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

Vibrational frequency scaling factors

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

Scale factor	How many		Source
	Molecules	Vibrations
0.949 ± 0.118	27	60	cccbdb

Jump to histogram

Formula	Name	Mode	Symmetry	Frequency			Count
				Theory	Experiment	ratio	molecules	vibrations
CH4	Methane	1	A1	3035	2917	0.961	1	1
		2	E	1570	1534	0.977	1	2
		3	T2	3154	3019	0.957	1	3
		4	T2	1343	1306	0.972	1	4
H2	Hydrogen diatomic	1	Σg	4410	4401	0.998	2	5
CS	carbon monosulfide	1	Σ	1253	1285	1.025	3	6
HO2	Hydroperoxy radical	1	A'	3674	3436	0.935	4	7
		2	A'	1430	1392	0.973	4	8
		3	A'	1116	1098	0.983	4	9
CH	Methylidyne	1	Σ	2834	2861	1.010	5	10
		1	Σ	3109	2861	0.920	5	11
		1	Σ	2834	3145	1.110	5	12
		1	Σ	3109	3145	1.012	5	13
		1	Σ	2834	2931	1.034	5	14
		1	Σ	3109	2931	0.943	5	15
OH	Hydroxyl radical	1	Σ	3738	3738	1.000	6	16
HCl	Hydrogen chloride	1	Σ	3000	2991	0.997	7	17
HF	Hydrogen fluoride	1	Σ	4178	4138	0.991	8	18
NH3	Ammonia	1	A1	3469	3337	0.962	9	19
		2	A1	1112	950	0.854	9	20
		3	E	3594	3444	0.958	9	21
		4	E	1688	1627	0.964	9	22
H2O	Water	1	A1	3838	3657	0.953	10	23
		2	A1	1668	1595	0.956	10	24
		3	B2	3943	3756	0.953	10	25
H2S	Hydrogen sulfide	1	A1	2717	2615	0.963	11	26
		2	A1	1204	1183	0.983	11	27
		3	B2	2733	2626	0.961	11	28
AlH3	aluminum trihydride	1	A1'	1940	1900	0.980	12	29
		2	A2"	717	698	0.973	12	30
		3	E'	1946	1883	0.967	12	31
		4	E'	791	783	0.990	12	32
PH3	Phosphine	1	A1	2411	2323	0.963	13	33
		2	A1	1018	992	0.974	13	34
		3	E	2420	2328	0.962	13	35
		4	E	1142	1118	0.979	13	36
SiH4	Silane	1	A1	2250	2187	0.972	14	37
		2	E	984	975	0.991	14	38
		3	T2	2258	2191	0.970	14	39
		4	T2	930	914	0.982	14	40
BH3	boron trihydride	2	A2"	1160	1148	0.989	15	41
		3	E'	2697	2602	0.964	15	42
		4	E'	1223	1197	0.979	15	43
PH2	Phosphino radical	1	A1	2385	2310	0.968	16	44
		2	A1	1124	1102	0.980	16	45
SiH3	silyl	1	A1	2218	2136	0.963	17	46
		2	A1	775	728	0.940	17	47
		3	E	2253	2185	0.970	17	48
		4	E	940	922	0.981	17	49
BH	Boron monohydride	1	Σ	2350	2367	1.007	18	50
NH2	Amino radical	1	A1	3364	3219	0.957	19	51
		2	A1	1558	1497	0.961	19	52
		3	B2	3456	3301	0.955	19	53
NH	Imidogen	1	Σ	3264	3283	1.006	20	54
		1	Σ	3322	3283	0.988	20	55
		1	Σ	3264	3314	1.015	20	56
		1	Σ	3322	3314	0.998	20	57
SiH	Silylidyne	1	Σ	2031	2043	1.006	21	58
SiH2	silicon dihydride	1	A1	2062	1996	0.968	22	59
		1	A1	2189	1996	0.912	22	60
		2	A1	1020	999	0.980	22	61
		2	A1	885	999	1.129	22	62
		3	B2	2060	1993	0.967	22	63
		3	B2	2251	1993	0.885	22	64
SH	Mercapto radical	1	Σ	2687	2696	1.003	23	65
PH	phosphorus monohydride	1	Σ	2352	2364	1.005	24	66
		1	Σ	2372	2364	0.996	24	67
		1	Σ	2352	2415	1.027	24	68
		1	Σ	2372	2415	1.018	24	69
		1	Σ	2352	2403	1.022	24	70
		1	Σ	2372	2403	1.013	24	71
AlH	aluminum monohydride	1	Σ	1681	1682	1.001	25	72
BH2	boron dihydride	2	A1	1018	954	0.937	26	73
AlH2	aluminum dihydride	1	A1	1847	1770	0.958	27	74
		2	A1	765	760	0.993	27	75
		3	B2	1883	1807	0.960	27	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.

	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