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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at AM1

Scale factor	How many		Source
	Molecules	Vibrations
0.954 ± 0.059	231	2457	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
H2CO	Formaldehyde	1	A1	3120	2782	0.892	1	1
		2	A1	2053	1746	0.850	1	2
		3	A1	1443	1500	1.039	1	3
		4	B1	1155	1167	1.011	1	4
		5	B2	3086	2843	0.921	1	5
		6	B2	1162	1249	1.074	1	6
C2H6	Ethane	1	A1g	3148	2896	0.920	2	7
		2	A1g	1444	1388	0.961	2	8
		3	A1g	1248	995	0.797	2	9
		4	A1u	203	289	1.424	2	10
		5	A2u	3164	2915	0.921	2	11
		6	A2u	1431	1370	0.958	2	12
		7	Eg	3050	2969	0.973	2	13
		8	Eg	1395	1468	1.052	2	14
		9	Eg	1168	1190	1.019	2	15
		10	Eu	3072	2974	0.968	2	16
		11	Eu	1395	1460	1.047	2	17
		12	Eu	889	822	0.924	2	18
CH3CH2CH2CH3	Butane	1	A	3156	2965	0.939	3	19
		2	A	3087	2872	0.930	3	20
		3	A	3062	2853	0.932	3	21
		4	A	3060	1460	0.477	3	22
		5	A	3012	1442	0.479	3	23
		6	A	1442	1382	0.959	3	24
		7	A	1430	1361	0.951	3	25
		8	A	1406	1151	0.818	3	26
		9	A	1398	1059	0.757	3	27
		10	A	1394	837	0.600	3	28
		11	A	1273	425	0.334	3	29
		12	A	1241	2968	2.392	3	30
		13	A	1193	2930	2.457	3	31
		14	A	1073	1461	1.362	3	32
		15	A	967	1257	1.300	3	33
		16	A	847	948	1.119	3	34
		17	A	349	731	2.094	3	35
		18	A	196	194	0.989	3	36
		19	A	71	102	1.434	3	37
		20	B	3156	2965	0.939	3	38
		21	B	3095	2912	0.941	3	39
		22	B	3063	1460	0.477	3	40
		23	B	3061	1300	0.425	3	41
		24	B	3018	1180	0.391	3	42
		25	B	1440	803	0.558	3	43
		26	B	1411	225	0.159	3	44
		27	B	1400	2968	2.120	3	45
		28	B	1393	2870	2.061	3	46
		29	B	1392	2853	2.050	3	47
		30	B	1243	1461	1.175	3	48
		31	B	1191	1461	1.227	3	49
		32	B	1089	1379	1.266	3	50
		33	B	1015	1290	1.271	3	51
		34	B	819	1009	1.232	3	52
		35	B	460	964	2.094	3	53
		36	B	149	271	1.819	3	54
C6H12	Cyclohexane	1	A	3098	2930	0.946	4	55
		2	A	3095	2852	0.921	4	56
		3	A	3092	1465	0.474	4	57
		4	A	3041	1157	0.380	4	58
		5	A	3017	802	0.266	4	59
		6	A	3011	383	0.127	4	60
		7	A	1426	1383	0.970	4	61
		8	A	1416	1157	0.817	4	62
		9	A	1415	1057	0.747	4	63
		10	A	1404	1437	1.023	4	64
		11	A	1401	1090	0.778	4	65
		12	A	1378	2915	2.115	4	66
		13	A	1256	2860	2.277	4	67
		14	A	1256	1437	1.144	4	68
		15	A	1196	1030	0.861	4	69
		16	A	1178	523	0.444	4	70
		17	A	1166	2930	2.513	4	71
		19	A	966	2897	2.999	4	72
		21	A	799	1443	1.805	4	73
		23	A	463	1347	2.909	4	74
		25	A	72	1266	17.586	4	75
		27	B	3093	1027	0.332	4	76
		29	B	3034	785	0.259	4	77
		31	B	3005	426	0.142	4	78
		33	B	1428	2933	2.054	4	79
		35	B	1396	2863	2.051	4	80
		37	B	1393	1457	1.046	4	81
		39	B	1205	1355	1.125	4	82
		41	B	1162	1261	1.086	4	83
		43	B	1038	907	0.874	4	84
		45	B	996	863	0.866	4	85
		47	B	616	248	0.403	4	86
C5H11N	Piperidine	1	A'	3408	3341	0.980	5	87
		2	A'	3104	2947	0.949	5	88
		3	A'	3096	2931	0.947	5	89
		4	A'	3043	2917	0.959	5	90
		5	A'	3037	2892	0.952	5	91
		6	A'	3019	2850	0.944	5	92
		7	A'	2949	2730	0.926	5	93
		8	A'	1483	1476	0.995	5	94
		9	A'	1419	1452	1.023	5	95
		10	A'	1411	1444	1.023	5	96
		11	A'	1403	1386	0.988	5	97
		12	A'	1387	1365	0.984	5	98
		13	A'	1253	1346	1.074	5	99
		14	A'	1239	1266	1.022	5	100
		15	A'	1185	1164	0.983	5	101
		16	A'	1179	1035	0.878	5	102
		17	A'	1078	1006	0.933	5	103
		18	A'	1038	906	0.873	5	104
		19	A'	1019	853	0.837	5	105
		20	A'	917	822	0.896	5	106
		21	A'	828	743	0.898	5	107
		22	A'	608	546	0.898	5	108
		23	A'	493	432	0.877	5	109
		24	A'	307	404	1.315	5	110
		25	A'	197	246	1.248	5	111
		26	A"	3102	2940	0.948	5	112
		27	A"	3039	2902	0.955	5	113
		28	A"	3033	2850	0.940	5	114
		29	A"	2948	2803	0.951	5	115
		30	A"	1546	1468	0.950	5	116
		31	A"	1462	1460	0.999	5	117
		32	A"	1417	1436	1.013	5	118
		33	A"	1401	1332	0.951	5	119
		34	A"	1385	1318	0.951	5	120
		35	A"	1376	1285	0.934	5	121
		36	A"	1320	1258	0.953	5	122
		37	A"	1246	1191	0.956	5	123
		38	A"	1218	1146	0.941	5	124
		39	A"	1141	1115	0.977	5	125
		40	A"	1140	1052	0.923	5	126
		41	A"	1037	964	0.930	5	127
		42	A"	989	874	0.884	5	128
		43	A"	847	810	0.956	5	129
		44	A"	500	445	0.890	5	130
		45	A"	194	254	1.312	5	131
		1	A'	3390	3341	0.986	5	132
		2	A'	3105	2947	0.949	5	133
		3	A'	3095	2931	0.947	5	134
		4	A'	3059	2917	0.953	5	135
		5	A'	3041	2892	0.951	5	136
		6	A'	3018	2850	0.944	5	137
		7	A'	2990	2730	0.913	5	138
		8	A'	1462	1476	1.010	5	139
		9	A'	1415	1452	1.026	5	140
		10	A'	1411	1444	1.024	5	141
		11	A'	1395	1386	0.993	5	142
		12	A'	1385	1365	0.985	5	143
		13	A'	1297	1346	1.038	5	144
		14	A'	1230	1266	1.029	5	145
		15	A'	1196	1164	0.973	5	146
		16	A'	1175	1035	0.881	5	147
		17	A'	1074	1006	0.936	5	148
		18	A'	1018	906	0.890	5	149
		19	A'	1000	853	0.853	5	150
		20	A'	947	822	0.868	5	151
		21	A'	848	743	0.876	5	152
		22	A'	620	546	0.881	5	153
		23	A'	492	432	0.877	5	154
		24	A'	334	404	1.211	5	155
		25	A'	211	246	1.168	5	156
		26	A"	3103	2940	0.947	5	157
		27	A"	3059	2902	0.949	5	158
		28	A"	3034	2850	0.939	5	159
		29	A"	2989	2803	0.938	5	160
		30	A"	1540	1468	0.953	5	161
		31	A"	1432	1460	1.019	5	162
		32	A"	1416	1436	1.014	5	163
		33	A"	1403	1332	0.950	5	164
		34	A"	1383	1318	0.953	5	165
		35	A"	1377	1285	0.933	5	166
		36	A"	1328	1258	0.947	5	167
		37	A"	1249	1191	0.954	5	168
		38	A"	1220	1146	0.939	5	169
		39	A"	1136	1115	0.982	5	170
		40	A"	1127	1052	0.934	5	171
		41	A"	1041	964	0.926	5	172
		42	A"	981	874	0.891	5	173
		43	A"	848	810	0.956	5	174
		44	A"	496	445	0.896	5	175
		45	A"	201	254	1.263	5	176
CF2	Difluoromethylene	1	A1	1435	1225	0.854	6	177
		2	A1	559	667	1.193	6	178
		3	B2	1487	1114	0.749	6	179
CH	Methylidyne	1	Σ	3322	2861	0.861	7	180
		1	Σ	3322	3145	0.947	7	181
		1	Σ	3322	2931	0.882	7	182
OH	Hydroxyl radical	1	Σ	3615	3738	1.034	8	183
FNO	Nitrosyl fluoride	1	A'	2185	1844	0.844	9	184
		2	A'	1207	766	0.635	9	185
		3	A'	726	520	0.717	9	186
C2	Carbon diatomic	1	Σg	1907	1855	0.973	10	187
NH	Imidogen	1	Σ	3497	3283	0.939	11	188
		1	Σ	3497	3314	0.948	11	189
NF	nitrogen fluoride	1	Σ	1431	1141	0.798	12	190
PH	phosphorus monohydride	1	Σ	2476	2364	0.955	13	191
		1	Σ	2476	2415	0.976	13	192
		1	Σ	2476	2403	0.971	13	193
PCl	phosphorus chloride	1	Σ	732	577	0.788	14	194
S2	Sulfur diatomic	1	Σg	774	726	0.937	15	195

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.

	70
	60
	50
	40
	30
	20
	10
	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