The Dealiasing Function File

When Jaguar fits a function’s grid point values to a basis set to find the applicable basis set coefficients for the function, it uses dealiasing functions to reduce errors. The dealiasing functions span the function space determined by the grid more completely than the basis functions, so a function on the grid can be better described using the dealiasing functions than by the basis functions alone. The basis set coefficients for the function can then be determined by using the overlap between the dealiasing functions and the basis set functions, which is determined analytically.

Some basis functions die off slowly and require long-range functions centered on each atom in the molecule, while others die off quickly over distance and can be described with short-range dealiasing functions centered on the nearby atoms. The latter type can employ different dealiasing functions, depending on the distance between the atom upon which the relevant basis function is centered and the atom upon which the short-range dealiasing functions are to be centered. If the atoms are the same, “home atom” dealiasing functions are used; otherwise, the distance between the two atoms determines whether the dealiasing functions used should be those for first-order or one of the other higher-order neighbors.1 To see this connectivity information for a system, set ip12 = 2 in the gen section. If the two atoms are further away than the farthest neighbor range specified, no dealiasing functions on one atom are used in calculating the contribution of a short-range basis function centered on the other atom.

The dealiasing functions themselves are simply Gaussian basis functions: s-type, p-type, and so on. Uncontracted dealiasing functions are formed by specifying the exponent of the Gaussian function. Contracted dealiasing functions are defined as linear combinations of the appropriate type of functions; the coefficients and exponents for the linear combination are the same as those used in the basis set for the contracted basis functions for the relevant function types (1s, 2s, 2p_x, etc.). Thus, a dealiasing uncontracted function can be specified with the type (s, p, d, etc.) and the exponent desired for the Gaussian, while a contracted Gaussian function can be specified with the type and a reference to the desired set of contraction coefficients and exponents.

Dealiasing Function File Format and Description describes the file that determines the dealiasing functions for a calculation. Sets of dealiasing functions must be provided for each grid used in the calculation. Comments about a sample file refer to the sample .daf file in Sample Dealiasing Function File.