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

Vibrational frequency scaling factors

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

Scale factor	How many		Source
	Molecules	Vibrations
0.934 ± 0.113	32	67	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CH4	Methane	1	A1	3097	2917	0.942	1	1
		2	E	1593	1534	0.963	1	2
		3	T2	3225	3019	0.936	1	3
		4	T2	1396	1306	0.936	1	4
H2	Hydrogen diatomic	1	Σg	4505	4401	0.977	2	5
CS	carbon monosulfide	1	Σ	1335	1285	0.963	3	6
HO2	Hydroperoxy radical	1	A'	3713	3436	0.925	4	7
		2	A'	1447	1392	0.962	4	8
		3	A'	1130	1098	0.971	4	9
CH	Methylidyne	1	Σ	2889	2861	0.990	5	10
		1	Σ	2889	3145	1.089	5	11
		1	Σ	2889	2931	1.014	5	12
OH	Hydroxyl radical	1	Σ	3769	3738	0.992	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	3064	2991	0.976	9	16
HF	Hydrogen fluoride	1	Σ	4151	4138	0.997	10	17
NH3	Ammonia	1	A1	3549	3337	0.940	11	18
		2	A1	1072	950	0.886	11	19
		3	E	3700	3444	0.931	11	20
		4	E	1713	1627	0.950	11	21
MgH2	magnesium dihydride	2	Σu	1619	1572	0.971	12	22
		3	Πu	447	440	0.984	12	23
H2O	Water	1	A1	3880	3657	0.943	13	24
		2	A1	1647	1595	0.969	13	25
		3	B2	4009	3756	0.937	13	26
H2S	Hydrogen sulfide	1	A1	2782	2615	0.940	14	27
		2	A1	1265	1183	0.935	14	28
		3	B2	2804	2626	0.936	14	29
AlH3	aluminum trihydride	1	A1'	1971	1900	0.964	15	30
		2	A2"	727	698	0.960	15	31
		3	E'	1984	1883	0.949	15	32
		4	E'	815	783	0.962	15	33
BeH2	beryllium dihydride	2	Σu	2293	2159	0.942	16	34
		3	Πu	717	698	0.973	16	35
PH3	Phosphine	1	A1	2470	2323	0.941	17	36
		2	A1	1068	992	0.929	17	37
		3	E	2483	2328	0.938	17	38
		4	E	1163	1118	0.961	17	39
SiH4	Silane	1	A1	2308	2187	0.948	18	40
		2	E	1002	975	0.973	18	41
		3	T2	2317	2191	0.946	18	42
		4	T2	961	914	0.951	18	43
BH3	boron trihydride	2	A2"	1192	1148	0.963	19	44
		3	E'	2769	2602	0.940	19	45
		4	E'	1253	1197	0.955	19	46
BeH	beryllium monohydride	1	Σ	2098	2061	0.983	20	47
PH2	Phosphino radical	1	A1	2439	2310	0.947	21	48
		2	A1	1169	1102	0.943	21	49
SiH3	silyl	1	A1	2278	2136	0.938	22	50
		2	A1	804	728	0.905	22	51
		3	E	2313	2185	0.945	22	52
		4	E	969	922	0.952	22	53
BH	Boron monohydride	1	Σ	2418	2367	0.979	23	54
NH2	Amino radical	1	A1	3420	3219	0.941	24	55
		2	A1	1559	1497	0.961	24	56
		3	B2	3530	3301	0.935	24	57
NH	Imidogen	1	Σ	3311	3283	0.992	25	58
		1	Σ	3311	3314	1.001	25	59
SiH	Silylidyne	1	Σ	2081	2043	0.981	26	60
SiH2	silicon dihydride	1	A1	2116	1996	0.943	27	61
		1	A1	2254	1996	0.886	27	62
		2	A1	1054	999	0.948	27	63
		2	A1	918	999	1.088	27	64
		3	B2	2118	1993	0.941	27	65
		3	B2	2313	1993	0.862	27	66
SH	Mercapto radical	1	Σ	2744	2696	0.983	28	67
PH	phosphorus monohydride	1	Σ	2398	2364	0.986	29	68
		1	Σ	2398	2415	1.007	29	69
		1	Σ	2398	2403	1.002	29	70
AlH	aluminum monohydride	1	Σ	1719	1682	0.979	30	71
MgH	magnesium monohydride	1	Σ	1473	1493	1.013	31	72
AlH2	aluminum dihydride	1	A1	1882	1770	0.940	32	73
		2	A1	790	760	0.962	32	74
		3	B2	1921	1807	0.940	32	75

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.

	50
	40
	30
	20
	10
	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