Solving large-scale sparse eigenproblems in Density Functional Theory (DFT) simulations is a critical bottleneck, especially for computationally demanding biomolecular systems. This research introduces a machine learning model, trained on 660 protein dimer calculations, to predict eigenvalues and Density of States (DoS). By providing high-quality initial guesses, the spectral prediction significantly accelerates Self-Consistent Field (SCF) convergence thus reducing iterations from tens to a few while maintaining spectral accuracy. Substantial computational savings enable efficient quantum simulations of large biomolecular assemblies, crucial in drug discovery and desing of new materials.