Hi all,

May I here ask a simple question about the symmetry of PySCF. I did a calculation on CH4 using keyword “mol.symmetry = True” or “False” I can get the same converged SCF energy and same molecular energies, where the top three MOs their energies are the same.
However, when “symmetry = False” is used the MOs are different, but also I find different MO coefficients each time I re-start the calculation. For example, the AO coefficients for the 3rd MO (which is one of the degenerated orbitals for CH4 molecule) are:

First run:
[ 8.20021408e-17 -7.93851527e-16 -4.72882826e-16 -4.16015875e-02
4.24168213e-01 1.43530136e-01 -1.85028054e-02 1.88653904e-01
6.38367506e-02 2.04123751e-01 1.72999922e-01 -9.27453436e-02
-7.86039699e-02 1.25027892e-01 1.05964227e-01 -2.36406300e-01
-2.00360179e-01]

Second run:
[ 1.59811632e-16 -3.02923196e-15 9.08140839e-15 3.94996482e-01
-1.64380398e-01 -1.38589788e-01 1.75679426e-01 -7.31101547e-02
-6.16394713e-02 3.57058896e-02 3.02616235e-02 -1.43250620e-01
-1.21408440e-01 -1.63263958e-01 -1.38370238e-01 2.70808689e-01
2.29517054e-01]

Third run:
[ 1.19134965e-15 2.83827922e-15 -2.32346205e-14 3.49355181e-01
2.60269433e-01 1.11629049e-01 1.55379910e-01 1.15757954e-01
4.96483592e-02 2.79843964e-01 2.37174673e-01 -1.93220583e-01
-1.63759217e-01 -7.78766573e-02 -6.60023909e-02 -8.74672398e-03
-7.41306465e-03]

But if I turn on the symmetry for my calculation each time I run it the MO coefficients have the same value, again for example, the AO coefficients for the 3rd MO:

Each run:
[ 0. 0. 0. 0. 0. 0.44972243
0. 0. 0.20001945 0.17449077 0.14788524 0.17449077
0.14788524 -0.17449077 -0.14788524 -0.17449077 -0.14788524]

So, it seems there is a randomness inside PySCF if not turning on the symmetry constrain. And what could possibly be the reason that with “symmetry = False” each time the MOs are different? And how can I reduce this changing of MOs with “symmetry = False”

Thank you!