linear response equations revisited

We present an algorithm to solve the linear response equations for Hartree-Fock, Density Functional Theory, and the Multiconfigurational Self-Consistent Field method that is both simple and efficient.
The algorithm makes use of the well-established symmetric and antisymmetric combinations of trial vectors but further orthogonalizes them with respect to the scalar product induced by the response matrix. This leads to a standard, symmetric block eigenvalue problem in the expansion subspace that can be solved by diagonalizing a symmetric, positive definite matrix half the size of the expansion space. Numerical tests showed that the algorithm is robust and stable.

Alessandro, I.; Giannì, I.; Pes, F.; Nottoli, T. & Lipparini, F.
J. Chem. Theory Comput. (2023)

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