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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)/cc-pV(T+d)Z

Scale factor	How many		Source
	Molecules	Vibrations
0.965 ± 0.021	51	179	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
H2CO	Formaldehyde	1	A1	2929	2782	0.950	1	1
		2	A1	1781	1746	0.980	1	2
		3	A1	1543	1500	0.972	1	3
		4	B1	1192	1167	0.979	1	4
		5	B2	2996	2843	0.949	1	5
		6	B2	1274	1249	0.980	1	6
HCOOH	Formic acid	1	A'	3764	3570	0.949	2	7
		2	A'	3089	2943	0.953	2	8
		3	A'	1825	1770	0.970	2	9
		4	A'	1416	1387	0.980	2	10
		5	A'	1326	1229	0.927	2	11
		6	A'	1137	1105	0.972	2	12
		7	A'	629	625	0.993	2	13
		8	A"	1062	1033	0.973	2	14
		9	A"	677	638	0.943	2	15
CH3OH	Methyl alcohol	1	A'	3865	3681	0.952	3	16
		2	A'	3129	3000	0.959	3	17
		3	A'	3010	2844	0.945	3	18
		4	A'	1522	1477	0.970	3	19
		5	A'	1487	1455	0.979	3	20
		6	A'	1394	1345	0.965	3	21
		7	A'	1095	1060	0.968	3	22
		8	A'	1064	1033	0.971	3	23
		9	A"	3065	2960	0.966	3	24
		10	A"	1507	1477	0.980	3	25
		11	A"	1179	1165	0.988	3	26
		12	A"	304	200	0.657	3	27
CH4	Methane	1	A1	3036	2917	0.961	4	28
		2	E	1570	1534	0.977	4	29
		3	T2	3155	3019	0.957	4	30
		4	T2	1343	1306	0.972	4	31
C2H6	Ethane	1	A1g	3040	2896	0.953	5	32
		2	A1g	1428	1388	0.972	5	33
		3	A1g	1015	995	0.980	5	34
		4	A1u	311	289	0.931	5	35
		5	A2u	3038	2915	0.959	5	36
		6	A2u	1407	1370	0.974	5	37
		7	Eg	3097	2969	0.959	5	38
		8	Eg	1511	1468	0.972	5	39
		9	Eg	1225	1190	0.971	5	40
		10	Eu	3120	2974	0.953	5	41
		11	Eu	1513	1460	0.965	5	42
		12	Eu	821	822	1.001	5	43
C2H4	Ethylene	1	Ag	3159	3026	0.958	6	44
		2	Ag	1671	1623	0.971	6	45
		3	Ag	1369	1342	0.981	6	46
		4	Au	1046	1023	0.978	6	47
		5	B1u	3141	2989	0.951	6	48
		6	B1u	1478	1444	0.977	6	49
		7	B2g	942	940	0.998	6	50
		8	B2u	3248	3105	0.956	6	51
		9	B2u	821	826	1.007	6	52
		10	B3g	3221	3086	0.958	6	53
		11	B3g	1241	1217	0.980	6	54
		12	B3u	966	949	0.982	6	55
C2H2	Acetylene	1	Σg	3512	3374	0.961	7	56
		2	Σg	2001	1974	0.986	7	57
		3	Σu	3411	3289	0.964	7	58
		4	Πg	577	612	1.060	7	59
		5	Πu	746	730	0.979	7	60
CH3Cl	Methyl chloride	1	A1	3080	2966	0.963	8	61
		2	A1	1385	1355	0.978	8	62
		3	A1	746	732	0.981	8	63
		4	E	3181	3042	0.956	8	64
		5	E	1493	1455	0.974	8	65
		6	E	1031	1015	0.984	8	66
HCN	Hydrogen cyanide	1	Σ	3444	3312	0.962	9	67
		2	Σ	2112	2089	0.989	9	68
		3	Π	716	712	0.994	9	69
CS2	Carbon disulfide	1	Σg	668	658	0.986	10	70
		2	Σu	1558	1535	0.985	10	71
		3	Πu	402	397	0.989	10	72
CO2	Carbon dioxide	1	Σg	1346	1333	0.990	11	73
		2	Σu	2396	2349	0.980	11	74
		3	Πu	660	667	1.010	11	75
CF2O	Carbonic difluoride	1	A1	1978	1928	0.975	12	76
		2	A1	984	965	0.981	12	77
		3	A1	588	584	0.993	12	78
		4	B1	786	774	0.985	12	79
		5	B2	1294	1249	0.965	12	80
		6	B2	626	626	1.000	12	81
C2N2	Cyanogen	1	Σg	2368	2330	0.984	13	82
		2	Σg	856	846	0.988	13	83
		3	Σu	2176	2158	0.992	13	84
		4	Πg	499	503	1.009	13	85
		5	Πu	236	234	0.990	13	86
CH2CCH2	allene	1	A1	3143	3015	0.959	14	87
		2	A1	1488	1443	0.970	14	88
		3	A1	1081	1073	0.993	14	89
		4	B1	871	865	0.993	14	90
		5	B2	3141	3007	0.957	14	91
		6	B2	2013	1957	0.972	14	92
		7	B2	1438	1398	0.972	14	93
		8	E	3225	3086	0.957	14	94
		9	E	1017	999	0.982	14	95
		10	E	857	841	0.981	14	96
		11	E	348	355	1.019	14	97
OCS	Carbonyl sulfide	1	Σ	2093	2062	0.985	15	98
		2	Σ	869	859	0.988	15	99
		3	Π	523	520	0.994	15	100
ClCN	chlorocyanogen	1	Σ	2240	2216	0.989	16	101
		2	Σ	740	744	1.005	16	102
		3	Π	384	378	0.984	16	103
CO	Carbon monoxide	1	Σ	2153	2170	1.008	17	104
		1	Σ	2153	1743	0.810	17	105
H2CS	Thioformaldehyde	1	A1	3083	2971	0.964	18	106
		2	A1	1500	1456	0.970	18	107
		3	A1	1069	1059	0.990	18	108
		4	B1	1008	990	0.982	18	109
		5	B2	3172	3025	0.953	18	110
		6	B2	1005	991	0.986	18	111
BeO	beryllium oxide	1	Σ	1458	1457	1.000	19	112
MgO	magnesium oxide	1	Σ	785	785	1.001	20	113
LiOH	lithium hydroxide	1	Σ	4021	3688	0.917	21	114
		2	Σ	961	871	0.906	21	115
		3	Π	324	257	0.791	21	116
H2	Hydrogen diatomic	1	Σg	4410	4401	0.998	22	117
CN	Cyano radical	1	Σ	2114	2069	0.978	23	118
CF2	Difluoromethylene	1	A1	1257	1225	0.974	24	119
		1	A1	1163	1225	1.054	24	120
		2	A1	673	667	0.991	24	121
		2	A1	517	667	1.290	24	122
		3	B2	1164	1114	0.958	24	123
		3	B2	1347	1114	0.827	24	124
HCO	Formyl radical	1	A'	2690	2434	0.905	25	125
		2	A'	1893	1868	0.987	25	126
		3	A'	1123	1081	0.962	25	127
CS	carbon monosulfide	1	Σ	1271	1285	1.011	26	128
HO2	Hydroperoxy radical	1	A'	3676	3436	0.935	27	129
		2	A'	1437	1392	0.969	27	130
		3	A'	1135	1098	0.967	27	131
CH	Methylidyne	1	Σ	2835	2861	1.009	28	132
		1	Σ	2835	3145	1.109	28	133
		1	Σ	2835	2931	1.034	28	134
OH	Hydroxyl radical	1	Σ	3740	3738	0.999	29	135
CF	Fluoromethylidyne	1	Σ	1321	1308	0.990	30	136
HNC	hydrogen isocyanide	1	Σ	3825	3653	0.955	31	137
		2	Σ	2046	2029	0.992	31	138
		3	Π	472	477	1.011	31	139
SO2	Sulfur dioxide	1	A1	1169	1151	0.985	32	140
		2	A1	519	518	0.997	32	141
		3	B2	1389	1362	0.980	32	142
LiH	Lithium Hydride	1	Σ	1395	1405	1.008	33	143
BF3	Borane, trifluoro-	1	A1'	899	888	0.987	34	144
		2	A2"	700	691	0.987	34	145
		3	E'	1494	1449	0.970	34	146
		4	E'	483	480	0.993	34	147
NaH	sodium hydride	1	Σ	1132	1172	1.035	35	148
HCl	Hydrogen chloride	1	Σ	3006	2991	0.995	36	149
HF	Hydrogen fluoride	1	Σ	4181	4138	0.990	37	150
NH3	Ammonia	1	A1	3471	3337	0.961	38	151
		2	A1	1112	950	0.854	38	152
		3	E	3596	3444	0.958	38	153
		4	E	1688	1627	0.964	38	154
NaF	sodium fluoride	1	Σ	549	536	0.976	39	155
MgH2	magnesium dihydride	2	Σu	1632	1572	0.963	40	156
		3	Πu	440	440	0.999	40	157
H2O2	Hydrogen peroxide	1	A	3810	3599	0.945	41	158
		2	A	1436	1402	0.976	41	159
		3	A	912	877	0.961	41	160
		4	A	363	371	1.023	41	161
		5	B	3809	3608	0.947	41	162
		6	B	1324	1266	0.956	41	163
N2	Nitrogen diatomic	1	Σg	2346	2359	1.005	42	164
H2O	Water	1	A1	3841	3657	0.952	43	165
		2	A1	1668	1595	0.956	43	166
		3	B2	3945	3756	0.952	43	167
F2	Fluorine diatomic	1	Σg	919	917	0.997	44	168
Cl2	Chlorine diatomic	1	Σg	549	560	1.019	45	169
H2S	Hydrogen sulfide	1	A1	2723	2615	0.960	46	170
		2	A1	1209	1183	0.978	46	171
		3	B2	2737	2626	0.959	46	172
F2O	Difluorine monoxide	1	A1	950	928	0.977	47	173
		2	A1	469	461	0.983	47	174
		3	B2	867	831	0.958	47	175
AlH3	aluminum trihydride	1	A1'	1940	1900	0.979	48	176
		2	A2"	715	698	0.976	48	177
		3	E'	1944	1883	0.969	48	178
		4	E'	797	783	0.983	48	179
BeH2	beryllium dihydride	2	Σu	2237	2159	0.965	49	180
		3	Πu	710	698	0.984	49	181
LiF	lithium fluoride	1	Σ	909	911	1.002	50	182
FNO	Nitrosyl fluoride	1	A'	1853	1844	0.995	51	183
		2	A'	804	766	0.953	51	184
		3	A'	549	520	0.947	51	185

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.

	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