Quantum and variational monte-carlo interaction potentials for li2 (x1-sigma-g+)

<span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">Optimized trial functions are used in quantum Monte Carlo and variational Monte Carlo calculations of the Li</span><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">2</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">(X </span><sup style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">1</sup><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">Σ</span><sup style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">+</sup><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">g</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">) potential curve. The trial functions used are a product of a Slater determinant of molecular orbitals multiplied by correlation functions of electron—nuclear and electron—electron separation. The parameters of the determinant and correlation functions are optimized simultaneously by reducing the deviations of the local energy </span><em style="border: 0px; font-size: 13px; margin: 0px; padding: 0px; vertical-align: baseline; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px; text-align: justify; word-spacing: -1px">E</em><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">L</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px"> (</span><em style="border: 0px; font-size: 13px; margin: 0px; padding: 0px; vertical-align: baseline; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px; text-align: justify; word-spacing: -1px">E</em><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">L</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">  Ψ</span><sup style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">−1</sup><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">T</sub><em style="border: 0px; font-size: 13px; margin: 0px; padding: 0px; vertical-align: baseline; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px; text-align: justify; word-spacing: -1px">H</em><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">Ψ</span><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">T</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">, where Ψ</span><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">T</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px"> denotes a trial function) over a fixed sample. At the equilibrium separation, the variational Monte Carlo and quantum Monte Carlo methods recover 68% and 98% of the correlation energy, respectively. At other points on the curves, these methods yield similar accuracies.</span>