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

Vibrational frequency scaling factors

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

Scale factor	How many		Source
	Molecules	Vibrations
0.959 ± 0.016	29	112	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
H2CO	Formaldehyde	1	A1	2954	2782	0.942	1	1
		2	A1	1792	1746	0.974	1	2
		3	A1	1556	1500	0.964	1	3
		4	B1	1207	1167	0.967	1	4
		5	B2	3000	2843	0.948	1	5
		6	B2	1286	1249	0.972	1	6
HCOOH	Formic acid	1	A'	3782	3570	0.944	2	7
		2	A'	3106	2943	0.948	2	8
		3	A'	1837	1770	0.964	2	9
		4	A'	1429	1387	0.971	2	10
		5	A'	1331	1229	0.924	2	11
		6	A'	1144	1105	0.966	2	12
		7	A'	634	625	0.986	2	13
		8	A"	1078	1033	0.958	2	14
		9	A"	682	638	0.935	2	15
CH4	Methane	1	A1	3054	2917	0.955	3	16
		2	E	1585	1534	0.968	3	17
		3	T2	3158	3019	0.956	3	18
		4	T2	1354	1306	0.965	3	19
C2H6	Ethane	1	A1g	3061	2896	0.946	4	20
		2	A1g	1439	1388	0.965	4	21
		3	A1g	1023	995	0.972	4	22
		4	A1u	338	289	0.856	4	23
		5	A2u	3060	2915	0.953	4	24
		6	A2u	1415	1370	0.968	4	25
		7	Eg	3101	2969	0.957	4	26
		8	Eg	1525	1468	0.963	4	27
		9	Eg	1235	1190	0.964	4	28
		10	Eu	3124	2974	0.952	4	29
		11	Eu	1526	1460	0.957	4	30
		12	Eu	828	822	0.993	4	31
C2H4	Ethylene	1	Ag	3181	3026	0.951	5	32
		2	Ag	1684	1623	0.964	5	33
		3	Ag	1378	1342	0.974	5	34
		4	Au	1051	1023	0.973	5	35
		5	B1u	3159	2989	0.946	5	36
		6	B1u	1487	1444	0.971	5	37
		7	B2g	954	940	0.985	5	38
		8	B2u	3250	3105	0.955	5	39
		9	B2u	827	826	0.999	5	40
		10	B3g	3216	3086	0.960	5	41
		11	B3g	1244	1217	0.978	5	42
		12	B3u	980	949	0.969	5	43
C2H2	Acetylene	1	Σg	3534	3374	0.955	6	44
		2	Σg	2016	1974	0.979	6	45
		3	Σu	3410	3289	0.965	6	46
		4	Πg	589	612	1.038	6	47
		5	Πu	754	730	0.969	6	48
HCN	Hydrogen cyanide	1	Σ	3459	3312	0.957	7	49
		2	Σ	2129	2089	0.981	7	50
		3	Π	727	712	0.980	7	51
CS2	Carbon disulfide	1	Σg	674	658	0.977	8	52
		2	Σu	1569	1535	0.978	8	53
		3	Πu	415	397	0.958	8	54
CO2	Carbon dioxide	1	Σg	1358	1333	0.982	9	55
		2	Σu	2413	2349	0.973	9	56
		3	Πu	666	667	1.002	9	57
CH2CCH2	allene	1	A1	3169	3015	0.952	10	58
		2	A1	1502	1443	0.961	10	59
		3	A1	1091	1073	0.984	10	60
		4	B1	877	865	0.986	10	61
		5	B2	3166	3007	0.950	10	62
		6	B2	2027	1957	0.965	10	63
		7	B2	1451	1398	0.963	10	64
		8	E	3231	3086	0.955	10	65
		9	E	1025	999	0.975	10	66
		10	E	877	841	0.959	10	67
		11	E	348	355	1.021	10	68
CO	Carbon monoxide	1	Σ	2171	2170	0.999	11	69
		1	Σ	2171	1743	0.803	11	70
H2CS	Thioformaldehyde	1	A1	3111	2971	0.955	12	71
		2	A1	1511	1456	0.964	12	72
		3	A1	1077	1059	0.984	12	73
		4	B1	1023	990	0.968	12	74
		5	B2	3178	3025	0.952	12	75
		6	B2	1013	991	0.978	12	76
MgO	magnesium oxide	1	Σ	798	785	0.984	13	77
CN	Cyano radical	1	Σ	2135	2069	0.969	14	78
OH	Hydroxyl radical	1	Σ	3763	3738	0.993	15	79
CF	Fluoromethylidyne	1	Σ	1332	1308	0.982	16	80
SO2	Sulfur dioxide	1	A1	1175	1151	0.980	17	81
		2	A1	522	518	0.991	17	82
		3	B2	1396	1362	0.976	17	83
LiH	Lithium Hydride	1	Σ	1412	1405	0.995	18	84
BF3	Borane, trifluoro-	1	A1'	904	888	0.982	19	85
		2	A2"	706	691	0.979	19	86
		3	E'	1500	1449	0.966	19	87
		4	E'	486	480	0.988	19	88
HF	Hydrogen fluoride	1	Σ	4197	4138	0.986	20	89
NH3	Ammonia	1	A1	3499	3337	0.954	21	90
		2	A1	1101	950	0.863	21	91
		3	E	3620	3444	0.951	21	92
		4	E	1694	1627	0.961	21	93
MgH2	magnesium dihydride	2	Σu	1711	1572	0.919	22	94
		3	Πu	529	440	0.832	22	95
H2O2	Hydrogen peroxide	1	A	3826	3599	0.941	23	96
		2	A	1442	1402	0.972	23	97
		3	A	917	877	0.957	23	98
		4	A	366	371	1.015	23	99
		5	B	3825	3608	0.943	23	100
		6	B	1331	1266	0.951	23	101
N2	Nitrogen diatomic	1	Σg	2366	2359	0.997	24	102
H2O	Water	1	A1	3859	3657	0.948	25	103
		2	A1	1667	1595	0.957	25	104
		3	B2	3964	3756	0.947	25	105
F2	Fluorine diatomic	1	Σg	921	917	0.995	26	106
Cl2	Chlorine diatomic	1	Σg	555	560	1.008	27	107
H2S	Hydrogen sulfide	1	A1	2725	2615	0.960	28	108
		2	A1	1218	1183	0.971	28	109
		3	B2	2737	2626	0.959	28	110
FNO	Nitrosyl fluoride	1	A'	1868	1844	0.987	29	111
		2	A'	806	766	0.951	29	112
		3	A'	551	520	0.944	29	113

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.

	80
	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