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the bug is located
It appears that the bug goes from Gaussian's routine for basis orthogonalization. NoBasisTransform option solves the problem, but significantly increases the job time:

Surprisingly, for gold all seems to be OK. Orthogonalization routine leaves only 168 of 177 basis functions as it does for nickel, but the total energy do not change.

So I think some kind of linear dependency problems do occur in the ANO-RCC basis set.

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