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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at B3LYP/6-311+G(3df,2pd)
Scale factor How many Source
Molecules Vibrations
0.964 ± 0.012 24 114 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4420 4161 0.941 1 1
LiH Lithium Hydride 1 Σ 1412 1360 0.963 2 2
Na2 Sodium diatomic 1 Σg 161 158 0.982 3 3
N2 Nitrogen diatomic 1 Σg 2446 2330 0.952 4 4
OH Hydroxyl radical 1 Σ 3721 3570 0.959 5 5
CO Carbon monoxide 1 Σ 2217 2143 0.967 6 6
HF Hydrogen fluoride 1 Σ 4092 3961 0.968 7 7
F2 Fluorine diatomic 1 Σg 1039 894 0.861 8 8
HCl Hydrogen chloride 1 Σ 2947 2886 0.979 9 9
Cl2 Chlorine diatomic 1 Σg 541 554 1.026 10 10
H2O Water 1 A1 3827 3657 0.956 11 11
    2 A1 1626 1595 0.981 11 12
    3 B2 3928 3756 0.956 11 13
CO2 Carbon dioxide 1 Σg 1374 1333 0.970 12 14
    2 Σu 2414 2349 0.973 12 15
    3 Πu 679 667 0.982 12 16
SO2 Sulfur dioxide 1 A1 1178 1151 0.977 13 17
    2 A1 519 518 0.998 13 18
    3 B2 1377 1362 0.989 13 19
C2H2 Acetylene 1 Σg 3508 3374 0.962 14 20
    2 Σg 2066 1974 0.955 14 21
    3 Σu 3409 3289 0.965 14 22
    4 Πg 660 612 0.928 14 23
    5 Πu 765 730 0.954 14 24
NH3 Ammonia 1 A1 3475 3337 0.960 15 25
    2 A1 1024 950 0.928 15 26
    3 E 3595 3444 0.958 15 27
    4 E 1663 1627 0.978 15 28
H2CO Formaldehyde 1 A1 2884 2782 0.965 16 29
    2 A1 1822 1746 0.959 16 30
    3 A1 1532 1500 0.979 16 31
    4 B1 1201 1167 0.972 16 32
    5 B2 2941 2843 0.967 16 33
    6 B2 1266 1249 0.987 16 34
BF3 Borane, trifluoro- 1 A1' 886 888 1.002 17 35
    2 A2" 685 691 1.009 17 36
    3 E' 1445 1449 1.003 17 37
    4 E' 475 480 1.010 17 38
AlF3 Aluminum trifluoride 1 A1' 680 690 1.015 18 39
    2 A2" 290 297 1.026 18 40
    3 E' 941 935 0.994 18 41
    4 E' 236 263 1.114 18 42
CH4 Methane 1 A1 3027 2917 0.964 19 43
    2 E 1560 1534 0.983 19 44
    3 T2 3130 3019 0.964 19 45
    4 T2 1342 1306 0.973 19 46
HCOOH Formic acid 1 A' 3741 3570 0.954 20 47
    2 A' 3049 2943 0.965 20 48
    3 A' 1818 1770 0.973 20 49
    4 A' 1404 1387 0.988 20 50
    5 A' 1300 1229 0.945 20 51
    6 A' 1126 1105 0.981 20 52
    7 A' 630 625 0.992 20 53
    8 A" 1054 1033 0.980 20 54
    9 A" 678 638 0.941 20 55
C2H4 Ethylene 1 Ag 3140 3026 0.964 21 56
    2 Ag 1689 1623 0.961 21 57
    3 Ag 1381 1342 0.972 21 58
    4 Au 1063 1023 0.962 21 59
    5 B1u 3126 2989 0.956 21 60
    6 B1u 1479 1444 0.976 21 61
    7 B2g 986 940 0.953 21 62
    8 B2u 3225 3105 0.963 21 63
    9 B2u 837 826 0.987 21 64
    10 B3g 3197 3086 0.965 21 65
    11 B3g 1246 1217 0.976 21 66
    12 B3u 979 949 0.970 21 67
C2H6 Ethane 1 A1g 3026 2954 0.976 22 68
    2 A1g 1422 1388 0.976 22 69
    3 A1g 996 995 0.999 22 70
    4 A1u 305 289 0.947 22 71
    5 A2u 3026 2896 0.957 22 72
    6 A2u 1413 1379 0.976 22 73
    7 Eg 3071 2969 0.967 22 74
    8 Eg 1504 1468 0.976 22 75
    9 Eg 1222 1190 0.974 22 76
    10 Eu 3096 2985 0.964 22 77
    11 Eu 1507 1469 0.975 22 78
    12 Eu 826 822 0.995 22 79
C3H6 Cyclopropane 1 A1' 3133 3038 0.970 23 80
    2 A1' 1521 1479 0.972 23 81
    3 A1' 1211 1188 0.981 23 82
    4 A1" 1154 1126 0.976 23 83
    5 A2' 1096 1070 0.976 23 84
    6 A2" 3221 3103 0.963 23 85
    7 A2" 862 854 0.990 23 86
    8 E' 3126 3025 0.968 23 87
    9 E' 1479 1438 0.973 23 88
    10 E' 1054 1029 0.976 23 89
    11 E' 879 866 0.985 23 90
    12 E" 3200 3082 0.963 23 91
    13 E" 1214 1188 0.979 23 92
    14 E" 743 739 0.994 23 93
CH2CHCH3 Propene 1 A' 3210 3090 0.963 24 94
    2 A' 3130 3013 0.963 24 95
    3 A' 3123 2991 0.958 24 96
    4 A' 3093 2954 0.955 24 97
    5 A' 3015 2871 0.952 24 98
    6 A' 1709 1650 0.966 24 99
    7 A' 1496 1470 0.983 24 100
    8 A' 1454 1420 0.977 24 101
    9 A' 1410 1378 0.978 24 102
    10 A' 1332 1297 0.973 24 103
    11 A' 1193 1171 0.982 24 104
    12 A' 952 963 1.012 24 105
    13 A' 923 920 0.996 24 106
    14 A' 428 428 1.000 24 107
    15 A" 3059 2954 0.966 24 108
    16 A" 1481 1443 0.974 24 109
    17 A" 1075 1045 0.972 24 110
    18 A" 1030 991 0.962 24 111
    19 A" 951 912 0.959 24 112
    20 A" 593 578 0.974 24 113
    21 A" 208 174 0.836 24 114

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