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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at CCD/cc-pVDZ

Scale factor	How many		Source
	Molecules	Vibrations
0.957 ± 0.024	42	342	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CCl4	Carbon tetrachloride	1	A1	469	459	0.979	1	1
		2	E	226	217	0.960	1	2
		3	T2	827	776	0.938	1	3
		4	T2	324	314	0.969	1	4
CH4	Methane	1	A1	3060	2917	0.953	2	5
		2	E	1560	1534	0.983	2	6
		3	T2	3197	3019	0.944	2	7
		4	T2	1344	1306	0.972	2	8
CH3NH2	methyl amine	1	A'	3508	3361	0.958	3	9
		2	A'	3110	2961	0.952	3	10
		3	A'	3018	2820	0.934	3	11
		4	A'	1677	1623	0.968	3	12
		5	A'	1504	1473	0.980	3	13
		6	A'	1468	1430	0.974	3	14
		7	A'	1206	1130	0.937	3	15
		8	A'	1093	1044	0.955	3	16
		9	A'	918	780	0.849	3	17
		10	A"	3588	3427	0.955	3	18
		11	A"	3151	2985	0.947	3	19
		12	A"	1522	1485	0.976	3	20
		13	A"	1376	1335	0.970	3	21
		14	A"	988	1195	1.210	3	22
		15	A"	341	268	0.786	3	23
CH3CH2NH2	Ethylamine	1	A'	3492	3345	0.958	4	24
		2	A'	3143	2985	0.950	4	25
		3	A'	3070	2840	0.925	4	26
		4	A'	3052	2860	0.937	4	27
		5	A'	1675	1622	0.968	4	28
		6	A'	1509	1487	0.985	4	29
		7	A'	1490	1465	0.983	4	30
		8	A'	1424	1378	0.968	4	31
		9	A'	1391	1397	1.005	4	32
		10	A'	1183	1016	0.858	4	33
		11	A'	1107	1086	0.981	4	34
		12	A'	947	892	0.942	4	35
		13	A'	903	773	0.856	4	36
		14	A'	405	403	0.994	4	37
		15	A"	3573	3412	0.955	4	38
		16	A"	3141	2924	0.931	4	39
		17	A"	3111	2906	0.934	4	40
		18	A"	1495	1455	0.973	4	41
		19	A"	1410	1238	0.878	4	42
		20	A"	1283	1293	1.007	4	43
		21	A"	1020	1117	1.095	4	44
		22	A"	783	816	1.042	4	45
		23	A"	324	259	0.798	4	46
		24	A"	266	218	0.820	4	47
HNCO	Isocyanic acid	1	A'	3702	3538	0.956	5	48
		2	A'	2362	2269	0.961	5	49
		3	A'	1346	1327	0.986	5	50
		4	A'	858	777	0.905	5	51
		5	A'	558	577	1.034	5	52
		6	A"	635	656	1.033	5	53
CH2CHCH3	Propene	1	A'	3267	3090	0.946	6	54
		2	A'	3182	3013	0.947	6	55
		3	A'	3169	2991	0.944	6	56
		4	A'	3154	2954	0.937	6	57
		5	A'	3060	2871	0.938	6	58
		6	A'	1743	1650	0.946	6	59
		7	A'	1496	1470	0.983	6	60
		8	A'	1460	1420	0.972	6	61
		9	A'	1413	1378	0.975	6	62
		10	A'	1325	1297	0.979	6	63
		11	A'	1197	1171	0.978	6	64
		12	A'	947	963	1.017	6	65
		13	A'	944	920	0.975	6	66
		14	A'	422	428	1.014	6	67
		15	A"	3132	2954	0.943	6	68
		16	A"	1482	1443	0.974	6	69
		17	A"	1071	1045	0.976	6	70
		18	A"	1021	991	0.971	6	71
		19	A"	938	912	0.972	6	72
		20	A"	584	578	0.990	6	73
		21	A"	199	174	0.874	6	74
C5H8	Cyclopentene	1	A'	3242	3066	0.946	7	75
		2	A'	3144	2958	0.941	7	76
		3	A'	3115	2916	0.936	7	77
		4	A'	3082	2902	0.942	7	78
		5	A'	3052	2852	0.934	7	79
		6	A'	1707	1616	0.947	7	80
		7	A'	1509	1467	0.972	7	81
		8	A'	1481	1449	0.978	7	82
		9	A'	1351	1302	0.964	7	83
		10	A'	1242	1284	1.034	7	84
		11	A'	1128	1213	1.075	7	85
		12	A'	1078	1048	0.972	7	86
		13	A'	993	964	0.970	7	87
		14	A'	932	962	1.032	7	88
		15	A'	842	904	1.074	7	89
		16	A'	719	692	0.962	7	90
		17	A'	597	603	1.009	7	91
		18	A'	179	254	1.415	7	92
		19	A"	3215	3039	0.945	7	93
		20	A"	3113	2967	0.953	7	94
		21	A"	3054	2927	0.958	7	95
		22	A"	1491	1467	0.984	7	96
		23	A"	1396	1432	1.026	7	97
		24	A"	1345	1356	1.008	7	98
		25	A"	1311	1302	0.993	7	99
		26	A"	1238	1297	1.047	7	100
		27	A"	1153	1207	1.047	7	101
		28	A"	1058	1113	1.052	7	102
		29	A"	964	1082	1.123	7	103
		30	A"	935	937	1.003	7	104
		31	A"	901	800	0.888	7	105
		32	A"	779	702	0.901	7	106
		33	A"	389	387	0.994	7	107
C8H8	cubane	1	A1g	3173	2995	0.944	8	108
		2	A1g	1036	1002	0.967	8	109
		3	A2u	3138	2978	0.949	8	110
		4	A2u	1043	839	0.804	8	111
		5	Eg	1143	1083	0.948	8	112
		6	Eg	920	912	0.991	8	113
		7	Eu	1169	1151	0.985	8	114
		8	Eu	624	617	0.989	8	115
		9	T1g	1162	1130	0.973	8	116
		10	T1u	3155	2978	0.944	8	117
		11	T1u	1284	1230	0.958	8	118
		12	T1u	874	853	0.976	8	119
		13	T2g	3147	2970	0.944	8	120
		14	T2g	1247	1182	0.948	8	121
		15	T2g	846	821	0.971	8	122
		16	T2g	674	665	0.987	8	123
		17	T2u	1102	1036	0.940	8	124
		18	T2u	842	829	0.984	8	125
C4H4N2	Pyrazine	1	Ag	3230	3055	0.946	9	126
		2	Ag	1678	1580	0.942	9	127
		3	Ag	1264	1233	0.976	9	128
		4	Ag	1055	1016	0.963	9	129
		5	Ag	608	602	0.991	9	130
		6	Au	1007	960	0.953	9	131
		7	Au	367	350	0.952	9	132
		8	B1g	955	927	0.970	9	133
		9	B1u	3208	3012	0.939	9	134
		10	B1u	1540	1483	0.963	9	135
		11	B1u	1177	1130	0.960	9	136
		12	B1u	1051	1018	0.969	9	137
		13	B2g	989	983	0.994	9	138
		14	B2g	768	756	0.984	9	139
		15	B2u	3225	3069	0.952	9	140
		16	B2u	1455	1411	0.970	9	141
		17	B2u	1175	1149	0.978	9	142
		18	B2u	1103	1063	0.963	9	143
		19	B3g	3207	3040	0.948	9	144
		20	B3g	1617	1525	0.943	9	145
		21	B3g	1375	1346	0.979	9	146
		22	B3g	718	704	0.981	9	147
		23	B3u	814	785	0.964	9	148
		24	B3u	431	418	0.970	9	149
C5H6	1,3-Cyclopentadiene	1	A1	3268	3091	0.946	10	150
		2	A1	3242	3075	0.949	10	151
		3	A1	3066	2886	0.941	10	152
		4	A1	1609	1500	0.933	10	153
		5	A1	1434	1378	0.961	10	154
		6	A1	1414	1365	0.965	10	155
		7	A1	1131	1106	0.978	10	156
		8	A1	1023	994	0.972	10	157
		9	A1	940	915	0.973	10	158
		10	A1	808	802	0.993	10	159
		11	A2	1137	1100	0.967	10	160
		12	A2	939	941	1.002	10	161
		13	A2	722	700	0.970	10	162
		14	A2	509	516	1.013	10	163
		15	B1	3110	2900	0.933	10	164
		16	B1	953	925	0.971	10	165
		17	B1	933	891	0.955	10	166
		18	B1	683	664	0.972	10	167
		19	B1	341	350	1.027	10	168
		20	B2	3259	3105	0.953	10	169
		21	B2	3233	3043	0.941	10	170
		22	B2	1675	1580	0.943	10	171
		23	B2	1339	1292	0.965	10	172
		24	B2	1284	1239	0.965	10	173
		25	B2	1113	1090	0.979	10	174
		26	B2	987	959	0.972	10	175
		27	B2	814	805	0.990	10	176
CH3CHCHCH3	2-Butene, (Z)-	1	A1	3193	3033	0.950	11	177
		2	A1	3178	2965	0.933	11	178
		3	A1	3066	2878	0.939	11	179
		4	A1	1772	1669	0.942	11	180
		5	A1	1497	1448	0.967	11	181
		6	A1	1427	1397	0.979	11	182
		7	A1	1292	1261	0.976	11	183
		8	A1	1028	986	0.959	11	184
		9	A1	885	880	0.995	11	185
		10	A1	291	290	0.998	11	186
		11	A2	3129	2988	0.955	11	187
		12	A2	1483	1464	0.987	11	188
		13	A2	1059	1037	0.980	11	189
		14	A2	1002	880	0.878	11	190
		15	A2	386	396	1.027	11	191
		17	B1	3129	2965	0.948	11	192
		18	B1	1488	1448	0.973	11	193
		19	B1	1070	986	0.921	11	194
		20	B1	702	673	0.959	11	195
		22	B2	3173	3033	0.956	11	196
		23	B2	3158	2965	0.939	11	197
		24	B2	3062	2900	0.947	11	198
		25	B2	1491	1448	0.971	11	199
		26	B2	1454	1420	0.977	11	200
		27	B2	1390	1397	1.005	11	201
		28	B2	1164	1135	0.975	11	202
		29	B2	999	986	0.987	11	203
		30	B2	563	583	1.036	11	204
CH3CHCHCH3	2-Butene, (E)-	1	Ag	3165	3011	0.951	12	205
		2	Ag	3152	2954	0.937	12	206
		3	Ag	3058	2874	0.940	12	207
		4	Ag	1780	1680	0.944	12	208
		5	Ag	1491	1457	0.977	12	209
		6	Ag	1424	1385	0.973	12	210
		7	Ag	1331	1309	0.984	12	211
		8	Ag	1177	1146	0.974	12	212
		9	Ag	886	866	0.977	12	213
		10	Ag	501	501	1.000	12	214
		11	Au	3128	2960	0.946	12	215
		12	Au	1481	1449	0.978	12	216
		13	Au	1073	1057	0.985	12	217
		14	Au	1001	964	0.963	12	218
		15	Au	245	224	0.914	12	219
		17	Bg	3129	2954	0.944	12	220
		18	Bg	1482	1457	0.983	12	221
		19	Bg	1065	1039	0.975	12	222
		20	Bg	749	750	1.001	12	223
		22	Bu	3171	3021	0.953	12	224
		23	Bu	3149	2960	0.940	12	225
		24	Bu	3057	2899	0.948	12	226
		25	Bu	1498	1449	0.968	12	227
		26	Bu	1424	1393	0.979	12	228
		27	Bu	1328	1311	0.987	12	229
		28	Bu	1104	1072	0.971	12	230
		29	Bu	987	987	1.000	12	231
		30	Bu	281	261	0.928	12	232
CH3SSCH3	Disulfide, dimethyl	1	A	3190	2990	0.937	13	233
		2	A	3176	2983	0.939	13	234
		3	A	3077	2913	0.947	13	235
		4	A	1481	1426	0.963	13	236
		5	A	1469	1419	0.966	13	237
		6	A	1362	1311	0.963	13	238
		7	A	983	955	0.971	13	239
		8	A	977	949	0.971	13	240
		9	A	727	694	0.955	13	241
		10	A	508	509	1.002	13	242
		11	A	237	240	1.012	13	243
		12	A	158	134	0.848	13	244
		13	A	97	117	1.211	13	245
		14	B	3190	2990	0.937	13	246
		15	B	3176	2983	0.939	13	247
		16	B	3075	2915	0.948	13	248
		17	B	1484	1430	0.963	13	249
		18	B	1463	1415	0.967	13	250
		19	B	1353	1303	0.963	13	251
		20	B	982	955	0.972	13	252
		21	B	975	949	0.973	13	253
		22	B	724	691	0.955	13	254
		23	B	267	274	1.024	13	255
		24	B	167	134	0.801	13	256
H2	Hydrogen diatomic	1	Σg	4399	4401	1.001	14	257
CF2	Difluoromethylene	1	A1	1283	1225	0.955	15	258
		1	A1	1169	1225	1.048	15	259
		2	A1	679	667	0.982	15	260
		2	A1	523	667	1.276	15	261
		3	B2	1199	1114	0.930	15	262
		3	B2	1367	1114	0.815	15	263
SF6	Sulfur Hexafluoride	1	A1g	770	774	1.005	16	264
		2	Eg	688	642	0.933	16	265
		3	T1u	1027	948	0.922	16	266
		4	T1u	598	616	1.029	16	267
		5	T2g	498	525	1.055	16	268
		6	T2u	341	347	1.016	16	269
C3H4	cyclopropene	1	A1	3335	3158	0.947	17	270
		2	A1	3094	2909	0.940	17	271
		3	A1	1729	1653	0.956	17	272
		4	A1	1525	1483	0.973	17	273
		5	A1	1191	1110	0.932	17	274
		6	A1	931	905	0.972	17	275
		7	A2	1020	996	0.977	17	276
		8	A2	840	820	0.977	17	277
		9	B1	3169	2995	0.945	17	278
		10	B1	1107	1088	0.983	17	279
		11	B1	592	569	0.962	17	280
		12	B2	3290	3124	0.950	17	281
		13	B2	1087	1043	0.960	17	282
		14	B2	1049	1011	0.964	17	283
		15	B2	808	769	0.952	17	284
CS	carbon monosulfide	1	Σ	1351	1285	0.951	18	285
CH	Methylidyne	1	Σ	2851	2861	1.004	19	286
		1	Σ	3154	2861	0.907	19	287
		1	Σ	2851	3145	1.103	19	288
		1	Σ	3154	3145	0.997	19	289
		1	Σ	2851	2931	1.028	19	290
		1	Σ	3154	2931	0.929	19	291
OH	Hydroxyl radical	1	Σ	3752	3738	0.996	20	292
SiH2Cl2	dichlorosilane	1	A1	2304	2224	0.965	21	293
		2	A1	961	954	0.993	21	294
		3	A1	529	527	0.997	21	295
		4	A1	188	188	1.002	21	296
		5	A2	725	710	0.979	21	297
		6	B1	2320	2237	0.964	21	298
		7	B1	601	602	1.001	21	299
		8	B2	896	876	0.978	21	300
		9	B2	596	590	0.990	21	301
HCl	Hydrogen chloride	1	Σ	3043	2991	0.983	22	302
HF	Hydrogen fluoride	1	Σ	4189	4138	0.988	23	303
NH3	Ammonia	1	A1	3474	3337	0.961	24	304
		2	A1	1178	950	0.806	24	305
		3	E	3601	3444	0.956	24	306
		4	E	1697	1627	0.959	24	307
H2O	Water	1	A1	3867	3657	0.946	25	308
		2	A1	1699	1595	0.939	25	309
		3	B2	3970	3756	0.946	25	310
H2S	Hydrogen sulfide	1	A1	2751	2615	0.951	26	311
		2	A1	1219	1183	0.970	26	312
		3	B2	2771	2626	0.948	26	313
AlH3	aluminum trihydride	1	A1'	1931	1900	0.984	27	314
		2	A2"	728	698	0.958	27	315
		3	E'	1940	1883	0.970	27	316
		4	E'	797	783	0.983	27	317
PH3	Phosphine	1	A1	2437	2323	0.953	28	318
		2	A1	1043	992	0.951	28	319
		3	E	2448	2328	0.951	28	320
		4	E	1155	1118	0.968	28	321
SiH4	Silane	1	A1	2256	2187	0.969	29	322
		2	E	986	975	0.989	29	323
		3	T2	2267	2191	0.966	29	324
		4	T2	936	914	0.977	29	325
BH3	boron trihydride	2	A2"	1163	1148	0.987	30	326
		3	E'	2713	2602	0.959	30	327
		4	E'	1218	1197	0.982	30	328
PH2	Phosphino radical	1	A1	2409	2310	0.959	31	329
		2	A1	1142	1102	0.965	31	330
SiH3	silyl	1	A1	2226	2136	0.960	32	331
		2	A1	786	728	0.927	32	332
		3	E	2262	2185	0.966	32	333
		4	E	944	922	0.977	32	334
BH	Boron monohydride	1	Σ	2362	2367	1.002	33	335
NH2	Amino radical	1	A1	3368	3219	0.956	34	336
		2	A1	1575	1497	0.951	34	337
		3	B2	3464	3301	0.953	34	338
NH	Imidogen	1	Σ	3259	3283	1.007	35	339
		1	Σ	3311	3283	0.991	35	340
		1	Σ	3259	3314	1.017	35	341
		1	Σ	3311	3314	1.001	35	342
SiH	Silylidyne	1	Σ	2045	2043	0.999	36	343
SiH2	silicon dihydride	1	A1	2080	1996	0.959	37	344
		1	A1	2207	1996	0.904	37	345
		2	A1	1042	999	0.959	37	346
		2	A1	892	999	1.120	37	347
		3	B2	2078	1993	0.959	37	348
		3	B2	2267	1993	0.879	37	349
SH	Mercapto radical	1	Σ	2720	2696	0.991	38	350
PH	phosphorus monohydride	1	Σ	2363	2364	1.000	39	351
		1	Σ	2393	2364	0.988	39	352
		1	Σ	2363	2415	1.022	39	353
		1	Σ	2393	2415	1.009	39	354
		1	Σ	2363	2403	1.017	39	355
		1	Σ	2393	2403	1.004	39	356
AlH	aluminum monohydride	1	Σ	1682	1682	1.000	40	357
BH2	boron dihydride	2	A1	1037	954	0.920	41	358
AlH2	aluminum dihydride	1	A1	1846	1770	0.959	42	359
		2	A1	773	760	0.984	42	360
		3	B2	1881	1807	0.960	42	361

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.

	200
	150
	100
	50
	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