I think I have the answer. The subroutine S^-1 is sm1_psi and S only changes if 
the ion positions change.

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________________________________
From: John McFarland
Sent: Saturday, July 13, 2019 1:00:39 PM
To: [email protected] <[email protected]>
Subject: Inverse of S operation

Dear all,

ESPRESSO has a subroutine calles s_psi() that applies the S matrix to the 
wavefunction. Is there a way to apply the inverse of S to the wavefunction?

Also, is S constant throught the SCF iterations?

Thanks in advance for any replies.

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