\begin{table}%t2
\caption{\label{tab_param}Torsion-rotation parameters needed for the global fit of
transitions involving $v_{\rm t} = 0$ and $v_{\rm t} = 1$ torsional energy levels of methyl formate (H$^{12}$COO$^{12}$CH$_3$) and torsion-rotation parameters needed for the global fit of transitions involving $v_{\rm t} = 0$  $^{13}$C$_2$-methyl formate   (HCOO$^{13}$CH$_3$).}
\par
%\centerline
{   
\begin{tabular}{cccccccccc}
\hline\hline           
 $nlm^{a}$ & Operator$^{b}$ & Parameter & HCOO$^{12}$CH$_3^{c}$ &
 HCOO$^{13}$CH$_3^{d}$ & $nlm$ & Operator & Parameter &
 HCOO$^{12}$CH$_3^{c}$ & HCOO$^{13}$CH$_3^{d}$\\
\hline
220 & $(1 - \cos 3 \gamma)/2$ & $V_3$ & 370.924(113) & 407.1549(147)$^{g}$ &
404 & --$P^4$ & $D_J$ & 0.42854(455) ~ 10$^{-6}$ & 0.15312(163) ~ 10$^{-6}$ 
\\
&$P_{\gamma}^2$ & $F$ & 5.49038(129) & 5.69168218$^{e}$ && --$P^2$ $P_{\rm a}^2$
& $D_{JK}$ & --0.19285(527) ~ $10^{-5}$  & 0.21223(170) ~ $10^{-5}$ 
\\
211& $P_{\gamma}$ $P_{\rm a}$ & $\rho$ & 0.08427127(723) & 0.0845207(106) && --$P_{\rm a}^4$ &
$D_K$ & 0.36534(594) ~ $10^{-5}$ & --0.17369(181) ~ $10^{-5}$ 
\\
202& $P_{\rm a}^2$ & A$^{\rm RAM}$ & 0.5884101(188) & 0.5857484(245) && --2$P^2$
$(P_{\rm b}^2- P_{\rm c}^2)$ & $\delta_J$ & 0.17990(227) ~ $10^{-6}$ & 0.39739(813) ~
$10^{-7}$ 
\\
&$P_{\rm b}^2$ & $B^{\rm RAM}$ & 0.3082455(179) & 0.2959971(182) && $-\{P_{\rm a}^2,(P_{\rm b}^2 -
P_{\rm c}^2)\}$ & $\delta_K$ & 0.28824(900) ~ $10^{-6}$ & 0.108794(621) ~ $10^{-5}$ 
\\
& $P_{\rm c}^2$ & $C^{\rm RAM}$ & 0.17711843(416) & 0.1729010(134) &&  $P^2 (P_{\rm a}
P_{\rm b} + P_{\rm b} P_{\rm a})$ & $D_{{\rm ab}J}$ & $0.0^{f}$  & 0.24287(221) ~ $10^{-6}$ 
\\
& $(P_{\rm a} P_{\rm b} + P_{\rm b} P_{\rm a})$ & $D_{\rm ab}$ & --0.1649794(162) & --0.1573691(747) &&
$(P_{\rm a}^3 P_{\rm b} + P_{\rm b} P_{\rm a}^3)$ & $D_{{\rm ab}K}$ & 0.20747(108) ~ $10^{-5}$ & 0.13608(491) ~ $10^{-5}$ 
\\
440& $P_{\gamma}^4$ & $k_4$ & 0.0004368(184) & $0.0^{f}$  & 642 & $(1-\cos
6 \gamma) P^2$ & $N_v$ & --0.507(127) ~ $10^{-4}$ & $0.0^{f}$  
\\
& $(1 - \cos 6 \gamma)/2 $& $V_6$ & 23.9018(636) & $0.0^{f}$  & & $(1 - \cos
6 \gamma) (P_{\rm b}^2- P_{\rm c}^2)$ & $c_{11}$ & --0.0014751(202) & $0.0^{f}$  
\\
431& $P_{\gamma}^3 P_{\rm a}$ & $k_3$ & --0.00012758(711) & $0.0^{f}$  && $2
P_{\gamma}^4 (P_{\rm b}^2 - P_{\rm c}^2)$ & $c_3$ & 0.45962(750) ~ $10^{-6}$ & $0.0^{f}$ 
\\
422& $P_{\gamma}^2 P^2$ & $G_v$ & 0.2709(432) ~ $10^{-5}$ & 0.4682(101) ~
$10^{-4}$ & 624 &$(1 - \cos 3 \gamma) P^4$ & $f_v$ & 0.9957(441) ~ $10^{-7}$
& $0.0^{f}$  
\\
& $2 P_{\gamma}^2 (P_{\rm b}^2- P_{\rm c}^2) $& $c_1$ & 0.000018117(264) &
$0.0^{f}$  && $(1 - \cos 3 \gamma) (P_{\rm b}^2- P_{\rm c}^2) P^2$ & $c_{2J}$ &
 0.5483(445)~ $10^{-7}$ & $0.0^{f}$  
 \\
 & $\sin 3 \gamma (P_{\rm a} P_{\rm c} + P_{\rm c} P_{\rm a})$ & $D_{\rm ac}$ & --0.0068896(540) &
--0.0040623(839) && $(1 - \cos 3 \gamma) \{P_{\rm a}^2, (P_{\rm b}^2 - P_{\rm c}^2)\}$ &
$c_{2K}$ & 0.24458(404) ~ $10^{-6}$ & $0.0^{f}$  
\\
& $(1 - \cos 3 \gamma) P^2$ & $F_v$ & --0.0025827(184) & --0.0007557(425) &&
$2 P_{\gamma}^2 (P_{\rm b}^2 - P_{\rm c}^2) P^2$ & $c_{1J}$ & 0.17386(211) ~ $10^{-8}$
& $0.0^{f}$  
\\
& $(1 - \cos 3 \gamma) P_{\rm a}^2$ & $k_5$ & 0.0112949(386) & 0.0124250(566) &&
$(1 - \cos 3 \gamma) (P_{\rm a} P_{\rm b} + P_{\rm b} P_{\rm a}) P^2$ & $d_{{\rm ab}J}$ & --0.12488(883) ~ $10^{-6}$ & 0.9060(708) ~ $10^{-7}$ 
\\
&$(1 - \cos 3 \gamma)(P_{\rm b}^2- P_{\rm c}^2)$ & $c_2$ & 0.0012608(253) & $0.0^{f}$ 
&& $(1- \cos 3 \gamma) (P_{\rm a}^3 P_{\rm b} + P_{\rm b} P_{\rm a}^3)$ & $d_{{\rm ab}K}$ & 0.19649(625) ~ $10^{-6}$ & 0.3349(260) ~ $10^{-6}$ 
\\
& $(1 - \cos 3 \gamma)(P_{\rm a} P_{\rm b} + P_{\rm b} P_{\rm a})$ &$d_{\rm ab}$
&--0.0063031(176)&--0.013852(236) &&$(1 - \cos 3 \gamma) P_{\rm a}^2 P^2$ &
$k_{5J}$ & --0.5853(125) ~ $10^{-6}$ & $0.0^{f}$ 
\\
&$P_{\gamma}^2 P_{\rm a}^2$ & $k_2$ & --0.2837(166) ~ $10^{-4}$ & $0.0^{f}$  &
633& $P_{\gamma}^3 P^2 P_{\rm a}$ & $k_{3J}$ & 0.7061(198) ~ $10^{-7}$ & $0.0^{f}$  
\\
& $P_{\gamma}^2 (P_{\rm a} P_{\rm b} + P_{\rm b} P_{\rm a})$ & $\Delta_{\rm ab}$ & --0.8874(434)
~ $10^{-5}$ & --0.16792(565) ~ $10^{-3}$ && $P_{\gamma}^3 P_{\rm a}^3$ & $k_{3K}$ &
--0.8230(461) ~ $10^{-7}$ & $0.0^{f}$  
\\
& $\sin 3 \gamma (P_{\rm b} P_{\rm c} + P_{\rm c} P_{\rm b})$ & $D_{\rm bc}$ & $0.0^{f} $ &
0.0010563(383) && $P_{\gamma}^3 \{P_{\rm a}, (P_{\rm b}^2 - P_{\rm c}^2)\}$ & $c_{12}$ & --0.6946(110) ~
$10^{-7}$ & $0.0^{f} $ 
\\
413 & $P_{\gamma} P_{\rm a} P^2$ & $L_v$ & 0.3932(110) ~
$10^{-5}$ & --0.2045(247) ~ $10^{-5}$ && $P_{\gamma}^3 \{P_{\rm a}^2, P_{\rm b}\}$ &
$\delta\delta_{\rm ab}$ & --0.61998(808) ~ $10^{-7}$ & $0.0^{f}$  
\\
& $P_{\gamma} P_{\rm a}^3$ & $k_1$ & --0.000000596(279) & $0.0^{f}$  & 606 & $P^6$ &
$H_J$ & 0.333(35) ~ $10^{-12}$ & --0.31(1) ~ $10^{-13}$ 
\\
& $P_{\gamma} \{P_{\rm a},(P_{\rm b}^2 - P_{\rm c}^2)\}$ & $c_4$ & 0.1100(561) ~ $10^{-6}$ &
0.39452(688) ~ $10^{-5}$ && $P^4 P_{\rm a}^2 $& $H_{JK}$ & 0.15998(570) ~
$10^{-10}$ & $0.0^{f}$  
\\
& $P_{\gamma} \{P_{\rm a}^2, P_{\rm b}\}$ & $\delta_{\rm ab}$ & --0.10141(145) ~ $10^{-4}$
&0.1707(107) ~ $10^{-4}$ && $P^2 P_{\rm a}^4$ & $H_{KJ}$ & --0.7620(187) ~
$10^{-10}$ & $0.0^{f} $ 
\\
&&&&&&$P_{\rm a}^6$ & $H_K$ & 0.9098(281) ~ $10^{-10}$ & $0.0^{f}$  
\\
&&&&&& $P^2 \{P_{\rm a}^2, (P_{\rm b}^2 - P_{\rm c}^2)\}$ & $h_{JK}$ &  $0.0^{f}$  & 0.1130(25) ~ $10^{-11}$ 
\\ 
&&&&&826& $(1 - \cos 3 \gamma) (P_{\rm b}^2 - P_{\rm c}^2) P^4$ & $c_{2JJ}$ &
0.1746(201) ~ $10^{-11}$ & $0.0^{f}$  
\\
&&&&&844&2 $P_{\gamma}^4 (P_{\rm b}^2 - P_{\rm c}^2) P^2$ & $c_{3J}$ & --0.29116(514) ~
$10^{-10}$ & $0.0^{f}$  
\\
\hline 
\end{tabular}}
 \medskip
\par
$^{a}$ Notation from \citet{ilyushin2003}; $n = l+m$,
  where $n$ is the total order of the operator, $l$ is the order of the
  torsional part and $m$ is the order of the rotational part. 
$^{b}$ Notation from   \citet{ilyushin2003}. $\{A, B\}=AB+BA$. The product of the parameter
  and operator from a given row yields the term actually used in the
  vibration-rotation-torsion Hamiltonian, except for $F$, $\rho$ and
  $A$, which occur in the Hamiltonian in the form $F(P_{\gamma}- \rho P_{\rm a})^2 + A^{\rm RAM} P_{\rm a}^2$.
$^{c}$ Values of the parameters in cm$^{-1}$, except for
  $\rho$ which is unitless, for the normal species from a fit of $v_{\rm t}
  = 0$ and $v_{\rm t} = 1$ data (from \citealt{carvajal2007}). The 3496 MW lines
  from $v_{\rm t} = 0$ fit with a standard deviation of 94~kHz and the 774
  MW lines from $v_{\rm t} = 1$ fit with a standard deviation of 84 kHz.  
$^{d}$ Values of the parameters from the present fit
  for the ground torsional state  $v_{\rm t} = 0$ of $^{13}$C$_2$ methyl formate. All values are in
  cm$^{-1}$, except for $\rho$ which is unitless. Statistical
  uncertainties are given in parentheses in units of the last quoted
  digit.   
$^{e}$ The internal rotation constant $F$ of
    $^{13}$C$_2$ methyl formate was kept fixed to the  ab initio 
    value calculated in the equilibrum structure (see Sect.~\ref{subsec-fit}).
$^{f}$ Kept fixed.
$^{g}$ Effective value, see text.
\end{table}