Borazine's EOM-CCSD gap is negative at def2-TZVP; 2b needs more memory

Abstract

Borazine’s EOM-CCSD gap changes from +117.6 meV at def2-SVP to -47.5 meV at def2-TZVP, a 165 meV decrease, while Amendment 1 is non-decisive under its frozen ±50 meV rule. This independent rematch of Shizu, Ishihara, Uratani, and Kaji’s Inorganic benzenes with inverted singlet-triplet gaps (2026) also reached a compute limit: we could not complete the 2b ADC(2)/def2-TZVP gap calculation on our MacBook Pro.¹ Boroxine stays positive, but borazine lies inside the frozen band. We prepared this experiment for a team with access to higher levels of compute to run. No completed 2b ADC(2) excitation energies or gap are available.

Introduction

The EOM-CCSD rerun at def2-TZVP reverses borazine’s positive def2-SVP gap from the first note, but the frozen Amendment 1 rule assigns a non-decisive verdict. The 2b ADC(2)/def2-TZVP attempt ended without a gap on our Mac, leaving its sign test inconclusive. The ADC(2) follow-up targets 2b (anth-BN), using the SI label; 2a (naph-BN) is our smaller completed comparison. The published 2b ADC(2)/def2-TZVP gap is +106 meV.¹ Its frozen S1 sign test fails if our gap is non-positive, and magnitude reproduction requires agreement within ±50 meV. The preregistration, frozen in 59824fd, remains unchanged by this report.

Computational Methods

The attempted calculation used PySCF 2.14.0 on the authors’ unchanged PBE0/6-31G(d) geometry: conventional RHF, density-fitted ADC(2), def2-TZVP, def2-TZVP-RI and 14 frozen core orbitals. PySCF supplies the independent implementation; we did not run the authors’ Turbomole code. The machine was an M1 Pro with 32 GiB RAM; --mem-mb 24000 was the solver memory setting. Software versions and threading limitations are in the environment record. We requested four singlet and eight unrestricted roots with the frozen script.² Code 1 records the exact Python invocation and working directory; the queue also used /usr/bin/time -l.

Code 1. The stopped 2b attempt used this command; the linked handoff gives a portable invocation for another machine.

cd ~/Molecules/ist-borazine/package/tier1
OMP_NUM_THREADS=8 ~/Molecules/ist-borazine/.venv/bin/python \
  run_adc2_pyscf.py 2b --basis def2-tzvp --mem-mb 24000 \
  --aux def2-tzvp-ri

The downloadable 2b handoff includes coordinates, script hash, basis and frozen-core settings, installation instructions, the JSON output schema, the frozen falsifier and the published comparison value. We have not completed the higher-resource calculation described there.

The EOM-CCSD runs used the frozen script, a conventional RHF reference, frozen core, and four singlet and four triplet roots. The exploratory 2b check used def2-SVP; Amendment 1 used def2-TZVP for borazine and boroxine on their unchanged published geometries. The retained logs for 2b, borazine and boroxine record convergence of SCF, CCSD and all requested EOM roots. Table 1 subtracts the lowest triplet energy from the lowest singlet energy in each completed JSON, then converts eV to meV. The basis shift uses unrounded values.

Results

The 2b log records 33 active occupied and 447 virtual orbitals. It prints MP2 reference correlation energy -2.03570034 Eh, then RADCEE Davidson settings, with no subsequent output. The journal records termination by SIGTERM, exit −15, on 30 September 2026 at 08:06:42 PDT after 70412 s (19.6 h). User plus system CPU time was 12.4 h. No 2b ADC(2) result JSON was written.

The final timing log records 25.57 decimal GB peak RSS and 73.46 decimal GB peak memory footprint. These are distinct counters. Table 1 records the follow-up outputs available at the status snapshot, last updated 2026-09-30T18:28:44+00:00.

Table 1. Completed EOM-CCSD gaps from the retained JSONs. The 2b def2-SVP check is exploratory; the borazine and boroxine def2-TZVP runs implement Amendment 1.

Compound	Method and basis	Recorded state	ΔEST (meV)
2b (anth-BN)	EOM-CCSD/def2-SVP	Completed	+186.4
1 (Borazine)	EOM-CCSD/def2-TZVP, A1	Completed	-47.5
11 (Boroxine)	EOM-CCSD/def2-TZVP, A1	Completed	+520.8

Discussion

The 2b sign test remains inconclusive because the attempt supplied no gap. Its failure to finish does not test the published sign. The completed 2a calculation had 24 occupied × 324 virtual orbitals and took 11.5 h with about 25 decimal GB peak RSS. A doubles-storage model proportional to \((ov)^2\) gives a 3.6× size ratio for 2b. Applying it to 2a’s measured RSS gives roughly 90 decimal GB for in-core storage. This extrapolation is a planning estimate; we have not verified either its memory requirement or runtime on a larger machine.

We observed a roughly 37 GB footprint and 28.4 of 29.7 GB swap in use while monitoring near the stop. Those operator observations are preserved in the archived prompt, but no monitor capture was retained to verify their timing or counter definitions. The final timing counters above are the retained machine record. We cannot accomplish this calculation without more compute within our budget; we will not occupy this Mac for weeks trying to obtain it.

Amendment 1, frozen in 8c0a21e before either def2-TZVP EOM-CCSD run, is non-decisive. Its rule first requires the boroxine gap to be positive; if ΔEST(11) ≤ 0, A1 is inconclusive. With the control satisfied, ΔEST(1) > +50 meV means method-driven sign disagreement at def2-TZVP; ΔEST(1) < −50 meV means the def2-SVP sign flip was basis-driven. The inclusive interval −50 to +50 meV is non-decisive. The control passes at +520.8 meV, while borazine at -47.5 meV remains inside that interval. The frozen rule therefore assigns neither a method-driven nor a basis-driven verdict.

The measured basis dependence is still substantial: borazine changes sign from +117.6 meV at def2-SVP to -47.5 meV at def2-TZVP, a 165 meV decrease. Boroxine stays positive, from +473.2 to +520.8 meV. The first note’s observation that EOM-CCSD never inverts within the completed set holds only at def2-SVP. These two basis sets do not establish convergence to the basis-set limit. The positive 2b EOM-CCSD/def2-SVP gap remains an exploratory small-basis cross-check and cannot supply the missing ADC(2) sign test.

Prompts and data

Code 2 quotes the compute budget in the handoff request. The full prompt is archived verbatim with a row in the prompt history.

Code 2. The follow-up prompt sets the Mac’s compute budget.

Peter's compute rule: nothing that would take weeks on this Mac.

The Amendment 1 update prompt is also archived verbatim.

The title and polish prompt records the request to lead with the borazine result while preserving the 2b handoff.

The publication manifest lists the inputs and retained evidence. A small metrics generator derives the resource figures, completed EOM-CCSD gaps and basis shift from the retained logs, journal and JSONs. The incomplete ADC(2) attempt still supplies no gap. The first post now has a dated update linking these results; the frozen calculation scripts are unchanged.

Conclusion

Amendment 1 is non-decisive under the frozen ±50 meV rule. Borazine’s gap changes from +117.6 to -47.5 meV, a 165 meV decrease, while boroxine remains positive. The basis-set limit remains untested.

Everything is prepared for anyone with the compute to complete this test. We welcome feedback, comments and results from anyone interested, through the Contact page or GitHub issues. Please send the environment, exact invocation, result JSON and full convergence log with any result.

References

Shizu, K.; Ishihara, K.; Uratani, H.; Kaji, H. Inorganic Benzenes with Inverted Singlet-Triplet Gaps. Communications Chemistry 2026. https://doi.org/10.1038/s42004-026-02141-0.

Sun, Q.; Zhang, X.; Banerjee, S.; Bao, P.; Barbry, M.; Blunt, N. S.; Bogdanov, N. A.; Booth, G. H.; Chen, J.; Cui, Z.-H.; Eriksen, J. J.; Gao, Y.; Guo, S.; Hermann, J.; Hermes, M. R.; Koh, K.; Koval, P.; Lehtola, S.; Li, Z.; Liu, J.; Mardirossian, N.; McClain, J. D.; Motta, M.; Mussard, B.; Pham, H. Q.; Pulkin, A.; Purwanto, W.; Robinson, P. J.; Ronca, E.; Sayfutyarova, E. R.; Scheurer, M.; Schurkus, H. F.; Smith, J. E. T.; Sun, C.; Sun, S.-N.; Upadhyay, S.; Wagner, L. K.; Wang, X.; White, A.; Whitfield, J. D.; Williamson, M. J.; Wouters, S.; Yang, J.; Yu, J. M.; Zhu, T.; Berkelbach, T. C.; Sharma, S.; Sokolov, A. Yu.; Chan, G. K.-L. Recent Developments in the PySCF Program Package. The Journal of Chemical Physics 2020, 153 (2), 024109. https://doi.org/10.1063/5.0006074.