Unified Time Evolution Approach for the Electronic Structure Calculation

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In imaginary-time evolution, the same technique, Crank–Nicolson’s method, as for the analysis of real-time evolution is employed. For the verification using the model oscillators such as quantum well, Morse, and harmonic potentials, practical density functional theory (DFT) calculations are performed for hydrogen atoms and molecules. The convergence is confirmed to be faster under appropriate initial and boundary conditions. The results are consistent with the analytical solutions and those of other DFT calculations. Imaginary-time evolution is quite convenient to subsequent real-time real-space time-dependent DFT calculation. Although the operators are different, similar evolution is adopted. This technique is expected to unify into practical electronic state calculations for the self-consistent electronic structure and system’s response due to perturbation because calculations are in the same framework as the time-dependent equation.