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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at B3LYP/aug-cc-pVQZ

Scale factor	How many		Source
	Molecules	Vibrations
0.969 ± 0.021	115	344	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
H2CO	Formaldehyde	1	A1	2882	2782	0.965	1	1
		2	A1	1816	1746	0.961	1	2
		3	A1	1533	1500	0.979	1	3
		4	B1	1200	1167	0.972	1	4
		5	B2	2937	2843	0.968	1	5
		6	B2	1267	1249	0.986	1	6
CH3OH	Methyl alcohol	1	A'	3831	3681	0.961	2	7
		2	A'	3106	3000	0.966	2	8
		3	A'	2991	2844	0.951	2	9
		4	A'	1511	1477	0.978	2	10
		5	A'	1481	1455	0.982	2	11
		6	A'	1368	1345	0.983	2	12
		7	A'	1079	1060	0.982	2	13
		8	A'	1043	1033	0.991	2	14
		9	A"	3036	2960	0.975	2	15
		10	A"	1499	1477	0.985	2	16
		11	A"	1174	1165	0.992	2	17
		12	A"	297	200	0.674	2	18
CH4	Methane	1	A1	3027	2917	0.964	3	19
		2	E	1559	1534	0.984	3	20
		3	T2	3130	3019	0.965	3	21
		4	T2	1342	1306	0.974	3	22
C2H6	Ethane	1	A1g	3025	2896	0.957	4	23
		2	A1g	1422	1388	0.976	4	24
		3	A1g	995	995	1.000	4	25
		4	A1u	303	289	0.954	4	26
		5	A2u	3026	2915	0.963	4	27
		6	A2u	1412	1370	0.970	4	28
		7	Eg	3070	2969	0.967	4	29
		8	Eg	1503	1468	0.977	4	30
		9	Eg	1222	1190	0.974	4	31
		10	Eu	3094	2974	0.961	4	32
		11	Eu	1506	1460	0.969	4	33
		12	Eu	826	822	0.995	4	34
C2H4	Ethylene	1	Ag	3138	3026	0.964	5	35
		2	Ag	1689	1623	0.961	5	36
		3	Ag	1381	1342	0.972	5	37
		4	Au	1064	1023	0.962	5	38
		5	B1u	3125	2989	0.956	5	39
		6	B1u	1480	1444	0.975	5	40
		7	B2g	987	940	0.952	5	41
		8	B2u	3222	3105	0.964	5	42
		9	B2u	837	826	0.987	5	43
		10	B3g	3194	3086	0.966	5	44
		11	B3g	1248	1217	0.975	5	45
		12	B3u	979	949	0.969	5	46
C2H2	Acetylene	1	Σg	3509	3374	0.962	6	47
		2	Σg	2067	1974	0.955	6	48
		3	Σu	3410	3289	0.965	6	49
		4	Πg	672	612	0.911	6	50
		5	Πu	767	730	0.952	6	51
CH3Cl	Methyl chloride	1	A1	3069	2966	0.967	7	52
		2	A1	1380	1355	0.982	7	53
		3	A1	715	732	1.024	7	54
		4	E	3163	3042	0.962	7	55
		5	E	1484	1455	0.980	7	56
		6	E	1028	1015	0.987	7	57
CH3NH2	methyl amine	1	A'	3500	3361	0.960	8	58
		2	A'	3055	2961	0.969	8	59
		3	A'	2966	2820	0.951	8	60
		4	A'	1661	1623	0.977	8	61
		5	A'	1500	1473	0.982	8	62
		6	A'	1462	1430	0.978	8	63
		7	A'	1169	1130	0.967	8	64
		8	A'	1055	1044	0.989	8	65
		9	A'	819	780	0.952	8	66
		10	A"	3575	3427	0.959	8	67
		11	A"	3090	2985	0.966	8	68
		12	A"	1519	1485	0.978	8	69
		13	A"	1345	1335	0.992	8	70
		14	A"	974	1195	1.227	8	71
		15	A"	294	268	0.910	8	72
HCN	Hydrogen cyanide	1	Σ	3438	3312	0.963	9	73
		2	Σ	2200	2089	0.949	9	74
		3	Π	759	712	0.939	9	75
CH3SH	Methanethiol	1	A'	3133	3000	0.958	10	76
		2	A'	3050	2931	0.961	10	77
		3	A'	2672	2597	0.972	10	78
		4	A'	1490	1475	0.990	10	79
		5	A'	1360	1335	0.982	10	80
		6	A'	1097	1074	0.979	10	81
		7	A'	799	803	1.005	10	82
		8	A'	699	708	1.013	10	83
		9	A"	3132	3000	0.958	10	84
		10	A"	1477	1430	0.968	10	85
		11	A"	974	976	1.002	10	86
N2H4	Hydrazine	1	A	3555	3398	0.956	11	87
		2	A	3462	3329	0.962	11	88
		3	A	1686	1642	0.974	11	89
		4	A	1325	1275	0.963	11	90
		5	A	1112	1076	0.968	11	91
		6	A	800	780	0.975	11	92
		7	A	442	377	0.852	11	93
		8	B	3561	3350	0.941	11	94
		9	B	3454	3314	0.959	11	95
		10	B	1674	1628	0.973	11	96
		11	B	1296	1275	0.984	11	97
		12	B	971	966	0.995	11	98
CH3F	Methyl fluoride	1	A1	3030	2930	0.967	12	99
		2	A1	1484	1464	0.986	12	100
		3	A1	1043	1049	1.006	12	101
		4	E	3110	3006	0.967	12	102
		5	E	1495	1467	0.981	12	103
		6	E	1194	1182	0.990	12	104
CH3PH2	Methyl phosphine	1	A'	3124	3000	0.960	13	105
		2	A'	3040	2938	0.966	13	106
		3	A'	2373	2297	0.968	13	107
		4	A'	1474	1450	0.983	13	108
		5	A'	1328	1238	0.932	13	109
		6	A'	1117	1086	0.972	13	110
		7	A'	994	977	0.983	13	111
		8	A'	738	740	1.002	13	112
		9	A'	669	677	1.012	13	113
		10	A"	3110	2992	0.962	13	114
		11	A"	2377	2312	0.973	13	115
		12	A"	1480	1450	0.980	13	116
		13	A"	1036	1017	0.982	13	117
		15	A"	228	207	0.908	13	118
CO	Carbon monoxide	1	Σ	2212	2170	0.981	14	119
		1	Σ	2212	1743	0.788	14	120
H2CS	Thioformaldehyde	1	A1	3060	2971	0.971	15	121
		2	A1	1495	1456	0.973	15	122
		3	A1	1087	1059	0.974	15	123
		4	B1	1031	990	0.960	15	124
		5	B2	3140	3025	0.963	15	125
		6	B2	1005	991	0.986	15	126
BeO	beryllium oxide	1	Σ	1550	1457	0.940	16	127
MgO	magnesium oxide	1	Σ	821	785	0.957	17	128
LiOH	lithium hydroxide	1	Σ	4000	3688	0.922	18	129
		2	Σ	952	871	0.914	18	130
		3	Π	341	257	0.752	18	131
NaOH	sodium hydroxide	1	Σ	3951	3637	0.921	19	132
		2	Σ	558	540	0.968	19	133
		3	Π	172	300	1.747	19	134
H2	Hydrogen diatomic	1	Σg	4420	4401	0.996	20	135
Si2H6	disilane	1	A1g	2220	2152	0.969	21	136
		2	A1g	928	909	0.980	21	137
		3	A1g	423	434	1.027	21	138
		4	A1u	137	131	0.954	21	139
		5	A2u	2212	2154	0.974	21	140
		6	A2u	855	844	0.987	21	141
		7	Eg	2217	2155	0.972	21	142
		8	Eg	946	929	0.982	21	143
		9	Eg	634	625	0.986	21	144
		10	Eu	2226	2179	0.979	21	145
		11	Eu	960	940	0.979	21	146
		12	Eu	375	379	1.011	21	147
CH2NH	Methanimine	1	A'	3432	3263	0.951	22	148
		2	A'	3108	3024	0.973	22	149
		3	A'	3013	2914	0.967	22	150
		4	A'	1710	1638	0.958	22	151
		5	A'	1492	1452	0.973	22	152
		6	A'	1368	1344	0.983	22	153
		7	A'	1074	1058	0.986	22	154
		8	A"	1163	1127	0.969	22	155
		9	A"	1103	1061	0.962	22	156
CN	Cyano radical	1	Σ	2153	2069	0.961	23	157
HCO	Formyl radical	1	A'	2649	2434	0.919	24	158
		2	A'	1934	1868	0.966	24	159
		3	A'	1105	1081	0.978	24	160
CS	carbon monosulfide	1	Σ	1306	1285	0.984	25	161
HO2	Hydroperoxy radical	1	A'	3595	3436	0.956	26	162
		2	A'	1435	1392	0.970	26	163
		3	A'	1166	1098	0.942	26	164
CH	Methylidyne	1	Σ	2830	2861	1.011	27	165
		1	Σ	3047	2861	0.939	27	166
		1	Σ	2830	3145	1.111	27	167
		1	Σ	3047	3145	1.032	27	168
		1	Σ	2830	2931	1.035	27	169
		1	Σ	3047	2931	0.962	27	170
OH	Hydroxyl radical	1	Σ	3703	3738	1.009	28	171
CF	Fluoromethylidyne	1	Σ	1293	1308	1.011	29	172
CCl	carbon monochloride	1	Σ	853	877	1.028	30	173
HCP	HCP	1	Σ	3348	3217	0.961	31	174
		2	Σ	1342	1278	0.952	31	175
		3	Π	721	674	0.936	31	176
HNC	hydrogen isocyanide	1	Σ	3800	3653	0.961	32	177
		2	Σ	2104	2029	0.964	32	178
		3	Π	468	477	1.019	32	179
LiCl	lithium chloride	1	Σ	640	643	1.004	33	180
LiH	Lithium Hydride	1	Σ	1420	1405	0.990	34	181
NaH	sodium hydride	1	Σ	1181	1172	0.993	35	182
HCl	Hydrogen chloride	1	Σ	2932	2991	1.020	36	183
NaCl	Sodium Chloride	1	Σ	358	365	1.020	37	184
HF	Hydrogen fluoride	1	Σ	4077	4138	1.015	38	185
NH3	Ammonia	1	A1	3472	3337	0.961	39	186
		2	A1	1018	950	0.933	39	187
		3	E	3593	3444	0.959	39	188
		4	E	1663	1627	0.978	39	189
NaF	sodium fluoride	1	Σ	525	536	1.021	40	190
MgH2	magnesium dihydride	2	Σu	1633	1572	0.962	41	191
		3	Πu	444	440	0.991	41	192
H2O2	Hydrogen peroxide	1	A	3764	3599	0.956	42	193
		2	A	1438	1402	0.975	42	194
		3	A	949	877	0.924	42	195
		4	A	374	371	0.993	42	196
		5	B	3763	3608	0.959	42	197
		6	B	1326	1266	0.955	42	198
N2	Nitrogen diatomic	1	Σg	2448	2359	0.964	43	199
H2O	Water	1	A1	3804	3657	0.961	44	200
		2	A1	1629	1595	0.979	44	201
		3	B2	3906	3756	0.962	44	202
F2	Fluorine diatomic	1	Σg	1045	917	0.877	45	203
Cl2	Chlorine diatomic	1	Σg	539	560	1.038	46	204
H2S	Hydrogen sulfide	1	A1	2686	2615	0.974	47	205
		2	A1	1210	1183	0.978	47	206
		3	B2	2700	2626	0.973	47	207
AlH3	aluminum trihydride	1	A1'	1943	1900	0.978	48	208
		2	A2"	712	698	0.980	48	209
		3	E'	1949	1883	0.966	48	210
		4	E'	799	783	0.981	48	211
BeH2	beryllium dihydride	2	Σu	2260	2159	0.955	49	212
		3	Πu	727	698	0.960	49	213
LiF	lithium fluoride	1	Σ	905	911	1.006	50	214
ClF	Chlorine monofluoride	1	Σ	786	783	0.996	51	215
HOCl	hypochlorous acid	1	A'	3770	3609	0.958	52	216
		2	A'	1260	1239	0.983	52	217
		3	A'	739	724	0.981	52	218
NH2OH	hydroxylamine	1	A'	3811	3650	0.958	53	219
		2	A'	3441	3294	0.957	53	220
		3	A'	1666	1605	0.963	53	221
		4	A'	1394	1353	0.971	53	222
		5	A'	1142	1115	0.977	53	223
		6	A'	929	895	0.963	53	224
		7	A"	3518	3359	0.955	53	225
		8	A"	1328	1295	0.975	53	226
		9	A"	417	386	0.925	53	227
PH3	Phosphine	1	A1	2387	2323	0.973	54	228
		2	A1	1018	992	0.975	54	229
		3	E	2393	2328	0.973	54	230
		4	E	1139	1118	0.982	54	231
SiH4	Silane	1	A1	2238	2187	0.977	55	232
		2	E	979	975	0.996	55	233
		3	T2	2240	2191	0.978	55	234
		4	T2	923	914	0.991	55	235
SiO	Silicon monoxide	1	Σ	1257	1242	0.988	56	236
SiF	silicon monofluoride	1	Σ	824	857	1.040	57	237
MgS	magnesium sulfide	1	Σ	526	529	1.005	58	238
SiN	Silicon nitride	1	Σ	1184	1151	0.973	59	239
C2	Carbon diatomic	1	Σg	1874	1855	0.990	60	240
		1	Σg	1693	1855	1.096	60	241
LiO	lithium oxide	1	Σ	814	815	1.001	61	242
P2	Phosphorus diatomic	1	Σg	808	781	0.967	62	243
BS	boron sulfide	1	Σ	1180	1180	1.000	63	244
AlS	Aluminum sulfide	1	Σ	594	617	1.038	64	245
CP	Carbon monophosphide	1	Σ	1281	1240	0.968	65	246
NaO	sodium monoxide	1	Σ	481	492	1.024	66	247
SiS	silicon monosulfide	1	Σ	744	750	1.008	67	248
BO	boron monoxide	1	Σ	1919	1885	0.982	68	249
Si2	Silicon diatomic	1	Σg	548	511	0.933	69	250
		1	Σg	600	511	0.852	69	251
BH3	boron trihydride	2	A2"	1161	1148	0.989	70	252
		3	E'	2690	2602	0.967	70	253
		4	E'	1206	1197	0.992	70	254
HCF	Fluoromethylene	1	A'	2762	2643	0.957	71	255
		2	A'	1438	1403	0.976	71	256
		3	A'	1198	1189	0.993	71	257
H2S2	HSSH	1	A	2620	2556	0.976	72	258
		2	A	889	882	0.993	72	259
		3	A	500	515	1.029	72	260
		4	A	428	417	0.976	72	261
		5	B	2622	2559	0.976	72	262
		6	B	889	878	0.987	72	263
SiH3Cl	chlorosilane	1	A1	2250	2201	0.978	73	264
		2	A1	954	949	0.995	73	265
		3	A1	532	551	1.036	73	266
		4	E	2259	2195	0.972	73	267
		5	E	959	954	0.994	73	268
		6	E	661	664	1.004	73	269
SiH3F	monofluorosilane	1	A1	2253	2206	0.979	74	270
		2	A1	992	990	0.998	74	271
		3	A1	857	872	1.017	74	272
		4	E	2256	2196	0.973	74	273
		5	E	967	956	0.989	74	274
		6	E	724	728	1.005	74	275
AlCl	Aluminum monochloride	1	Σ	454	482	1.062	75	276
AlF	Aluminum monofluoride	1	Σ	770	802	1.041	76	277
BeF	Beryllium monofluoride	1	Σ	1255	1247	0.994	77	278
BeH	beryllium monohydride	1	Σ	2063	2061	0.999	78	279
BeS	beryllium sulfide	1	Σ	1011	998	0.987	79	280
PH2	Phosphino radical	1	A1	2365	2310	0.977	80	281
		2	A1	1126	1102	0.978	80	282
SiH3	silyl	1	A1	2190	2136	0.975	81	283
		2	A1	770	728	0.945	81	284
		3	E	2227	2185	0.981	81	285
		4	E	938	922	0.983	81	286
BH	Boron monohydride	1	Σ	2354	2367	1.005	82	287
NH2	Amino radical	1	A1	3355	3219	0.960	83	288
		2	A1	1531	1497	0.978	83	289
		3	B2	3444	3301	0.958	83	290
NH	Imidogen	1	Σ	3262	3283	1.006	84	291
		1	Σ	3303	3283	0.994	84	292
		1	Σ	3262	3314	1.016	84	293
		1	Σ	3303	3314	1.003	84	294
SiH	Silylidyne	1	Σ	2021	2043	1.011	85	295
BeCl	beryllium chloride	1	Σ	832	847	1.018	86	296
HPO	HPO	1	A'	2090	2095	1.003	87	297
		2	A'	1220	1188	0.974	87	298
		3	A'	1002	986	0.984	87	299
SiH2	silicon dihydride	1	A1	2042	1996	0.977	88	300
		2	A1	1022	999	0.977	88	301
		3	B2	2041	1993	0.976	88	302
SO	Sulfur monoxide	1	Σ	1152	1151	0.999	89	303
		1	Σ	1152	1151	0.999	89	304
SH	Mercapto radical	1	Σ	2666	2696	1.012	90	305
SiCl	Clorosilylidyne	1	Σ	507	536	1.056	91	306
NF	nitrogen fluoride	1	Σ	1150	1141	0.993	92	307
		1	Σ	1197	1141	0.954	92	308
PH	phosphorus monohydride	1	Σ	2337	2364	1.011	93	309
		1	Σ	2356	2364	1.003	93	310
		1	Σ	2337	2415	1.033	93	311
		1	Σ	2356	2415	1.025	93	312
		1	Σ	2337	2403	1.028	93	313
		1	Σ	2356	2403	1.020	93	314
AlH	aluminum monohydride	1	Σ	1644	1682	1.023	94	315
HOF	Hypofluorous acid	1	A'	3727	3537	0.949	95	316
		2	A'	1409	1393	0.989	95	317
		3	A'	981	886	0.903	95	318
HNO	Nitrosyl hydride	1	A'	2856	2684	0.940	96	319
		2	A'	1668	1565	0.939	96	320
		3	A'	1562	1501	0.961	96	321
MgH	magnesium monohydride	1	Σ	1463	1493	1.021	97	322
Li2	Lithium diatomic	1	Σg	342	351	1.027	98	323
BH2	boron dihydride	2	A1	986	954	0.967	99	324
AlH2	aluminum dihydride	1	A1	1823	1770	0.971	100	325
		2	A1	772	760	0.985	100	326
		3	B2	1864	1807	0.969	100	327
HBS	hydrogen boron sulfide	1	Σ	2838	2736	0.964	101	328
		2	Σ	1187	1172	0.988	101	329
MgF	Magnesium monofluoride	1	Σ	695	712	1.024	102	330
MgCl	magnesium monochloride	1	Σ	444	462	1.040	103	331
ClO	Monochlorine monoxide	1	Σ	855	854	0.999	104	332
SCl	sulfur monochloride	1	Σ	559	575	1.027	105	333
PF	phosphorus monofluoride	1	Σ	820	847	1.032	106	334
		1	Σ	832	847	1.017	106	335
SF	Monosulfur monofluoride	1	Σ	820	838	1.021	107	336
PCl	phosphorus chloride	1	Σ	528	577	1.092	108	337
		1	Σ	549	577	1.051	108	338
PN	Phosphorus mononitride	1	Σ	1403	1337	0.953	109	339
B2H6	Diborane	1	Ag	2619	2524	0.964	110	340
		2	Ag	2176	2104	0.967	110	341
		3	Ag	1207	1180	0.978	110	342
		4	Ag	801	794	0.992	110	343
		5	Au	852	833	0.978	110	344
		6	B1g	2693	2591	0.962	110	345
		7	B1g	942	915	0.972	110	346
		8	B1u	1993	1915	0.961	110	347
		9	B1u	992	973	0.980	110	348
		10	B2g	1859	1768	0.951	110	349
		11	B2g	895	850	0.950	110	350
		12	B2u	2707	2612	0.965	110	351
		13	B2u	956	950	0.994	110	352
		14	B2u	365	368	1.009	110	353
		15	B3g	1024	1012	0.989	110	354
		16	B3u	2606	2525	0.969	110	355
		17	B3u	1716	1602	0.933	110	356
		18	B3u	1200	1177	0.981	110	357
BCl	boron monochloride	1	Σ	819	840	1.026	111	358
HBO	Boron hydride oxide	1	Σ	2892	2850	0.986	112	359
		2	Σ	1867	1826	0.978	112	360
		3	Π	775	756	0.975	112	361
BeOH	beryllium hydroxide	2	A'	1281	1246	0.972	113	362
S2	Sulfur diatomic	1	Σg	713	726	1.017	114	363
		1	Σg	709	726	1.023	114	364
Na2	Sodium diatomic	1	Σg	161	159	0.991	115	365

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.

	180
	160
	140
	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