The phrase "auxiliary basis" is correct and usable in written English.
It can be used in contexts related to support systems, frameworks, or additional resources that assist a primary function or structure.
Example: "The project was built on an auxiliary basis to ensure that all necessary resources were available for the main objectives."
Alternatives: "supporting framework" or "supplementary foundation".
We instead use the free-space Green's kernel for the near field, add auxiliary basis functions for the far field, and enforce periodicity in an expanded linear system; this is robust for all parameters.
Resolution of identity (RI-J) and chain of spheres (COSX) approximations were utilized with the equivalent quality auxiliary basis set.
These "density-based QMFFs" prefit an accurate ab initio electron density with an auxiliary basis that interacts through a density-overlap model and is allowed to respond under the principle of chemical potential equalization.
In this paper, we study different ways of treating singularities, and in particular, the method of auxiliary mapping coupled with the use of supplementary basis functions.
Among the various ways of doing so (through supplementary basis functions, eigenfunction expansions, and graded meshes), the method of auxiliary mapping proves to be particularly effective.
To remove the jagged edges caused by the appearance of the sun in the sea-skyline (which causes target detection errors), introduce the image brightness as an auxiliary judgment basis.
V nZ-F12 is used herein due to better availability of auxiliary F12 basis sets for Br, I and At.
Periodizing then combines fast multipole summation of nearest neighbors with an auxiliary global Helmholtz basis expansion to represent the distant contributions, and enforcing quasiperiodicity and radiation conditions on the unit cell walls.
On this basis, the auxiliary device to impress the external force during LO bending was implemented.
These auxiliary domains are the basis for the common classification of remodelers into four subfamilies: SWI/SNF, ISWI, CHD, and INO80 (Clapier and Cairns, 2009).
53 For density functional calculations, resolution of the identity (RI) approximation with the auxiliary TZV/J Coulomb fitting basis sets and PBE functional were employed.
