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

Vibrational frequency scaling factors

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

Scale factor	How many		Source
	Molecules	Vibrations
0.960 ± 0.026	33	68	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CH4	Methane	1	A1	3083	2917	0.946	1	1
		2	E	1585	1534	0.968	1	2
		3	T2	3212	3019	0.940	1	3
		4	T2	1389	1306	0.941	1	4
NaOH	sodium hydroxide	1	Σ	3992	3637	0.911	2	5
		2	Σ	549	540	0.984	2	6
		3	Π	320	300	0.937	2	7
H2	Hydrogen diatomic	1	Σg	4505	4401	0.977	3	8
CS	carbon monosulfide	1	Σ	1281	1285	1.003	4	9
CH	Methylidyne	1	Σ	2875	2861	0.995	5	10
		1	Σ	2875	3145	1.094	5	11
		1	Σ	2875	2931	1.019	5	12
OH	Hydroxyl radical	1	Σ	3747	3738	0.997	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	4127	4138	1.003	10	17
NH3	Ammonia	1	A1	3525	3337	0.947	11	18
		2	A1	1075	950	0.884	11	19
		3	E	3679	3444	0.936	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	3856	3657	0.949	13	24
		2	A1	1640	1595	0.973	13	25
		3	B2	3987	3756	0.942	13	26
H2S	Hydrogen sulfide	1	A1	2766	2615	0.945	14	27
		2	A1	1256	1183	0.942	14	28
		3	B2	2790	2626	0.941	14	29
AlH3	aluminum trihydride	1	A1'	1966	1900	0.967	15	30
		2	A2"	724	698	0.963	15	31
		3	E'	1979	1883	0.951	15	32
		4	E'	812	783	0.964	15	33
BeH2	beryllium dihydride	2	Σu	2291	2159	0.943	16	34
		3	Πu	716	698	0.975	16	35
PH3	Phosphine	1	A1	2459	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	0.969	17	39
SiH4	Silane	1	A1	2299	2187	0.951	18	40
		2	E	997	975	0.978	18	41
		3	T2	2310	2191	0.949	18	42
		4	T2	956	914	0.956	18	43
BH3	boron trihydride	2	A2"	1189	1148	0.965	19	44
		3	E'	2763	2602	0.942	19	45
		4	E'	1250	1197	0.958	19	46
BeH	beryllium monohydride	1	Σ	2092	2061	0.985	20	47
PH2	Phosphino radical	1	A1	2425	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	2411	2367	0.981	23	54
NH2	Amino radical	1	A1	3397	3219	0.948	24	55
		2	A1	1551	1497	0.965	24	56
		3	B2	3509	3301	0.941	24	57
NH	Imidogen	1	Σ	3289	3283	0.998	25	58
		1	Σ	3289	3314	1.008	25	59
SiH	Silylidyne	1	Σ	2071	2043	0.986	26	60
SiH2	silicon dihydride	1	A1	2107	1996	0.947	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	0.944	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	1.013	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	1469	1493	1.016	31	72
BH2	boron dihydride	2	A1	1060	954	0.899	32	73
AlH2	aluminum dihydride	1	A1	1875	1770	0.944	33	74
		2	A1	788	760	0.964	33	75
		3	B2	1915	1807	0.943	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