The surface energy penalty term is designed to constrain atoms to fit within a surface or move them out of the space enclosed by a surface.The surfaces are represented by spherical harmonics of user-specified order. The penalty term has the form:

H[ rij- rsurfi- ti ] ksurfi ( rij - rsurfi - ti )n, for inclusion surfaces
   H[ rsurfi- ti - rij ] ksurfi ( rsurfi- ti - rij )n, for exclusion surfaces
   

where k_surfi is the force constant for surf_i, r_ij is the distance between the center of the surface surf_i and the atom atom_j, r_surfi is the distance between a corresponding point on surf_i and its center, t_i is the thickness of surf_i, n is zero or a positive integer power and H[r] is the Heaviside step function in which H[r<0] = 1, H[r=0] = 1/2 and H[r>0] = 0. Surfaces can be of inclusion or exclusion types and sets of surfaces can be OR or AND type:

Surface Characteristics	Effects on Atoms	Special Requirements
inclusion	An energy penalty is imposed on atoms that stray outside such a surface	.
exclusion	An energy penalty is imposed on atoms that stray inside such a surface	.
OR	Sets of surfaces, each enclosing or excluding an identical set of atoms. Energy penalty on an atom is imposed based on one surface only, the closest surface to that atom.	A set of OR surfaces should have an identical atom list (this is not checked). Group OR surfaces together based on their order.
AND	Energy from each surface is imposed on an atom.	.

Spherical harmonics surfaces can be constructed from ms (Mike Connolly) srf files, using the program SPHINX (Nelson Max & Elizabeth Getzoff, © Scripps Clinic & Research Foundation).

The surf record in the descriptor has the form:

surf	Nsurf	n	qcutoff
	surfi	ksurfi	ti	surforder	surftype	Nj
	xc	yc	zc
		i	j	Cij
		...	...	...
		atomj	...
	...	...	...	...	...	...

The record starts with the keyword surf followed by the number of surfaces N_surf, the power n and the angle cutoff q_cutoff. The spherical harmonics are recalculated only when certain angular parameters have changed by more than q_cutoff.. Following the header line are N_surf lists:

Each list consists of the surface number surf_i, the force constant k_surfi, the thickness of that surface t_i, the surface order surf_order, the surface type surf_type and the number of atoms N_j. The list continues with the coordinates of the center of the surface x_c, y_c and z_c, then the listing of the spherical harmonic coefficients:

The spherical harmonic coefficients must be listed in the following specific way, first the indices i and j, then the coefficient C_ij, with i running from 0 to surf_order and j, the inner index, running from 1 to 2i+1.

The list for surf_i is concluded with a listing of the N_j atoms atom_j that are associated with the surface.

The surface type surf_type is a code that is interpreted in the following way:

surftype	Number of Surfaces	Positioning of Atoms	Combination of Surfaces
0	none	ignored	none
1	single	inclusion	AND
-1	single	exclusion	AND
2 to 9998	sets of	inclusion	OR
-2 to -9998	sets of	exclusion	OR

Example:

surf   1   2   0.001

1   50   10   2   1   9
 
9.7199   57.231   0.96117
 
0   1   195.2891693115
1   1   -10.7412862778
1   2    -1.9537516832
1   3    -1.3621480465
2   1    -9.7586975098
2   2    -4.4064025879
2   3     6.7076225281
2   4    -1.5868632793
2   5    -5.5846691132
 
1   12   13   24   25   62   75   89   93

The header line starts with the keyword surf, then declares 1 surface, a power of 2 and an angular cutoff of 0.001 radians (which effectively means no angular cutoff).

In the first surface, the force constant is 50 CEU/Ų, the surface thickness is 10Å, the surface order is 2, the surface type is 1 and there are 9 atoms associated with that surface. The coordinates for the center of the surface are listed next. Then, the listing of indices and the spherical harmonics coefficients. The first index runs from 0 to 2 (the surface order). The second index runs from 1 to twice the first index plus 1. Following the coefficients are the nine atoms that are associated with this surface.

If there are more than one surface, the listing for the other surfaces would follow in the same manner.