III.B.3.b. (XIII.C.2.)

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at CISD/3-21G

Scale factor	How many		Source
	Molecules	Vibrations
0.939 ± 0.031	19	263	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
HCN	Hydrogen cyanide	1	Σ	3513	3312	0.943	1	1
		2	Σ	2179	2089	0.959	1	2
		3	Π	864	712	0.824	1	3
C3H8	Propane	1	A1	3155	2977	0.943	2	4
		2	A1	3097	2962	0.956	2	5
		3	A1	3090	2887	0.934	2	6
		4	A1	1616	1476	0.913	2	7
		5	A1	1598	1462	0.915	2	8
		6	A1	1514	1392	0.920	2	9
		7	A1	1239	1158	0.935	2	10
		8	A1	869	869	1.000	2	11
		9	A1	386	369	0.957	2	12
		10	A2	3147	2967	0.943	2	13
		11	A2	1599	1451	0.907	2	14
		12	A2	1393	1278	0.917	2	15
		13	A2	978	940	0.961	2	16
		14	A2	233	216	0.926	2	17
		15	B1	3161	2973	0.940	2	18
		16	B1	3121	2968	0.951	2	19
		17	B1	1615	1472	0.912	2	20
		18	B1	1292	1192	0.923	2	21
		19	B1	788	748	0.949	2	22
		20	B1	281	268	0.954	2	23
		21	B2	3152	2968	0.942	2	24
		22	B2	3086	2887	0.936	2	25
		23	B2	1605	1464	0.912	2	26
		24	B2	1496	1378	0.921	2	27
		25	B2	1440	1338	0.929	2	28
		26	B2	1060	1054	0.995	2	29
		27	B2	983	922	0.938	2	30
CH3CH2NH2	Ethylamine	1	A'	3466	3345	0.965	3	31
		2	A'	3155	2985	0.946	3	32
		3	A'	3110	2840	0.913	3	33
		4	A'	3086	2860	0.927	3	34
		5	A'	1780	1622	0.911	3	35
		6	A'	1608	1487	0.925	3	36
		7	A'	1592	1465	0.920	3	37
		8	A'	1498	1378	0.920	3	38
		9	A'	1442	1397	0.969	3	39
		10	A'	1193	1016	0.851	3	40
		11	A'	1048	1086	1.037	3	41
		12	A'	914	892	0.975	3	42
		13	A'	808	773	0.957	3	43
		14	A'	403	403	1.000	3	44
		15	A"	3557	3412	0.959	3	45
		16	A"	3161	2924	0.925	3	46
		17	A"	3135	2906	0.927	3	47
		18	A"	1605	1455	0.907	3	48
		19	A"	1445	1238	0.857	3	49
		20	A"	1343	1293	0.963	3	50
		21	A"	1053	1117	1.061	3	51
		22	A"	807	816	1.011	3	52
		23	A"	316	259	0.821	3	53
		24	A"	262	218	0.831	3	54
HNCO	Isocyanic acid	1	A'	3823	3538	0.926	4	55
		2	A'	2391	2269	0.949	4	56
		3	A'	1343	1327	0.988	4	57
		4	A'	609	777	1.275	4	58
		5	A'	510	577	1.131	4	59
		6	A"	590	656	1.113	4	60
CH3SCH3	Dimethyl sulfide	1	A1	3218	2998	0.932	5	61
		2	A1	3123	2930	0.938	5	62
		3	A1	1585	1444	0.911	5	63
		4	A1	1450	1331	0.918	5	64
		5	A1	1092	973	0.891	5	65
		6	A1	636	695	1.092	5	66
		7	A1	248	282	1.135	5	67
		8	A2	3211	2952	0.919	5	68
		9	A2	1568	1420	0.906	5	69
		10	A2	995	919	0.924	5	70
		12	B1	3208	2970	0.926	5	71
		13	B1	1577	1439	0.912	5	72
		14	B1	1024	973	0.950	5	73
		15	B1	164	182	1.109	5	74
		16	B2	3218	2998	0.932	5	75
		17	B2	3122	2930	0.939	5	76
		18	B2	1577	1444	0.915	5	77
		19	B2	1424	1315	0.923	5	78
		20	B2	969	903	0.932	5	79
		21	B2	683	743	1.087	5	80
CH3COOCH3	methyl acetate	1	A'	3250	3035	0.934	6	81
		2	A'	3249	3031	0.933	6	82
		3	A'	3150	2966	0.941	6	83
		4	A'	3146	2964	0.942	6	84
		5	A'	1844	1771	0.960	6	85
		6	A'	1623	1460	0.899	6	86
		7	A'	1588	1440	0.907	6	87
		8	A'	1557	1430	0.919	6	88
		9	A'	1503	1375	0.915	6	89
		10	A'	1314	1248	0.950	6	90
		11	A'	1243	1159	0.933	6	91
		12	A'	1125	1060	0.942	6	92
		13	A'	1015	980	0.966	6	93
		14	A'	850	844	0.993	6	94
		15	A'	654	639	0.977	6	95
		16	A'	418	429	1.027	6	96
		17	A'	276	303	1.099	6	97
		18	A"	3212	3005	0.935	6	98
		19	A"	3210	2994	0.933	6	99
		20	A"	1608	1460	0.908	6	100
		21	A"	1596	1430	0.896	6	101
		22	A"	1220	1187	0.973	6	102
		23	A"	1151	1036	0.900	6	103
		24	A"	618	607	0.982	6	104
		25	A"	174	187	1.073	6	105
		26	A"	116	136	1.177	6	106
		27	A"	105	110	1.048	6	107
CH2CHCH3	Propene	1	A'	3263	3090	0.947	7	108
		2	A'	3195	3013	0.943	7	109
		3	A'	3181	2991	0.940	7	110
		4	A'	3152	2954	0.937	7	111
		5	A'	3084	2871	0.931	7	112
		6	A'	1754	1650	0.941	7	113
		7	A'	1604	1470	0.916	7	114
		8	A'	1542	1420	0.921	7	115
		9	A'	1507	1378	0.915	7	116
		10	A'	1401	1297	0.926	7	117
		11	A'	1248	1171	0.938	7	118
		12	A'	1019	963	0.945	7	119
		13	A'	917	920	1.003	7	120
		14	A'	449	428	0.954	7	121
		15	A"	3135	2954	0.942	7	122
		16	A"	1591	1443	0.907	7	123
		17	A"	1146	1045	0.912	7	124
		18	A"	1064	991	0.931	7	125
		19	A"	994	912	0.918	7	126
		20	A"	607	578	0.952	7	127
		21	A"	187	174	0.928	7	128
CH3OCH3	Dimethyl ether	1	A1	3182	2996	0.941	8	129
		2	A1	3057	2817	0.921	8	130
		3	A1	1630	1464	0.898	8	131
		4	A1	1571	1452	0.924	8	132
		5	A1	1288	1244	0.966	8	133
		6	A1	907	928	1.023	8	134
		7	A1	412	418	1.015	8	135
		8	A2	3090	2952	0.955	8	136
		9	A2	1594	1464	0.918	8	137
		10	A2	1190	1150	0.967	8	138
		11	A2	239	203	0.851	8	139
		12	B1	3090	2925	0.947	8	140
		13	B1	1602	1464	0.914	8	141
		14	B1	1222	1179	0.965	8	142
		15	B1	246	242	0.986	8	143
		16	B2	3179	2996	0.943	8	144
		17	B2	3046	2817	0.925	8	145
		18	B2	1617	1464	0.906	8	146
		19	B2	1529	1452	0.950	8	147
		20	B2	1199	1227	1.024	8	148
		21	B2	1117	1102	0.987	8	149
CH3CH2CHO	Propanal	1	A'	3193	2981	0.934	9	150
		2	A'	3128	2904	0.928	9	151
		3	A'	3105	2895	0.933	9	152
		4	A'	3017	2809	0.931	9	153
		5	A'	1782	1743	0.978	9	154
		6	A'	1611	1460	0.906	9	155
		7	A'	1572	1416	0.901	9	156
		8	A'	1523	1390	0.912	9	157
		9	A'	1493	1376	0.922	9	158
		10	A'	1420	1335	0.940	9	159
		11	A'	1153	1093	0.948	9	160
		12	A'	1041	993	0.954	9	161
		13	A'	861	848	0.985	9	162
		14	A'	702	668	0.952	9	163
		15	A'	280	271	0.966	9	164
		16	A"	3197	2992	0.936	9	165
		17	A"	3133	2942	0.939	9	166
		18	A"	1613	1451	0.900	9	167
		19	A"	1365	1250	0.916	9	168
		20	A"	1220	1118	0.916	9	169
		21	A"	967	892	0.923	9	170
		22	A"	737	660	0.895	9	171
		23	A"	240	220	0.917	9	172
		24	A"	135	135	1.000	9	173
C2H5N	Aziridine	1	A'	3438	3338	0.971	10	174
		2	A'	3301	3079	0.933	10	175
		3	A'	3207	3015	0.940	10	176
		4	A'	1599	1482	0.927	10	177
		5	A'	1335	1237	0.926	10	178
		6	A'	1212	1211	0.999	10	179
		7	A'	1128	1090	0.966	10	180
		8	A'	1026	998	0.973	10	181
		9	A'	867	856	0.987	10	182
		10	A'	751	773	1.029	10	183
		11	A"	3286	3079	0.937	10	184
		12	A"	3195	3015	0.944	10	185
		13	A"	1583	1463	0.924	10	186
		14	A"	1321	1268	0.960	10	187
		15	A"	1215	1131	0.931	10	188
		16	A"	1171	1095	0.935	10	189
		17	A"	935	904	0.967	10	190
		18	A"	812	817	1.006	10	191
C5H8	1,4-Pentadiene	1	A	3289	3080	0.936	11	192
		2	A	3223	3012	0.934	11	193
		3	A	3207	3012	0.939	11	194
		4	A	3102	2900	0.935	11	195
		5	A	1776	1644	0.926	11	196
		6	A	1584	1433	0.905	11	197
		7	A	1558	1413	0.907	11	198
		8	A	1403	1295	0.923	11	199
		9	A	1341	1263	0.942	11	200
		10	A	1150	1120	0.974	11	201
		11	A	1080	995	0.921	11	202
		12	A	1020	918	0.900	11	203
		13	A	949	876	0.923	11	204
		14	A	703	562	0.800	11	205
		15	A	392	421	1.075	11	206
		16	A	318	137	0.430	11	207
		17	A	86	102	1.190	11	208
		18	B	3289	3080	0.936	11	209
		19	B	3222	3012	0.935	11	210
		20	B	3207	3012	0.939	11	211
		21	B	3143	2982	0.949	11	212
		22	B	1760	1640	0.932	11	213
		23	B	1553	1413	0.910	11	214
		24	B	1405	1314	0.935	11	215
		25	B	1393	1280	0.919	11	216
		26	B	1227	1060	0.864	11	217
		27	B	1081	995	0.920	11	218
		28	B	1019	995	0.976	11	219
		29	B	985	920	0.934	11	220
		30	B	945	760	0.804	11	221
		31	B	637	721	1.132	11	222
		32	B	474	421	0.888	11	223
		33	B	90	331	3.663	11	224
CH3SSCH3	Disulfide, dimethyl	1	A	3249	2990	0.920	12	225
		2	A	3228	2983	0.924	12	226
		3	A	3140	2913	0.928	12	227
		4	A	1578	1426	0.904	12	228
		5	A	1572	1419	0.903	12	229
		6	A	1443	1311	0.909	12	230
		7	A	1026	955	0.931	12	231
		8	A	1021	949	0.929	12	232
		9	A	656	694	1.059	12	233
		10	A	434	509	1.173	12	234
		11	A	201	240	1.194	12	235
		12	A	138	134	0.972	12	236
		13	A	78	117	1.500	12	237
		14	B	3249	2990	0.920	12	238
		15	B	3227	2983	0.924	12	239
		16	B	3137	2915	0.929	12	240
		17	B	1582	1430	0.904	12	241
		18	B	1566	1415	0.904	12	242
		19	B	1435	1303	0.908	12	243
		20	B	1030	955	0.927	12	244
		21	B	1018	949	0.932	12	245
		22	B	651	691	1.061	12	246
		23	B	235	274	1.167	12	247
		24	B	150	134	0.894	12	248
CS	carbon monosulfide	1	Σ	1162	1285	1.106	13	249
HCP	HCP	1	Σ	3402	3217	0.946	14	250
		2	Σ	1264	1278	1.011	14	251
		3	Π	701	674	0.961	14	252
HOCl	hypochlorous acid	1	A'	3439	3609	1.050	15	253
		2	A'	1272	1239	0.973	15	254
		3	A'	663	724	1.093	15	255
LiO	lithium oxide	1	Σ	892	815	0.913	16	256
NaO	sodium monoxide	1	Σ	493	492	0.998	17	257
HOF	Hypofluorous acid	1	A'	3463	3537	1.021	18	258
		2	A'	1343	1393	1.037	18	259
		3	A'	1017	886	0.871	18	260
HBO	Boron hydride oxide	1	Σ	2967	2850	0.960	19	261
		2	Σ	1826	1826	1.000	19	262
		3	Π	788	756	0.959	19	263

How do we calculate the scaling factor?

Histogram of vibrational frequency ratios

Ratios greater than 1.35 are in the 1.35 bin. Ratios less than 0.7 are in the 0.7 bin.

	120
	100
	80
	60
	40
	20
	0
		0.70			0.75			0.80			0.85			0.90			0.95			1.00			1.05			1.10			1.15			1.20			1.25			1.30			1.35
Ratio of experimental frequency to calculated frequency