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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD(T)/aug-cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.978 ± 0.028 32 157 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4344 4161 0.958 1 1
LiH Lithium Hydride 1 Σ 1344 1360 1.012 2 2
Li2 Lithium diatomic 1 Σg 339 346 1.022 3 3
Na2 Sodium diatomic 1 Σg 149 158 1.057 4 4
CH Methylidyne 1 Σ 2814 2733 0.971 5 5
    1 Σ 3078     5 6
Si2 Silicon diatomic 1 Σg 522 507 0.970 6 7
N2 Nitrogen diatomic 1 Σg 2313 2330 1.007 7 8
    1 Σg 1700 1733 1.020 7 9
PH phosphorus monohydride 1 Σ 2327 2276 0.978 8 10
    1 Σ 2354 2319 0.985 8 11
OH Hydroxyl radical 1 Σ 3678 3570 0.971 9 12
CO Carbon monoxide 1 Σ 2092 2143 1.024 10 13
    1 Σ 1711     10 14
SO Sulfur monoxide 1 Σ 1065 1138 1.069 11 15
    1 Σ 1004 1054 1.050 11 16
HF Hydrogen fluoride 1 Σ 4079 3961 0.971 12 17
F2 Fluorine diatomic 1 Σg 831 894 1.076 13 18
HCl Hydrogen chloride 1 Σ 2970 2886 0.972 14 19
BeH2 beryllium dihydride 2 Σu 2229 2159 0.968 15 20
    3 Πu 724 698 0.964 15 21
H2O Water 1 A1 3785 3657 0.966 16 22
    2 A1 1636 1595 0.975 16 23
    3 B2 3904 3756 0.962 16 24
CO2 Carbon dioxide 1 Σg 1307 1333 1.020 17 25
    2 Σu 2328 2349 1.009 17 26
    3 Πu 656 667 1.017 17 27
OCS Carbonyl sulfide 1 Σ 2031 2062 1.015 18 28
    2 Σ 844 859 1.017 18 29
    3 Π 508 520 1.023 18 30
SO2 Sulfur dioxide 1 A1 1032 1151 1.115 19 31
    2 A1 470 518 1.101 19 32
    3 B2 1201 1362 1.134 19 33
C2H2 Acetylene 1 Σg 3479 3374 0.970 20 34
    2 Σg 1967 1974 1.004 20 35
    3 Σu 3385 3289 0.972 20 36
    4 Πg 364 612 1.684 20 37
    5 Πu 690 730 1.058 20 38
NH3 Ammonia 1 A1 3432 3337 0.972 21 39
    2 A1 1070 950 0.888 21 40
    3 E 3570 3444 0.965 21 41
    4 E 1650 1627 0.986 21 42
H2CO Formaldehyde 1 A1 2928 2782 0.950 22 43
    2 A1 1734 1746 1.007 22 44
    3 A1 1514 1500 0.991 22 45
    4 B1 1166 1167 1.001 22 46
    5 B2 3004 2843 0.946 22 47
    6 B2 1243 1249 1.005 22 48
BF3 Borane, trifluoro- 1 A1' 838 888 1.060 23 49
    2 A2" 707 691 0.977 23 50
    3 E' 1400 1449 1.035 23 51
    4 E' 456 480 1.052 23 52
AlF3 Aluminum trifluoride 1 A1' 665 690 1.037 24 53
    2 A2" 293 297 1.014 24 54
    3 E' 924 935 1.012 24 55
    4 E' 245 263 1.075 24 56
CH4 Methane 1 A1 3017 2917 0.967 25 57
    2 E 1535 1534 1.000 25 58
    3 T2 3144 3019 0.960 25 59
    4 T2 1319 1306 0.990 25 60
C2H4 Ethylene 1 Ag 3148 3026 0.961 26 61
    2 Ag 1653 1623 0.982 26 62
    3 Ag 1352 1342 0.993 26 63
    4 Au 1016 1023 1.007 26 64
    5 B1u 3130 2989 0.955 26 65
    6 B1u 1459 1444 0.989 26 66
    7 B2g 927 940 1.014 26 67
    8 B2u 3245 3105 0.957 26 68
    9 B2u 813 826 1.016 26 69
    10 B3g 3217 3086 0.959 26 70
    11 B3g 1223 1217 0.995 26 71
    12 B3u 957 949 0.992 26 72
C2H6 Ethane 1 A1g 3023 2954 0.977 27 73
    2 A1g 1408 1388 0.986 27 74
    3 A1g 1011 995 0.984 27 75
    4 A1u 312 289 0.926 27 76
    5 A2u 3018 2896 0.959 27 77
    6 A2u 1380 1379 1.000 27 78
    7 Eg 3085 2969 0.963 27 79
    8 Eg 1483 1468 0.990 27 80
    9 Eg 1206 1190 0.987 27 81
    10 Eu 3106 2985 0.961 27 82
    11 Eu 1484 1469 0.990 27 83
    12 Eu 809 822 1.017 27 84
C3H5 Allyl radical 1 A1 3249 3114 0.958 28 85
    2 A1 3156 3048 0.966 28 86
    4 A1 1512 1488 0.984 28 87
    5 A1 1259 1245 0.989 28 88
    6 A1 1025 1066 1.040 28 89
    7 A1 420 427 1.017 28 90
    9 A2 546 549 1.005 28 91
    10 B1 982 968 0.986 28 92
    11 B1 790 802 1.015 28 93
    12 B1 524 518 0.988 28 94
    13 B2 3246 3105 0.957 28 95
    14 B2 3139 3016 0.961 28 96
    15 B2 1504 1463 0.972 28 97
    16 B2 1405 1389 0.989 28 98
    17 B2 1185 1182 0.997 28 99
C3H6 Cyclopropane 1 A1' 3140 3038 0.967 29 100
    2 A1' 1506 1479 0.982 29 101
    3 A1' 1201 1188 0.989 29 102
    4 A1" 1136 1126 0.991 29 103
    5 A2' 1050 1070 1.019 29 104
    6 A2" 3236 3103 0.959 29 105
    7 A2" 837 854 1.020 29 106
    8 E' 3128 3025 0.967 29 107
    9 E' 1453 1438 0.990 29 108
    10 E' 1031 1029 0.998 29 109
    11 E' 876 866 0.989 29 110
    12 E" 3216 3082 0.958 29 111
    13 E" 1193 1188 0.995 29 112
    14 E" 722 739 1.024 29 113
CH2CHCH3 Propene 1 A' 3225 3090 0.958 30 114
    2 A' 3143 3013 0.959 30 115
    3 A' 3127 2991 0.956 30 116
    4 A' 3099 2954 0.953 30 117
    5 A' 3010 2871 0.954 30 118
    6 A' 1679 1650 0.983 30 119
    7 A' 1476 1470 0.996 30 120
    8 A' 1437 1420 0.988 30 121
    9 A' 1384 1378 0.996 30 122
    10 A' 1305 1297 0.994 30 123
    11 A' 1178 1171 0.994 30 124
    12 A' 928 963 1.037 30 125
    13 A' 925 920 0.995 30 126
    14 A' 414 428 1.033 30 127
    15 A" 3076 2954 0.960 30 128
    16 A" 1459 1443 0.989 30 129
    17 A" 1046 1045 0.999 30 130
    18 A" 987 991 1.004 30 131
    19 A" 911 912 1.001 30 132
    20 A" 570 578 1.014 30 133
    21 A" 199 174 0.874 30 134
CH3CHClCH3 Propane, 2-chloro- 1 A' 3124 3005 0.962 31 135
    2 A' 3102 2955 0.953 31 136
    3 A' 3078 2927 0.951 31 137
    4 A' 3019 2878 0.953 31 138
    5 A' 1486 1472 0.991 31 139
    6 A' 1472 1454 0.988 31 140
    7 A' 1399 1390 0.994 31 141
    8 A' 1272 1270 0.999 31 142
    9 A' 1176 1163 0.989 31 143
    10 A' 1065 1065 1.000 31 144
    11 A' 901 888 0.985 31 145
    12 A' 621 633 1.019 31 146
    13 A' 417 418 1.001 31 147
    14 A' 334 336 1.006 31 148
    15 A' 266 253 0.950 31 149
    16 A" 3120 2997 0.961 31 150
    17 A" 3094 2985 0.965 31 151
    18 A" 3015 2947 0.977 31 152
    19 A" 1465 1472 1.004 31 153
    20 A" 1460 1454 0.996 31 154
    21 A" 1390 1377 0.991 31 155
    22 A" 1342 1334 0.994 31 156
    23 A" 1152 1123 0.975 31 157
    24 A" 943 972 1.030 31 158
    25 A" 923 936 1.014 31 159
    26 A" 321 317 0.987 31 160
    27 A" 233 276 1.184 31 161

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 90 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 80 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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