Quantum computing is emerging as a useful paradigm for solving highly complex computational problems. Unfortunately, current quantum computers are too noisy to achieve sufficient accuracy, and quantum-classical hybrid algorithms have emerged as a solution. Variational Quantum Eigensolver (VQE) and its extension, Variational Quantum Deflation (VQD), represent promising algorithms for computing ground-state and excited-state energy eigenvalues of Hamiltonians, particularly in quantum physics, chemistry, and materials science. We investigated the robustness of these hybrid quantum-classical schemes for tight-binding models of diamond and zincblende crystal structures (Sn, C, Si, Ge, AlP, AlAs, AlSb, and GaP). We analyzed the performance of these methods by comparing their results with those of classical solutions and assessing their convergence to the exact eigenvalues obtained via the classical diagonalization method. Based on our findings, we critically discuss the implications of implementing VQD on current noisy intermediate-scale quantum (NISQ) devices.