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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)=FULL/cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.966 ± 0.023 40 108 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4404 4161 0.945 1 1
LiH Lithium Hydride 1 Σ 1412 1360 0.963 2 2
Li2 Lithium diatomic 1 Σg 372 346 0.932 3 3
NaH sodium hydride 1 Σ 1421 1133 0.798 4 4
Na2 Sodium diatomic 1 Σg 249 158 0.634 5 5
BeH beryllium monohydride 1 Σ 2053 1987 0.968 6 6
C2 Carbon diatomic 1 Σg 1869 1827 0.978 7 7
N2 Nitrogen diatomic 1 Σg 2369 2330 0.984 8 8
    1 Σg 1753 1733 0.989 8 9
PH phosphorus monohydride 1 Σ 2362 2276 0.964 9 10
    1 Σ 2379 2319 0.975 9 11
P2 Phosphorus diatomic 1 Σg 784 775 0.989 10 12
OH Hydroxyl radical 1 Σ 3752 3570 0.951 11 13
BeO beryllium oxide 1 Σ 1490 1435 0.962 12 14
CO Carbon monoxide 1 Σ 2177 2143 0.984 13 15
    1 Σ 1809     13 16
HS Mercapto radical 1 Σ 2693 2599 0.965 14 17
SO Sulfur monoxide 1 Σ 1156 1138 0.985 15 18
    1 Σ 1100 1054 0.958 15 19
HF Hydrogen fluoride 1 Σ 4167 3961 0.951 16 20
F2 Fluorine diatomic 1 Σg 925 894 0.966 17 21
SF Monosulfur monofluoride 1 Σ 845 829 0.981 18 22
HCl Hydrogen chloride 1 Σ 2998 2886 0.963 19 23
NaCl Sodium Chloride 1 Σ 329 361 1.097 20 24
AlCl Aluminum monochloride 1 Σ 507 478 0.942 21 25
SCl sulfur monochloride 1 Σ 578 577 0.998 22 26
Cl2 Chlorine diatomic 1 Σg 556 554 0.996 23 27
BeH2 beryllium dihydride 2 Σu 2238 2159 0.965 24 28
    3 Πu 699 698 0.999 24 29
SiH2 silicon dihydride 1 A1 2124 1996 0.940 25 30
    2 A1 1035 999 0.965 25 31
    3 B2 2120 1993 0.940 25 32
HCN Hydrogen cyanide 1 Σ 3447 3312 0.961 26 33
    2 Σ 2134 2089 0.979 26 34
    3 Π 722 712 0.986 26 35
H2O Water 1 A1 3854 3657 0.949 27 36
    2 A1 1663 1595 0.959 27 37
    3 B2 3960 3756 0.948 27 38
CO2 Carbon dioxide 1 Σg 1360 1333 0.980 28 39
    2 Σu 2411 2349 0.974 28 40
    3 Πu 673 667 0.991 28 41
N2O Nitrous oxide 1 Σ 2306 2224 0.965 29 42
    2 Σ 1313 1285 0.979 29 43
    3 Π 611 589 0.964 29 44
BH3 boron trihydride 2 A2" 1167 1148 0.983 30 45
    3 E' 2719 2602 0.957 30 46
    4 E' 1232 1197 0.971 30 47
C2H2 Acetylene 1 Σg 3511 3374 0.961 31 48
    2 Σg 2013 1974 0.981 31 49
    3 Σu 3417 3289 0.962 31 50
    4 Πg 597 612 1.026 31 51
    5 Πu 756 730 0.966 31 52
NH3 Ammonia 1 A1 3495 3337 0.955 32 53
    2 A1 1082 950 0.878 32 54
    3 E 3622 3444 0.951 32 55
    4 E 1685 1627 0.965 32 56
H2CO Formaldehyde 1 A1 2945 2782 0.945 33 57
    2 A1 1791 1746 0.975 33 58
    3 A1 1544 1500 0.971 33 59
    4 B1 1195 1167 0.976 33 60
    5 B2 3015 2843 0.943 33 61
    6 B2 1278 1249 0.977 33 62
BF3 Borane, trifluoro- 1 A1' 903 888 0.983 34 63
    2 A2" 702 691 0.984 34 64
    3 E' 1492 1449 0.971 34 65
    4 E' 486 480 0.988 34 66
AlF3 Aluminum trifluoride 1 A1' 731 690 0.945 35 67
    2 A2" 315 297 0.942 35 68
    3 E' 1012 935 0.924 35 69
    4 E' 262 263 1.003 35 70
CH4 Methane 1 A1 3049 2917 0.957 36 71
    2 E 1575 1534 0.974 36 72
    3 T2 3170 3019 0.952 36 73
    4 T2 1348 1306 0.969 36 74
C2H4 Ethylene 1 Ag 3169 3026 0.955 37 75
    2 Ag 1680 1623 0.966 37 76
    3 Ag 1373 1342 0.977 37 77
    4 Au 1052 1023 0.973 37 78
    5 B1u 3153 2989 0.948 37 79
    6 B1u 1479 1444 0.976 37 80
    7 B2g 958 940 0.981 37 81
    8 B2u 3260 3105 0.952 37 82
    9 B2u 824 826 1.003 37 83
    10 B3g 3234 3086 0.954 37 84
    11 B3g 1242 1217 0.980 37 85
    12 B3u 973 949 0.976 37 86
CH3OH Methyl alcohol 1 A' 3882 3681 0.948 38 87
    2 A' 3145 3000 0.954 38 88
    3 A' 3028 2844 0.939 38 89
    4 A' 1528 1477 0.967 38 90
    5 A' 1492 1455 0.975 38 91
    6 A' 1390 1345 0.968 38 92
    7 A' 1098 1060 0.965 38 93
    8 A' 1069 1033 0.966 38 94
    9 A" 3085 2960 0.959 38 95
    10 A" 1516 1477 0.974 38 96
    11 A" 1187 1165 0.981 38 97
    12 A" 297 200 0.674 38 98
C2H6 Ethane 1 A1g 3052 2954 0.968 39 99
    2 A1g 1433 1388 0.968 39 100
    3 A1g 1021 995 0.975 39 101
    4 A1u 307 289 0.941 39 102
    5 A2u 3052 2896 0.949 39 103
    6 A2u 1412 1379 0.976 39 104
    7 Eg 3112 2969 0.954 39 105
    8 Eg 1517 1468 0.968 39 106
    9 Eg 1230 1190 0.967 39 107
    10 Eu 3135 2985 0.952 39 108
    11 Eu 1517 1469 0.968 39 109
    12 Eu 826 822 0.995 39 110

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.

40 70 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 60 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 50 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 40 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 30 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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