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Is there any standard file format (.txt, .dat etc) for storing one and two electron integrals (generated from ab initio packages) which doesn't compromise on precision and is convenient for reading into HPC routines in Fortran for calculations (and also, maybe, Python for some trivial calculations).

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The FCIDUMP format is probably the closest thing to what you are seeking. More than a dozen different quantum chemistry programs already have a built-in mechanism to read or write one- and two-electron integrals in FCIDUMP format, as described here: How do the various programs read or write integrals in FCIDUMP format?

"which doesn't compromise on precision"

I've also never seen an FCIDUMP file in which the integrals were not stored with double-precision.

"and is convenient for reading into HPC routines in Fortran for calculations (and also, maybe, Python for some trivial calculations)."

Many of those programs listed in the body of the question linked above, already have some FORTRAN or Python code written for reading (and/or writing) FCIDUMP files.

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