Correlation-driven stabilization and dimensional crossover in germanium clusters from quantum Monte Carlo

We investigate the structural and energetic properties of neutral germanium clusters Ge_n (n = 2-15) using fixed-node diffusion Monte Carlo (FN-DMC), Hartree-Fock (HF), and density functional theory (DFT) simulations. We analyze optimized geometries, weighted average bond lengths (ranging from 2.28 to 2.70 Å), effective coordination numbers (from 1.00 to 5.16), surface areas, volumes, binding energies, electron-correlation contributions, dissociation energies, and second energy differences. The FN-DMC binding energies are in excellent agreement with available experimental data, with deviations below 7%. For n > 4, the correlation contribution to binding relative to the HF reference amounts to 47.3-52.5% of the total binding energy, reaching a maximum of 86.6% for Ge₄. Electron correlation changes the dissociation energies by up to several electronvolts, underscoring its crucial role in cluster stability. A liquid-drop model analysis yields an extrapolated bulk cohesive energy of -3.94(1) eV and a surface tension of 0.637(8) J m^-2, both consistent with experimental values. The most stable clusters, identified by minima in the dissociation energy ΔE and maxima in the second energy difference Δ²E, are Ge₄ and Ge₁₀. These results highlight the essential role of accurate electron-correlation treatment in describing the energetics and size-dependent stability of medium-sized semiconductor clusters.