Hermiticity and Diagonal term in the Hamiltonian and Overlap Matrices |
- Date: 2026/01/28 12:09
- Name: Kieran
<masrfa@googlemail.com>
- Dear All,
I extracted the Kohn-Sham Hamiltonian and Overlap matrices from OpenMX and used ZHEGV to obtain the eigen value and eigen vector. Then I used the eigen value to plot the band structure and the eigen vector to calculate the spin texture. I found that the band structure and spin texture can re-produce those from OpenMX code well.
Then, I also checked the hermiticity and diagonal term in the Hamiltonian and overlap matrices, with the following Fortran code.
!Checking the Hermicity in both Hamiltonian and Overlap matrics
print*, 'Check S Hermiticity:', MAXVAL(ABS(overlap - CONJG(TRANSPOSE(overlap))))
print*, 'Check H Hermiticity:', MAXVAL(ABS(hamiltonian - CONJG(TRANSPOSE(hamiltonian))))
!Checking the diagonal term in the overlap matrix
print*, 'overlap_mini_max', &
MINVAL(REAL([(b(i,i), i=1, 2*numtatorb)])), &
MAXVAL(REAL([(b(i,i), i=1, 2*numtatorb)]))
!
I obtained the following output.
Check S Hermiticity: 3.8857805861880479E-016
Check H Hermiticity: 4.4522200459995241E-002
overlap_mini_max -1.2840000003658771E-004 1.8735611999999986
I suppose the hermicity value for both Hamiltonian and overlap matrices should be smaller than 1.0d-5; while, that for Hamiltonian is 4.4522200459995241E-002.
I also suppose that the diagonal term in the overlap matrix should be something very close to 1.0; while, those in the overlap matrix varies between -1.2840000003658771E-004 and 1.8735611999999986. I also wonder why there is negative value showing up.
I would really appreciate it if anyone could provide any explanation/suggestions on these issues to me?
Kind regards,
Kieran
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