Calculating Ground State Energy of Helium by using Variational Monte Carlo Methods

Sri Purwaningsih, Nehru Nehru, Cicyn Riantoni

Abstract

Variational Quantum Monte Carlo (VQMC) is a computational approach that combines the variational principle of quantum mechanics with stochastic Monte Carlo integration to estimate ground-state properties of many-body systems. In this study, the VQMC method is employed to calculate the ground-state energy of the helium atom, a fundamental two-electron system that serves as a benchmark for testing quantum methods. The evaluation of multidimensional integrals arising in the expectation value of the Hamiltonian is performed using importance sampling based on the Metropolis algorithm, which enhances computational efficiency and accuracy. A key advantage of the VQMC approach lies in its flexibility in selecting analytically tractable trial wave functions, enabling systematic improvement of results through parameter optimization. Using an appropriately constructed trial wave function that incorporates electron–electron correlation effects, the calculated ground-state energy of helium is found to be −77.645 eV. This result shows good agreement with the exact reference value, demonstrating that the VQMC method provides reliable and accurate estimations for atomic systems. The findings confirm the effectiveness of VQMC as a powerful tool for solving quantum many-body problems. 

Keywords

Monte Carlo; Ground State energy; Helium

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References

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DOI: https://doi.org/10.13057/ijap.v16i1.94513

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