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

Vibrational frequency scaling factors

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

Scale factor	How many		Source
	Molecules	Vibrations
0.941 ± 0.119	27	60	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CH4	Methane	1	A1	3052	2917	0.956	1	1
		2	E	1581	1534	0.971	1	2
		3	T2	3169	3019	0.953	1	3
		4	T2	1356	1306	0.963	1	4
H2	Hydrogen diatomic	1	Σg	4410	4401	0.998	2	5
CS	carbon monosulfide	1	Σ	1325	1285	0.970	3	6
HO2	Hydroperoxy radical	1	A'	3724	3436	0.923	4	7
		2	A'	1467	1392	0.949	4	8
		3	A'	1171	1098	0.938	4	9
CH	Methylidyne	1	Σ	2853	2861	1.003	5	10
		1	Σ	2853	3145	1.102	5	11
		1	Σ	2853	2931	1.027	5	12
OH	Hydroxyl radical	1	Σ	3773	3738	0.991	6	13
HCl	Hydrogen chloride	1	Σ	3020	2991	0.990	7	14
HF	Hydrogen fluoride	1	Σ	4216	4138	0.982	8	15
NH3	Ammonia	1	A1	3502	3337	0.953	9	16
		2	A1	1109	950	0.856	9	17
		3	E	3626	3444	0.950	9	18
		4	E	1700	1627	0.957	9	19
H2O	Water	1	A1	3875	3657	0.944	10	20
		2	A1	1678	1595	0.950	10	21
		3	B2	3979	3756	0.944	10	22
H2S	Hydrogen sulfide	1	A1	2737	2615	0.956	11	23
		2	A1	1219	1183	0.970	11	24
		3	B2	2751	2626	0.954	11	25
AlH3	aluminum trihydride	1	A1'	1946	1900	0.976	12	26
		2	A2"	721	698	0.968	12	27
		3	E'	1951	1883	0.965	12	28
		4	E'	796	783	0.985	12	29
PH3	Phosphine	1	A1	2429	2323	0.956	13	30
		2	A1	1030	992	0.963	13	31
		3	E	2436	2328	0.956	13	32
		4	E	1154	1118	0.969	13	33
SiH4	Silane	1	A1	2260	2187	0.968	14	34
		2	E	989	975	0.985	14	35
		3	T2	2266	2191	0.967	14	36
		4	T2	939	914	0.973	14	37
BH3	boron trihydride	2	A2"	1165	1148	0.985	15	38
		3	E'	2705	2602	0.962	15	39
		4	E'	1229	1197	0.974	15	40
PH2	Phosphino radical	1	A1	2403	2310	0.961	16	41
		2	A1	1137	1102	0.969	16	42
SiH3	silyl	1	A1	2228	2136	0.959	17	43
		2	A1	785	728	0.927	17	44
		3	E	2261	2185	0.966	17	45
		4	E	947	922	0.973	17	46
BH	Boron monohydride	1	Σ	2361	2367	1.002	18	47
NH2	Amino radical	1	A1	3396	3219	0.948	19	48
		2	A1	1567	1497	0.955	19	49
		3	B2	3487	3301	0.947	19	50
NH	Imidogen	1	Σ	3295	3283	0.996	20	51
		1	Σ	3295	3314	1.006	20	52
SiH	Silylidyne	1	Σ	2044	2043	0.999	21	53
SiH2	silicon dihydride	1	A1	2075	1996	0.962	22	54
		1	A1	2202	1996	0.906	22	55
		2	A1	1034	999	0.966	22	56
		2	A1	894	999	1.117	22	57
		3	B2	2072	1993	0.962	22	58
		3	B2	2261	1993	0.881	22	59
SH	Mercapto radical	1	Σ	2707	2696	0.996	23	60
PH	phosphorus monohydride	1	Σ	2371	2364	0.997	24	61
		1	Σ	2371	2415	1.018	24	62
		1	Σ	2371	2403	1.013	24	63
AlH	aluminum monohydride	1	Σ	1688	1682	0.997	25	64
BH2	boron dihydride	2	A1	1023	954	0.932	26	65
AlH2	aluminum dihydride	1	A1	1856	1770	0.954	27	66
		2	A1	770	760	0.987	27	67
		3	B2	1890	1807	0.956	27	68

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