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

Vibrational frequency scaling factors

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

Scale factor	How many		Source
	Molecules	Vibrations
0.937 ± 0.113	33	68	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CH4	Methane	1	A1	3093	2917	0.943	1	1
		2	E	1608	1534	0.954	1	2
		3	T2	3225	3019	0.936	1	3
		4	T2	1397	1306	0.935	1	4
H2	Hydrogen diatomic	1	Σg	4505	4401	0.977	2	5
CS	carbon monosulfide	1	Σ	1258	1285	1.022	3	6
HO2	Hydroperoxy radical	1	A'	3688	3436	0.932	4	7
		2	A'	1426	1392	0.976	4	8
		3	A'	1101	1098	0.997	4	9
CH	Methylidyne	1	Σ	2848	2861	1.004	5	10
		1	Σ	2848	3145	1.104	5	11
		1	Σ	2848	2931	1.029	5	12
OH	Hydroxyl radical	1	Σ	3762	3738	0.993	6	13
LiH	Lithium Hydride	1	Σ	1374	1405	1.023	7	14
NaH	sodium hydride	1	Σ	1137	1172	1.031	8	15
HCl	Hydrogen chloride	1	Σ	3056	2991	0.979	9	16
HF	Hydrogen fluoride	1	Σ	4180	4138	0.990	10	17
NH3	Ammonia	1	A1	3511	3337	0.950	11	18
		2	A1	1146	950	0.829	11	19
		3	E	3653	3444	0.943	11	20
		4	E	1724	1627	0.944	11	21
MgH2	magnesium dihydride	2	Σu	1618	1572	0.972	12	22
		3	Πu	445	440	0.989	12	23
H2O	Water	1	A1	3869	3657	0.945	13	24
		2	A1	1693	1595	0.942	13	25
		3	B2	3995	3756	0.940	13	26
H2S	Hydrogen sulfide	1	A1	2771	2615	0.944	14	27
		2	A1	1259	1183	0.940	14	28
		3	B2	2795	2626	0.940	14	29
AlH3	aluminum trihydride	1	A1'	1960	1900	0.969	15	30
		2	A2"	722	698	0.966	15	31
		3	E'	1975	1883	0.953	15	32
		4	E'	808	783	0.970	15	33
BeH2	beryllium dihydride	2	Σu	2300	2159	0.939	16	34
		3	Πu	723	698	0.966	16	35
PH3	Phosphine	1	A1	2461	2323	0.944	17	36
		2	A1	1065	992	0.932	17	37
		3	E	2476	2328	0.940	17	38
		4	E	1156	1118	0.967	17	39
SiH4	Silane	1	A1	2295	2187	0.953	18	40
		2	E	996	975	0.979	18	41
		3	T2	2307	2191	0.950	18	42
		4	T2	954	914	0.958	18	43
BH3	boron trihydride	2	A2"	1193	1148	0.962	19	44
		3	E'	2773	2602	0.938	19	45
		4	E'	1256	1197	0.953	19	46
BeH	beryllium monohydride	1	Σ	2093	2061	0.985	20	47
PH2	Phosphino radical	1	A1	2427	2310	0.952	21	48
		2	A1	1163	1102	0.948	21	49
SiH3	silyl	1	A1	2265	2136	0.943	22	50
		2	A1	797	728	0.913	22	51
		3	E	2303	2185	0.949	22	52
		4	E	963	922	0.958	22	53
BH	Boron monohydride	1	Σ	2389	2367	0.991	23	54
NH2	Amino radical	1	A1	3389	3219	0.950	24	55
		2	A1	1591	1497	0.941	24	56
		3	B2	3495	3301	0.944	24	57
NH	Imidogen	1	Σ	3274	3283	1.003	25	58
		1	Σ	3274	3314	1.012	25	59
SiH	Silylidyne	1	Σ	2068	2043	0.988	26	60
SiH2	silicon dihydride	1	A1	2105	1996	0.948	27	61
		1	A1	2241	1996	0.891	27	62
		2	A1	1047	999	0.954	27	63
		2	A1	912	999	1.096	27	64
		3	B2	2109	1993	0.945	27	65
		3	B2	2302	1993	0.866	27	66
SH	Mercapto radical	1	Σ	2738	2696	0.985	28	67
PH	phosphorus monohydride	1	Σ	2384	2364	0.992	29	68
		1	Σ	2384	2415	1.013	29	69
		1	Σ	2384	2403	1.008	29	70
AlH	aluminum monohydride	1	Σ	1710	1682	0.984	30	71
MgH	magnesium monohydride	1	Σ	1467	1493	1.018	31	72
BH2	boron dihydride	2	A1	1079	954	0.884	32	73
AlH2	aluminum dihydride	1	A1	1870	1770	0.946	33	74
		2	A1	783	760	0.971	33	75
		3	B2	1910	1807	0.946	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