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https://github.com/maroba/findiff Eventually it will be a runtime dependency, so that a (static) perturbation can be done numerically and not just analytically.
**** SCF Summaries ****
Total Energy = -317.654569137503472
Nuclear Repulsion Energy = 248.175936966105979
One-electron Energy = -929.029398755747252
Two-electron Energy = 363.198892652137829
[-2.45747929 1.7516888 -2.01564383]
[-2.45055712 1.7498966 -2.01522139]
[-2.45925283 1.75661295 -2.01578952]
[-2.45707171 1.75153706 -2.00968794]
FD polarizability 1
[[27.23389041 -7.05107969 1.66201956]
[-6.97762021 19.37304047 -0.57316094]
[ 1.60353844 -0.5969904 23.43223982]]
FD polarizability 2
[[27.23389041 -7.05107969 1.66201956]
[-6.97762021 19.37304047 -0.57316094]
[ 1.60353844 -0.5969904 23.43223982]]
Analytical polarizability
[[27.31719954 -7.04241525 1.65887012]
[-7.04241525 19.48068656 -0.62010082]
[ 1.65887012 -0.62010082 23.46302403]]
Reference Q-Chem results are:
20 -317.6545691370 1.88E-12 Convergence criterion met
---------------------------------------
One-Electron Energy = -929.0293991645
Total Coulomb Energy = 404.5797863304
Alpha Exchange Energy = -20.6904466050
Beta Exchange Energy = -20.6904466050
DFT Exchange Energy = 0.0000000000
DFT Correlation Energy = 0.0000000000
Nuclear Repu. Energy = 248.1759369070
Nuclear Attr. Energy = -1243.8031596459
Kinetic Energy = 314.7737604814
[-0.96685375 0.68917099 -0.79299712]
forward terms
[-1.01847174 0.70246892 -0.79614456]
[-0.95355583 0.65234596 -0.79181683]
[-0.96996185 0.69035128 -0.83733666]
backward terms
[-0.91523576 0.67587307 -0.78984968]
[-0.98015168 0.72595668 -0.79417741]
[-0.96370631 0.68799071 -0.74865758]
finite difference (forward)
[[ 27.3150084 -7.03694576 1.66554929]
[ -7.03694576 19.48692672 -0.62458098]
[ 1.64472993 -0.62458098 23.46342566]]
finite difference (backward)
[[ 27.3150084 -7.03694576 1.66554929]
[ -7.03694576 19.46610736 -0.62458098]
[ 1.66554929 -0.62458098 23.46342566]]
finite difference (central)
[[ 27.3150084 -7.03694576 1.66554929]
[ -7.03694576 19.47651704 -0.62458098]
[ 1.65513961 -0.62458098 23.46342566]]
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Closes #181