Topological Organization of the Gas-Phase Glycine Dipeptide Energy Landscape

Conformational potential energy surfaces encode the energetic hierarchy and connectivity of molecular configurations, but their global organization becomes difficult to characterize when multiple torsional degrees of freedom are coupled. Here, sublevel-set persistent homology (SSPH) was applied to the gas-phase conformational landscape of N-acetylglycine-N′-methylamide (Ace–Gly–NMe). A relaxed two-dimensional scan of the backbone dihedral angles ϕ and ψ was performed at the B3LYP-D3(BJ)/def2-SVP level. The periodic angular domain was modeled as S1×S1≅T2 and analyzed through a periodic cubical lower-star filtration. At the reporting threshold εpers=0.045kcalmol−1, the filtration retained five H0, six H1, and one H2 classes, corresponding to persistence-derived event counts (m0,m1,m2)=(5,10,5). The five retained basin components became connected by 3.168kcalmol−1, while the essential classes recovered the Betti numbers (1,2,1) expected for the toroidal domain. while the essential classes recovered the Betti numbers (1,2,1) expected for the toroidal domain. Independent unconstrained optimization and harmonic frequency analysis confirmed the five H0-birth configurations as local minima and the four finite H0-death configurations as first-order saddle points. Bidirectional displacement along their imaginary modes identified the local basin connections associated with these saddle points. These results show that SSPH can provide a compact global description of basin hierarchy and periodic-domain topology while also directing subsequent stationary-point calculations toward chemically relevant regions of the energy landscape. The remaining persistence-derived events retain a discrete topological interpretation and are not, without independent validation, molecular stationary points or kinetic pathways.