Point Charge Embedding

Non-Iterative

EC-MFCC Charges

Introduced by Jiang et al.37. The description is a bit vague, but the idea seems to be to only put charges on the most electronegative/electropositive atoms. In the original presentation proteins with charged termini were fragmented. When a terminus did not show up in the fragment it was replaced by a point charge. How this would generalize to other systems is not immediately clear.

EE-MB-A

One of two charge embedding schemes proposed by Dahlke and Truhlar9 for the EE-MB method.

  1. Compute charges for the supersystem

  2. Let \(Q_i\) be the charge of atom \(i\), \(A_i\)

  3. For each \(n\)-mer, loop over atoms in the supersystem. If \(A_i\) is not in the \(n\)-mer, place \(Q_i\) at the location of \(A_i\)

EE-MB-B

The second embedding scheme proposed by Dahlke and Truhlar9.

  1. Compute charges for each monomer

  2. Let \(Q_i\) be the charge of atom \(i\), \(A_i\)

  3. For each \(n\)-mer, loop over atoms in the supersystem. If \(A_i\) is not in the \(n\)-mer, place \(Q_i\) at the location of \(A_i\)

Iterative Point Charge Embedding

Iterative point charge embedding requires the use of point charges that in some shape or form respond to changes in the electronic structure. Typically this means one:

  1. Compute point charges for each fragment in vacuum

  2. Recompute the point charges for each fragment. This time instead of neglecting atoms outside the fragment, replace them with their computed point charge.

  3. Repeat the previous step until convergence or for a set number of iterations

Variations

For disjoint fragments the above is straightforward; however, when the fragments intersect there is some ambiguity as to what the charge of an atom is since it can appear in multiple fragments. In the context of GEBF 59 this ambiguity is resolved by taking the point charges from the fragment which resulted from the pseudoatom which contains the atom. This assumes that the GEBF fragmentation method has been used.

Screened Charge Model

In the context of the EE-MB method, Tempkin et al.85 introduced a screened point charge. For the \(i`\)-th atom, \(A_i\), the screened charge at a distance \(r_i\) from \(A_i\), \(q_i^*\left(r_i\right)\), is given by:

\[ \begin{align}\begin{aligned}\newcommand{\zi}{Z_i} \newcommand{\Zei}{\zeta_{\zi}} \newcommand{\ri}{r_i} \newcommand{\fi}{f\left(\Zei\ri\right)}\\Q_i^*(\ri) = Q_i + m \fi\exp\left(-2\Zei\ri\right)\end{aligned}\end{align} \]

where:

  • \(Q_i\) is the unscreened charge of \(A_i\)

  • \(m\) is the number of electrons in the orbital

  • \(Z_i\) is the atomic number of \(A_i\)

  • \(\zeta_{z_i}\) is the exponent of the Slater orbital, and

  • \(f\) is a polynomial that depends on the principal quantum number of \(A_i\)

N.B. the details of the polynomial, as well as values for \(\zeta_{z_i}\) are given in 86.