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Recenty,I am reading the source code of the first-principle software.I meet some words that I haven't found in those DFT books.For example,it mentions the first-variational and second-variational eigenvectors. Similarly,the first-variational and second-variational eigenvalues are mentioned.In my opinion,the first-vatiational eigenvectors and eigenvalues should be the wave functions and eigen energies of Kohn-sham equation.But what is the meaning of the second-variational eigenvectors and eigenvalues ?

Regards.

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# First-variational and second-variational eigenvectors

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