Multiconfigurational nature of the chemical bond in beryllium molecule

Context: Despite having only eight electrons, accurate prediction of the dissociation energy of the weakly bound beryllium molecule remains a stringent test for quantum chemical methods. Although its formal bond order is zero, Be₂ exhibits an unusual bond that is stronger than dispersion forces yet weaker than typical chemical bonds, arising from the interplay of nondynamical and dynamical correlation effects. In this work, a detailed first-principles study of the ground state of Be₂ is presented. An accurate ab initio potential energy curve (PEC) is computed and extrapolated to the complete basis set (CBS) limit. The contributions of nondynamical and dynamical correlation effects to the dissociation energy are rigorously analyzed within the Nonclosed Shell Many Electron Theory (NCMET) framework. NCMET(ND) predicted that the binding energy results predominantly from the nondynamical correlation, with a significant but smaller contribution from dynamical correlation. It is further found that the triple excitations play the crucial role in locating the correct minimum. An eight-parameter model potential is proposed, and new values for dispersion coefficients are reported. The inclusion of the C₁₀ term was found essential to support the full set of twelve vibrational states observed experimentally. The vibrational states are obtained by solving the Lippmann–Schwinger equation in momentum space using the developed potential. Methods: An accurate ab initio PEC was computed using a range of quantum chemical methods, including Nonclosed Shell Many Electron Theory (NCMET), high-order perturbation theory (MP8 and MP9), and full CI in pentuple-zeta basis and extrapolated to the CBS limit. The nondynamical correlation energy of Be₂ was calculated using NCMET(ND), including internal and semi-internal correlations, while dynamical correlation effects were described using second-order configuration interaction (SOCI) and near-NCMET wave functions. Multiconfigurational (MC) wave functions were constructed within the MCCI framework using CSFs under D_2h symmetry, with an active space of approximately thirty orbitals in frozen core approximation. Correlation-consistent augmented basis sets (aug-cc-pVXZ, X=3–5) were employed. Core correlation effects were estimated using all-electron coupled-cluster singles, doubles, and noniterative triples (CCSD(T)) method with aug-cc-pCVXZ basis sets. The relativistic effects and the diagonal Born–Oppenheimer correction (DBOC) were included. Dissociation energy was calculated using a supermolecular approach at a large separation to ensure size consistency. All NCMET(ND), SOCI, near-NCMET, full CI, and relativistic calculations were performed in MOLPRO, while multireference coupled cluster (Mk-MRCC), symmetry-adapted perturbation theory (SAPT), and MPn calculations were carried out in PSI4.