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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)/aug-cc-pVDZ

Scale factor	How many		Source
	Molecules	Vibrations
0.982 ± 0.029	23	65	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CH4	Methane	1	A1	3017	2917	0.967	1	1
		2	E	1535	1534	0.999	1	2
		3	T2	3144	3019	0.960	1	3
		4	T2	1319	1306	0.990	1	4
C2H2	Acetylene	1	Σg	3478	3374	0.970	2	5
		2	Σg	1970	1974	1.002	2	6
		3	Σu	3384	3289	0.972	2	7
		4	Πg	368	612	1.663	2	8
		5	Πu	692	730	1.056	2	9
HCN	Hydrogen cyanide	1	Σ	3416	3312	0.969	3	10
		2	Σ	2078	2089	1.005	3	11
		3	Π	692	712	1.028	3	12
CO2	Carbon dioxide	1	Σg	1316	1333	1.013	4	13
		2	Σu	2339	2349	1.004	4	14
		3	Πu	659	667	1.012	4	15
CO	Carbon monoxide	1	Σ	2104	2170	1.031	5	16
		1	Σ	2104	1743	0.829	5	17
H2	Hydrogen diatomic	1	Σg	4344	4401	1.013	6	18
CN	Cyano radical	1	Σ	2077	2069	0.996	7	19
HCl	Hydrogen chloride	1	Σ	2969	2991	1.008	8	20
HF	Hydrogen fluoride	1	Σ	4084	4138	1.013	9	21
NH3	Ammonia	1	A1	3434	3337	0.972	10	22
		2	A1	1071	950	0.887	10	23
		3	E	3571	3444	0.964	10	24
		4	E	1651	1627	0.986	10	25
H2O2	Hydrogen peroxide	1	A	3753	3599	0.959	11	26
		2	A	1409	1402	0.995	11	27
		3	A	842	877	1.042	11	28
		4	A	385	371	0.964	11	29
		5	B	3754	3608	0.961	11	30
		6	B	1301	1266	0.973	11	31
N2	Nitrogen diatomic	1	Σg	2319	2359	1.017	12	32
H2O	Water	1	A1	3787	3657	0.966	13	33
		2	A1	1638	1595	0.973	13	34
		3	B2	3905	3756	0.962	13	35
F2	Fluorine diatomic	1	Σg	824	917	1.113	14	36
Cl2	Chlorine diatomic	1	Σg	502	560	1.114	15	37
N2O	Nitrous oxide	1	Σ	2242	2224	0.992	16	38
		2	Σ	1277	1285	1.006	16	39
		3	Π	567	589	1.039	16	40
C2	Carbon diatomic	1	Σg	1814	1855	1.023	17	41
		1	Σg	1605	1855	1.156	17	42
P2	Phosphorus diatomic	1	Σg	747	781	1.045	18	43
Si2	Silicon diatomic	1	Σg	525	511	0.974	19	44
		1	Σg	537	511	0.951	19	45
BH3	boron trihydride	2	A2"	1146	1148	1.001	20	46
		3	E'	2676	2602	0.972	20	47
		4	E'	1203	1197	0.995	20	48
SO	Sulfur monoxide	1	Σ	1071	1151	1.074	21	49
		1	Σ	1006	1151	1.144	21	50
NF	nitrogen fluoride	1	Σ	1080	1141	1.056	22	51
		1	Σ	1124	1141	1.016	22	52
B2H6	Diborane	1	Ag	2604	2524	0.969	23	53
		2	Ag	2160	2104	0.974	23	54
		3	Ag	1190	1180	0.991	23	55
		4	Ag	801	794	0.991	23	56
		5	Au	833	833	1.000	23	57
		6	B1g	2680	2591	0.967	23	58
		7	B1g	923	915	0.991	23	59
		8	B1u	1979	1915	0.968	23	60
		9	B1u	982	973	0.991	23	61
		10	B2g	1873	1768	0.944	23	62
		11	B2g	876	850	0.970	23	63
		12	B2u	2697	2612	0.969	23	64
		13	B2u	962	950	0.988	23	65
		14	B2u	366	368	1.006	23	66
		15	B3g	1051	1012	0.963	23	67
		16	B3u	2588	2525	0.976	23	68
		17	B3u	1741	1602	0.920	23	69
		18	B3u	1174	1177	1.002	23	70

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.

	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