Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exchange splitting of the interaction energy and the multipole expansion
  of the wave function   The exchange splitting $J$ of the interaction energy of the hydrogen atom
with a proton is calculated using the conventional surface-integral formula
$J_{\textrm{surf}}[\varphi]$, the volume-integral formula of the
symmetry-adapted perturbation theory $J_{\textrm{SAPT}}[\varphi]$, and a
variational volume-integral formula $J_{\textrm{var}}[\varphi]$. The
calculations are based on the multipole expansion of the wave function
$\varphi$, which is divergent for any internuclear distance $R$. Nevertheless,
the resulting approximations to the leading coefficient $j_0$ in the large-$R$
asymptotic series $J(R) = 2 e^{-R-1} R ( j_0 + j_1 R^{-1} + j_2 R^{-2} +\cdots
) $ converge, with the rate corresponding to the convergence radii equal to 4,
2, and 1 when the $J_{\textrm{var}}[\varphi]$, $J_{\textrm{surf}}[\varphi]$,
and $J_{\textrm{SAPT}}[\varphi]$ formulas are used, respectively. Additionally,
we observe that also the higher $j_k$ coefficients are predicted correctly when
the multipole expansion is used in the $J_{\textrm{var}}[\varphi]$ and
$J_{\textrm{surf}}[\varphi]$ formulas. The SAPT formula
$J_{\textrm{SAPT}}[\varphi]$ predicts correctly only the first two
coefficients, $j_0$ and $j_1$, gives a wrong value of $j_2$, and diverges for
higher $j_n$. Since the variational volume-integral formula can be easily
generalized to many-electron systems and evaluated with standard basis-set
techniques of quantum chemistry, it provides an alternative for the
determination of the exchange splitting and the exchange contribution of the
interaction potential in general.

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The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph