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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at MP4=FULL/cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.963 ± 0.029 42 231 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1424 1360 0.955 1 1
Li2 Lithium diatomic 1 Σg 345 346 1.004 2 2
NaH sodium hydride 1 Σ 1088 1133 1.042 3 3
Na2 Sodium diatomic 1 Σg 179 158 0.882 4 4
BeH beryllium monohydride 1 Σ 2085 1987 0.953 5 5
C2 Carbon diatomic 1 Σg 1766 1827 1.035 6 6
N2 Nitrogen diatomic 1 Σg 2215 2330 1.052 7 7
P2 Phosphorus diatomic 1 Σg 732 775 1.059 8 8
OH Hydroxyl radical 1 Σ 3779 3570 0.945 9 9
BeO beryllium oxide 1 Σ 1035 1435 1.386 10 10
HS Mercapto radical 1 Σ 2712 2599 0.958 11 11
SO Sulfur monoxide 1 Σ 1108 1138 1.027 12 12
HF Hydrogen fluoride 1 Σ 4183 3961 0.947 13 13
SF Monosulfur monofluoride 1 Σ 830 829 0.998 14 14
HCl Hydrogen chloride 1 Σ 3011 2886 0.958 15 15
NaCl Sodium Chloride 1 Σ 358 361 1.008 16 16
AlCl Aluminum monochloride 1 Σ 488 478 0.980 17 17
SCl sulfur monochloride 1 Σ 573 577 1.006 18 18
Cl2 Chlorine diatomic 1 Σg 555 554 0.999 19 19
BeH2 beryllium dihydride 2 Σu 2249 2159 0.960 20 20
    3 Πu 720 698 0.970 20 21
SiH2 silicon dihydride 1 A1 2086 1996 0.957 21 22
    2 A1 1031 999 0.969 21 23
    3 B2 2088 1993 0.955 21 24
HCN Hydrogen cyanide 1 Σ 3453 3312 0.959 22 25
    2 Σ 2033 2089 1.028 22 26
    3 Π 717 712 0.993 22 27
CO2 Carbon dioxide 1 Σg 1283 1333 1.039 23 28
    2 Σu 2365 2349 0.993 23 29
    3 Πu 641 667 1.041 23 30
N2O Nitrous oxide 1 Σ 2198 2224 1.012 24 31
    2 Σ 1244 1285 1.033 24 32
    3 Π 593 589 0.993 24 33
SO2 Sulfur dioxide 1 A1 1039 1151 1.108 25 34
    2 A1 487 518 1.063 25 35
    3 B2 1260 1362 1.081 25 36
BH3 boron trihydride 2 A2" 1158 1148 0.991 26 37
    3 E' 2733 2602 0.952 26 38
    4 E' 1221 1197 0.980 26 39
C2H2 Acetylene 1 Σg 3534 3374 0.955 27 40
    2 Σg 1977 1974 0.999 27 41
    3 Σu 3414 3289 0.963 27 42
    4 Πg 577 612 1.061 27 43
    5 Πu 750 730 0.973 27 44
NH3 Ammonia 1 A1 3498 3337 0.954 28 45
    2 A1 1097 950 0.866 28 46
    3 E 3624 3444 0.950 28 47
    4 E 1692 1627 0.961 28 48
H2CO Formaldehyde 1 A1 2941 2782 0.946 29 49
    2 A1 1756 1746 0.994 29 50
    3 A1 1545 1500 0.971 29 51
    4 B1 1203 1167 0.970 29 52
    5 B2 2985 2843 0.952 29 53
    6 B2 1277 1249 0.978 29 54
BF3 Borane, trifluoro- 1 A1' 893 888 0.994 30 55
    2 A2" 699 691 0.988 30 56
    3 E' 1485 1449 0.976 30 57
    4 E' 482 480 0.996 30 58
AlF3 Aluminum trifluoride 1 A1' 683 690 1.010 31 59
    2 A2" 300 297 0.990 31 60
    3 E' 951 935 0.983 31 61
    4 E' 237 263 1.111 31 62
CH4 Methane 1 A1 3058 2917 0.954 32 63
    2 E 1587 1534 0.967 32 64
    3 T2 3166 3019 0.953 32 65
    4 T2 1353 1306 0.965 32 66
C2H4 Ethylene 1 Ag 3184 3026 0.950 33 67
    2 Ag 1678 1623 0.967 33 68
    3 Ag 1378 1342 0.974 33 69
    4 Au 1059 1023 0.966 33 70
    5 B1u 3161 2989 0.945 33 71
    6 B1u 1485 1444 0.972 33 72
    7 B2g 955 940 0.984 33 73
    8 B2u 3255 3105 0.954 33 74
    9 B2u 825 826 1.001 33 75
    10 B3g 3221 3086 0.958 33 76
    11 B3g 1242 1217 0.980 33 77
    12 B3u 982 949 0.967 33 78
CH3OH Methyl alcohol 1 A' 3873 3681 0.950 34 79
    2 A' 3138 3000 0.956 34 80
    3 A' 3030 2844 0.939 34 81
    4 A' 1536 1477 0.962 34 82
    5 A' 1496 1455 0.972 34 83
    6 A' 1391 1345 0.967 34 84
    7 A' 1098 1060 0.965 34 85
    8 A' 1064 1033 0.971 34 86
    9 A" 3074 2960 0.963 34 87
    10 A" 1520 1477 0.971 34 88
    11 A" 1185 1165 0.983 34 89
    12 A" 309 200 0.648 34 90
CHONH2 formamide 1 A' 3765 3564 0.946 35 91
    2 A' 3626 3439 0.949 35 92
    3 A' 2986 2854 0.956 35 93
    4 A' 1788 1754 0.981 35 94
    5 A' 1629 1577 0.968 35 95
    6 A' 1428 1390 0.974 35 96
    7 A' 1281 1258 0.982 35 97
    8 A' 1047 1046 0.998 35 98
    9 A' 562 581 1.034 35 99
    10 A" 1059 1021 0.964 35 100
    11 A" 646 603 0.933 35 101
    12 A" 89 289 3.226 35 102
CH2N4 1H-Tetrazole 1 A' 3679 3447 0.937 36 103
    2 A' 3314 3102 0.936 36 104
    3 A' 1486 1441 0.970 36 105
    4 A' 1460 1384 0.948 36 106
    5 A' 1253 1259 1.005 36 107
    6 A' 1220 1159 0.950 36 108
    7 A' 1148 1084 0.944 36 109
    8 A' 1057 1015 0.960 36 110
    9 A' 1043 1002 0.960 36 111
    10 A' 999 969 0.970 36 112
    11 A' 950 925 0.974 36 113
    12 A" 879 906 1.031 36 114
    13 A" 737 663 0.900 36 115
    14 A" 693 658 0.949 36 116
    15 A" 603 578 0.959 36 117
C2H6 Ethane 1 A1g 3062 2954 0.965 37 118
    2 A1g 1436 1388 0.966 37 119
    3 A1g 1023 995 0.973 37 120
    4 A1u 336 289 0.861 37 121
    5 A2u 3062 2896 0.946 37 122
    6 A2u 1414 1379 0.976 37 123
    7 Eg 3108 2969 0.955 37 124
    8 Eg 1525 1468 0.963 37 125
    9 Eg 1233 1190 0.965 37 126
    10 Eu 3131 2985 0.953 37 127
    11 Eu 1525 1469 0.963 37 128
    12 Eu 827 822 0.993 37 129
C3H6 Cyclopropane 1 A1' 3180 3038 0.955 38 130
    2 A1' 1536 1479 0.963 38 131
    3 A1' 1227 1188 0.969 38 132
    4 A1" 1168 1126 0.964 38 133
    5 A2' 1092 1070 0.980 38 134
    6 A2" 3257 3103 0.953 38 135
    7 A2" 863 854 0.989 38 136
    8 E' 3170 3025 0.954 38 137
    9 E' 1487 1438 0.967 38 138
    10 E' 1062 1029 0.969 38 139
    11 E' 901 866 0.961 38 140
    12 E" 3237 3082 0.952 38 141
    13 E" 1221 1188 0.973 38 142
    14 E" 744 739 0.993 38 143
CH2CHCH3 Propene 1 A' 3237 3090 0.955 39 144
    2 A' 3172 3013 0.950 39 145
    3 A' 3157 2991 0.947 39 146
    4 A' 3120 2954 0.947 39 147
    5 A' 3048 2871 0.942 39 148
    6 A' 1703 1650 0.969 39 149
    7 A' 1512 1470 0.972 39 150
    8 A' 1463 1420 0.970 39 151
    9 A' 1413 1378 0.975 39 152
    10 A' 1328 1297 0.976 39 153
    11 A' 1198 1171 0.978 39 154
    12 A' 947 963 1.017 39 155
    13 A' 937 920 0.981 39 156
    14 A' 420 428 1.020 39 157
    15 A" 3099 2954 0.953 39 158
    16 A" 1499 1443 0.963 39 159
    17 A" 1078 1045 0.969 39 160
    18 A" 1032 991 0.960 39 161
    19 A" 947 912 0.963 39 162
    20 A" 597 578 0.969 39 163
    21 A" 210 174 0.829 39 164
CHCCH2CH3 1-Butyne 1 A' 3480 3332 0.958 40 165
    2 A' 3132 2988 0.954 40 166
    3 A' 3067     40 167
    4 A' 3058     40 168
    5 A' 2141 2116 0.988 40 169
    6 A' 1523 1470 0.965 40 170
    7 A' 1495 1446 0.967 40 171
    8 A' 1419 1385 0.976 40 172
    9 A' 1361 1322 0.971 40 173
    10 A' 1100 1070 0.973 40 174
    11 A' 1041 1008 0.968 40 175
    12 A' 855 840 0.983 40 176
    13 A' 635 634 0.999 40 177
    14 A' 510 509 0.998 40 178
    15 A' 194 197 1.014 40 179
    16 A" 3137 2988 0.953 40 180
    17 A" 3082 2939 0.954 40 181
    18 A" 1517 1462 0.964 40 182
    19 A" 1303 1261 0.968 40 183
    20 A" 1117 1090 0.976 40 184
    21 A" 789 782 0.991 40 185
    22 A" 638 630 0.987 40 186
    23 A" 357 344 0.961 40 187
    24 A" 231 213 0.921 40 188
CH3CHClCH3 Propane, 2-chloro- 1 A' 3146 3005 0.955 41 189
    2 A' 3127 2955 0.945 41 190
    3 A' 3104 2927 0.943 41 191
    4 A' 3059 2878 0.941 41 192
    5 A' 1521 1472 0.968 41 193
    6 A' 1510 1454 0.963 41 194
    7 A' 1423 1390 0.977 41 195
    8 A' 1300 1270 0.977 41 196
    9 A' 1197 1163 0.972 41 197
    10 A' 1086 1065 0.981 41 198
    11 A' 916 888 0.969 41 199
    12 A' 648 633 0.977 41 200
    13 A' 420 418 0.994 41 201
    14 A' 336 336 1.001 41 202
    15 A' 279 253 0.908 41 203
    16 A" 3140 2997 0.954 41 204
    17 A" 3117 2985 0.958 41 205
    18 A" 3055 2947 0.965 41 206
    19 A" 1502 1472 0.980 41 207
    20 A" 1496 1454 0.972 41 208
    21 A" 1411 1377 0.976 41 209
    22 A" 1372 1334 0.972 41 210
    23 A" 1165 1123 0.964 41 211
    24 A" 959 972 1.014 41 212
    25 A" 942 936 0.994 41 213
    26 A" 322 317 0.986 41 214
    27 A" 242 276 1.142 41 215

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.

40 140 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