Spectral signatures of electron correlation: a denominator-based perspective on excitation complexity

Understanding and quantifying electronic structure complexity remains a central challenge in quantum chemistry. In this work, we introduce a spectral framework based on the distribution of second-order Møller–Plesset (MP2) excitation denominators, providing a statistical characterization of the excitation-energy landscape underlying perturbative correlation treatments. We define a set of descriptors that capture complementary features of the denominator spectrum, including its energetic span, the accumulation of low-energy excitations, and its statistical organization through entropy. These quantities enable a resolved characterization of the excitation manifold beyond single-parameter descriptions. Applying this framework to the S22 benchmark set (57 molecules), we identify systematic relationships between the proposed spectral descriptors across chemically diverse systems. In particular, the behavior of the I_ND^MAX I ND MAX diagnostic is found to correlate with distinct regions of the spectral descriptor space, suggesting a connection between occupation-based diagnostics and the organization of excitation energies. The results indicate that systems with compressed denominator spectra tend to exhibit higher spectral entropies and larger I_ND^MAX I ND MAX values, whereas broader spectra are generally associated with lower entropy and smaller diagnostic values. The present work introduces a complementary perspective for analyzing electronic structure complexity through the statistical properties of the MP2 denominator spectrum and provides a framework for exploring relationships between excitation-energy distributions and established electronic structure diagnostics.