The relationship between unpaired electron delocalization and nearest-neighbor atomic relaxations in the vacancies of diamond has been determined in order to understand the microscopic reason behind the neighboring atomic relaxation. The Density Functional Theory (DFT) cluster method is applied to calculate the single-electron wavefunction of the vacancy in different charge states. Depending on the charge and spin state of the vacancies, at outward relaxations, 84-90 per cent of the unpaired electron densities are localized on the first neighboring atoms. The calculated spin localizations on the first neighboring atoms in the ground state of the negatively charged vacancy and in the spin quintet excited state of the neutral vacancy are in good agreement with Electron Paramagnetic Resonance (EPR) measurements. The calculated spin localization of the positively charged vacancy contrasts with the tentative assignment of the NIRIM-3 EPR signal to this center in (p-type) semiconductor diamond. The sign of the lattice relaxation in the diamond vacancy is explained based on the effect of electron delocalization on nearest-neighbor ion-ion screening, and also its effect on the bond length of neighboring atoms.