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Re: ESP mapped onto vdW surface: Statistics either area weighted or not

dummy@example.com (sobereva) — Fri, 22 May 2020 20:35:09 +0000

The variances printed by Multiwfn are closely related to your quantity:

The only difference is that the average of ESP is taken into account. I think this definition is somewhat more meaningful.

However, if you indeed want to drop the average term from the above equation, I will modify the code so that Multiwfn can directly output the quantity that you need.

Re: ESP mapped onto vdW surface: Statistics either area weighted or not

dummy@example.com (Dominic M Di Toro) — Fri, 22 May 2020 10:45:59 +0000

Thank you for the prompt reply. Very helpful.
I'd like to calculate the vdW ( = iso electron density) surface integral of the square of the ESP.

surface integral (vdW) (phi )^2 dA

This integral is useful for estimating Abraham parameters as demonstrated in
Arey, JS, WH Green, and PM Gschwend. “The Electrostatic Origin of Abraham’s Solute Polarity Parameter.” JOURNAL OF PHYSICAL CHEMISTRY B 109, no. 15 (April 21, 2005): 7564–73.

I suspect that it can be calculated by squaring the ESP cube and using that as the mapped function. Is this possible and straightforward? I'd appreciate sending the workflow required.

I've just encountered Multiwfn and it is a wonderful analysis program. I look forward to using it and passing it along to my colleagues that use quantum chemistry to solve environmental engineering problems.

Re: ESP mapped onto vdW surface: Statistics either area weighted or not

dummy@example.com (sobereva) — Thu, 21 May 2020 03:29:26 +0000

1 In the latter equation, it is assumed that areas of all facets are identical, therefore the facet area is not explicitly shown in the equation. In actual calculation, the facet area is always taken into account.

2 Multiwfn can export ESP of all vertices (see post-process menu), but there is no option to export ESP and area of all facets, since they are rarely useful for users. If you really need it, you should modify source code.

Exporting electron density of facets is meaningless, since all facets in principle has identical electron density, which is 0.001 a.u. by default.

ESP mapped onto vdW surface: Statistics either area weighted or not

dummy@example.com (Dominic M Di Toro) — Thu, 21 May 2020 01:43:34 +0000

There are two definitions of the statistics: average, variance etc of the ESP
Manual page 145
Statistics are weighted by the facet surface areas
e.g. Vs bar = (1/ Atot) Sum (i=1 to N) Ai Fi

Manual page 140
e.g. Vs bar = (1/t) Sum (k=1 to k=t) V(rk)

Which of these statistics is computed for the command sequence
Multiwfn < H2O_fchk_v1.inp > H2O_fchk_v1.out

H2O_fchk_v1.inp

which contains
H2O_gas.fchk
12
0

The output file is
H2O_fchk_v1.out

which contains

================= Summary of surface analysis =================

Volume: 189.82511 Bohr^3 ( 28.12918 Angstrom^3)
Estimated density according to mass and volume (M/V): 1.0635 g/cm^3
Minimal value: -33.30519 kcal/mol Maximal value: 43.10833 kcal/mol
Overall surface area: 160.97471 Bohr^2 ( 45.07752 Angstrom^2)
Positive surface area: 80.20354 Bohr^2 ( 22.45928 Angstrom^2)
Negative surface area: 80.77117 Bohr^2 ( 22.61823 Angstrom^2)
Overall average value: 0.00270967 a.u. ( 1.70034 kcal/mol)
Positive average value: 0.03701499 a.u. ( 23.22728 kcal/mol)
Negative average value: -0.03135457 a.u. ( -19.67530 kcal/mol)
Overall variance (sigma^2_tot): 0.00060805 a.u.^2 ( 239.43218 (kcal/mol)^2)
Positive variance: 0.00036929 a.u.^2 ( 145.41673 (kcal/mol)^2)
Negative variance: 0.00023876 a.u.^2 ( 94.01545 (kcal/mol)^2)
Balance of charges (nu): 0.23847813
Product of sigma^2_tot and nu: 0.00014501 a.u.^2 ( 57.09934 (kcal/mol)^2)
Internal charge separation (Pi): 0.03422669 a.u. ( 21.47759 kcal/mol)

Second question
How to output the ESP for each facet and the area for each facit and the electron density of each facet.