Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Downfolding approaches to electron-ion coupling: Constrained
  density-functional perturbation theory for molecules   Constrained electronic-structure theories enable the construction of
effective low-energy models consisting of partially dressed particles. However,
the interpretation and physical content of these theories is not
straightforward. Here, we carefully explore the properties of downfolding
theories for electron-ion problems, in particular constrained
density-functional perturbation theory (cDFPT). We show that the dipole
selection rules determine whether the partially dressed phonons satisfy
Goldstone's theorem, and we prove that electronic screening always lowers the
phonon frequencies. We illustrate the theory with cDFPT calculations for
minimal example systems: the nitrogen and benzene molecule as well as graphene.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga