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Home All issues Volume 500 / No 3 (June IV 2009) A&A, 500 3 (2009) 1109-1118 Full HTML
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Table 2:

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 (H12COO12CH3) and torsion-rotation parameters needed for the global fit of transitions involving $v_{\rm t} = 0$ 13C2-methyl formate (HCOO13CH3).
nlma Operatorb Parameter HCOO12CH3c HCOO13CH3d nlm Operator Parameter HCOO12CH3c HCOO13CH3d
220 $(1 - \cos 3 \gamma)/2$ V3 370.924(113) 407.1549(147)g 404 -P4 DJ 0.42854(455)   10-6 0.15312(163)   10-6
  $P_{\gamma}^2$ F 5.49038(129) 5.69168218e   -P2 $P_{\rm a}^2$ DJK -0.19285(527)   10-5 0.21223(170)   10-5
211 $P_{\gamma}$ $P_{\rm a}$ $\rho$ 0.08427127(723) 0.0845207(106)   - $P_{\rm a}^4$ DK 0.36534(594)   10-5 -0.17369(181)   10-5
202 $P_{\rm a}^2$ A $^{\rm RAM}$ 0.5884101(188) 0.5857484(245)   -2P2 $(P_{\rm b}^2- P_{\rm c}^2)$ $\delta_J$ 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)   $P^2 (P_{\rm a} P_{\rm b} + P_{\rm b} P_{\rm a})$ $D_{{\rm ab}J}$ 0.0f 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 $P_{\gamma}^4$ k4 0.0004368(184) 0.0f 642 $(1-\cos 6 \gamma) P^2$ Nv -0.507(127)   10-4 0.0f
  $(1 - \cos 6 \gamma)/2 $ V6 23.9018(636) 0.0f   $(1 - \cos 6 \gamma) (P_{\rm b}^2- P_{\rm c}^2)$ c11 -0.0014751(202) 0.0f
431 $P_{\gamma}^3 P_{\rm a}$ k3 -0.00012758(711) 0.0f   $2 P_{\gamma}^4 (P_{\rm b}^2 - P_{\rm c}^2)$ c3 0.45962(750)   10-6 0.0f
422 $P_{\gamma}^2 P^2$ Gv 0.2709(432)   10-5 0.4682(101)   10-4 624 $(1 - \cos 3 \gamma) P^4$ fv 0.9957(441)   10-7 0.0f
  $2 P_{\gamma}^2 (P_{\rm b}^2- P_{\rm c}^2) $ c1 0.000018117(264) 0.0f   $(1 - \cos 3 \gamma) (P_{\rm b}^2- P_{\rm c}^2) P^2$ c2J 0.5483(445)  10-7 0.0f
  $\sin 3 \gamma (P_{\rm a} P_{\rm c} + P_{\rm c} P_{\rm a})$ $D_{\rm ac}$ -0.0068896(540) -0.0040623(839)   $(1 - \cos 3 \gamma) \{P_{\rm a}^2, (P_{\rm b}^2 - P_{\rm c}^2)\}$ c2K 0.24458(404)   10-6 0.0f
  $(1 - \cos 3 \gamma) P^2$ Fv -0.0025827(184) -0.0007557(425)   $2 P_{\gamma}^2 (P_{\rm b}^2 - P_{\rm c}^2) P^2$ c1J 0.17386(211)   10-8 0.0f
  $(1 - \cos 3 \gamma) P_{\rm a}^2$ k5 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
  $(1 - \cos 3 \gamma)(P_{\rm b}^2- P_{\rm c}^2)$ c2 0.0012608(253) 0.0f   $(1- \cos 3 \gamma) (P_{\rm a}^3 P_{\rm b} + P_{\rm b} P_{\rm a}^3)$ $d_{{\rm ab}K}$ 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)   $(1 - \cos 3 \gamma) P_{\rm a}^2 P^2$ k5J -0.5853(125)   10-6 0.0f
  $P_{\gamma}^2 P_{\rm a}^2$ k2 -0.2837(166)   10-4 0.0f 633 $P_{\gamma}^3 P^2 P_{\rm a}$ k3J 0.7061(198)   10-7 0.0f
  $P_{\gamma}^2 (P_{\rm a} P_{\rm b} + P_{\rm b} P_{\rm a})$ $\Delta_{\rm ab}$ -0.8874(434)   10-5 -0.16792(565)   10-3   $P_{\gamma}^3 P_{\rm a}^3$ k3K -0.8230(461)   10-7 0.0f
  $\sin 3 \gamma (P_{\rm b} P_{\rm c} + P_{\rm c} P_{\rm b})$ $D_{\rm bc}$ 0.0f 0.0010563(383)   $P_{\gamma}^3 \{P_{\rm a}, (P_{\rm b}^2 - P_{\rm c}^2)\}$ c12 -0.6946(110)   10-7 0.0f
413 $P_{\gamma} P_{\rm a} P^2$ Lv 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 0.0f
  $P_{\gamma} P_{\rm a}^3$ k1 -0.000000596(279) 0.0f 606 P6 HJ 0.333(35)   10-12 -0.31(1)   10-13
  $P_{\gamma} \{P_{\rm a},(P_{\rm b}^2 - P_{\rm c}^2)\}$ c4 0.1100(561)   10-6 0.39452(688)   10-5   $P^4 P_{\rm a}^2 $ HJK 0.15998(570)   10-10 0.0f
  $P_{\gamma} \{P_{\rm a}^2, P_{\rm b}\}$ $\delta_{\rm ab}$ -0.10141(145)   10-4 0.1707(107)   10-4   $P^2 P_{\rm a}^4$ HKJ -0.7620(187)   10-10 0.0f
            $P_{\rm a}^6$ HK 0.9098(281)   10-10 0.0f
            $P^2 \{P_{\rm a}^2, (P_{\rm b}^2 - P_{\rm c}^2)\}$ hJK 0.0f 0.1130(25)   10-11
          826 $(1 - \cos 3 \gamma) (P_{\rm b}^2 - P_{\rm c}^2) P^4$ c2JJ 0.1746(201)   10-11 0.0f
          844 2 $P_{\gamma}^4 (P_{\rm b}^2 - P_{\rm c}^2) P^2$ c3J -0.29116(514)   10-10 0.0f
a Notation from Ilyushin et al. (2003); 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 Ilyushin et al. (2003). $\{A, B\}=AB+BA$. 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 Carvajal et al. 2007). 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 13C2 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 13C2 methyl formate was kept fixed to the ab initio value calculated in the equilibrum structure (see Sect. 3.2). f Kept fixed. g Effective value, see text.

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