions of theŜ 2 operator. In some situations, having a spin adapted wave function is essential for the proper convergence of the method. We propose an efficient algorithm which, given an arbitrary determinant space, generates all the missing Slater determinants allowing one to obtain spin adapted wave functions while avoiding working with configuration state functions. For example, generating all the possible determinants with 6 up-spin and 6 down-spin electrons in 12 open shells takes 21 CPU cycles per generated Slater determinant. We also propose a modification of the denominators in the Epstein-Nesbet perturbation theory reducing significantly the non-invariance of the second order correction with respect to different values of the spin quantum number m s. The computational cost of this correction is also negligible.
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