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Table A.1

Fitted parameters of the RAM Hamiltonian for the CH317OH molecule

ntra Par.b Operatorc Valued,e
22,0 (1/2)V3 (1 − cos 3α) 186.94207(64)
22,0 F pα2$\[p_{\alpha}^{2}\]$ 27.5312352(20)
21,1 ρ Papα 0.8094036988(18)
20,2 ARAM Pa2$\[P_{a}^{2}\]$ 4.22572(28)
20,2 BRAM Pb2$\[P_{b}^{2}\]$ 0.8051588(47)
20,2 CRAM Pc2$\[P_{c}^{2}\]$ 0.7753620(35)
20,2 2Dab (1/2){Pa,Pb} −0.0108380(64)
44,0 (1/2)V6 (1 − cos 6α) −0.8414(44)
44,0 Fm pα4$\[p_{\alpha}^{4}\]$ −0.8818018(89) × 10−2
43,1 ρm Papα3$\[P_{a} p_{\alpha}^{3}\]$ −0.3441336(28) × 10−1
42,2 V3J P2(1 − cos 3α) −0.233190(20) × 10−2
42,2 V3K Pa2(1−cos 3α)$\[P_{a}^{2}(1-\cos ~3 \alpha)\]$ 0.12153(13) × 10−1
42,2 V3bc (Pb2−Pc2)(1−cos 3α)$\[\left(P_{b}^{2}-P_{c}^{2}\right)(1-\cos ~3 \alpha)\]$ −0.4030(86) × 10−4
42,2 V3ab (1/2){Pa,Pb}(1 − cos 3α) 0.178794(29) × 10−1
42,2 FJ P2pα2$\[P^{2} p_{\alpha}^{2}\]$ −0.11533011(92) × 10−3
42,2 FK Pa2pα2$\[P_{a}^{2} p_{\alpha}^{2}\]$ −0.5093083(33) × 10−1
42,2 Fbc (Pb2−Pc2)pα2$\[\left(P_{b}^{2}-P_{c}^{2}\right) p_{\alpha}^{2}\]$ −0.1251(12) × 10−3
42,2 Fab (1/2){Pa,Pb}pα2$\[(1 / 2)\left\{P_{a}, P_{b}\right\} p_{\alpha}^{2}\]$ 0.1538(16) × 10−5
42,2 D3ac (1/2){Pa,Pc} sin 3α 0.256158(44) × 10−1
42,2 D3bc (1/2){Pb,Pc} sin 3α −0.138(16) × 10−3
41,3 ρJ P2 Papα −0.1856334(19) × 10−3
41,3 ρK Pa3pα$\[P_{a}^{3} p_{\alpha}\]$ −0.3354061(19) × 10−1
41,3 ρbc (1/2){Pa,(Pb2−Pc2)}pα$\[(1 / 2)\left\{P_{a},\left(P_{b}^{2}-P_{c}^{2}\right)\right\} p_{\alpha}\]$ −0.2183(12) × 10−3
40,4 −ΔJ P4 −0.1626985(20) × 10−5
40,4 −ΔJK P2Pa2$\[P^{2} P_{a}^{2}\]$ −0.10148(27) × 10−3
40,4 −ΔK Pa4$\[P_{a}^{4}\]$ −0.8286520(49) × 10−2
40,4 −2δJ P2(Pb2−Pc2)$\[P^{2}\left(P_{b}^{2}-P_{c}^{2}\right)\]$ −0.1107985(58) × 10−6
40,4 −2δK (1/2){Pa2,(Pb2−Pc2)}$\[(1 / 2)\left\{P_{a}^{2},\left(P_{b}^{2}-P_{c}^{2}\right)\right\}\]$ −0.91153(87) × 10−4
40,4 DabJ (1/2)P2{Pa,Pb} −0.16976(77) × 10−6
66,0 (1/2)V9 (1 − cos 9α) 0.786(17)
66,0 Fmm pα6$\[p_{\alpha}^{6}\]$ 0.10069(20) × 10−4
65,1 ρmm Papα5$\[P_{a} p_{\alpha}^{5}\]$ 0.67059(99) × 10−4
64,2 V6J P2(1 − cos 6α) −0.456(14) × 10−4
64,2 V6K Pa2(1−cos 6α)$\[P_{a}^{2}(1-\cos ~6 \alpha)\]$ −0.8042(92) × 10−2
64,2 V6bc (Pb2−Pc2)(1−cos 6α)$\[\left(P_{b}^{2}-P_{c}^{2}\right)(1-\cos ~6 \alpha)\]$ −0.2379(12) × 10−4
64,2 V6ab (1/2){Pa,Pb}(1 − cos 6α) −0.1611(91) × 10−3
64,2 FmJ P2pα4$\[P^{2} p_{\alpha}^{4}\]$ 0.8956(10) × 10−7
64,2 FmK Pa2pα4$\[P_{a}^{2} p_{\alpha}^{4}\]$ 0.18102(20) × 10−3
64,2 Fmab (1/2){Pa,Pb}pα4$\[(1 / 2)\left\{P_{a}, P_{b}\right\} p_{\alpha}^{4}\]$ −0.250(11) × 10−8
64,2 D6ac (1/2){Pa,Pc} sin 6α −0.3458(40) × 10−2
63,3 ρmJ P2Papα3$\[P^{2} P_{a} p_{\alpha}^{3}\]$ 0.34612(28) × 10−6
63,3 ρmK Pa3pα3$\[P_{a}^{3} p_{\alpha}^{3}\]$ 0.25554(22) × 10−3
63,3 ρ3bc (1/2){Pa,Pb,Pc,pα, sin 3α} 0.412(11) × 10−4
62,4 V3JJ P4(1 − cos 3α) 0.10480(28) × 10−7
62,4 V3JK P2Pa2(1−cos 3α)$\[P^{2} P_{a}^{2}(1-\cos ~3 \alpha)\]$ −0.3861(21) × 10−6
62,4 V3KK Pa4(1−cos 3α)$\[P_{a}^{4}(1-\cos ~3 \alpha)\]$ 0.6713(36) × 10−6
62,4 V3bcJ P2(Pb2−Pc2)(1−cos 3α)$\[P^{2}\left(P_{b}^{2}-P_{c}^{2}\right)(1-\cos ~3 \alpha)\]$ 0.24337(62) × 10−8
62,4 V3bcK (1/2){Pa2,(Pb2−Pc2)}(1−cos 3α)$\[(1 / 2)\left\{P_{a}^{2},\left(P_{b}^{2}-P_{c}^{2}\right)\right\}(1-\cos ~3 \alpha)\]$ −0.2185(64) × 10−5
62,4 V3b2c2 (1/2){Pb2,Pc2}cos 3α$\[(1 / 2)\left\{P_{b}^{2}, P_{c}^{2}\right\} \cos ~3 \alpha\]$ 0.4618(62) × 10−7
62,4 V3abJ (1/2)P2{Pa,Pb}(1 − cos 3α) −0.2421(10) × 10−6
62,4 V3abK (1/2){Pa3,Pb}(1−cos 3α)$\[(1 / 2)\left\{P_{a}^{3}, P_{b}\right\}(1-\cos ~3 \alpha)\]$ −0.1439(16) × 10−5
62,4 FJJ P4pα2$\[P^{4} p_{\alpha}^{2}\]$ 0.5256(26) × 10−9
62,4 FJK P2Pa2pα2$\[P^{2} P_{a}^{2} p_{\alpha}^{2}\]$ 0.51158(30) × 10−6
62,4 FKK Pa4pα2$\[P_{a}^{4} p_{\alpha}^{2}\]$ 0.20008(14) × 10−3
62,4 D3acJ (1/2)P2{Pa,Pc} sin 3α −0.5868(21) × 10−6
62,4 D3acK (1/2){Pa3,Pc}sin 3α$\[(1 / 2)\left\{P_{a}^{3}, P_{c}\right\} \sin ~3 \alpha\]$ −0.1263(22) × 10−5
62,4 D3bcJ (1/2)P2{Pb,Pc} sin 3α −0.1123(17) × 10−7
62,4 D3bcK (1/2){Pa2,Pb,Pc}sin 3α$\[(1 / 2)\left\{P_{a}^{2}, P_{b}, P_{c}\right\} \sin ~3 \alpha\]$ 0.2956(79) × 10−4
62,4 D3acbc (1/2)({Pa,Pb2,Pc}−{Pa,Pc3})sin 3α$\[(1 / 2)\left(\left\{P_{a}, P_{b}^{2}, P_{c}\right\}-\left\{P_{a}, P_{c}^{3}\right\}\right) \sin ~3 \alpha\]$ −0.3816(13) × 10−6
62,4 D3bcbc (1/2)({Pb3,Pc}−{Pb,Pc3})sin 3α$\[(1 / 2)\left(\left\{P_{b}^{3}, P_{c}\right\}-\left\{P_{b}, P_{c}^{3}\right\}\right) \sin ~3 \alpha\]$ −0.891(29) × 10−8
61,5 ρJJ P4 PaPα 0.8080(23) × 10−9
61,5 ρJK P2Pa3pα$\[P^{2} P_{a}^{3} p_{\alpha}\]$ 0.33885(19) × 10−6
61,5 ρKK Pa5pα$\[P_{a}^{5} p_{\alpha}\]$ 0.82693(47) × 10−4
60,6 ΦJ P6 −0.7082(40) × 10−12
60,6 ΦJK P4Pa2$\[P^{4} P_{a}^{2}\]$ 0.4015(15) × 10−9
60,6 ΦKJ P2Pa4$\[P^{2} P_{a}^{4}\]$ 0.84566(56) × 10−7
60,6 ΦK Pa6$\[P_{a}^{6}\]$ 0.141352(69) × 10−4
60,6 2ϕJ P4(Pb2−Pc2)$\[P^{4}\left(P_{b}^{2}-P_{c}^{2}\right)\]$ 0.1743(20) × 10−12
60,6 2ϕ JK (1/2)P2{Pa2,(Pb2−Pc2)}$\[(1 / 2) P^{2}\left\{P_{a}^{2},\left(P_{b}^{2}-P_{c}^{2}\right)\right\}\]$ 0.2724(70) × 10−10
60,6 2ϕK (1/2){Pa4,(Pb2−Pc2)}$\[(1 / 2)\left\{P_{a}^{4},\left(P_{b}^{2}-P_{c}^{2}\right)\right\}\]$ 0.124(11) × 10−9
60,6 Db2c2bc (1/2)({Pb4,Pc2}−{Pb2,Pc4})$\[(1 / 2)\left(\left\{P_{b}^{4}, P_{c}^{2}\right\}-\left\{P_{b}^{2}, P_{c}^{4}\right\}\right)\]$ −0.862(14) × 10−12
60,6 DabJJ (1/2)P4{Pa,Pb} −0.443(18) × 10−11
60,6 DabJK (1/2)P2{Pa3,Pb}$\[(1 / 2) P^{2}\left\{P_{a}^{3}, P_{b}\right\}\]$ −0.618(72) × 10−10
88,0 Fmmm pα8$\[p_{\alpha}^{8}\]$ 0.10917(86) × 10−8
86,2 V9J P2(1 − cos 9α) 0.1605(52) × 10−3
86,2 V9K Pa2(1−cos 9α)$\[P_{a}^{2}(1-\cos ~9 \alpha)\]$ 0.3053(36) × 10−1
86,2 FmmJ P2pα6$\[P^{2} p_{\alpha}^{6}\]$ 0.484(11) × 10−10
86,2 FmmK Pa2pα6$\[P_{a}^{2} p_{\alpha}^{6}\]$ −0.4440(33) × 10−8
86,2 D9ac (1/2){Pa,Pc} sin 9α 0.1404(17) × 10−1
85,3 ρmmJ P2Papα5$\[P^{2} P_{a} p_{\alpha}^{5}\]$ 0.928(23) × 10−10
85,3 ρmmbc (1/2){Pa,(Pb2−Pc2)}pα5$\[(1 / 2)\left\{P_{a},\left(P_{b}^{2}-P_{c}^{2}\right)\right\} p_{\alpha}^{5}\]$ −0.1085(80) × 10−11
85,3 D6b2cm (1/2){Pb2,Pc,pα,sin 6α}$\[(1 / 2)\left\{P_{b}^{2}, P_{c}, p_{\alpha}, \sin ~6 \alpha\right\}\]$ −0.977(48) × 10−7
84,4 V6JK P2Pa2(1−cos 6α)$\[P^{2} P_{a}^{2}(1-\cos ~6 \alpha)\]$ −0.8483(86) × 10−6
84,4 V6bcK (1/2){Pa2,(Pb2−Pc2)}(1−cos 6α)$\[(1 / 2)\left\{P_{a}^{2},\left(P_{b}^{2}-P_{c}^{2}\right)\right\}(1-\cos ~6 \alpha)\]$ −0.1329(47) × 10−5
84,4 V6b2c2 (1/2){Pb2,Pc2}cos 6α$\[(1 / 2)\left\{P_{b}^{2}, P_{c}^{2}\right\} \cos ~6 \alpha\]$ −0.1068(11) × 10−7
84,4 V6abK (1/2){Pa3,Pb}(1−cos 6α)$\[(1 / 2)\left\{P_{a}^{3}, P_{b}\right\}(1-\cos ~6 \alpha)\]$ −0.462(12) × 10−6
84,4 FmJK P2Pa2pα4$\[P^{2} P_{a}^{2} p_{\alpha}^{4}\]$ 0.466(13) × 10−10
84,4 FmKK Pa4pα4$\[P_{a}^{4} p_{\alpha}^{4}\]$ 0.8020(55) × 10−8
84,4 D6bcK (1/2){Pa2,Pb,Pc}sin 6α$\[(1 / 2)\left\{P_{a}^{2}, P_{b}, P_{c}\right\} \sin ~6 \alpha\]$ 0.107(11) × 10−5
84,4 D3acmJ (1/2)P2{Pa,Pc,pα2,sin 3α}$\[(1 / 2) P^{2}\left\{P_{a}, P_{c}, p_{\alpha}^{2}, \sin ~3 \alpha\right\}\]$ 0.464(13) × 10−8
84,4 D3bcmK (1/2){Pa2,Pb,Pc,pα2,sin 3α}$\[(1 / 2)\left\{P_{a}^{2}, P_{b}, P_{c}, p_{\alpha}^{2}, \sin ~3 \alpha\right\}\]$ −0.2284(51) × 10−8
82,6 V3JJJ P6(1 − cos 3α) −0.5682(45) × 10−12
82,6 V3JJK P4Pa2(1−cos 3α)$\[P^{4} P_{a}^{2}(1-\cos ~3 \alpha)\]$ −0.285(15) × 10−10
82,6 V3KKK Pa6(1−cos 3α)$\[P_{a}^{6}(1-\cos ~3 \alpha)\]$ 0.3046(67) × 10−8
82,6 V3b2c2J (1/2)P2{Pb2,Pc2}cos 3α$\[(1 / 2) P^{2}\left\{P_{b}^{2}, P_{c}^{2}\right\} \cos ~3 \alpha\]$ −0.3766(36) × 10−11
82,6 V3b2c2K (1/2){Pa2,Pb2,Pc2}cos 3α$\[(1 / 2)\left\{P_{a}^{2}, P_{b}^{2}, P_{c}^{2}\right\} \cos ~3 \alpha\]$ −0.3881(93) × 10−9
82,6 V3abJJ (1/2)P4{Pab,Pb}(1−cos 3α)$\[(1 / 2) P^{4}\left\{P_{a}^{b}, P_{b}\right\}(1-\cos ~3 \alpha)\]$ 0.966(22) × 10−11
82,6 V3abKK (1/2){Pa5,Pb}(1−cos 3α)$\[(1 / 2)\left\{P_{a}^{5}, P_{b}\right\}(1-\cos ~3 \alpha)\]$ 0.315(11) × 10−8
82,6 FJJK P4Pa2pα2$\[P^{4} P_{a}^{2} p_{\alpha}^{2}\]$ 0.741(22) × 10−13
82,6 FKKK Pa6pα2$\[P_{a}^{6} p_{\alpha}^{2}\]$ −0.11704(75) × 10−7
82,6 D3acJK (1/2)P2{Pa3,Pc}sin 3α$\[(1 / 2) P^{2}\left\{P_{a}^{3}, P_{c}\right\} \sin ~3 \alpha\]$ −0.2798(77) × 10−8
82,6 D3bcJJ (1/2)P4{Pb,Pc} sin 3α 0.2201(79) × 10−12
82,6 D3bcbcJ (1/2)P2({Pb3,Pc}−{Pb,Pc3})sin 3α$\[(1 / 2) P^{2}\left(\left\{P_{b}^{3}, P_{c}\right\}-\left\{P_{b}, P_{c}^{3}\right\}\right) \sin ~3 \alpha\]$ 0.1724(14) × 10−11
81,7 ρKKK Pa7pα$\[P_{a}^{7} p_{\alpha}\]$ −0.9200(56) × 10−8
81,7 ρbcJJ (1/2)P4{Pa,(Pb2−Pc2)}pα$\[(1 / 2) P^{4}\left\{P_{a},\left(P_{b}^{2}-P_{c}^{2}\right)\right\} p_{\alpha}\]$ 0.281(24) × 10−14
80,8 LKKJ P2Pa6$\[P^{2} P_{a}^{6}\]$ −0.1362(47) × 10−11
80,8 LK Pa8$\[P_{a}^{8}\]$ −0.2175(12) × 10−8
108,2 FmmmK Pa2pα8$\[P_{a}^{2} p_{\alpha}^{8}\]$ 0.1511(67) × 10−12
107,3 ρ9bc (1/2){Pa,Pb,Pc,Pα, sin 9α} −0.805(13) × 10−5
106,4 FmmKK Pa4pα6$\[P_{a}^{4} p_{\alpha}^{6}\]$ −0.881(46) × 10−13
106,4 D9bcJ (1/2)P2{Pb,Pc} sin 9α 0.6674(82) × 10−8
104,6 V6JJK P4Pa2(1−cos 6α)$\[P^{4} P_{a}^{2}(1-\cos ~6 \alpha)\]$ −0.307(16) × 10−10
104,6 V6KKK Pa6(1−cos 6α)$\[P_{a}^{6}(1-\cos ~6 \alpha)\]$ −0.5642(92) × 10−8
104,6 FmabJK (1/2)P2{Pa3,Pb}pα4$\[(1 / 2) P^{2}\left\{P_{a}^{3}, P_{b}\right\} p_{\alpha}^{4}\]$ 0.547(27) × 10−14
102,8 V3JJJK P6Pa2(1−cos 3α)$\[P^{6} P_{a}^{2}(1-\cos ~3 \alpha)\]$ 0.756(59) × 10−15
102,8 V3KKKK Pa8(1−cos 3α)$\[P_{a}^{8}(1-\cos ~3 \alpha)\]$ −0.284(22) × 10−11
102,8 V3b2c2JJ (1/2)P4{Pb2,Pc2}cos 3α$\[(1 / 2) P^{4}\left\{P_{b}^{2}, P_{c}^{2}\right\} \cos ~3 \alpha\]$ −0.146(12) × 10−15
128,4 V12JK P2Pa2(1−cos 12α)$\[P^{2} P_{a}^{2}(1-\cos ~12 \alpha)\]$ 0.1899(28) × 10−4
χaa −0.27527(18) × 10−3
χbb −0.9514(37) × 10−4
2χab −0.261(29) × 10−3

Notes. an=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. bThe 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$\[F\left(p_\alpha+\rho P_a\right)^2+A_{\mathrm{RAM}} P_a^2\]$. dValues of the parameters in units of cm−1, 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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