Illustrative calculations

Here some illustrative calculations can be seen

SCF with and without DIIS

The used geometry can be seen below:

10;;;
1;1.63803684;1.136548823;0
8;0;-0.143225817;0
1;-1.63803684;1.136548823;0

The used settings can be seen below:

basisset;6-31ppGss
DIIS;Yes
SCF Energy Threshold;1e-5
SCF RMSD Threshold;1e-5
basisset;6-31ppGss
DIIS;No
SCF Energy Threshold;1e-5
SCF RMSD Threshold;1e-5

First a SCF calculation was performed with DIIS enabled giving:

Iter          Eel                     Etot                    dE                       rmsD                    DIIS
0             -134.1449183618         -126.1425513008
1             -61.4018313732          -53.3994643122           7.27430870e+01          1.37140022e+01
2             -82.1748278956          -74.1724608346          -2.07729965e+01          1.34573050e+01          7.81843771e-01
3             -83.5297539977          -75.5273869367          -1.35492610e+00          1.33204239e-01          7.81843771e-01
4             -84.0658119442          -76.0634448831          -5.36057946e-01          4.78581548e-02          7.81843771e-01
5             -84.0523274324          -76.0499603713           1.34845118e-02          8.49130680e-03          7.81843771e-01
6             -84.0148299835          -76.0124629225           3.74974488e-02          2.96875516e-03          7.81843771e-01
7             -83.9935874709          -75.9912204099           2.12425126e-02          1.76964818e-03          7.81843771e-01
8             -83.9947637830          -75.9923967219          -1.17631206e-03          2.26414594e-04          1.16112494e-01
9             -83.9947955055          -75.9924284444          -3.17225082e-05          1.66077078e-05          3.21096922e-02
10            -83.9948061725          -75.9924391115          -1.06670263e-05          6.54369763e-06          3.03280249e-03

Then a SCF calculation was performed without DIIS giving:

Iter          Eel                     Etot                    dE                      rmsD
0             -134.1449183618         -126.1425513008
1             -61.4018313732          -53.3994643122           7.27430870e+01          1.37140022e+01
2             -104.9615819231         -96.9592148621          -4.35597505e+01          1.35548186e+01
3             -64.7628958717          -56.7605288107           4.01986861e+01          1.25781385e+01
4             -102.8062267026         -94.8038596416          -3.80433308e+01          1.25633760e+01
5             -65.5183313906          -57.5159643295           3.72878953e+01          1.23251505e+01
6             -102.3075211689         -94.3051541079          -3.67891898e+01          1.23221102e+01
7             -65.7017602918          -57.6993932308           3.66057609e+01          1.22666435e+01
8             -102.1836707293         -94.1813036683          -3.64819104e+01          1.22659169e+01
9             -65.7473338650          -57.7449668040           3.64363369e+01          1.22524386e+01
......
96            -102.1421225328         -94.1397554718          -3.63795182e+01          1.22477235e+01
97            -65.7626043489          -57.7602372879           3.63795182e+01          1.22477235e+01
98            -102.1421225328         -94.1397554718          -3.63795182e+01          1.22477235e+01
99            -65.7626043489          -57.7602372879           3.63795182e+01          1.22477235e+01

As it can bee seen the one with DIIS converges in 10 iterations, whereas without DIIS it never converges

Hartee-Fock H2 dissociation

Under the Hartee-Fock approximation the dissociation of dihydrogen can be considered. To investigate this the following geometry input was used:

2;;;
1;0.0;0.0;0.0
1;x;0.0;0.0

Here x is varied to make the dissociation curve. The following settings were used:

Initial method;HF
basisset;3-21G

and,

Initial method;UHF
basisset;3-21G

For x varried from 0.5 to 13 a.u. the following curve can be made:

_images/H2dissociation.png

For a script to calculate the curves see SlowQuant/data/notebooks/H2 dissociation HF vs UHF.ipynb

It can be seen from the curve that (R)HF and UHF converges to two different values. By calculating H- and H radical it can be seen that RHF converges to H- and H+, whereas UHF converges towards 2x H radicals. This can be understood since RHF is a closed-shell method. When H2 dissociates it is expected that each hydrogen will be associated with one electron, this cannot be descirbed with RHF. UHF can describe open-shells and therefore, seem to have a better describtion of the dissocation. UHF have other problems like spin contamination to be aware of.