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Table A.1

Fitted parameters of the RAM Hamiltonian for the CH3OD molecule.

ntra Par.b Operatorc Valued,e
22,0 (1/2)V3 (1 − cos 3α) 183.171569(21)
22,0 F pα2$\[p_\alpha^2\]$ 17.42797209(17)
21,1 ρ Papα 0.6993446726(21)
20,2 ARAM Pa2$\[P_a^2\]$ 3.675099(14)
20,2 BRAM Pb2$\[P_b^2\]$ 0.783150(12)
20,2 CRAM Pc2$\[P_c^2\]$ 0.733527(12)
20,2 2Dab (1/2){Pa,Pb} 0.055955652(61)
44,0 (1/2)V6 (1 − cos 6α) −0.807349(95)
44,0 Fm pα4$\[p_\alpha^4\]$ −0.2945328(17) × 10−2
43,1 ρm Papα3$\[P_a p_\alpha^3\]$ −0.11189627(44) × 10−1
42,2 V3J P2(1 − cos 3α) −0.2211486(94) × 10−2
42,2 V3K Pa2(1−cos⁡3α)$\[P_a^2(1-\cos 3 \alpha)\]$ 0.125539(11) × 10−1
42,2 V3bc (Pb2−Pc2)(1−cos⁡3α)$\[\left(P_b^2-P_c^2\right)(1-\cos 3 \alpha)\]$ −0.137249(22) × 10−3
42,2 V3ab (1/2){Pa,Pb}(1 − cos 3α) 0.15619469(62) × 10−1
42,2 FJ P2pα2$\[P^2 p_\alpha^2\]$ −0.8417192(26) × 10−4
42,2 FK Pa2pα2$\[P_a^2 p_\alpha^2\]$ −0.16465226(55) × 10−1
42,2 Fbc (Pb2−Pc2)pα2$\[\left(P_b^2-P_c^2\right) p_\alpha^2\]$ −0.8781804(46) × 10−4
42,2 Fab (1/2){Pa,Pb}pα2$\[(1 / 2)\left\{P_a, P_b\right\} p_\alpha^2\]$ 0.123059(61) × 10−3
42,2 D3ac (1/2){Pa,Pc} sin 3α 0.287840(14) × 10−1
41,3 ρJ P2Papα −0.12144162(39) × 10−3
41,3 ρK Pa3pα$\[P_a^3 p_\alpha\]$ −0.10794357(36) × 10−1
41,3 ρbc (1/2){Pa,(Pb2−Pc2)}pα$\[(1 / 2)\left\{P_a,\left(P_b^2-P_c^2\right)\right\} p_\alpha\]$ −0.1589380(32) × 10−3
41,3 ρab (1/2){Pa2,Pb}pα$\[(1 / 2)\left\{P_a^2, P_b\right\} p_\alpha\]$ 0.115410(57) × 10−3
40,4 −ΔJ P4 −0.144728(12) × 10−5
40,4 −ΔJK P2Pa2$\[P^2 P_a^2\]$ −0.46863(83) × 10−4
40,4 −ΔK Pa4$\[P_a^4\]$ −0.26562002(84) × 10−2
40,4 −2δJ P2(Pb2−Pc2)$\[P^2\left(P_b^2-P_c^2\right)\]$ −0.1984984(31) × 10−6
40,4 −2δK (1/2){Pa2,(Pb2−Pc2)}$\[(1 / 2)\left\{P_a^2,\left(P_b^2-P_c^2\right)\right\}\]$ −0.726533(26) × 10−4
40,4 DabJ (1/2)P2{Pa,Pb} −0.69723(14) × 10−6
66,0 (1/2)V9 (1 − cos 9α) 0.1588(23) × 10−1
66,0 Fmm pα6$\[p_\alpha^6\]$ 0.22823(16) × 10−5
65,1 ρmm Papα5$\[P_a p_\alpha^5\]$ 0.150802(69) × 10−4
64,2 V6J P2(1 − cos 6α) −0.6128(78) × 10−4
64,2 V6K Pa2(1−cos⁡6α)$\[P_a^2(1-\cos 6 \alpha)\]$ 0.1056(50) × 10−3
64,2 V6bc (Pb2−Pc2)(1−cos⁡6α)$\[\left(P_b^2-P_c^2\right)(1-\cos 6 \alpha)\]$ −0.28947(72) × 10−4
64,2 V6ab (1/2){Pa,Pb}(1 − cos 6α) −0.2335(10) × 10−4
64,2 FmJ P2pα4$\[P^2 p_\alpha^4\]$ 0.25716(24) × 10−7
64,2 FK Pa2pα4$\[P_a^2 p_\alpha^4\]$ 0.40075(13) × 10−4
64,2 D6ac (1/2){Pa,Pc} sin 6α 0.10499(12) × 10−3
63,3 ρmJ P2Papα3$\[P^2 P_a p_\alpha^3\]$ 0.89234(68) × 10−7
63,3 ρmK Pa3pα3$\[P_a^3 p_\alpha^3\]$ 0.55525(14) × 10−4
63,3 ρ3bc (1/2){Pa,Pb,Pc,pα, sin 3α} 0.17326(13) × 10−5
62,4 V3JJ P4(1 − cos 3α) 0.13288(18) × 10−7
62,4 V3JK P2Pa2(1−cos⁡3α)$\[P^2 P_a^2(1-\cos 3 \alpha)\]$ −0.108198(83) × 10−5
62,4 V3KK Pa4(1−cos⁡3α)$\[P_a^4(1-\cos 3 \alpha)\]$ 0.12335(14) × 10−5
62,4 V3bcJ P2(Pb2−Pc2)(1−cos⁡3α)$\[P^2\left(P_b^2-P_c^2\right)(1-\cos 3 \alpha)\]$ 0.54564(17) × 10−8
62,4 V3bcK (1/2){Pa2,(Pb2−Pc2)}(1−cos⁡3α)$\[(1 / 2)\left\{P_a^2,\left(P_b^2-P_c^2\right)\right\}(1-\cos 3 \alpha)\]$ −0.6019(59) × 10−7
62,4 V3b2c2 (1/2){Pb2,Pc2}cos⁡3α$\[(1 / 2)\left\{P_b^2, P_c^2\right\} \cos 3 \alpha\]$ 0.36950(15) × 10−7
62,4 V3abJ (1/2)P2{Pa,Pb}(1 − cos 3α) −0.34986(11) × 10−6
62,4 V3abK (1/2){Pa3,Pb}(1−cos⁡3α)$\[(1 / 2)\left\{P_a^3, P_b\right\}(1-\cos 3 \alpha)\]$ −0.16693(13) × 10−5
62,4 V3abc2 (1/2){Pa,Pb,Pc2}cos⁡3α$\[(1 / 2)\left\{P_a, P_b, P_c^2\right\} \cos 3 \alpha\]$ −0.41168(30) × 10−6
62,4 FJJ P4pα2$\[P^4 p_\alpha^2\]$ 0.52398(53) × 10−9
62,4 FJK P2Pa2pα2$\[P^2 P_a^2 p_\alpha^2\]$ 0.120708(76) × 10−6
62,4 FKK Pa4pα2$\[P_a^4 p_\alpha^2\]$ 0.426507(90) × 10−4
62,4 FbcJ P2(Pb2−Pc2)pα2$\[P^2\left(P_b^2-P_c^2\right) p_\alpha^2\]$ 0.747(35) × 10−9
62,4 FabJ (1/2)P2{Pa,Pb}pα2$\[(1 / 2) P^2\left\{P_a, P_b\right\} p_\alpha^2\]$ −0.1940(17) × 10−8
62,4 D3acJ (1/2)P2{Pa,Pc} sin 3α −0.21496(33) × 10−6
62,4 D3acK (1/2){Pa3,Pc}sin⁡3α$\[(1 / 2)\left\{P_a^3, P_c\right\} \sin 3 \alpha\]$ −0.27643(22) × 10−5
62,4 D3bcJ (1/2)P2{Pb,Pc} sin 3α −0.1440(78) × 10−7
62,4 D3acb2 (1/2){Pa,Pb2,Pc}sin⁡3α$\[(1 / 2)\left\{P_a, P_b^2, P_c\right\} \sin 3 \alpha\]$ −0.63621(23) × 10−6
62,4 D3bcbc (1/2)({Pb3,Pc}−{Pb,Pc3})sin⁡3α$\[(1 / 2)\left(\left\{P_b^3, P_c\right\}-\left\{P_b, P_c^3\right\}\right) \sin 3 \alpha\]$ −0.15526(13) × 10−7
61,5 ρJJ P4 Papα 0.76489(73) × 10−9
61,5 ρJK P2Pa3pα$\[P^2 P_a^3 p_\alpha\]$ 0.72735(40) × 10−7
61,5 ρKK Pa5pα$\[P_a^5 p_\alpha\]$ 0.173086(31) × 10−4
61,5 ρbcJ (1/2)P2{Pa,(Pb2−Pc2)}pα$\[(1 / 2) P^2\left\{P_a,\left(P_b^2-P_c^2\right)\right\} p_\alpha\]$ 0.1779(33) × 10−8
60,6 ΦJ P6 −0.839(30) × 10−13
60,6 ΦJK P4Pa2$\[P^4 P_a^2\]$ 0.30696(29) × 10−9
60,6 ΦKJ P2Pa4$\[P^2 P_a^4\]$ 0.17819(12) × 10−7
60,6 ΦK Pa6$\[P_a^6\]$ 0.290869(45) × 10−5
60,6 2ϕJ P4(Pb2−Pc2)$\[P^4\left(P_b^2-P_c^2\right)\]$ 0.6901(12) × 10−12
60,6 2ϕJK (1/2)P2{Pa2,(Pb2−Pc2)}$\[(1 / 2) P^2\left\{P_a^2,\left(P_b^2-P_c^2\right)\right\}\]$ 0.102073(94) × 10−8
60,6 2ϕK (1/2){Pa4,(Pb2−Pc2)}$\[(1 / 2)\left\{P_a^4,\left(P_b^2-P_c^2\right)\right\}\]$ 0.2973(18) × 10−8
60,6 Db2c2bc (1/2)({Pb4,Pc2}−{Pb2,Pc4})$\[(1 / 2)\left(\left\{P_b^4, P_c^2\right\}-\left\{P_b^2, P_c^4\right\}\right)\]$ −0.32957(53) × 10−11
60,6 DabJK (1/2)P2{Pa3,Pb}$\[(1 / 2) P^2\left\{P_a^3, P_b\right\}\]$ 0.1662(15) × 10−8
60,6 Dabc4 (1/2){Pa,Pb,Pc4}$\[(1 / 2)\left\{P_a, P_b, P_c^4\right\}\]$ 0.1892(15) × 10−10
88,0 Fmmm pα8$\[p_\alpha^8\]$ 0.2592(24) × 10−8
86,2 V9J P2(1 − cos 9α) 0.3021(47) × 10−3
86,2 V9K Pa2(1−cos⁡9α)$\[P_a^2(1-\cos 9 \alpha)\]$ −0.657(12) × 10−3
86,2 FmmK Pa2pα6$\[P_a^2 p_\alpha^6\]$ −0.5042(33) × 10−7
86,2 D9bc (1/2){Pb,Pc} sin 9α 0.78071(91) × 10−4
85,3 ρmmK Pa3pα5$\[P_a^3 p_\alpha^5\]$ −0.16973(94) × 10−6
85,3 ρ3bcm (1/2){Pa,Pb,Pc,pα3,sin⁡3α}$\[(1 / 2)\left\{P_a, P_b, P_c, p_\alpha^3, \sin 3 \alpha\right\}\]$ −0.770(13) × 10−8
84,4 V6JJ P4(1 − cos 6α) 0.2170(71) × 10−8
84,4 V6JK P2Pa2(1−cos⁡6α)$\[P^2 P_a^2(1-\cos 6 \alpha)\]$ −0.5615(58) × 10−6
84,4 V6KK Pa4(1−cos⁡6α)$\[P_a^4(1-\cos 6 \alpha)\]$ 0.1808(27) × 10−6
84,4 V6bcJ P2(Pb2−Pc2)(1−cos⁡6α)$\[P^2\left(P_b^2-P_c^2\right)(1-\cos 6 \alpha)\]$ 0.14457(44) × 10−8
84,4 V6bcK (1/2){Pa2,(Pb2−Pc2)}(1−cos⁡6α)$\[(1 / 2)\left\{P_a^2,\left(P_b^2-P_c^2\right)\right\}(1-\cos 6 \alpha)\]$ 0.4650(41) × 10−7
84,4 FmKK Pa4pα4$\[P_a^4 p_\alpha^4\]$ −0.2700(13) × 10−6
84,4 D6bcJ (1/2)P2{Pb,Pc} sin 6α −0.461(16) × 10−9
84,4 D6bcbc (1/2)({Pb,Pc3}−{Pb3,Pc})sin⁡6α$\[(1 / 2)\left(\left\{P_b, P_c^3\right\}-\left\{P_b^3, P_c\right\}\right) \sin 6 \alpha\]$ 0.2259(44) × 10−8
84,4 D3acb2m (1/2){Pa,Pb2,Pc,pα2,sin⁡3α}$\[(1 / 2)\left\{P_a, P_b^2, P_c, p_\alpha^2, \sin 3 \alpha\right\}\]$ 0.859(12) × 10−9
83,5 ρmKK Pa5pα3$\[P_a^5 p_\alpha^3\]$ −0.2464(11) × 10−6
83,5 ρ3bcK (1/2){Pa3,Pb,Pc,pα,sin⁡3α}$\[(1 / 2)\left\{P_a^3, P_b, P_c, p_\alpha, \sin 3 \alpha\right\}\]$ 0.4437(26) × 10−7
82,6 V3JJJ P6(1 − cos 3α) −0.576(19) × 10−13
82,6 V3KKK Pa6(1−cos⁡3α)$\[P_a^6(1-\cos 3 \alpha)\]$ −0.3463(78) × 10−9
82,6 V3bcKK (1/2){Pa4,(Pb2−Pc2)}(1−cos⁡3α)$\[(1 / 2)\left\{P_a^4,\left(P_b^2-P_c^2\right)\right\}(1-\cos 3 \alpha)\]$ −0.2770(18) × 10−8
82,6 V3b2c2bc (1/2)({Pb4,Pc2}−{Pb2,Pc4})cos⁡3α$\[(1 / 2)\left(\left\{P_b^4, P_c^2\right\}-\left\{P_b^2, P_c^4\right\}\right) \cos 3 \alpha\]$ 0.7702(54) × 10−12
82,6 V3abJJ (1/2)P4{Pa,Pb}(1 − cos 3α) 0.3300(70) × 10−11
82,6 V3abc4 (1/2){Pa,Pb,Pc4}cos⁡3α$\[(1 / 2)\left\{P_a, P_b, P_c^4\right\} \cos 3 \alpha\]$ 0.1252(17) × 10−10
82,6 FJJJ P6pα2$\[P^6 p_\alpha^2\]$ −0.363(21) × 10−14
82,6 FKKK Pa6pα2$\[P_a^6 p_\alpha^2\]$ −0.13293(51) × 10−6
82,6 D3acJJ (1/2)P4{Pa,Pc} sin 3α −0.2388(78) × 10−11
82,6 D3acKK (1/2){Pa5,Pc}sin⁡3α$\[(1 / 2)\left\{P_a^5, P_c\right\} \sin 3 \alpha\]$ 0.3398(79) × 10−9
82,6 D3bcJJ (1/2)P4{Pb,Pc} sin 3α 0.4091(84) × 10−12
82,6 D3bcKK (1/2){Pa4,Pb,Pc}sin⁡3α$\[(1 / 2)\left\{P_a^4, P_b, P_c\right\} \sin 3 \alpha\]$ 0.2557(16) × 10−7
82,6 D3acb2J (1/2)P2{Pa,Pb2,Pc}sin⁡3α$\[(1 / 2) P^2\left\{P_a, P_b^2, P_c\right\} \sin 3 \alpha\]$ 0.1579(16) × 10−10
82,6 D3acb2K (1/2){Pa3,Pb2,Pc}sin⁡3α$\[(1 / 2)\left\{P_a^3, P_b^2, P_c\right\} \sin 3 \alpha\]$ −0.5322(48) × 10−9
82,6 D3bcbcJ (1/2)P2({Pb3,Pc}−{Pb,Pc3})sin⁡3α$\[(1 / 2) P^2\left(\left\{P_b^3, P_c\right\}-\left\{P_b, P_c^3\right\}\right) \sin 3 \alpha\]$ 0.3740(28) × 10−12
81,7 ρJJJ P6 Papα −0.710(29) × 10−14
81,7 ρKKK Pa7pα$\[P_a^7 p_\alpha\]$ −0.3969(14) × 10−7
80,8 Lj P8 −0.1082(61) × 10−16
80,8 LJJK P6Pa2$\[P^6 P_a^2\]$ −0.355(10) × 10−14
80,8 LK Pa8$\[P_a^8\]$ −0.5083(16) × 10−8
80,8 2lK (1/2){Pa6,(Pb2−Pc2)}$\[(1 / 2)\left\{P_a^6,\left(P_b^2-P_c^2\right)\right\}\]$ −0.254(13) × 10−12
108,2 V12J P2(1 − cos 12α) −0.992(16) × 10−3
108,2 V12bc (Pb2−Pc2)(1−cos⁡12α)$\[\left(P_b^2-P_c^2\right)(1-\cos 12 \alpha)\]$ −0.8712(96) × 10−4
106,4 V9JJ P4(1 − cos 9α) −0.326(18) × 10−8
106,4 V9JK P2Pa2(1−cos⁡9α)$\[P^2 P_a^2(1-\cos 9 \alpha)\]$ 0.2026(32) × 10−5
106,4 V9b2c2 (1/2){Pb2,Pc2}cos⁡9α$\[(1 / 2)\left\{P_b^2, P_c^2\right\} \cos 9 \alpha\]$ 0.544(16) × 10−8
106,4 D9acK (1/2){Pa3,Pc}sin⁡9α$\[(1 / 2)\left\{P_a^3, P_c\right\} \sin 9 \alpha\]$ −0.5240(98) × 10−6
106,4 D6acmK (1/2){Pa3,Pc,pα2,sin⁡6α}$\[(1 / 2)\left\{P_a^3, P_c, p_\alpha^2, \sin 6 \alpha\right\}\]$ 0.1717(33) × 10−7
104,6 V6JJJ P6(1 − cos 6α) −0.551(35) × 10−13
104,6 V6JKK P2Pa4(1−cos⁡6α)$\[P^2 P_a^4(1-\cos 6 \alpha)\]$ 0.8775(30) × 10−9
104,6 V6KKK Pa6(1−cos⁡6α)$\[P_a^6(1-\cos 6 \alpha)\]$ 0.214(14) × 10−9
104,6 V6bcJJ P4(Pb2−Pc2)(1−cos⁡6α)$\[P^4\left(P_b^2-P_c^2\right)(1-\cos 6 \alpha)\]$ −0.808(19) × 10−13
104,6 V6b2c2K (1/2){Pa2,Pb2,Pc2}cos⁡6α$\[(1 / 2)\left\{P_a^2, P_b^2, P_c^2\right\} \cos 6 \alpha\]$ −0.580(19) × 10−10
104,6 D6acKK (1/2){Pa5,Pc}sin⁡6α$\[(1 / 2)\left\{P_a^5, P_c\right\} \sin 6 \alpha\]$ −0.842(15) × 10−8
103,7 ρ3bcKK (1/2){Pa5,Pb,Pc,pα,sin⁡3α}$\[(1 / 2)\left\{P_a^5, P_b, P_c, p_\alpha, \sin 3 \alpha\right\}\]$ 0.1553(41) × 10−11
102,8 V3JKKK P2Pa6(1−cos⁡3α)$\[P^2 P_a^6(1-\cos 3 \alpha)\]$ 0.548(14) × 10−13
102,8 D3b3c3J (1/2)P2{Pb3,Pc3}sin⁡3α$\[(1 / 2) P^2\left\{P_b^3, P_c^3\right\} \sin 3 \alpha\]$ −0.977(46) × 10−16
128,4 V12JK P2Pa2(1−cos⁡12α)$\[P^2 P_a^2(1-\cos 12 \alpha)\]$ −0.408(11) × 10−5
126,6 V9JKK P2Pa4(1−cos⁡9α)$\[P^2 P_a^4(1-\cos 9 \alpha)\]$ −0.23634(86) × 10−8
126,6 V9b2c2K (1/2){Pa2,Pb2,Pc2}cos⁡9α$\[(1 / 2)\left\{P_a^2, P_b^2, P_c^2\right\} \cos 9 \alpha\]$ 0.639(42) × 10−10
124,8 D6bcJJK (1/2)P4{Pa2,Pb,Pc}sin⁡6α$\[(1 / 2) P^4\left\{P_a^2, P_b, P_c\right\} \sin 6 \alpha\]$ 0.492(18) × 10−14

Notes. a n=t+r, where n is the total order of the operator, t is the order of the torsional part, and r is the order of the rotational part, respectively. The ordering scheme of Nakagawa et al. (1987) is used. b The parameter nomenclature is based on the subscript procedure of Xu et al. (2008).c {A, B, C, D, E} = ABCDE + EDCBA. {A, B, C, D} = ABCD + DCBA. {A, B, C} = ABC + CBA. {A, B} = AB + BA. The product of the operator in the third column of a given row and the parameter in the second 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 F(pα+ρPa)2+ARAMPa2.d$\[F\left(p_\alpha+\rho P_a\right)^2+A_{\mathrm{RAM}} P_a^2.{ }^d\]$. Values of the parameters are in units of reciprocal centimeters, except for ρ, which is unitless.e Statistical uncertainties are given in parentheses as one standard uncertainty in units of the last digits.

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