Spectrum energies do not perfectly match with valence energies when using Feynman Sigm

Agreement is to parts in <math-renderer class="js-inline-math" style="display: inline"

Spectrum stability with Feynman Sigma about ampsci HOT 1 OPEN

benroberts999 commented on August 31, 2024

Spectrum stability with Feynman Sigma

from ampsci.

Comments (1)

benroberts999 commented on August 31, 2024

Agreement is to parts in $10^6$ comparing Finite-Difference Hartree-Fock energies to basis/spectrum energies.
Roughly the same level of agreement between Brueckner orbitals and Spectrum orbitals using Goldstone technique for $\Sigma$.
However, agreement drops to parts in $\sim 10^4$ when using Feynman technique.

Could be related to B-spline code, but more likely is due to calculation of $\Sigma \psi$.

HF	HF/Bruckner	Spectrum
$6s_{1/2}$	-0.1273682	-0.1273681	1E-06
$7s_{1/2}$	-0.0551874	-0.0551874	9E-07
$8s_{1/2}$	-0.0309525	-0.0309525	6E-07
$9s_{1/2}$	-0.0198146	-0.0198146	-1E-06
Goldstone(2)
$6s_{1/2}$	-0.1475863	-0.1475867	-3E-06
$7s_{1/2}$	-0.0593160	-0.0593161	-2E-06
$8s_{1/2}$	-0.0325347	-0.0325347	-6E-07
$9s_{1/2}$	-0.0205929	-0.0205930	-2E-06
Feynman(2)
$6s_{1/2}$	-0.1478421	-0.1478491	-5E-05
$7s_{1/2}$	-0.0593860	-0.0593874	-2E-05
$8s_{1/2}$	-0.0325636	-0.0325641	-2E-05
$9s_{1/2}$	-0.0206073	-0.0206076	-1E-05
Feynman($\infty$)
$6s_{1/2}$	-0.1432236	-0.1431959	2E-04
$7s_{1/2}$	-0.0584265	-0.0584218	8E-05
$8s_{1/2}$	-0.0321932	-0.0321915	5E-05
$9s_{1/2}$	-0.0204248	-0.0204240	4E-05