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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD/aug-cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.962 ± 0.017 27 127 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4403 4161 0.945 1 1
LiH Lithium Hydride 1 Σ 1386 1360 0.981 2 2
Li2 Lithium diatomic 1 Σg 345 346 1.004 3 3
Na2 Sodium diatomic 1 Σg 151 158 1.041 4 4
N2 Nitrogen diatomic 1 Σg 2385 2330 0.977 5 5
    1 Σg 1757 1733 0.987 5 6
OH Hydroxyl radical 1 Σ 3750 3570 0.952 6 7
CO Carbon monoxide 1 Σ 2180 2143 0.983 7 8
    1 Σ 1814     7 9
HF Hydrogen fluoride 1 Σ 4159 3961 0.952 8 10
F2 Fluorine diatomic 1 Σg 1007 894 0.888 9 11
HCl Hydrogen chloride 1 Σ 3009 2886 0.959 10 12
AlCl Aluminum monochloride 1 Σ 473 478 1.009 11 13
BeH2 beryllium dihydride 2 Σu 2234 2159 0.966 12 14
    3 Πu 710 698 0.983 12 15
H2O Water 1 A1 3846 3657 0.951 13 16
    2 A1 1658 1595 0.962 13 17
    3 B2 3953 3756 0.950 13 18
CO2 Carbon dioxide 1 Σg 1368 1333 0.974 14 19
    2 Σu 2393 2349 0.981 14 20
    3 Πu 682 667 0.978 14 21
SO2 Sulfur dioxide 1 A1 1185 1151 0.972 15 22
    2 A1 523 518 0.989 15 23
    3 B2 1374 1362 0.991 15 24
C2H2 Acetylene 1 Σg 3525 3374 0.957 16 25
    2 Σg 2035 1974 0.970 16 26
    3 Σu 3413 3289 0.964 16 27
    4 Πg 632 612 0.969 16 28
    5 Πu 769 730 0.949 16 29
NH3 Ammonia 1 A1 3494 3337 0.955 17 30
    2 A1 1068 950 0.890 17 31
    3 E 3620 3444 0.951 17 32
    4 E 1686 1627 0.965 17 33
H2CO Formaldehyde 1 A1 2956 2782 0.941 18 34
    2 A1 1802 1746 0.969 18 35
    3 A1 1544 1500 0.971 18 36
    4 B1 1203 1167 0.970 18 37
    5 B2 3022 2843 0.941 18 38
    6 B2 1275 1249 0.980 18 39
BF3 Borane, trifluoro- 1 A1' 899 888 0.988 19 40
    2 A2" 698 691 0.991 19 41
    3 E' 1485 1449 0.976 19 42
    4 E' 481 480 0.999 19 43
NF3 Nitrogen trifluoride 1 A1 1078 1032 0.958 20 44
    2 A1 676 647 0.956 20 45
    3 E 982 907 0.924 20 46
    4 E 515 492 0.955 20 47
AlF3 Aluminum trifluoride 1 A1' 694 690 0.994 21 48
    2 A2" 300 297 0.991 21 49
    3 E' 958 935 0.976 21 50
    4 E' 245 263 1.074 21 51
CH4 Methane 1 A1 3042 2917 0.959 22 52
    2 E 1584 1534 0.969 22 53
    3 T2 3158 3019 0.956 22 54
    4 T2 1363 1306 0.958 22 55
C2H4 Ethylene 1 Ag 3172 3026 0.954 23 56
    2 Ag 1694 1623 0.958 23 57
    3 Ag 1382 1342 0.971 23 58
    4 Au 1037 1023 0.987 23 59
    5 B1u 3152 2989 0.948 23 60
    6 B1u 1487 1444 0.971 23 61
    7 B2g 956 940 0.982 23 62
    8 B2u 3258 3105 0.953 23 63
    9 B2u 829 826 0.997 23 64
    10 B3g 3231 3086 0.955 23 65
    11 B3g 1253 1217 0.971 23 66
    12 B3u 979 949 0.970 23 67
C2H6 Ethane 1 A1g 3050 2954 0.969 24 68
    2 A1g 1445 1388 0.960 24 69
    3 A1g 1021 995 0.975 24 70
    4 A1u 311 289 0.929 24 71
    5 A2u 3048 2896 0.950 24 72
    6 A2u 1427 1379 0.966 24 73
    7 Eg 3106 2969 0.956 24 74
    8 Eg 1527 1468 0.962 24 75
    9 Eg 1239 1190 0.960 24 76
    10 Eu 3128 2985 0.954 24 77
    11 Eu 1528 1469 0.961 24 78
    12 Eu 831 822 0.990 24 79
C3H5 Allyl radical 1 A1 3267 3114 0.953 25 80
    2 A1 3175 3048 0.960 25 81
    4 A1 1535 1488 0.969 25 82
    5 A1 1282 1245 0.971 25 83
    6 A1 1042 1066 1.023 25 84
    7 A1 423 427 1.010 25 85
    9 A2 547 549 1.003 25 86
    10 B1 999 968 0.969 25 87
    11 B1 802 802 1.000 25 88
    12 B1 526 518 0.984 25 89
    13 B2 3264 3105 0.951 25 90
    14 B2 3162 3016 0.954 25 91
    15 B2 1523 1463 0.961 25 92
    16 B2 1428 1389 0.973 25 93
    17 B2 1186 1182 0.997 25 94
C3H6 Cyclopropane 1 A1' 3170 3038 0.958 26 95
    2 A1' 1545 1479 0.958 26 96
    3 A1' 1226 1188 0.969 26 97
    4 A1" 1166 1126 0.966 26 98
    5 A2' 1099 1070 0.974 26 99
    6 A2" 3259 3103 0.952 26 100
    7 A2" 857 854 0.997 26 101
    8 E' 3158 3025 0.958 26 102
    9 E' 1490 1438 0.965 26 103
    10 E' 1067 1029 0.964 26 104
    11 E' 902 866 0.960 26 105
    12 E" 3239 3082 0.952 26 106
    13 E" 1223 1188 0.971 26 107
    14 E" 743 739 0.995 26 108

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