Table 1
Fitted parameters of the RAM Hamiltonian for 13C acetaldehyde isotopologs.
Operator1 |
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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) × 10−5 | 0.10255(12) × 10−5 |
{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.
{ 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 .
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