Implement the 13 integrals missing relative to libcint 6.1.3

[susilehtola]

As I reported in October 2025 in pyscf/pyscf#3021, some PySCF tests failed with missing symbols. This turned out to be due to a mismatch in qcint and libcint: the former was missing some integral classes. This PR implements those missing integral types.

AI summary

qcint 6.1.3 does not export 13 integrals that libcint 6.1.3 provides. Five of them — int1e_r{2,4}_origi_ip2 and int3c1e_ip1_r{2,4,6}_origk — are required by PySCF >= 2.13 for nuclear gradients with GTH pseudopotentials, so PySCF built against qcint aborts with undefined-symbol AttributeErrors in pyscf.gto.pp_int / pyscf.pbc.gto.pseudo.pp_int. This was found while enabling the PySCF test suite in Fedora, where qcint provides libcint on x86-64; 10 tests fail.

Generated code (via scripts/gen-code.cl, which reproduces all previously committed autocode byte-for-byte):

• src/autocode/deriv4.c (new): int1e_ipiprinvipip, int1e_ipipiprinvip, int1e_ipipipiprinv — already declared in auto_intor.cl, but the file had never been generated;
• src/autocode/lresc.c (new): int1e_iprinvr, int1e_iprinviprip, int1e_rinvipiprip, int1e_ipiprinvrip;
• src/autocode/int3c1e.c: int3c1e_ipip1, int3c1e_ip1ip2, int3c1e_ipvip1, int3c1e_ipip2;
• src/cint1e_a.c / src/cint3c1e_a.c: the five PySCF-critical integrals listed above.

Hand-ported to the SIMD framework: int4c1e (src/g4c1e.c + src/cint4c1e.c, behind the same WITH_4C1E option as libcint). CINTg4c1e_ovlp vectorizes libcint's algorithm with one primitive quartet per SIMD lane, reusing the existing CINTg0_{lj,kj,il,ik}_4d expansion routines; the primitive loop follows CINT3c1e_loop_nopt extended to four shells.

A separate first commit adds src/autocode/deriv3.c to CMakeLists.txt: the file was in the tree and its integrals declared in cint_funcs.h, but it was never compiled, so int1e_ipipipnuc, int1e_ipipiprinv, int1e_ipipnucip, and int1e_ipiprinvip were also absent from the built library. include/cint_funcs.h is updated to declare the same integral set as libcint.

Validation. Every new integral was compared against libcint 6.1.3 over all shell tuples of a mixed s/p/d/f contracted/primitive basis, in both _sph and _cart forms: agreement is at machine precision (<= 3e-13; int4c1e at 1e-13). A smoke test of 17 pre-existing integrals shows no regressions. int3c1e_ip1_r6_origk was additionally validated against finite differences of int3c1e_r6_origk, because libcint's own hand-written version of that integral has a bug in its y component (an uninitialized g76 read; fix submitted separately as sunqm/libcint#132).

🤖 Generated with Claude Code

https://claude.ai/code/session_01TTc5De7stABc2q58NHV22E

[susilehtola]

CI note: qcint's workflow downloads the test scripts from libcint master at run time (curl -O https://raw.githubusercontent.com/sunqm/libcint/master/testsuite/...). libcint master's test_int3c1e.py currently crashes with an undefined-symbol AttributeError on any pyscf release, because it compares the int3c1e_ipip1/ip1ip2/ipvip1/ipip2 integrals (added post-6.1.3 by libcint PR #129) against the installed pyscf's libcgto.so, which does not provide them. sunqm/libcint#132 fixes the test to skip integrals the installed pyscf lacks and adds self-contained finite-difference checks for int3c1e_ip1_r{2,4,6}_origk; once it lands, this PR's CI should be able to pass.

Also note that pyscf cannot serve as a numerical reference for int3c1e_ip1_r6_origk: released libcint <= 6.1.3 computes its y component from an uninitialized buffer (see sunqm/libcint#132), which is why that integral was validated here against finite differences of int3c1e_r6_origk instead.