You can get the very same energies each time by running in serial instead of parallel mode. I am guessing that you want to do larger calculations also where this is not a practical workaround. I tried running 25 instances of your initial input and then 25 instances of the variation suggested by Edoapra. Within each group of 25, Edoapra's had modestly lower standard deviation among energies, 3.51759317924e-05 vs. 4.32143681234e-05. The maximum absolute difference was very close in the two groups: a maximum difference of 0.0001303668269940772 in the first group, 0.0001303645710066803 in the second group.
Here's the little Python script I used to automate and process the multiple runs, plus the log files:
http://www.sciencemadness.org/cc/iodine-sodft-test.zip
And here's the energy results and differences from the first group and the second. I had to trim the differences to only show the 10 greatest differences from each group, otherwise the post was too long. Download the script if you want to see all differences.
ENERGIES I
[-111.264029798081,
-111.26402979805,
-111.263985503976,
-111.263981695197,
-111.263980619461,
-111.263980548577,
-111.263980543614,
-111.263927334838,
-111.263908317052,
-111.263907897043,
-111.263905806428,
-111.263903650468,
-111.263903504641,
-111.263903153903,
-111.263902852252,
-111.26390126782,
-111.263900925281,
-111.263900687624,
-111.263900544382,
-111.263899898156,
-111.263899655918,
-111.263899623602,
-111.263899435115,
-111.263899431433,
-111.263899431254]
STANDARD DEVIATION 4.32143681234e-05
DIFFERENCES I
[0.00013014213200790437,
0.0001301421630017785,
0.0001301744480031175,
0.00013017447899699164,
0.00013036293501045293,
0.00013036296600432706,
0.00013036661700027707,
0.0001303666479941512,
0.00013036679600020307,
0.0001303668269940772]
ENERGIES II
[-111.264029795362,
-111.263984337878,
-111.263982310785,
-111.26398054393,
-111.263926319113,
-111.2639117327,
-111.263904505574,
-111.263904339896,
-111.2639019858,
-111.263901272317,
-111.263900885848,
-111.263900840543,
-111.263900472191,
-111.263899699611,
-111.263899640777,
-111.263899534106,
-111.263899531909,
-111.263899497567,
-111.263899476559,
-111.263899441205,
-111.263899437064,
-111.26389943464,
-111.263899431947,
-111.263899431344,
-111.263899430791]
STANDARD DEVIATION 3.51759317924e-05
DIFFERENCES II
[0.00013026125600390515,
0.00013026345300204412,
0.0001302977950103923,
0.0001303188030021829,
0.0001303541570081279,
0.00013035829800855936,
0.00013036072201089155,
0.00013036341501049264,
0.00013036401800547992,
0.0001303645710066803]
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