Thank you for your advice!

Kind regards,

Georg

Thank you for your reply!

I am looking forward to use your latest application in Multiwfn, this is a very interesting topic.

Concerning my topic of extremely high electrostatic and polarization energies in GAMESS-US EDA, I did some further investigations, which I would like to share, in case you or the members of the forum are interested in.

GAMESS - EDA is described in lit. J. Chem. Phys. 131, 014102  (2009) by Peifeng Su and Hui Li.

It seems that electrostatic energy ( 50676.28 kcal/mol) in GAMESS EDA involves a huge interaction energy, which is mostly neutralized by the polarization energy (-50782.52 kcal/mol). Indeed, adding these two terms gives −106,24 kcal/mol, which sounds quite reasonable.

Also the total fragment interaction energy is calculated correctly, as I have been able to reproduce these values by calculating them "by hand". Hence, the mathematics behind it seems to be OK.

It seems, as far as I have read the study above, that nucleus-nucleus repulsion energy for the complex molecule  (E-nuc-X) is involved in the calculation of the KS-orbitals of the fragments (instead of E-nuc frag only), resulting in a huge positive electrostatic energy term. This results (seemingly) in a correspondingly large Delta - E, when comparing it to the final, SCF - calculated complex electron structure. This large Delta - E is represented in GAMESS - EDA polarization energy.

However, I am not definitely sure about that yet.

The repulsion energy calculated in GAMESS-US EDA might be an equivalent to Pauli Repulsion, since it is calculated in the same manner by switching from nonorthonormal to orthonormal wavefunction, as described in GAMESS-US output.

----------------------------------------------------------------------
SUPER MOLECULE ENERGY  USING ANTISYMMETRIC NONORTHONORMAL WAVEFUNCTION
(EXCHANGE ENERGY: ONLY X CHANGES)
----------------------------------------------------------------------

              FROM OWN BASIS      FROM ALL BASIS
T             1403.12890958       1403.08427349
V            -7592.41629433      -7592.40280098
X               37.50933497         37.51658975
J             2696.67754203       2696.67759754
N             2062.03362382       2062.03362382
EC              -6.72465000         -6.72306280
E            -1399.79153393      -1399.81377917

-----------------------------------------------------------------------
SUPER MOLECULE ENERGY  USING ANTISYMMETRIC AND ORTHONORMAL WAVEFUNCTION
(REPULSION ENERGY: T V X J CHANGE)
-----------------------------------------------------------------------

              FROM OWN BASIS      FROM ALL BASIS
T             1403.73815072       1403.75815248
V            -7593.22649878      -7593.28389320
X               37.48194256         37.49069044
J             2697.02385325       2697.04743699
N             2062.03362382       2062.03362382
EC              -6.72465000         -6.72306280
E            -1399.67357843      -1399.67705227

However, I am not sure about that either, since I am not very familiar with Löwdin orthonormalization.

If anyone knows some literature concerning Löwdin orthonormalization, I would be thankful if this literature is shared.

Kind regards,

Georg

"-50782.52" is a quite abnormal value, I don't think it has any physical meaning.

By the way, sobEDA energy decomposition analysis method recently proposed by me is able to calculate orbital interaction energy, see J. Phys. Chem. A 2023, 127, 7023−7035, it is worth to try.

Best,

Tian

Thank you very much for providing ETS-NOCV within Multiwfn.

I have tried to combine EDA-results as provided in GAMESS-US with ETS-NOCV from Multiwfn.

The result for ETS-NOCV for my fragmented molecule is:

"Sum of NOCV eigenvalues:   0.00002
Sum of pair energies:     -38.70 kcal/mol"

As far as I have understood, the Delta-E-orb consists mainly of inter- and intrafragent polarization energies.

However, when calculating the same molecule (with the same fragmentation) with GAMESS-US, RUNTYP=EDA,

one gets as a result:

                      SUMMARY OF CMOEDA RESULTS
                      - PEIFENG SU AND HUI LI -
                   *******************************

-------------
OWN BASIS SET                                       HARTREE          KCAL/MOL
-------------
ELECTROSTATIC ENERGY                  ES=         80.757731          50676.28
EXCHANGE ENERGY                       EX=         -0.014236             -8.93
REPULSION ENERGY                     REP=          0.117956             74.02
POLARIZATION ENERGY                  POL=        -80.927031         -50782.52
DFT DISPERSION ENERGY               DISP=         -0.017444            -10.95
TOTAL INTERACTION ENERGY HF OR DFT     E=         -0.083025            -52.10
 
Obviously, the polarization energy obtained with the latter is much larger than with ETS-NOCV.

This has lead to my questions: Are there different definitions used for polarization / electrostatic energy?

Is the repulsion energy calculated by GAMESS an equivalent to the Pauli Repulsion mentioned in Multiwfn manual?

Thank you very much in advance for your reply!

Kind regards,

Georg