Fix uninitialized read in int3c1e_ip1_r6_origk y component

[susilehtola]

This PR is an offshoot of sunqm/qcint#24: it turned out that libcint was missing a term that exists in qcint, which is added in this PR. libcint is currently returning incorrect results.

AI summary

CINTgout1e_int3c1e_ip1_r6_origk (src/cint3c1e_a.c) computes the y-component s[1] with the term 6*g48[ix]*g76[iy]*g3[iz], but g76 is never initialized — the G1E_D_I call for it is missing from the recurrence list. The y component of the integral is therefore computed from stale scratch-buffer contents; the x and z components are unaffected.

g76 must hold G1E_D_I applied to g12, consistent with the pointer layout in which every bra-derivative array sits 64 slots above its base (g64=D(g0), g67=D(g3), g79=D(g15), g112=D(g48), g124=D(g60), g127=D(g63)). This PR adds the missing line:

G1E_D_I(g76, g12, envs->i_l+0, envs->j_l, envs->k_l);

Validation. With one single-primitive shell per center, -d/dR_i <i|r^6|jk> = <nabla i|r^6|jk> exactly, so central differences of int3c1e_r6_origk give an independent reference. Before the fix, the y component deviates from the numerical derivative by up to ~0.2 (on values of order 1) for an s/p/d/f test basis; after the fix, all components of all shell tuples agree to 1e-10 (the finite-difference truncation level). The fixed code also agrees with qcint's machine-generated implementation of the same integral to ~1e-10.

Impact. PySCF >= 2.13 uses int3c1e_ip1_r6_origk for the C4 term of GTH pseudopotential nuclear gradients (pyscf/gto/pp_int.py:99, pyscf/pbc/gto/pseudo/pp_int.py:186), so molecular and PBC gradients of elements whose GTH local potential includes the r^6 term have had a silently wrong y component.

🤖 Generated with Claude Code

https://claude.ai/code/session_01TTc5De7stABc2q58NHV22E

[susilehtola]

Note on the earlier ubuntu-latest CI failure: it was pre-existing on master, not caused by this fix. testsuite/test_int3c1e.py takes reference values from the installed pyscf wheel's libcgto.so, and the int3c1e_ipip1/ip1ip2/ipvip1/ipip2 integrals (added in #129, after the v6.1.3 release) are not present in any released pyscf, so the script crashed with an undefined-symbol AttributeError.

The second commit fixes this by skipping integrals the installed pyscf does not provide, and adds self-contained finite-difference checks for int3c1e_ip1_r{2,4,6}_origk (bra shell on its own atom, so -d/dR_i of the base integral equals the ip1 integral exactly). The new FD check fails on the unfixed int3c1e_ip1_r6_origk and passes with the fix — pyscf cannot serve as the reference for that integral, since released libcint computes its y component from an uninitialized buffer.