FewBodyECG.jl

Installation

Get the latest stable release with Julia's package manager:

julia ] add FewBodyECG

Example

We consider a system of a positron and two electrons. The energy of this system has been very accurately calculated by various approaches and it has been found to be -0.262005 in atomic units (a.u.). We calculate the ground-state energy of this systems using correlated Gaussian bases constructed stochastically with pseudorandom and quasirandom sequences. The Hamiltonian of the system is given by

\[H = - \sum_{i=1}^{3} \frac{1}{2m_i}\frac{\partial^2}{\partial \boldsymbol{r}_i^2} + \sum_{i<j=1}^3 \frac{q_i q_j}{|\boldsymbol{r}_i-\boldsymbol{r}_j|}\]

The masses of the three constituents are m_i = {1, 1, 1} and the charges q_i = {+1, −1, −1}. We can estimate the ground state of this Coulombic three-body system using 50 Gaussians

using FewBodyECG
using LinearAlgebra
using Plots
using QuasiMonteCarlo

masses = [1.0, 1.0, 1.0]

Λmat = Λ(masses)
kin = KineticOperator(Λmat)

J, U = _jacobi_transform(masses)
w_list = [[1, -1, 0], [1, 0, -1], [0, 1, -1]]
w_raw = [U' * w for w in w_list]

coeffs = [+1.0, -1.0, -1.0]
coulomb_ops = [CoulombOperator(c, w) for (c, w) in zip(coeffs, w_raw)]

ops = Operator[kin; coulomb_ops...]

result = solve_ECG(ops, 250, sampler = SobolSample(); scale = 0.2)
n, E = convergence(result)
plot(n, E)