TABLE X.

Anharmonic fundamental vibrational wavenumbers (in cm⁻¹) of trans-2,3-dimethyloxirane computed with hybrid schemes and the best estimated anharmonic IR intensities (in km mol ⁻¹).

Mode	Symmetry	B3LYPa	CAMa	B2PLYPb/		best cheapc/			Best IRd	Assignmente
				B3LYP	B2PLYP	B3LYP	CAM	B2PLYP
1	A	2968	3003	2998	2994	2993	2996	2989	3.92	CH3 ∥ bend
2	A	2944	2983	2976	2974	2975	2978	2973	29.65	CH3 ⊥ bend
3	A	2914	2957	2946	2943	2944	2934	2936	2.97	asym C-CH3 str
4	A	2930	2958	2962	2959	2958	2960	2951	3.28	CH3 rocking
5	A	1482	1496	1492	1490	1494	1493	1492	6.79	∥CH
6	A	1441	1454	1465	1461	1462	1462	1454	12.53	CH3 asym def
7	A	1424	1441	1436	1433	1438	1441	1434	0.76	CH3 sym stretch
8	A	1375	1384	1392	1388	1386	1386	1383	0.19	CH3 asym stretch +CH str
9	A	1249	1268	1259	1258	1253	1253	1253	1.25	CH3 torsion
10	A	1156	1175	1164	1165	1161	1167	1171	0.57	CH3 ⊥ bend
11	A	1108	1126	1121	1121	1118	1118	1118	6.39	ring CC stretching
12	A	1015	1031	1027	1030	1024	1022	1027	13.44	⊥ CH + CH3 rock
13	A	886	909	888	887	890	889	889	17.37	∥CH + ring bretching
14	A	801	820	811	809	813	812	811	19.56	CH3 umbrella sym
15	A	458	463	459	460	459	458	459	0.01	Ring breathing
16	A	245	249	250	248	250	249	249	2.14	CH sym stretch
17	A	173	174	189	185	188	178	183	0.32	CH3 asym stretch +CH str
18	B	2971	3006	3001	2994	2996	2998	2989	54.01	CH3 torsion
19	B	2944	2983	2976	2973	2974	2977	2971	4.72	CO asym stretching
20	B	2953	2991	2987	2967	2980	2982	2960	25.02	CH3 rocking + ⊥ CH
21	B	2933	2954	2967	2966	2963	2962	2959	30.46	⊥ CH + CH3 rock
22	B	1451	1459	1470	1467	1468	1468	1465	8.86	CH3 umbrella asym
23	B	1434	1443	1456	1453	1453	1451	1449	5.75	CH3 asym def
24	B	1376	1390	1392	1389	1391	1390	1388	14.43	CH asym stretch
25	B	1333	1344	1346	1345	1334	1334	1334	8.69	CH3 asym stretch +CH str
26	B	1146	1163	1158	1176	1154	1154	1171	1.33	CH3 ∥ bend
27	B	1095	1114	1111	1109	1115	1115	1113	10.08	ring def + C-CH3 str
28	B	1004	1025	1012	1008	1015	1021	1012	10.75	CH3 rocking
29	B	951	960	965	966	959	959	960	1.87	⊥ CH
30	B	730	766	727	727	731	730	731	11.52	CH3 asym def
31	B	472	480	469	472	468	468	468	5.50	CH3 asym def
32	B	281	283	282	283	281	281	282	0.46	CH3 sym stretch
33	B	191	193	208	203	209	200	204	0.27	CH3 asym stretch
MAEf		12.3	9.3	5.8	3.9	4.0	4.3
∣MAX∣f		28.8	34.7	27.8	11.5	20.5	22.5

^aComputed with the SNSD basis set.

^bComputed with the aug-cc-pVTZ basis set.

^cBest-estimated (best) harmonic wavenumbers obtained by means of the “cheap” scheme according to Eq. (5).

^dBest estimated anharmonic IR intensities computed at the best cheap/B2PLYP level.

^eNotation adopted from Ref.¹¹; ⊥: perpendicular and ∥= parallel to the C₂C₃C_5/7 plane (Figure 1), respectively.

^fMean absolute error (MAE) and maximum absolute deviations (∣MAX∣) with respect to the best theoretical estimate (best cheap/B2PLYP).