Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact factorization-based density functional theory of electrons and
  nuclei   The ground state energy of a system of electrons and nuclei is proven to be a
variational functional of the conditional electronic density $n_R(\mathbf{r})$,
the nuclear wavefunction $\chi(R)$ and an induced vector potential $A_{\mu}(R)$
and quantum geometric tensor $\mathcal{T}_{\mu\nu}(R)$ derived from the
conditional electronic wavefunction $\Phi_R(r)$ over nuclear configuration
space, where $r=\mathbf{r}_1,\mathbf{r}_2,\ldots$ are electronic coordinates
and $R=\mathbf{R}_1,\mathbf{R}_2,\ldots$ are nuclear coordinates. The ground
state $(n_R,\chi,A_{\mu},\mathcal{T}_{\mu\nu})$ can be calculated by solving
self-consistently (i) conditional Kohn-Sham equations containing an effective
potential $v_{\rm s}(\mathbf{r})$ that depends parametrically on $R$, (ii) the
Schr\"odinger equation for $\chi(R)$ and (iii) Euler-Lagrange equations that
determine $\mathcal{T}_{\mu\nu}$. The theory is applied to the $E\otimes e$
Jahn-Teller model.

2
The categories of this paper are: math
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg