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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at QCISD(T)/6-31+G**

Scale factor	How many		Source
	Molecules	Vibrations
0.939 ± 0.112	33	68	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CH4	Methane	1	A1	3081	2917	0.947	1	1
		2	E	1585	1534	0.968	1	2
		3	T2	3211	3019	0.940	1	3
		4	T2	1388	1306	0.941	1	4
H2	Hydrogen diatomic	1	Σg	4505	4401	0.977	2	5
CS	carbon monosulfide	1	Σ	1263	1285	1.017	3	6
HO2	Hydroperoxy radical	1	A'	3676	3436	0.935	4	7
		2	A'	1417	1392	0.982	4	8
		3	A'	1084	1098	1.012	4	9
CH	Methylidyne	1	Σ	2874	2861	0.995	5	10
		1	Σ	2874	3145	1.094	5	11
		1	Σ	2874	2931	1.020	5	12
OH	Hydroxyl radical	1	Σ	3745	3738	0.998	6	13
LiH	Lithium Hydride	1	Σ	1375	1405	1.022	7	14
NaH	sodium hydride	1	Σ	1138	1172	1.030	8	15
HCl	Hydrogen chloride	1	Σ	3048	2991	0.981	9	16
HF	Hydrogen fluoride	1	Σ	4122	4138	1.004	10	17
NH3	Ammonia	1	A1	3524	3337	0.947	11	18
		2	A1	1076	950	0.883	11	19
		3	E	3677	3444	0.937	11	20
		4	E	1705	1627	0.954	11	21
MgH2	magnesium dihydride	2	Σu	1617	1572	0.972	12	22
		3	Πu	446	440	0.986	12	23
H2O	Water	1	A1	3853	3657	0.949	13	24
		2	A1	1639	1595	0.973	13	25
		3	B2	3985	3756	0.942	13	26
H2S	Hydrogen sulfide	1	A1	2766	2615	0.946	14	27
		2	A1	1256	1183	0.942	14	28
		3	B2	2789	2626	0.941	14	29
AlH3	aluminum trihydride	1	A1'	1965	1900	0.967	15	30
		2	A2"	724	698	0.964	15	31
		3	E'	1979	1883	0.951	15	32
		4	E'	812	783	0.965	15	33
BeH2	beryllium dihydride	2	Σu	2291	2159	0.943	16	34
		3	Πu	715	698	0.975	16	35
PH3	Phosphine	1	A1	2458	2323	0.945	17	36
		2	A1	1061	992	0.935	17	37
		3	E	2473	2328	0.941	17	38
		4	E	1153	1118	0.970	17	39
SiH4	Silane	1	A1	2299	2187	0.951	18	40
		2	E	997	975	0.978	18	41
		3	T2	2309	2191	0.949	18	42
		4	T2	956	914	0.957	18	43
BH3	boron trihydride	2	A2"	1189	1148	0.965	19	44
		3	E'	2762	2602	0.942	19	45
		4	E'	1249	1197	0.958	19	46
BeH	beryllium monohydride	1	Σ	2092	2061	0.985	20	47
PH2	Phosphino radical	1	A1	2424	2310	0.953	21	48
		2	A1	1160	1102	0.950	21	49
SiH3	silyl	1	A1	2268	2136	0.942	22	50
		2	A1	799	728	0.911	22	51
		3	E	2305	2185	0.948	22	52
		4	E	964	922	0.956	22	53
BH	Boron monohydride	1	Σ	2410	2367	0.982	23	54
NH2	Amino radical	1	A1	3396	3219	0.948	24	55
		2	A1	1551	1497	0.965	24	56
		3	B2	3508	3301	0.941	24	57
NH	Imidogen	1	Σ	3288	3283	0.998	25	58
		1	Σ	3288	3314	1.008	25	59
SiH	Silylidyne	1	Σ	2071	2043	0.986	26	60
SiH2	silicon dihydride	1	A1	2106	1996	0.948	27	61
		1	A1	2243	1996	0.890	27	62
		2	A1	1046	999	0.955	27	63
		2	A1	913	999	1.094	27	64
		3	B2	2110	1993	0.945	27	65
		3	B2	2304	1993	0.865	27	66
SH	Mercapto radical	1	Σ	2728	2696	0.988	28	67
PH	phosphorus monohydride	1	Σ	2383	2364	0.992	29	68
		1	Σ	2383	2415	1.014	29	69
		1	Σ	2383	2403	1.008	29	70
AlH	aluminum monohydride	1	Σ	1713	1682	0.982	30	71
MgH	magnesium monohydride	1	Σ	1468	1493	1.017	31	72
BH2	boron dihydride	2	A1	1060	954	0.899	32	73
AlH2	aluminum dihydride	1	A1	1873	1770	0.945	33	74
		2	A1	786	760	0.967	33	75
		3	B2	1913	1807	0.945	33	76

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