The vlat energy is the sum over N_atom atoms where for each atom, the energy and gradient depends on the position of the atom in space. Space is divided into two regions, the region inside a unit cell centered on the origin and the space outside. The unit cell has sides of lengths a, b, and c and angles alpha, beta, and gamma, and could be further divided by L, M, and N times into volume elements or voxels of sides of lengths a/L, b/M and c/N. Each voxel would have associated with it an energy and gradients. If an atom of atom type j is within the unit cell and is therefore in a voxel, let us say i, it will be credited with the energy W_jE_i and gradients W_ju_i, W_j v_i, and W_j w_i. E_i, u_i, v_i and w_i are values stored for that voxel and these numbers are based on the rectangular laboratory coordinates and not on the possibly oblique coordinate system of the unit cell. W_j is a weighting factor based on the atom type. The lowest energy stored is E_min and the highest energy is E_max. If the atom is outside the unit cell, it will be credited with an energy of W_j E_max and a gradient that directs the atom towards a default destination (x_o,y_o,z_o) which again is expressed relative to the rectangular laboratory coordinates. The components of the gradient are:

( x - xo )
( y - yo ) W j ( Emax - Emin ) / [ ( x - xo )2 + ( y - yo )2 + ( z - zo )2 ]
( z - zo )
   

This term is further scaled by a factor K which has a preset value of 1 and which can be modified during a simulation. The vlat record in the descriptor file has the form

vlat	L	M	N	Ntype
	a	b	c
	alpha	beta	gamma
	xo	yo	zo
	Emin	Emax	Dmin	Dmax
	Wj	...
	Ei	ui	vi	wi
	...	...	...	...

The vlat record starts with the keyword vlat followed by the number of divisions of the unit cell L, M and N and the number of atom types N_type.The last number must be at least as large as the largest atom type stored in the type record. Following the header line are the cell dimensions a, b, and c and angles alpha, beta and gamma. This is followed by the coordinates of the default destination x_o, y_o and z_o. Next are the minimum and maximum energies E_min and E_max and two other numbers D_min and D_max which are not used in the energy calculation. This is followed by N_type weights W_j. Finally, the energy E_i and the three components of the gradient u_i, v_i, and w_i are listed for LMN voxels.

The energies and gradients are listed for the three-dimensional array of voxels with the first index varying fastest, i.e., (1,1,1), (2,1,1), (3,1,1), ..., ( L,1,1), (1,2,1), (2,2,1), ..., ( L, M,1), ..., ( L, M,N). The weights can have any values including negative ones but should be limited to the range of 0 to 1. With a weight of 0, this atom type will not be affected by this term. With a weight of 1 the full effect of this term is felt.

One use of the vlat term is for refinement of a structure subject to a low resolution electron density map. A procedure to translate electron density to a vector lattice elec2vlat is available. This procedure will save the minimum and maximum electron densities within the vlat record as D_min and D_max and the electron density can be partly recovered from the vector lattice term.

The vector lattice term can be uniformly scaled during a simulation. See the documentation for the yammp scripting language. The location of every atom within the vector lattice can be reported. See the exam documentation.

Example

vlat    2        2        2        3
 
        1000     1000     1000
        1.0472   2.094    1.5708
        0        0        0
       -249.28   249.28   1        1
 
        1        1        1
 
 249.28   -0.332   -0.997   -0.470
-249.28    0        0        0
 249.28   -0.997    0.997   -1.410
 249.28    0        0.997    0
 249.28   -0.997   -0.332    0.470
 249.28   -0.499    0.499    0.705
-249.28    0        0        0
 249.28   -0.166    0.499    0.235

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A vlat record with a unit cell of equal sides 1000Å and angles 60° (1.0472 radian), 120° (2.094 radian) and 90° (1.5708 radian), subdivided into two on each side and therefore into eight voxels. The default destination is the origin (0,0,0). The energy ranges from a minimum of -0.6 kcal/mol (-249.28 CEU) to 0.6 kcal/mol (249.28 CEU). Three weights are given. The minimum energy occurs in two voxels (2,1,1) and (1,2,2) and the gradients for these voxels have zero component values.