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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCD/aug-cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.965 ± 0.022 39 203 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4360 4161 0.954 1 1
LiH Lithium Hydride 1 Σ 1349 1360 1.008 2 2
Li2 Lithium diatomic 1 Σg 341 346 1.017 3 3
Na2 Sodium diatomic 1 Σg 151 158 1.047 4 4
CH Methylidyne 1 Σ 3110     5 5
Si2 Silicon diatomic 1 Σg 514 507 0.986 6 6
PH phosphorus monohydride 1 Σ 2354 2276 0.967 7 7
    1 Σ 2386 2319 0.972 7 8
OH Hydroxyl radical 1 Σ 3744 3570 0.953 8 9
CO Carbon monoxide 1 Σ 2203 2143 0.973 9 10
SO Sulfur monoxide 1 Σ 1148 1138 0.991 10 11
    1 Σ 1095 1054 0.963 10 12
HF Hydrogen fluoride 1 Σ 4142 3961 0.956 11 13
F2 Fluorine diatomic 1 Σg 963 894 0.928 12 14
HCl Hydrogen chloride 1 Σ 3000 2886 0.962 13 15
AlCl Aluminum monochloride 1 Σ 447 478 1.068 14 16
BeH2 beryllium dihydride 2 Σu 2236 2159 0.966 15 17
    3 Πu 727 698 0.960 15 18
HCN Hydrogen cyanide 1 Σ 3453 3312 0.959 16 19
    2 Σ 2157 2089 0.968 16 20
    3 Π 725 712 0.982 16 21
H2O Water 1 A1 3842 3657 0.952 17 22
    2 A1 1651 1595 0.966 17 23
    3 B2 3957 3756 0.949 17 24
CO2 Carbon dioxide 1 Σg 1378 1333 0.967 18 25
    2 Σu 2405 2349 0.977 18 26
    3 Πu 692 667 0.964 18 27
H2S Hydrogen sulfide 1 A1 2722 2615 0.961 19 28
    2 A1 1203 1183 0.984 19 29
    3 B2 2742 2626 0.958 19 30
OCS Carbonyl sulfide 1 Σ 2123 2062 0.971 20 31
    2 Σ 876 859 0.981 20 32
    3 Π 532 520 0.977 20 33
SO2 Sulfur dioxide 1 A1 1147 1151 1.004 21 34
    2 A1 505 518 1.026 21 35
    3 B2 1319 1362 1.032 21 36
C2H2 Acetylene 1 Σg 3508 3374 0.962 22 37
    2 Σg 2030 1974 0.972 22 38
    3 Σu 3409 3289 0.965 22 39
    4 Πg 455 612 1.344 22 40
    5 Πu 720 730 1.014 22 41
NH3 Ammonia 1 A1 3475 3337 0.960 23 42
    2 A1 1069 950 0.888 23 43
    3 E 3614 3444 0.953 23 44
    4 E 1664 1627 0.978 23 45
H2CO Formaldehyde 1 A1 2966 2782 0.938 24 46
    2 A1 1810 1746 0.965 24 47
    3 A1 1539 1500 0.975 24 48
    4 B1 1196 1167 0.976 24 49
    5 B2 3047 2843 0.933 24 50
    6 B2 1266 1249 0.987 24 51
BF3 Borane, trifluoro- 1 A1' 856 888 1.037 25 52
    2 A2" 721 691 0.958 25 53
    3 E' 1427 1449 1.015 25 54
    4 E' 464 480 1.033 25 55
NF3 Nitrogen trifluoride 1 A1 1064 1032 0.970 26 56
    2 A1 666 647 0.971 26 57
    3 E 978 907 0.928 26 58
    4 E 506 492 0.972 26 59
AlF3 Aluminum trifluoride 1 A1' 678 690 1.017 27 60
    2 A2" 298 297 0.997 27 61
    3 E' 940 935 0.995 27 62
    4 E' 249 263 1.057 27 63
CH4 Methane 1 A1 3038 2917 0.960 28 64
    2 E 1546 1534 0.992 28 65
    3 T2 3167 3019 0.953 28 66
    4 T2 1331 1306 0.981 28 67
CH2F2 Methane, difluoro- 1 A1 3111 2948 0.948 29 68
    2 A1 1528 1508 0.987 29 69
    3 A1 1119 1111 0.993 29 70
    4 A1 521 529 1.015 29 71
    5 A2 1271 1262 0.993 29 72
    6 B1 3193 3014 0.944 29 73
    7 B1 1180 1178 0.999 29 74
    8 B2 1460 1435 0.983 29 75
    9 B2 1114 1090 0.978 29 76
CH3Cl Methyl chloride 1 A1 3088 2966 0.960 30 77
    2 A1 1377 1355 0.984 30 78
    3 A1 747 732 0.980 30 79
    4 E 3198 3042 0.951 30 80
    5 E 1474 1455 0.987 30 81
    6 E 1033 1015 0.983 30 82
CF2Cl2 difluorodichloromethane 1 A1 1129 1101 0.976 31 83
    2 A1 665 667 1.003 31 84
    3 A1 462 458 0.992 31 85
    4 A1 269 262 0.974 31 86
    5 A2 328 322 0.983 31 87
    6 B1 943 902 0.956 31 88
    7 B1 445 437 0.982 31 89
    8 B2 1184 1159 0.979 31 90
    9 B2 443 446 1.006 31 91
C2H4 Ethylene 1 Ag 3175 3026 0.953 32 92
    2 Ag 1694 1623 0.958 32 93
    3 Ag 1377 1342 0.975 32 94
    4 Au 1036 1023 0.987 32 95
    5 B1u 3155 2989 0.947 32 96
    6 B1u 1476 1444 0.978 32 97
    7 B2g 964 940 0.975 32 98
    8 B2u 3269 3105 0.950 32 99
    9 B2u 826 826 1.000 32 100
    10 B3g 3242 3086 0.952 32 101
    11 B3g 1237 1217 0.984 32 102
    12 B3u 981 949 0.968 32 103
CH2CF2 Ethene, 1,1-difluoro- 1 A1 3225 3070 0.952 33 104
    2 A1 1808 1728 0.956 33 105
    3 A1 1417 1360 0.960 33 106
    4 A1 927 926 0.999 33 107
    5 A1 538 550 1.022 33 108
    6 A2 726 714 0.984 33 109
    7 B1 847 803 0.948 33 110
    8 B1 616 611 0.992 33 111
    9 B2 3338 3154 0.945 33 112
    10 B2 1328 1302 0.981 33 113
    11 B2 965 955 0.989 33 114
    12 B2 437 438 1.003 33 115
C2H6 Ethane 1 A1g 3049 2954 0.969 34 116
    2 A1g 1426 1388 0.973 34 117
    3 A1g 1024 995 0.972 34 118
    4 A1u 316 289 0.915 34 119
    5 A2u 3045 2896 0.951 34 120
    6 A2u 1396 1379 0.988 34 121
    7 Eg 3112 2969 0.954 34 122
    8 Eg 1495 1468 0.982 34 123
    9 Eg 1219 1190 0.976 34 124
    10 Eu 3133 2985 0.953 34 125
    11 Eu 1497 1469 0.981 34 126
    12 Eu 818 822 1.005 34 127
C3H5 Allyl radical 1 A1 3284 3114 0.948 35 128
    2 A1 3190 3048 0.956 35 129
    4 A1 1537 1488 0.968 35 130
    5 A1 1290 1245 0.965 35 131
    6 A1 1050 1066 1.015 35 132
    7 A1 430 427 0.994 35 133
    9 A2 574 549 0.957 35 134
    10 B1 1034 968 0.936 35 135
    11 B1 844 802 0.950 35 136
    12 B1 550 518 0.942 35 137
    13 B2 3281 3105 0.946 35 138
    14 B2 3172 3016 0.951 35 139
    15 B2 1507 1463 0.971 35 140
    16 B2 1419 1389 0.979 35 141
    17 B2 1151 1182 1.027 35 142
C3H6 Cyclopropane 1 A1' 3168 3038 0.959 36 143
    2 A1' 1530 1479 0.967 36 144
    3 A1' 1223 1188 0.971 36 145
    4 A1" 1150 1126 0.979 36 146
    5 A2' 1074 1070 0.996 36 147
    6 A2" 3263 3103 0.951 36 148
    7 A2" 849 854 1.006 36 149
    8 E' 3155 3025 0.959 36 150
    9 E' 1471 1438 0.978 36 151
    10 E' 1052 1029 0.978 36 152
    11 E' 896 866 0.967 36 153
    12 E" 3243 3082 0.950 36 154
    13 E" 1208 1188 0.983 36 155
    14 E" 733 739 1.008 36 156
CH2CHCH3 Propene 1 A' 3252 3090 0.950 37 157
    2 A' 3171 3013 0.950 37 158
    3 A' 3155 2991 0.948 37 159
    4 A' 3127 2954 0.945 37 160
    5 A' 3037 2871 0.945 37 161
    6 A' 1725 1650 0.957 37 162
    7 A' 1490 1470 0.986 37 163
    8 A' 1456 1420 0.975 37 164
    9 A' 1403 1378 0.982 37 165
    10 A' 1326 1297 0.978 37 166
    11 A' 1194 1171 0.981 37 167
    12 A' 941 963 1.023 37 168
    13 A' 938 920 0.980 37 169
    14 A' 422 428 1.015 37 170
    15 A" 3104 2954 0.952 37 171
    16 A" 1473 1443 0.980 37 172
    17 A" 1065 1045 0.981 37 173
    18 A" 1009 991 0.982 37 174
    19 A" 945 912 0.965 37 175
    20 A" 583 578 0.992 37 176
    21 A" 200 174 0.871 37 177
CH3CHClCH3 Propane, 2-chloro- 1 A' 3151 3005 0.954 38 178
    2 A' 3131 2955 0.944 38 179
    3 A' 3107 2927 0.942 38 180
    4 A' 3048 2878 0.944 38 181
    5 A' 1501 1472 0.981 38 182
    6 A' 1487 1454 0.978 38 183
    7 A' 1419 1390 0.980 38 184
    8 A' 1299 1270 0.978 38 185
    9 A' 1192 1163 0.976 38 186
    10 A' 1084 1065 0.983 38 187
    11 A' 917 888 0.968 38 188
    12 A' 647 633 0.979 38 189
    13 A' 425 418 0.983 38 190
    14 A' 341 336 0.986 38 191
    15 A' 273 253 0.928 38 192
    16 A" 3146 2997 0.953 38 193
    17 A" 3123 2985 0.956 38 194
    18 A" 3044 2947 0.968 38 195
    19 A" 1480 1472 0.994 38 196
    20 A" 1476 1454 0.985 38 197
    21 A" 1410 1377 0.976 38 198
    22 A" 1360 1334 0.981 38 199
    23 A" 1166 1123 0.963 38 200
    24 A" 958 972 1.015 38 201
    25 A" 936 936 1.000 38 202
    26 A" 329 317 0.963 38 203
    27 A" 239 276 1.153 38 204

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.

40 100 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