PLB140846140846S0370-2693(26)00697-010.1016/j.physletb.2026.140846The AuthorsFig. 1Total and excitation energies of low-lying states of 78Ni from SHCI and particle-hole truncated shell-model calculations. The extrapolation error of the SHCI is very small and is not clearly represented in the figure. The dimension of the full configuration-interaction model space is 2.10 × 1011. The numbers shown in panel (b) denote the dimensions of selected SHCI and the corresponding particle-hole truncated spaces. The values at ϵ1=0 in panel (b) are obtained by subtracting the extrapolated energies of low-lying states in panel (a).Fig. 1 dummy alt textFig. 2Low-lying spectra and neutron occupations for the N=50 isotones 80Zn, 79Cu, 78Ni, 77Co, and 76Fe, calculated with VS-IMSRG+SHCI and compared with available experimental data [1,11,49]. Negative values indicate depletion below the N=50 closure, while positive values indicate occupation above the closure.Fig. 2 dummy alt textFig. 3Ground-state energies, two-neutron separation energies, and empirical two-neutron shell gaps of Ni, Cu, and Zn isotopes calculated with VS-IMSRG+SHCI up to the predicted neutron drip lines. The error bars of the SHCI results indicate the extrapolation uncertainties; unless otherwise visible, they are smaller than the corresponding plotting symbols. The results are compared with available experimental and extrapolated masses from AME2020 [51], and used to identify the neutron-rich limits and the evolution of the N=50 shell closure.Fig. 3 dummy alt textFig. 4First 2+ excitation energies of even-even Ni and Zn isotopes calculated with VS-IMSRG+SHCI and compared with available experimental data [49].Fig. 4 dummy alt textLetterSemistochastic heat-bath configuration interaction with ab initio valence-space Hamiltonians for neutron-rich Ni, Cu, and Zn isotopesSemistochastic heat-bath configuration interaction with ab initio valence-space Hamiltonians for neutron-rich Ni, Cu, and Zn isotopesP.Y.WangabK.H.LiacQ.YuanadW.J.HuangbJ.G.Li⁎adejianguo_li@impcas.ac.cnaState Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, ChinaState Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics Chinese Academy of Sciences Lanzhou 730000 ChinaState Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, ChinabAdvanced Energy Science and Technology Guangdong Laboratory, Huizhou, 516007, ChinaAdvanced Energy Science and Technology Guangdong Laboratory Huizhou 516007 ChinaAdvanced Energy Science and Technology Guangdong Laboratory, Huizhou, 516007, ChinacCollege of Physics, Center for Theoretical Physics, Henan Normal University, Xinxiang, 453007, ChinaCollege of Physics, Center for Theoretical Physics, Henan Normal University Xinxiang 453007 ChinaCollege of Physics, Center for Theoretical Physics, Henan Normal University, Xinxiang, 453007, ChinadSchool of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, ChinaSchool of Nuclear Science and Technology, University of Chinese Academy of Sciences Beijing 100049 ChinaSchool of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, ChinaeSouthern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou, 516000, Guangdong Province, ChinaSouthern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences Huizhou Guangdong Province 516000 ChinaSouthern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou, 516000, Guangdong Province, China⁎Corresponding author.Editor: Baha BalantekinAbstractNeutron-rich nuclei around 78Ni provide an important testing ground for the N=50 shell closure and cross-shell correlations. We develop a nuclear-structure implementation of the semistochastic heat-bath configuration interaction (SHCI) method and apply it, for the first time, to nuclear structure calculations with ab initio valence-space Hamiltonians. SHCI builds a compact variational space through heat-bath selection and accounts for remaining correlations using semistochastic second-order perturbation theory. Combined with valence-space in-medium similarity renormalization group Hamiltonians derived from chiral two- and three-nucleon interactions, SHCI provides a large-space solver for extended proton-pf and neutron-gds valence spaces beyond conventional exact diagonalization. Benchmark calculations for 78Ni show that SHCI achieves faster convergence of low-lying spectra than comparable particle-hole truncations, demonstrating the efficiency of determinant-based selection. We further study the N=50 isotones and the Ni, Cu, and Zn isotopic chains toward the predicted neutron-rich limits. The results indicate a robust but gradually weakened N=50 shell closure from Ni to Zn, predict the drip-line nuclei, and suggest a possible weak subshell structure near N=58. This work establishes SHCI as a systematically improvable large-space solver for ab initio nuclear structure.KeywordsSemistochastic heat-bath configuration interactionAb initio valence-space HamiltoniansN=50 shell closure78NiData availabilityData will be made available on request.1IntroductionThe region around 78Ni is one of the clearest laboratories for testing how traditional magic numbers evolve at the neutron-rich frontier. Spectroscopy of 78Ni established a high 21+ excitation energy and a strong closed-shell character, while also revealing low-lying structures associated with deformed intruder configurations [1–3]. Earlier isomer and mass measurements in neighboring Zn isotopes already pointed to a robust N=50 gap near Z=30 and connected this region to the r-process waiting point at 80Zn [4–6]. Thus, nuclei around 78Ni simultaneously probe shell evolution, deformation, neutron-rich limits, and astrophysical input for rapid neutron capture.Recent experiments have provided stringent probes of shell evolution and collectivity in the neighboring Cu and Zn isotopes around 78Ni [7–9]. Precision mass measurements of 75−79Cu constrain the neutron-separation-energy systematics up to N=50, one proton above 78Ni, and therefore provide direct information on the persistence of the shell gap [10]. In-beam γ-ray spectroscopy of 79Cu and electromagnetic-moment measurements of neutron-rich Cu isotopes further support a largely persistent Z=28 closure and reduced dynamical correlations toward N=50 [11,12]. For neutron-rich Zn isotopes, transfer reactions and in-beam γ-ray spectroscopy of 79−84Zn have mapped single-particle strength, low-lying collective states, and intruder configurations associated with neutron particle-hole excitations across N=50 [13–17]. Recent in-flight fission experiments at RIKEN have extended the known neutron-rich boundary in this region, including the identification of very neutron-rich Cu isotopes up to 85Cu [18]. Together, these developments make the description of spectra, ground-state energies, separation energies, and neutron-rich limits in the Ni, Cu, and Zn region a stringent test of nuclear models.The same region has also been investigated extensively from the theoretical side using large-scale shell model [3,19–21], Monte Carlo shell-model (MCSM) [22], beyond-mean-field [23], and ab initio approaches [2,24–26]. Despite differences in many-body frameworks and interactions, these studies consistently indicate that 78Ni behaves as a strong, but not inert, doubly magic core. The N=50 neutron gap and the Z=28 proton gap remain pronounced, while neighboring nuclei are strongly affected by quadrupole correlations, proton-neutron monopole effects, and cross-shell excitations. Such correlations can lower intruder configurations and generate shape coexistence or enhanced collectivity away from 78Ni [3,19–21,24]. Recent valence-space in-medium similarity renormalization group (VS-IMSRG) combined with the density matrix renormalization group (DMRG) has provided a description of the erosion of the N=50 shell closure south of 78Ni, highlighting multi-particle–multi-hole correlations beyond conventional truncations [25,27].The remaining challenge is to treat the relevant many-body correlations in a large many-body space. VS-IMSRG calculations provide nonempirical valence-space Hamiltonians derived from chiral two- and three-nucleon interactions [28–33]. However, once neutron orbitals above the N=50 shell closure are included explicitly, the resulting valence spaces rapidly exceed the reach of full diagonalization. This dimensional bottleneck has motivated hybrid and truncated solvers, including VS-IMSRG+DMRG and importance-truncated shell-model [25,34,35]. Here we employ the semistochastic heat-bath configuration interaction (SHCI) method as a complementary large-space solver for nuclear structure. SHCI selects the most important Slater determinants with a heat-bath criterion and accounts for the remaining correlation energy through a semistochastic perturbative correction [36–39]. Compared with DMRG, SHCI does not rely on orbital ordering or matrix-product-state compression, and it provides a direct determinant-selection criterion together with a perturbative correction and extrapolation scheme.In this work, we develop a nuclear-structure implementation of the SHCI as a large-space solver and combine it with VS-IMSRG effective Hamiltonians. We first apply this framework to the spectroscopy of 78Ni, where the low-lying spectrum directly probes its doubly magic character. We then extend the calculations to neighboring N=50 isotones from Fe to Zn, to quantify the evolution of the N=50 shell closure. Finally, we investigate the neutron-rich limits of Ni, Cu, and Zn isotopic chains. The predicted ground-state energies, two-neutron separation energies, and drip-line locations provide a unified description of shell evolution from 78Ni toward the neutron drip line.2Theoretical framework2.1VS-IMSRG HamiltoniansWe start from chiral effective field theory nuclear interactions and, in the present calculations, employ the EM1.8/2.0 interaction [40–42]. Valence-space Hamiltonians are constructed using the VS-IMSRG [28,29,31–33]. The Hamiltonian is normal ordered with respect to an ensemble reference state,(1)H=E0+∑ijfij{ai†aj}+14∑ijklΓijkl{ai†aj†alak}+…,where E0, f, and Γ are the zero-, one-, and two-body terms. The IMSRG evolution decouples the chosen core and valence space from excluded configurations, and the Magnus formulation is used to obtain the evolved Hamiltonian and consistently transformed operators [30]. The valence space contains proton pf orbitals and neutron orbitals spanning the N=50 shell closure, including the relevant gds degrees of freedom. The VS-IMSRG effective Hamiltonians are derived using the IMSRG++ code [43]. The two- and three-nucleon matrix elements of the chiral EM1.8/2.0 interaction are generated with the NuHamil code [44]. The nuclear interaction is calculated using Nmax=14, E3max=24, and ℏω=16 MeV.2.2Semistochastic heat-bath configuration interaction as a nuclear many-body solverOriginally developed in quantum chemistry, SHCI is employed here as a selected-CI solver for VS-IMSRG valence-space Hamiltonians in nuclear spaces beyond full diagonalization [36–39]. It provides a complementary route to large-scale shell-model calculations by constructing a compact variational space from the Slater determinants that contribute most strongly to the target states.The variational wave function in SHCI is written as |Ψvar〉=∑Di∈Vci|Di〉, where V denotes the selected determinant space. Starting from an initial trial space, new determinants are iteratively added according to the heat-bath criterion(2)|Haici|>ϵ1,where Di∈V, Da∉V, and ϵ1 controls the size of the variational space. Eq. (2) is an existence condition and does not imply a summation over the Di∈V. The new determinant Da is retained if it has a sufficiently large coupling to at least one determinant in the current variational space. This differs from the importance measures based on the first-order wave-function correction, such as the IT-NCSM [35,45–48] method, which involve the coherent sum ∑iHaici together with an energy denominator and therefore require the evaluation of matrix-vector products. The absence of this summation makes the heat-bath criterion particularly efficient: for each variational determinant Di, only those connected determinants satisfying |Hai| ≥ ϵ1/|ci| need to be generated. The many connected determinants that cannot satisfy the threshold are therefore never explicitly examined. The iterative selection procedure is continued until the number of newly added determinants falls below 0.1 % of the dimension of the current variational space. The resulting Hamiltonian is diagonalized only in the selected subspace, yielding variational energies and wave functions for the targeted low-lying states.The residual correlation energy from determinants outside V is estimated by a second-order Epstein–Nesbet perturbative correction (PT2),(3)ΔEPT2=∑Da∉V|∑Di∈VHaici|2Evar−Haa.To overcome the storage bottleneck of Eq. (3), which requires a sum over all external determinants connected to the selected space V, SHCI introduces the second threshold ϵ2 < ϵ1 in the perturbative step, where the restricted sum includes only terms satisfying |Haici| ≥ ϵ2. Large PT2 contributions are evaluated deterministically, while the remaining small contributions can be included semistochastically [36–39]. At a finite selection threshold, the SHCI energy is ESHCI=Evar+ΔEPT2. Calculations are repeated for a sequence of decreasing ϵ1 values, producing a set of variational energies and PT2 corrections. The selected-space limit is obtained by extrapolating ESHCI as a function of |ΔEPT2| to |ΔEPT2|=0 [38]. Linear extrapolations are used as the default, and the selected-space extrapolation uncertainty is estimated by varying the fit window.As a validation, we first benchmark the SHCI in 71Ni using the valence space Hamiltonian. Using ϵ1=2×10−4, 1×10−4, 9×10−5, 8×10−5, and 7×10−5, with ϵ2=1×10−10, the zero-PT2 extrapolated energy is −164.098985±0.000028 MeV, which differs from the exact value of −164.098659 MeV by 0.33 keV. We further examine the sensitivity to the ϵ1 sequence using 79Cu. The above sequence gives −216.674865±0.000834 MeV, while an alternative sequence, ϵ1=2×10−4, 1.6×10−4, 1.3×10−4, 1×10−4, and 9×10−5, gives −216.675453±0.001006 MeV. The difference is only about 0.5 keV, showing that the extrapolation is insensitive to the adopted ϵ1 sequence and that the residual external-space contribution is sufficiently small for a stable zero-PT2 extrapolation. For all remaining calculations, we use the first ϵ1 sequence for isotopes with N ≤ 52 and the alternative one for N > 52, with ϵ2 fixed at 1×10−10 throughout.Beyond providing converged energies, the dominant determinants, particle-hole content, and orbital occupations can be extracted from the same calculation, making it possible to connect the evolution of ground-state energies and spectra with the underlying shell structure and many-body correlations. Thus, the VS-IMSRG+SHCI combines ab initio effective Hamiltonians with a systematically improvable large-space solver and provides quantitative spectroscopic information and microscopic wave-function diagnostics for exotic nuclei.3Results and discussion3.1SHCI convergence and spectroscopy of 78NiWe now apply the VS-IMSRG+SHCI framework introduced above to neutron-rich nuclei around 78Ni. Its low-lying spectrum tests whether the selected SHCI space captures the dominant closed-shell configuration and the leading cross-shell correlations. For comparison, we also perform shell model calculations with explicit mpmh truncations across the Z=28 and N=50 shells, where m=3–6 is the maximum number of particles excited across the shell closures. Fig. 1 summarizes the convergence of the lowest four states of 78Ni from SHCI and compares them with the truncated shell-model results.Fig. 1 (a) shows the SHCI total energies as functions of |ΔEPT2|, together with the zero-PT2 extrapolations and truncated shell-model results. As ϵ1 is lowered, the selected space grows while |ΔEPT2| decreases, showing the systematic recovery of correlations outside the variational space. The nearly linear behavior of the final SHCI points supports the zero-PT2 extrapolation, with uncertainties of only several keV from different fitting windows and fit errors. The convergence is state dependent: the ground state has the smallest |ΔEPT2| and converges fastest, consistent with its closed-shell character, whereas the excited states have larger PT2 corrections and are more sensitive to cross-shell correlations. A similar trend appears in the mpmh calculations, where the ground-state energy converges faster than the excitation spectrum, indicating stronger correlations in the low-lying excited states.The excitation energies relative to the ground state are displayed in Fig. 1(b). For each finite selection threshold ϵ1, the excitation energies shown in Fig. 1(b) are calculated directly as ExJ(ϵ1)=EtotalJ(ϵ1)−Etotal0+(ϵ1). Each point in Fig. 1(b) corresponds to the total-energy results obtained at the same value of ϵ1 in Fig. 1(a), so that there is no extrapolation of the excitation energies with respect to ϵ1. The values shown at ϵ1=0 are obtained from the differences between the independently extrapolated total energies in Fig. 1(a). They converge more smoothly than the absolute energies due to the partial cancellation of residual correlations. The SHCI spectrum shows the characteristic pattern of a doubly magic nucleus, with the 21+ state around 3 MeV. As ϵ1 decreases, Ex(21+) moves toward the experimental value of approximately 2.7 MeV [1]. The zero-PT2 extrapolation gives Ex(21+)≈2.93 MeV, preserving the characteristic high-lying 21+ state of a doubly magic nucleus. The particle-hole truncated spectra approach the SHCI results as the truncation is enlarged, but more slowly: even in the 6p6h space, which is slightly larger than the selected SHCI space at ϵ1=7×10−5, Ex(21+) remains about 200 keV above the finite-ϵ1 SHCI value and about 400 keV above the SHCI extrapolation. This demonstrates that low-lying spectra are governed not only by the total many-body dimension, but also by the efficient selection of relevant cross-shell configurations. In SHCI, such configurations are selected variationally through the heat-bath criterion, and the residual correlation energy is incorporated through the PT2 extrapolation, leading to faster convergence.3.2Spectroscopy of N=50 isotonesWe next investigate the low-lying spectroscopy of the N=50 isotones 80Zn, 79Cu, 78Ni, 77Co, and 76Fe, to examine the proton-number dependence of the N=50 shell closure across Z=28. For each nucleus, the lowest four states are calculated using the VS-IMSRG+SHCI framework and compared with the available experimental data [1,11,49], as shown in Fig. 2. We also analyze neutron occupations relative to the naive N=50 filling, where positive values above the gap and corresponding depletion below the gap quantify neutron particle-hole excitations across N=50. This isotonic chain therefore probes the robustness of the N=50 gap from the proton-particle side above Ni to the proton-hole side below Z=28.For the even-even isotones, the most striking feature is the much lower 21+ energy in 76Fe than in 80Zn and 78Ni. This asymmetry indicates a pronounced weakening of the N=50 shell closure below 78Ni, where proton holes below Z=28 enhance quadrupole correlations and promote neutron particle-hole excitations across the shell gap. This behavior is consistent with previous shell-model and ab initio studies showing that 78Ni is strongly, but not inertly, doubly magic and that mpmh configurations become increasingly important toward the proton-hole side [3,21,24,27]. The occupations support this interpretation: in 76Fe, the sizable population of neutron orbitals above N=50, especially the ds and g7/2 orbitals, signals strong cross-shell mixing and substantial erosion of the N=50 closure.In contrast, 80Zn, with two protons above the Z=28 shell closure, still retains a relatively high E(21+), supporting the persistence of a sizable N=50 shell gap on the proton-particle side of 78Ni. The calculated 21+ energy is about 500 keV above experiment, giving a slight overestimate of the N=50 shell stiffness in 80Zn. The calculated 21+ energy of 82Zn is 0.770 MeV, lower than that of 80Zn, indicating enhanced collectivity once neutrons are added above N=50. This behavior suggests that the N=50 gap remains visible at Z=30, but the closed-shell rigidity is softened beyond the shell closure. Consistently, the occupation analysis shows stronger neutron cross-shell excitations in 80Zn than in 78Ni, indicating that two protons outside the Z=28 core already enhance quadrupole correlations and slightly weaken the ideal closed-shell picture. However, these cross-shell excitations remain much weaker than those in 76Fe. This conclusion is consistent with experimental studies of neutron-rich Zn isotopes and mass measurements around N=50, which point to a robust but gradually evolving shell closure from 78Ni to 82Ge [5,14–16,50]. For the odd-Z isotones 79Cu and 77Co, the low-lying spectra provide a complementary probe of proton-particle and proton-hole structures around the 78Ni core [10–12]. The calculated level ordering in 79Cu also agrees with the MCSM calculations [11].The selected SHCI dimensions further reflect the different correlation strengths in 76Fe and 78Ni. At ϵ1=7×10−5, the selected space for 76Fe reaches about 2.1 × 108 Slater determinants, larger than that for 78Ni with 1.31 × 108 Slater determinants, despite the larger full many-body dimension of 78Ni. This indicates a more fragmented wave function in 76Fe. While 78Ni is dominated by near-spherical closed-shell configurations, proton holes below Z=28 in 76Fe enhance quadrupole correlations and neutron particle-hole excitations across N=50. Consequently, more determinants are required to describe its deformed and strongly mixed low-lying states, signaling a stronger erosion of the closed-shell structure.3.3Neutron-rich limits and shell evolutionHaving established from the N=50 isotones that the shell closure evolves with proton number, we now examine its consequences along the Ni, Cu, and Zn isotopic chains. The mass systematics provide a complementary probe of the same physics: ground-state energies determine the neutron-rich limits, while separation energies and empirical shell gaps quantify the persistence and softening of the shell closure away from 78Ni. Fig. 3 shows the ground-state energies, two-neutron separation energies (S2n), and empirical two-neutron shell gaps for neutron-rich Ni, Cu, and Zn isotopes. The calculated VS-IMSRG+SHCI results are compared with available experimental and extrapolated masses from AME2020 [51].Fig. 3 (a) shows that the calculated ground-state energies follow the experimental systematics from Ni to Zn. The remaining deviations vary smoothly along each isotopic chain, suggesting that the relative trends are more robust than the absolute ground-state energies. We use these ground-state energies to determine the neutron-rich limits. The one- and two-neutron drip lines are identified separately. The last isotope with positive Sn defines the one-neutron drip line, while the last isotope with positive S2n defines the two-neutron drip line. Although only S2n is shown in Fig. 3, the one-neutron separation energies are calculated from the same ground-state energies and are used to identify the one-neutron drip lines. Within the present Hamiltonian and valence-space truncation, the predicted drip-line nuclei from the one-neutron criterion are 83Ni, 86Cu, and 87Zn. For the two-neutron criterion, the predicted last bound nuclei are 86Ni, 91Cu, and 92Zn.Experimentally, the neutron-rich frontier in the Ni, Cu, and Zn region has been steadily extended at RIKEN. The most neutron-rich isotopes observed so far include 81,82Ni, 85Cu, and 84,85Zn, while recent precision mass measurements have reached neutron-rich Zn isotopes such as 83Zn [7,18,52,53]. These limits remain well inside the region covered by the present VS-IMSRG+SHCI calculations. Global mass models, such as Skyrme-HFB and FRDM(2012), also place the Ni, Cu, and Zn drip lines far beyond the known isotopes, although the detailed locations differ among models [54–56]. The present results provide a complementary ab initio prediction based on chiral interactions and a systematically improvable selected-CI solver. Near the drip line, however, the small separation energies make the exact locations sensitive to residual uncertainties from the VS-IMSRG Hamiltonian, SHCI calculation, and omitted continuum coupling.We now turn to the shell evolution encoded in the same mass systematics. Fig. 3(b) shows the S2n, which measures the additional binding gained by adding two neutrons. In all three isotopic chains, S2n decreases with increasing neutron number, with a visible change of slope across N=50. This behavior reflects the persistence of the neutron shell closure around 78Ni. The effect is most pronounced in the Ni chain, where the drop of S2n beyond N=50 is steeper. For Cu and Zn, the decrease beyond N=50 is smoother, indicating that valence protons outside the Z=28 core enhance proton-neutron correlations and reduce the rigidity of the N=50 shell closure.To quantify this shell effect, we consider the empirical two-neutron shell gap, Δ2n(Z,N)=S2n(Z,N)−S2n(Z,N+2). As shown in Fig. 3(c), Δ2n exhibits a clear peak at N=50 for Ni, Cu, and Zn. The largest peak appears in the Ni chain, consistent with a robust N=50 shell closure at 78Ni. Moving from Ni to Cu and Zn, the peak at N=50 is reduced, showing that the shell gap is gradually weakened by the addition of one or two protons outside the Z=28 core. The results are in agreement with the occupation analysis presented above. Away from N=50, Δ2n is smaller and varies more smoothly, indicating that the enhanced stability is localized around the shell closure rather than being a smooth bulk effect. The combined S2n and Δ2n systematics therefore show that the N=50 shell closure remains strongest at Z=28, but becomes progressively softened toward Cu and Zn as proton-neutron correlations and neutron cross-shell excitations increase.The shell evolution inferred from masses is further tested by the first 2+ excitation energies of even-even Ni and Zn isotopes, shown in Fig. 4. The Ex(21+) is a sensitive spectroscopic indicator of the competition between shell closure and quadrupole collectivity: a high Ex(21+) is characteristic of a closed-shell configuration, whereas a rapid decrease signals enhanced correlations and deformation. In the Ni chain, the calculated Ex(21+) exhibits a pronounced maximum at N=50, consistent with the doubly magic character of 78Ni. Away from N=50, the Ex(21+) decreases, indicating the onset of collectivity as the closed-shell configuration is broken.A similar but softened pattern is found in the Zn chain. The calculated 21+ energy also increases around N=50, showing that the neutron shell gap remains visible when two protons are added outside the Z=28 core. However, the peak is lower than in Ni and the decrease beyond N=50 is more gradual. This is consistent with the S2n and Δ2n trends: the N=50 shell closure persists in Zn, but proton-neutron correlations and neutron particle-hole excitations across the gap reduce the rigidity of the closed-shell structure. Beyond the dominant N=50 closure, Δ2n shows weak local enhancements near N=58 and N=62. These features are much smaller than the N=50 peak. The 21+ systematics provide partial support only for the N=58 feature, where a mild increase of Ex(21+) is found, whereas no corresponding enhancement appears near N=62. This suggests a possible weak subshell structure around N=58, which should be tested by future mass and spectroscopy measurements.Overall, Figs. 3 and 4 connect the predicted neutron-rich limits with shell evolution around 78Ni. The ground-state and separation energies determine how far the Ni, Cu, and Zn chains remain bound, while Δ2n and the 21+ energies quantify the persistence and gradual softening of the N=50 shell closure. In this context, the SHCI method provides a crucial computational tool that makes such large-scale valence-space calculations feasible, extending well beyond conventional shell-model diagonalization capabilities.4SummaryWe have developed a nuclear-structure implementation of the semistochastic heat-bath configuration interaction method and applied it for the first time to nuclear structure calculations with ab initio valence-space Hamiltonians. Important Slater determinants are selected through a heat-bath criterion, while remaining correlations are treated by semistochastic second-order perturbation theory and zero-PT2 extrapolation. Combined with VS-IMSRG Hamiltonians, SHCI provides a systematically improvable solver for large valence spaces beyond conventional exact diagonalization.As a benchmark, we studied 78Ni with VS-IMSRG+SHCI. SHCI yields stable low-lying energies with uncertainties of only several keV and converges faster than comparable particle-hole truncation schemes, highlighting its ability to efficiently capture the most important cross-shell configurations. We then investigated the N=50 isotones from 76Fe to 80Zn. The results show that the N=50 shell closure is strongest near 78Ni but evolves with proton number. Proton holes below Z=28 enhance quadrupole correlations and neutron excitations, significantly weakening the closure in 76Fe, whereas 80Zn retains a visible shell gap despite signs of gradual softening. Finally, we extended the Ni, Cu, and Zn isotopic chains toward the neutron drip line. The last bound nuclei are predicted to be 83Ni, 86Cu, and 87Zn from Sn, and 86Ni, 91Cu, and 92Zn from S2n. Systematics of S2n, Δ2n, and 21+ excitation energies indicate a robust N=50 shell closure at Z=28 that gradually weakens toward Zn, while weak signatures around N=58 suggest a possible subshell structure.This work establishes SHCI as a powerful, systematically improvable selected-CI solver for large-scale nuclear structure calculations, demonstrating its capability for ab initio calculations combined with valence-space Hamiltonians.Declaration of competing interestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.AcknowledgementsThis work has been supported by the National Key R&D Program of China under Grant Nos. 2024YFE0109800, 2024YFE0109802, and 2023YFA1606403; The National Natural Science Foundation of China under Grant Nos. 12405141, 12347106, 12441506, 12575124, 12375123. 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