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saeed_E

Member

Registered: 2019-12-21

Posts: 297

Using CDA to compute fragment orbitals responsible for Pauli

Dear Tian,
As you nicely did guide me to use CDA for obtaining the value of Pauli repulsion between occupied orbitals of two interacting fragments (and, evaluating corresponding overlap), I did follow the below steps one-by-one. Please, if possible, let me know if my approach is quite correct:

1- The TS structure is fully optimized using, for instance, M062X/def2TZVPP level (TS includes two interacting fragments f1 and f2 which include some very heavy atoms such as Sn and, thus, I employed this basis set so that pseudo potentials are applied for such atoms).
2- After full optimization of TS, I changed number of atoms so that the electron-donor fragment (f1) to be the first fragment and electron-acceptor (f2) to be the second fragment.
3- Taking fully optimized TS structure, a SP is performed using "M062X/def2TZVPP nosymm pop=full iop(3/33=1)" keywords and, generated "chk" file is converted into "fch".
4- Taking the fully optimized structure of TS (whose atom numbering has been changed as described), f1 and f2 will be generated following a SP over each fragment using "M062X/def2-TZVPP nosymm pop=full" keywords and, "chk" files are converted into "fch" ones.
5-Multiwfn boots up, and the "fch" file of TS is loaded. Then 16 is chosen. I also enter 2 as there are two fragments. Then, the "fch" file of f1 (electron-donor) and "fch" file of f2 will be entered, respectively. The below data are presented:

Orb.      Occ.          d           b        d - b          r
       1    2.000000   -0.000003    0.000025   -0.000029    0.000014
       2    2.000000   -0.000005   -0.000212    0.000206   -0.000071
       3    2.000000   -0.000004   -0.000086    0.000082   -0.000026
       4    2.000000    0.000445   -0.000000    0.000445    0.000024
       5    2.000000    0.000304   -0.000001    0.000305    0.000043
       6    2.000000   -0.000006   -0.000178    0.000171   -0.000065
       7    2.000000   -0.000114   -0.001880    0.001766    0.022417
       8    2.000000    0.005204    0.000709    0.004495    0.065189
       9    2.000000    0.000370    0.002808   -0.002438   -0.003814
      10    2.000000   -0.001802   -0.008178    0.006376   -0.011103
      11    2.000000    0.003259    0.002135    0.001124    0.106547
      12    2.000000   -0.005901   -0.000438   -0.005464   -0.101433
      13    2.000000   -0.001358   -0.002066    0.000708    0.041290
      14    2.000000    0.002171   -0.000691    0.002862    0.006158
      15    2.000000   -0.001241   -0.001562    0.000321   -0.032240
      16    2.000000    0.000064    0.002083   -0.002020    0.018551
      17    2.000000    0.003422   -0.001551    0.004973    0.128120
      18    2.000000    0.001397   -0.000052    0.001449    0.025455
      19    2.000000    0.008062   -0.001752    0.009813   -0.089066
      20    2.000000    0.018289    0.016942    0.001347   -0.159743
      21    2.000000    0.051780   -0.002916    0.054697   -0.403971
      22    2.000000   -0.000894    0.062648   -0.063542   -0.141167
-------------------------------------------------------------------
Sum:      44.000000    0.083437    0.065789    0.017649   -0.528892

As can be seen, the last four MO orbitals of complex (TS), 19-22, display a significant negative "r" value. So, one can conclude that the fragments orbitals participating in these MOs are responsible for the Pauli repulsion. Consequently, we should first decompose MOs 19-22 to the fragments orbitals. Now, we should select option "6, Decompose complex orbital contribution to CDA" to find which fragments orbital participate in the formation of MO 19. Once we select 6 followed by 19, and enter a threshold value such as 0.005, the following information is displayed:

Occupation number of orbital    19 of the complex:  2.00000000
FragA Orb(Occ.)  FragB Orb(Occ.)      d           b        d - b          r
    6( 2.0000)       7( 2.0000)    0.000000    0.000000    0.000000   -0.009978
    6( 2.0000)       9( 2.0000)    0.000000    0.000000    0.000000   -0.026962
    6( 2.0000)      10( 2.0000)    0.000000    0.000000    0.000000   -0.014043
    6( 2.0000)      12( 2.0000)    0.000000    0.000000    0.000000   -0.021881
    7( 2.0000)       7( 2.0000)    0.000000    0.000000    0.000000   -0.007323
    7( 2.0000)       9( 2.0000)    0.000000    0.000000    0.000000   -0.005278
    7( 2.0000)      12( 2.0000)    0.000000    0.000000    0.000000    0.007499
    7( 2.0000)      13( 2.0000)    0.000000    0.000000    0.000000   -0.008777

Among NEGATIVE "r" values, the MOST NEGATIVE "r" is -0.026962 associated with a Pauli repulsion between orbital 6 of f1 and orbital 9 of f2. If we again repeat this calculation for orbitals 20, 21, 22 of TS and look for the most negative "r" value, we finally find that:

MO-19----> O-6_f1+O-9_f2
MO-20----> O-7_f1+O-13_f2
MO-21----> O-7_f1+O-13_f2
MO-22----> O-7_f1+O-15_f2

A simple visualization of the f1-orbitals (f1.fch is loaded into gview) one can see that orbitals 6 and 7 in f1 are HOMO-1 and HOM, respectively. These two orbitals are degenerate located over pi-orbitals of C-C triple bond of acetylene. On the other hand, a simple visualization of the f2-orbitals (f2.fch is loaded into gview), one can see that orbitals 9, 13, and 15 f2 are HOMO-6, HOMO-2, and HOMO, respectively. We should compute the value of S(i,j), the overlap integral, between:

orbital 6 of f1 and orbital 9 of f2
and
orbital 7 of f1 and each of orbitals 13 and 15 of f2.

To compute S(i,j) for f1 orbitals and f2 orbitals mentioned above, we should initially save TS.fch, f1.fch, and f2.fch as gaussian input files (gjf). Then, a SP is performed over TS.gjf using "M062X/def2TZVPP nosymm guess(save,only pop=none)" keywords and, corresponding chk file is converted into fch. A SP is also performed over each of f1.gjf and f2.gjf using "M062X/def2TZVPP nosymm" keywords and generated chk files are converted into fch ones. Now, Multiwfn boots up and TS.fch (newly generated as explained) is loaded. Then we select 100 followed by 15. The f1.fch and f2.fch is loaded, respectively and finally we enter 6,9. Then, we generate "whole overlap integral matrix to ovlpint.txt in current folder". From this file, one can see that:

S(6,9)= 0.056
S(7,13)= -0.126
S(7,15)= -0.031

We should consider the absolute value for negative S(I,j). Consequently, the Pauli repulsion between fragments orbitals at the TS structure increases as:
7,15<6,9<7,13

Please accept my highest apology for such a lengthy explanation.

Best Regards,
Saeed

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,973

Website

Re: Using CDA to compute fragment orbitals responsible for Pauli

Dear Saeed,

Your description is correct. However, I would like to mention that in fact you can directly obtain overlap integral between fragment orbitals via option "4 Export overlap matrix between fragment orbitals" in Multiwfn CDA module, it is more convenient. Also it should be noted that magnitude of overlap integral is just a very crude estimation of contribution to Pauli repulsion, the value should not be overly discussed.

Best,

Tian

saeed_E

Member

Registered: 2019-12-21

Posts: 297

Re: Using CDA to compute fragment orbitals responsible for Pauli

Dear Tian,
Your highly kind attention to prompt reply with much valuable and informative comments is extremely appreciated. Thank you very very much for the valuable time you so kindly assigned to my post.
Given your comments, do you have any other solutions to analyze Pauli repulsion between fragments in a given TS structure?
In addition, you have mentioned option 4 of CDA can directly give the overlap matrix. Isn't it necessary to first find the fragments' orbitals participating in the Pauli repulsion? Indeed, we should first find which fragment orbitals and in which complex orbital repeal each other due to Pauli repulsion.

Please also let me state that you cod "GauIRC2xyz" immediately crashes if the IRC.log file includes a TS comprising of three fragments (diene+dienophile+catalyst). Could you please change your code to be appropriate for three fragments?

Sincerely yours,
Saeed

Last edited by saeed_E (2025-04-27 16:39:24)

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,973

Website

Re: Using CDA to compute fragment orbitals responsible for Pauli

Dear Saeed,

The ETS-NOCV in Multiwfn is also able to study Pauli repulsion interaction, but it doesn't represent the interaction as fragment orbital interactions.

In the CDA interface, you should also need to first identify the fragment orbitals that heavily participlate in the repulsion term. I mention "4 Export overlap matrix between fragment orbitals" because you do not need to use subfunction 15 of main function 100.

I don't know how did you represent fragments in IRC.log. If something like C(fragment=2) appears in the log file, GauIRC2xyz doesn't formally support this very special case, and I don't have intention to modify the code.

Best,

Tian

saeed_E

Member

Registered: 2019-12-21

Posts: 297

Re: Using CDA to compute fragment orbitals responsible for Pauli

Dear Tian,
Many thanks for your nice and professional comments.

Best regards,
Saeed