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Table 1

Fitted parameters of the RAM Hamiltonian for 13C acetaldehyde isotopologs.

Operator1 Parameter 12CH312CHO 13CH312CHO 12CH313CHO
Value3 (cm-1) Value3 (cm-1) Value3 (cm-1)

pα2 220 F 7.56708175(35) 7.5652791(19) 7.5068034(55)
(1/2) (1−cos(3α)) 220 V 3 407.59768(20) 407.91172(18) 407.58042(26)
pαPa 211 ρ 0.328632673(20) 0.328300981(35) 0.322541154(65)
Pa2 202 A RAM 1.884881309(61) 1.88013742(13) 1.848976496(63)
Pb2 202 B RAM 0.348706489(16) 0.337726802(58) 0.348720666(61)
Pc2 202 C RAM 0.3031840478(44) 0.294817724(11) 0.302179145(18)
{Pa,Pb} 202 D ab 0.122669037(94) 0.11817144(38) 0.12175149(39)
(1/2) (1−cos(6α)) 440 V 6 −11.63964(50) −11.67172(20) −11.71571(65)
pα4 440 F m 0.424416(38) × 10-3 0.427829(96) × 10-3 0.42834(12) × 10-3
pα3Pa 431 ρ m 0.832163(52) × 10-3 0.82821(11) × 10-3 −0.81162(16)× 10-3
P2(1−cos(3α)) 422 V 3 J 0.5577894(41) × 10-3 0.524776(16) × 10-3 0.529795(22) × 10-3
Pa2(1−cos(3α)) 422 V 3 K 0.19313906(98) × 10-1 0.1898291(17) × 10-1 0.1953217(29) × 10-1
(Pb2 Pc2)(1−cos(3α)) 422 V 3 bc 0.2114597(52) × 10-3 0.192215(19) × 10-3 0.213208(15) × 10-3
(1/2){Pa,Pb}(1−cos(3α)) 422 V 3 ab 0.4235363(70) × 10-2 0.405222(33) × 10-2 0.443922(36) × 10-2
pα2P2 422 F J 0.291704(53) × 10-5 0.26533(11) × 10-5 0.31536(19) × 10-5
pα2Pa2 422 F K 0.982545(30) × 10-3 0.972792(46) × 10-3 0.944979(89) × 10-3
pα2(Pb2 Pc2) 422 F bc 0.14720(12) × 10-5 0.13745(31) × 10-5 0.16632(37) × 10-5
(1/2){Pa,Pc}sin(3α) 422 D 3 ac 0.1405503(49) × 10-1 0.135881(17) × 10-1 0.142957(18) × 10-1
(1/2){Pb,Pc}sin(3α) 422 D 3 bc 0.59173(13) × 10-3 0.55489(43) × 10-3 0.63859(48) × 10-3
pαPaP2 413 ρ J 0.958253(42) × 10-5 0.91984(11) × 10-5 0.91075(15) × 10-5
pαPa3 413 ρ K 0.571407(12) × 10-3 0.564681(12) × 10-3 0.549548(31) × 10-3
(1/2){Pa,(Pb2 Pc2)}pα 413 ρ bc 0.5536(12) × 10-6 0.5763(36) × 10-6 0.2887(35) × 10-6
P4 404 Δ J 0.3244101(54) × 10-6 0.306742(20) × 10-6 0.325255(24) × 10-6
P2Pa2 404 Δ JK 0.581770(50) × 10-5 0.556079(86) × 10-5 0.571647(79) × 10-5
Pa4 404 Δ K 0.1308173(26) × 10-3 0.1292582(29) × 10-3 0.1263888(56) × 10-3
2P2(Pb2 Pc2) 404 δ J 0.778472(23) × 10-7 0.709225(70) × 10-7 0.786517(69) × 10-7
{Pa2,(Pb2 Pc2)} 404 δ K 0.94268 (17) × 10-6 0.105094(90) × 105 0.10255(12) × 105
{Pa,Pb}P2 404 D abJ 0.867443(32) × 10-6 0.81273(20) × 10-6 0.85179(14) × 10-6
{Pa3,Pb} 404 D abK 0.30498(25) × 10-5 0.29239(46) × 10-5 0.27116(33) × 10-5

Notes. A complete version up to 8th order is available in Table 7.

(1)

{ A,B } = AB + BA; { A,B,C } = ABC + CBA; { A,B,C,D } = ABCD + DCBA. The product of the operator in the first column of a given row and the parameter in the third column of that row gives the term actually used in the torsion-rotation Hamiltonian of the program, except for F, ρ, and ARAM, which occur in the Hamiltonian in the form .

(2)

n = t + r, where n is the total order of the operator, t is the order of the torsional part, and r the order of the rotational part.

(3)

All values are in cm-1, except ρ, which is unitless. Statistical uncertainties are shown as one standard uncertainty in the units of the last two digits.

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