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There are four algorithms used in calculating the nonbonded energies, each making different approximations in an attempt to speed the calculation. Electrostatic interactions are the most difficult to deal with for two reasons. They do not fall off quickly with distance (so it is inappropriate to simply ignore all interactions beyond some cutoff), and they depend on odd powers of r necessitating expensive square root calculations for each pair evaluated. The approximations used to make the electrostatics calculation more tractable are setting the dielectric constant equal to r or using a constant dielectric but only calculating distant interactions periodically (and storing the value in between).

Setting the dielectric constant equal to the atom atom distance
times a constant factor (determined by the `EPS` keyword value)
makes the computation easier by eliminating the need to calculate square
roots and by making the calculated contribution fall off more quickly.
It also introduces problems. The force calculated using an *r* dependent
dielectric will be larger than the force from a constant dielectric at
short distances (5.0 angstroms or less by comparsion to a constant
dielectric of 2.5). In addition, the electrostatic contribution still
falls off relatively slowly and large distance cutoffs are needed. As
the number of atom pairs included will be proportional to the cutoff
cubed, this is a significant disadvantage.

The `RESI` options use an *r*
dependent dielectric (as do all of Bruce Gelin's protein calculations).
In the `RESI` searches,
the program constructs a rectangular box around every residue, and examines
every residue–residue pair that can yield atom atom pairs within the
cutoff. Every atom–atom pair within
those residue–residue pairs is added to the non-bonded list.
When switching functions are used, `RESI` and `ATOM`
will yield the same energy, but `RESI` will generate a longer list.

The `SHFT` option is similar to `ATOM` except, the potential:

E= (QI*QJ/EPS)*( 1.0/R**2 + R**4/(2.0*CTOFNB**6) - 1.5/CTOFNB**2 )
is used when ( R < `CTOFNB` ) and zero otherwise. This potential
and it first derivative approach zero as R becomes `CTOFNB`,
without the messy computation of switching functions and steep
forces at large R.

The `EXEL` and `EXFL` routines use a constant dielectric at large
distances joined to the short distance function. The long distance terms
are approximated using interpolation and periodic updating. At `CUTNB` the
constant dielectric potential is joined to a dielectric equal to *r*
potential with a shift and scale that preserve the continuity of the
energy and forces.
`CONS` uses a constant dielectric everywhere. This requires a square root
to be calculated in the inner loop of `ENBOND`

, slowing things down a bit,
but it is physically more reasonable and widely employed by other groups
doing empirical energy modelling (ex. ST2 water).

This form allows a small `CUTNB` (5.0 angstroms with
`EPS`=2.5) even though the electrostatic terms are still varying
rapidly at that distance. The short range forces are identical to those
calculated with the other options, reflecting the decrease in dielectric
shielding at short ranges. For the long range forces there is
effectively no cutoff in the electrostatic energy. Interactions between
atoms beyond the `CUTNB` are calculated when the list is updated and
stored together with their first (`EXFL`,`CONS`) or first and
second (`EXEL`) derivatives. The energy is calculated by explicitly
evaluating pairs in the list and using the stored potentials, fields,
and gradients to approximate the distant pairs. In essence the routines
assume that for distant pairs the atom movements will be small enough
that the changes in their electrostatic interactions can be accurately
calculated using local expansions.

The constant dielectric routines compile the close contact list using the same two stage minimum rectangle box search that is described above. In this way the efficiency of a residue by residue search is exploited while being certain that all necessary pairs are included. For close residue pairs an atom by atom search is then performed. Atom pairs are either included in the list of close contacts or their electrostatic interactions are calculated and stored.

An option is offered to increase the accuracy of residue residue
interactions by using a multipole expansion of one residue evaluated for
each atom of the other. This cutoff for this treatment is `CUTMP`.
For residue pairs outside of `CUTMP` only a single multipole
evaluation is made and second order polynomial expansion is used to
extrapolate to each atom. Ordinarily this is sufficient and `CUTMP`
is set to 0.0.

The `DUMMY` option results in no non-bonded interactions
whatsoever. The creation of a dummy list can be done very quickly. This
is useful when one is analyzing only the other terms in the energy.