I am currently trying to diagonalize the elements of a Fock matrix, $F'$ in an STO-nG basis. That is, I'm solving the Roothaan equations, $$F'C'=C'\epsilon,$$ by diagonalising $F'$ through taking its eigenvectors to obtain $C'$. Note that $\epsilon$ is a diagonal matrix (namely the eigenvalues of $F'$). However, the issue I'm having is that my column vectors in $C'$ can take on arbitrary sign. That is, if $C'=[\mathbf{a},\mathbf{b}]$ for column vectors $\mathbf{a}$ and $\mathbf{b}$, then $F'$ is also diagonalized by $C'=[-\mathbf{a},\mathbf{b}]$. This is an issue in my SCF procedure and is causing me to iterate to incorrect values. How should I choose my diagonalisation of the Fock operator to obtain physically correct results?

  • $\begingroup$ After you diagonalize the Fock matrix, are you transforming back to the original non-orthogonal basis: $C = S^{-1/2} C'$? $\endgroup$ Commented Feb 6, 2018 at 21:23


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