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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at MP4=FULL/6-31G*
Scale factor How many Source
Molecules Vibrations
0.962 ± 0.053 43 239 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1357 1360 1.002 1 1
Li2 Lithium diatomic 1 Σg 342 346 1.011 2 2
NaH sodium hydride 1 Σ 1149 1133 0.986 3 3
Na2 Sodium diatomic 1 Σg 164 158 0.962 4 4
BeH beryllium monohydride 1 Σ 2093 1987 0.950 5 5
C2 Carbon diatomic 1 Σg 1774 1827 1.030 6 6
N2 Nitrogen diatomic 1 Σg 2202 2330 1.058 7 7
P2 Phosphorus diatomic 1 Σg 729 775 1.064 8 8
OH Hydroxyl radical 1 Σ 3664 3570 0.974 9 9
BeO beryllium oxide 1 Σ 658 1435 2.181 10 10
HS Mercapto radical 1 Σ 2696 2599 0.964 11 11
SO Sulfur monoxide 1 Σ 1085 1138 1.049 12 12
HF Hydrogen fluoride 1 Σ 4014 3961 0.987 13 13
SF Monosulfur monofluoride 1 Σ 836 829 0.991 14 14
HCl Hydrogen chloride 1 Σ 2987 2886 0.966 15 15
NaCl Sodium Chloride 1 Σ 368 361 0.980 16 16
AlCl Aluminum monochloride 1 Σ 498 478 0.958 17 17
SCl sulfur monochloride 1 Σ 552 577 1.046 18 18
Cl2 Chlorine diatomic 1 Σg 510 554 1.086 19 19
BeH2 beryllium dihydride 2 Σu 2281 2159 0.947 20 20
    3 Πu 723 698 0.966 20 21
SiH2 silicon dihydride 1 A1 2089 1996 0.956 21 22
    2 A1 1033 999 0.967 21 23
    3 B2 2094 1993 0.951 21 24
HCN Hydrogen cyanide 1 Σ 3472 3312 0.954 22 25
    2 Σ 2046 2089 1.021 22 26
    3 Π 703 712 1.012 22 27
CO2 Carbon dioxide 1 Σg 1269 1333 1.051 23 28
    2 Σu 2371 2349 0.991 23 29
    3 Πu 622 667 1.073 23 30
N2O Nitrous oxide 1 Σ 2192 2224 1.015 24 31
    2 Σ 1232 1285 1.043 24 32
    3 Π 561 589 1.050 24 33
SO2 Sulfur dioxide 1 A1 982 1151 1.172 25 34
    2 A1 467 518 1.107 25 35
    3 B2 1212 1362 1.123 25 36
BH3 boron trihydride 2 A2" 1170 1148 0.981 26 37
    3 E' 2750 2602 0.946 26 38
    4 E' 1230 1197 0.973 26 39
C2H2 Acetylene 1 Σg 3531 3374 0.956 27 40
    2 Σg 1994 1974 0.990 27 41
    3 Σu 3439 3289 0.956 27 42
    4 Πg 337 612 1.817 27 43
    5 Πu 733 730 0.995 27 44
NH3 Ammonia 1 A1 3445 3337 0.969 28 45
    2 A1 1181 950 0.805 28 46
    3 E 3589 3444 0.960 28 47
    4 E 1749 1627 0.930 28 48
H2CO Formaldehyde 1 A1 2947 2782 0.944 29 49
    2 A1 1770 1746 0.986 29 50
    3 A1 1557 1500 0.964 29 51
    4 B1 1186 1167 0.984 29 52
    5 B2 3009 2843 0.945 29 53
    6 B2 1279 1249 0.977 29 54
BF3 Borane, trifluoro- 1 A1' 883 888 1.006 30 55
    2 A2" 696 691 0.993 30 56
    3 E' 1494 1449 0.970 30 57
    4 E' 479 480 1.001 30 58
AlF3 Aluminum trifluoride 1 A1' 704 690 0.980 31 59
    2 A2" 300 297 0.990 31 60
    3 E' 989 935 0.946 31 61
    4 E' 259 263 1.014 31 62
CH4 Methane 1 A1 3063 2917 0.952 32 63
    2 E 1602 1534 0.958 32 64
    3 T2 3190 3019 0.946 32 65
    4 T2 1397 1306 0.935 32 66
C2H4 Ethylene 1 Ag 3182 3026 0.951 33 67
    2 Ag 1696 1623 0.957 33 68
    3 Ag 1393 1342 0.964 33 69
    4 Au 1057 1023 0.968 33 70
    5 B1u 3163 2989 0.945 33 71
    6 B1u 1504 1444 0.960 33 72
    7 B2g 918 940 1.023 33 73
    8 B2u 3267 3105 0.950 33 74
    9 B2u 840 826 0.983 33 75
    10 B3g 3244 3086 0.951 33 76
    11 B3g 1253 1217 0.972 33 77
    12 B3u 968 949 0.980 33 78
CH3OH Methyl alcohol 1 A' 3756 3681 0.980 34 79
    2 A' 3163 3000 0.948 34 80
    3 A' 3023 2844 0.941 34 81
    4 A' 1557 1477 0.948 34 82
    5 A' 1522 1455 0.956 34 83
    6 A' 1416 1345 0.950 34 84
    7 A' 1102 1060 0.962 34 85
    8 A' 1075 1033 0.961 34 86
    9 A" 3081 2960 0.961 34 87
    10 A" 1544 1477 0.957 34 88
    11 A" 1191 1165 0.978 34 89
    12 A" 351 200 0.570 34 90
CHONH2 formamide 1 A' 3736 3564 0.954 35 91
    2 A' 3598 3439 0.956 35 92
    3 A' 2982 2854 0.957 35 93
    4 A' 1805 1754 0.972 35 94
    5 A' 1643 1577 0.960 35 95
    6 A' 1431 1390 0.972 35 96
    7 A' 1294 1258 0.972 35 97
    8 A' 1061 1046 0.986 35 98
    9 A' 560 581 1.038 35 99
    10 A" 1037 1021 0.985 35 100
    11 A" 650 603 0.928 35 101
    12 A" 187i 289 -1.541 35 102
B2Cl4 Diboron tetrachloride 1 A1 1170 1122 0.959 36 103
    2 A1 417 401 0.961 36 104
    3 A1 179 176 0.982 36 105
    5 B2 758 728 0.960 36 106
    6 B2 305 289 0.947 36 107
    7 E 962 917 0.954 36 108
    8 E 512 512 1.000 36 109
    9 E 102 104 1.018 36 110
CH2N4 1H-Tetrazole 1 A' 3644 3447 0.946 37 111
    2 A' 3306 3102 0.938 37 112
    3 A' 1491 1441 0.967 37 113
    4 A' 1468 1384 0.943 37 114
    5 A' 1256 1259 1.002 37 115
    6 A' 1227 1159 0.944 37 116
    7 A' 1154 1084 0.939 37 117
    8 A' 1060 1015 0.958 37 118
    9 A' 1046 1002 0.958 37 119
    10 A' 999 969 0.970 37 120
    11 A' 950 925 0.974 37 121
    12 A" 819 906 1.106 37 122
    13 A" 725 663 0.915 37 123
    14 A" 684 658 0.962 37 124
    15 A" 560 578 1.033 37 125
C2H6 Ethane 1 A1g 3062 2954 0.965 38 126
    2 A1g 1477 1388 0.940 38 127
    3 A1g 1035 995 0.961 38 128
    4 A1u 323 289 0.894 38 129
    5 A2u 3062 2896 0.946 38 130
    6 A2u 1450 1379 0.951 38 131
    7 Eg 3129 2969 0.949 38 132
    8 Eg 1549 1468 0.948 38 133
    9 Eg 1258 1190 0.946 38 134
    10 Eu 3150 2985 0.948 38 135
    11 Eu 1554 1469 0.945 38 136
    12 Eu 840 822 0.979 38 137
C3H6 Cyclopropane 1 A1' 3172 3038 0.958 39 138
    2 A1' 1569 1479 0.943 39 139
    3 A1' 1244 1188 0.955 39 140
    4 A1" 1185 1126 0.951 39 141
    5 A2' 1109 1070 0.965 39 142
    6 A2" 3260 3103 0.952 39 143
    7 A2" 876 854 0.975 39 144
    8 E' 3162 3025 0.957 39 145
    9 E' 1515 1438 0.949 39 146
    10 E' 1101 1029 0.934 39 147
    11 E' 915 866 0.947 39 148
    12 E" 3242 3082 0.951 39 149
    13 E" 1242 1188 0.957 39 150
    14 E" 761 739 0.971 39 151
CH2CHCH3 Propene 1 A' 3250 3090 0.951 40 152
    2 A' 3167 3013 0.951 40 153
    3 A' 3156 2991 0.948 40 154
    4 A' 3136 2954 0.942 40 155
    5 A' 3048 2871 0.942 40 156
    6 A' 1720 1650 0.959 40 157
    7 A' 1542 1470 0.953 40 158
    8 A' 1486 1420 0.956 40 159
    9 A' 1450 1378 0.950 40 160
    10 A' 1343 1297 0.966 40 161
    11 A' 1215 1171 0.964 40 162
    12 A' 965 963 0.998 40 163
    13 A' 945 920 0.974 40 164
    14 A' 427 428 1.003 40 165
    15 A" 3115 2954 0.948 40 166
    16 A" 1527 1443 0.945 40 167
    17 A" 1092 1045 0.957 40 168
    18 A" 1020 991 0.972 40 169
    19 A" 910 912 1.002 40 170
    20 A" 584 578 0.989 40 171
    21 A" 196 174 0.888 40 172
CHCCH2CH3 1-Butyne 1 A' 3482 3332 0.957 41 173
    2 A' 3149 2988 0.949 41 174
    3 A' 3067     41 175
    4 A' 3052     41 176
    5 A' 2158 2116 0.981 41 177
    6 A' 1550 1470 0.949 41 178
    7 A' 1529 1446 0.946 41 179
    8 A' 1456 1385 0.951 41 180
    9 A' 1384 1322 0.955 41 181
    10 A' 1116 1070 0.959 41 182
    11 A' 1051 1008 0.959 41 183
    12 A' 860 840 0.977 41 184
    13 A' 543 634 1.168 41 185
    14 A' 452 509 1.125 41 186
    15 A' 173 197 1.134 41 187
    16 A" 3159 2988 0.946 41 188
    17 A" 3092 2939 0.951 41 189
    18 A" 1542 1462 0.948 41 190
    19 A" 1315 1261 0.959 41 191
    20 A" 1132 1090 0.963 41 192
    21 A" 801 782 0.976 41 193
    22 A" 509 630 1.239 41 194
    23 A" 319 344 1.075 41 195
    24 A" 207 213 1.028 41 196
CH3CHClCH3 Propane, 2-chloro- 1 A' 3165 3005 0.950 42 197
    2 A' 3147 2955 0.939 42 198
    3 A' 3107 2927 0.942 42 199
    4 A' 3064 2878 0.939 42 200
    5 A' 1551 1472 0.949 42 201
    6 A' 1537 1454 0.946 42 202
    7 A' 1466 1390 0.948 42 203
    8 A' 1342 1270 0.947 42 204
    9 A' 1222 1163 0.951 42 205
    10 A' 1115 1065 0.955 42 206
    11 A' 926 888 0.959 42 207
    12 A' 655 633 0.967 42 208
    13 A' 432 418 0.967 42 209
    14 A' 348 336 0.966 42 210
    15 A' 283 253 0.895 42 211
    16 A" 3162 2997 0.948 42 212
    17 A" 3141 2985 0.950 42 213
    18 A" 3061 2947 0.963 42 214
    19 A" 1532 1472 0.961 42 215
    20 A" 1526 1454 0.953 42 216
    21 A" 1452 1377 0.948 42 217
    22 A" 1395 1334 0.957 42 218
    23 A" 1181 1123 0.951 42 219
    24 A" 980 972 0.991 42 220
    25 A" 962 936 0.973 42 221
    26 A" 329 317 0.962 42 222
    27 A" 256 276 1.080 42 223

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.

40 160 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 140 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 120 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 100 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 60 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 20 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