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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)=FULL/6-31G*

Scale factor	How many		Source
	Molecules	Vibrations
0.971 ± 0.031	30	95	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
H2CO	Formaldehyde	1	A1	2956	2782	0.941	1	1
		2	A1	1795	1746	0.973	1	2
		3	A1	1566	1500	0.958	1	3
		4	B1	1185	1167	0.985	1	4
		5	B2	3021	2843	0.941	1	5
		6	B2	1285	1249	0.972	1	6
HCOOH	Formic acid	1	A'	3661	3570	0.975	2	7
		2	A'	3113	2943	0.945	2	8
		3	A'	1846	1770	0.959	2	9
		4	A'	1432	1387	0.968	2	10
		5	A'	1344	1229	0.915	2	11
		6	A'	1153	1105	0.958	2	12
		7	A'	626	625	0.998	2	13
		8	A"	1054	1033	0.980	2	14
		9	A"	701	638	0.911	2	15
CH4	Methane	1	A1	3056	2917	0.954	3	16
		2	E	1598	1534	0.960	3	17
		3	T2	3178	3019	0.950	3	18
		4	T2	1395	1306	0.936	3	19
C2H6	Ethane	1	A1g	3055	2896	0.948	4	20
		2	A1g	1476	1388	0.940	4	21
		3	A1g	1034	995	0.962	4	22
		4	A1u	322	289	0.898	4	23
		5	A2u	3054	2915	0.955	4	24
		6	A2u	1449	1370	0.946	4	25
		7	Eg	3116	2969	0.953	4	26
		8	Eg	1546	1468	0.950	4	27
		9	Eg	1256	1190	0.948	4	28
		10	Eu	3138	2974	0.948	4	29
		11	Eu	1551	1460	0.941	4	30
		12	Eu	839	822	0.980	4	31
C2H2	Acetylene	1	Σg	3520	3374	0.959	5	32
		2	Σg	2024	1974	0.976	5	33
		3	Σu	3425	3289	0.960	5	34
		4	Πg	358	612	1.708	5	35
		5	Πu	735	730	0.993	5	36
HCN	Hydrogen cyanide	1	Σ	3466	3312	0.955	6	37
		2	Σ	2130	2089	0.981	6	38
		3	Π	714	712	0.998	6	39
CS2	Carbon disulfide	1	Σg	673	658	0.977	7	40
		2	Σu	1571	1535	0.977	7	41
		3	Πu	397	397	1.000	7	42
CO2	Carbon dioxide	1	Σg	1349	1333	0.988	8	43
		2	Σu	2417	2349	0.972	8	44
		3	Πu	644	667	1.035	8	45
ClCN	chlorocyanogen	1	Σ	2264	2216	0.979	9	46
		2	Σ	741	744	1.004	9	47
		3	Π	355	378	1.065	9	48
CO	Carbon monoxide	1	Σ	2159	2170	1.005	10	49
		1	Σ	2159	1743	0.807	10	50
H2CS	Thioformaldehyde	1	A1	3111	2971	0.955	11	51
		2	A1	1544	1456	0.943	11	52
		3	A1	1071	1059	0.989	11	53
		4	B1	1009	990	0.981	11	54
		5	B2	3200	3025	0.945	11	55
		6	B2	1036	991	0.957	11	56
MgO	magnesium oxide	1	Σ	747	785	1.051	12	57
CN	Cyano radical	1	Σ	2120	2069	0.976	13	58
CH	Methylidyne	1	Σ	3174	2861	0.901	14	59
		1	Σ	3174	3145	0.991	14	60
		1	Σ	3174	2931	0.923	14	61
OH	Hydroxyl radical	1	Σ	3630	3738	1.030	15	62
CF	Fluoromethylidyne	1	Σ	1310	1308	0.999	16	63
SO2	Sulfur dioxide	1	A1	1111	1151	1.036	17	64
		2	A1	499	518	1.038	17	65
		3	B2	1324	1362	1.028	17	66
LiH	Lithium Hydride	1	Σ	1332	1405	1.055	18	67
BF3	Borane, trifluoro-	1	A1'	892	888	0.995	19	68
		2	A2"	701	691	0.985	19	69
		3	E'	1505	1449	0.963	19	70
		4	E'	483	480	0.994	19	71
HCl	Hydrogen chloride	1	Σ	2962	2991	1.010	20	72
HF	Hydrogen fluoride	1	Σ	4006	4138	1.033	21	73
NH3	Ammonia	1	A1	3435	3337	0.972	22	74
		2	A1	1180	950	0.805	22	75
		3	E	3576	3444	0.963	22	76
		4	E	1747	1627	0.932	22	77
MgH2	magnesium dihydride	2	Σu	1583	1572	0.993	23	78
		3	Πu	442	440	0.996	23	79
H2O2	Hydrogen peroxide	1	A	3698	3599	0.973	24	80
		2	A	1455	1402	0.964	24	81
		3	A	879	877	0.998	24	82
		4	A	326	371	1.137	24	83
		5	B	3701	3608	0.975	24	84
		6	B	1311	1266	0.965	24	85
N2	Nitrogen diatomic	1	Σg	2346	2359	1.006	25	86
H2O	Water	1	A1	3726	3657	0.981	26	87
		2	A1	1742	1595	0.916	26	88
		3	B2	3856	3756	0.974	26	89
F2	Fluorine diatomic	1	Σg	889	917	1.031	27	90
Cl2	Chlorine diatomic	1	Σg	503	560	1.112	28	91
H2S	Hydrogen sulfide	1	A1	2702	2615	0.968	29	92
		2	A1	1257	1183	0.941	29	93
		3	B2	2726	2626	0.963	29	94
AlH3	aluminum trihydride	1	A1'	1924	1900	0.988	30	95
		2	A2"	702	698	0.994	30	96
		3	E'	1942	1883	0.970	30	97
		4	E'	786	783	0.997	30	98

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.

	45
	40
	35
	30
	25
	20
	15
	10
	5
	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