# What is the definition of energy-independent basis?

I am reading this article by Zatsarinny and Fischer [1]. At some point they span a wave function $$\Psi_{E}$$ in terms of energy independent basis

$$\Psi_{E}=\sum_{k} A_{E k} \Psi_{k}$$

For example, The Structures of Binary Compounds mentions that LCAO is an energy-independent basis [2] (Google Books):

The non-linearity of the one-electron eigenvalue problem represents a considerable complication of this scheme, which does not occur if an energy-independent basis set, such as the LCAO, is used.

What is the energy-independent basis?

### Reference

1. Zatsarinny, O.; Fischer, C. F. The Use of Basis Splines and Non-Orthogonal Orbitals in $$R$$-Matrix Calculations: Application to Li Photoionization. J. Phys. B: At. Mol. Opt. Phys. 2000, 33 (3), 313–341. DOI: 10.1088/0953-4075/33/3/303.
2. The Structures of Binary Compounds; Boer, F. R. de, Pettifor, D. G., Hafner, J., Eds.; Cohesion and structure; North-Holland: Amsterdam, 1989. ISBN 978-0-444-87478-8.