This app allows you to upload a basis set or generate a new, random basis set for 1 and 2 electron atoms.
For 1 electron, we use a gaussian orbital basis set, which requires 1 α coefficient per basis function:
ψ = Σ cie-αir2
For 2 electrons, we use an explicitly correlated gaussian geminal basis set, which requires 3 coefficients per
basis function: an α for each electron and a β coefficient which correlates the two electrons:
ψ = 𝒴 Σ ci e-α1,ir12
-α2,ir22 -β12,ir122
𝒴 is the young operator, which maintains permutational symmetry (Pauli Principle adherence).
When uploading a basis set text file, the first line should have the word "coefficients" and then be followed by: an α
for each basis function for 1 electron (each on a new line), or by a set of α, β, α for each basis function for 2 electrons
(each on a new line).
Once a basis set is uploaded or generated, you can calculate the energy via the Rayleigh quotient:
= < ψ| H | ψ > / < ψ| ψ >
You may also perform a stochastic optimization on the basis set, which uses random numbers to modify the basis set
until a lower energy value if found. This works due to the variational principle.
Target values for H and He are: -0.5000 au and -2.9033 au.
NOTE: if your randomly generated basis set contains α values that are too similar, you develop linear dependence and break the variational
principle.
Number of electrons:
Nuclear charge:
Press here to generate a random initial basis set.
coefficients:
Press here to calculate the ground state energy with the current basis set.
Press here to perform a stochastic optimization of the basis set.
This is the work of Dr. Mauricio Cafiero and may be used widely though attribution is appreciated.
