Hydrogen Bonds correction - ProkopHapala/FireCore GitHub Wiki

General principle

We model hydrogen bonds by two methods

1. we decrease repulsive of non-covalent interatomic pairwise potential ( i.e. Pauli repulsion, modeled by $A/r_{ij}^{12}$ in Lennard-Jones or by $A \exp(-2 a r_{ij})$ in Morse and Buckingham.
   • This is done by multiplying amplitude of repulsion $A$ by some constant, $A_H = A(1 + H_{ij})$ where $H_{ij} = H_i H_j$
   • This correction is in effect only for atoms which have opposite Hbond correction charges $H_i, H_j$, which means $H_{ij}<0$.
2. we add electron pairs as dummy atoms at certain distance (~0.5A) from host Hbond-acceptor (e.g. electronegative O,N atoms). We transfer some charge (0.1-0.6e) from host atom to electron pair.
   • The electron pair is typically closer to Hbond-donor
   • This is supposed to simulate the angular dependence of hydrogen bonds

Only for selected atoms

• Fit REQ only for atoms which have non-zero Hb correction ( like if(abs(Hbond)<1e-300) continue; )
  • Or we may make a flag bool* bHBs; if(bHBs[ia]) continue
  • Or we may make Hb atoms selection int* iHbs; for(int ia in iHbs){ ... };
  • Or we may make new temp array which lists only hydrogen-bond corrected atoms
• For all of this we need do non-Hbonded reference
  • we compute reference Hbond energy first (using non-corrected LJQ or MorseQ) and store it in temporary array atoms->userData->Emodel0
  • to evaluate error we simply substract dE = Eref - Emodel0 - Ecor where Emodel0 is pre-calculated and Ecor is calculated just for selected Hbonded atoms.

Electron pairs - short-range

• Electron pairs have certain charge on itself ( which is subtracted from host atom)
• However they can have also some short range function (e.g. $\exp(-a r_{ij})$ ) which is attractive for all Hbond-donors (electron depleted Hydrogen atoms).
  • we can check this by Hb[ja]>0

Remaping $H_i$, $H_j$ mixing to charge mixing

For Lenard-Jones $H_{ij}$ coefficient must be close to 1 in order to have meaningful effect. The dependece is extremely steep for $H_{ij} \to 0$. Therefor it would be better to remap these coefficent so that they have more reasonable values, and ideally if they are somewhat proportional to partial charges of atoms. This can be probably done using some reciprocal function, e.g.

$H_{ij} = 1 - \frac{1}{(1+ \alpha Q_i Q_j )^\beta}$ where $\alpha~10 ... 100$ and $\beta$ could be derived from Lennard-Jones potential to be in the order of 6 (?).

Directional subtraction of barrier