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III.B.3.b. (XIII.C.2.)

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
H2CO Formaldehyde 1 A1 2966 2782 0.938 1 1
    2 A1 1810 1746 0.965 1 2
    3 A1 1539 1500 0.975 1 3
    4 B1 1196 1167 0.976 1 4
    5 B2 3047 2843 0.933 1 5
    6 B2 1266 1249 0.987 1 6
CH4 Methane 1 A1 3038 2917 0.960 2 7
    2 E 1546 1534 0.992 2 8
    3 T2 3167 3019 0.953 2 9
    4 T2 1331 1306 0.981 2 10
C2H6 Ethane 1 A1g 3049 2896 0.950 3 11
    2 A1g 1426 1388 0.973 3 12
    3 A1g 1024 995 0.972 3 13
    4 A1u 316 289 0.915 3 14
    5 A2u 3045 2915 0.957 3 15
    6 A2u 1396 1370 0.981 3 16
    7 Eg 3112 2969 0.954 3 17
    8 Eg 1495 1468 0.982 3 18
    9 Eg 1219 1190 0.976 3 19
    10 Eu 3133 2974 0.949 3 20
    11 Eu 1497 1460 0.975 3 21
    12 Eu 818 822 1.005 3 22
C2H4 Ethylene 1 Ag 3175 3026 0.953 4 23
    2 Ag 1694 1623 0.958 4 24
    3 Ag 1377 1342 0.975 4 25
    4 Au 1036 1023 0.987 4 26
    5 B1u 3155 2989 0.947 4 27
    6 B1u 1476 1444 0.978 4 28
    7 B2g 964 940 0.975 4 29
    8 B2u 3269 3105 0.950 4 30
    9 B2u 826 826 1.000 4 31
    10 B3g 3242 3086 0.952 4 32
    11 B3g 1237 1217 0.984 4 33
    12 B3u 981 949 0.968 4 34
C2H2 Acetylene 1 Σg 3508 3374 0.962 5 35
    2 Σg 2030 1974 0.972 5 36
    3 Σu 3409 3289 0.965 5 37
    4 Πg 455 612 1.344 5 38
    5 Πu 720 730 1.014 5 39
CH3Cl Methyl chloride 1 A1 3088 2966 0.960 6 40
    2 A1 1377 1355 0.984 6 41
    3 A1 747 732 0.980 6 42
    4 E 3198 3042 0.951 6 43
    5 E 1474 1455 0.987 6 44
    6 E 1033 1015 0.983 6 45
HCN Hydrogen cyanide 1 Σ 3453 3312 0.959 7 46
    2 Σ 2157 2089 0.968 7 47
    3 Π 725 712 0.982 7 48
CH2F2 Methane, difluoro- 1 A1 3111 2948 0.948 8 49
    2 A1 1528 1508 0.987 8 50
    3 A1 1119 1111 0.993 8 51
    4 A1 521 529 1.015 8 52
    5 A2 1271 1262 0.993 8 53
    6 B1 3193 3014 0.944 8 54
    7 B1 1180 1178 0.999 8 55
    8 B2 1460 1435 0.983 8 56
    9 B2 1114 1090 0.978 8 57
C3H6 Cyclopropane 1 A1' 3168 3038 0.959 9 58
    2 A1' 1530 1479 0.967 9 59
    3 A1' 1223 1188 0.971 9 60
    4 A1" 1150 1126 0.979 9 61
    5 A2' 1074 1070 0.996 9 62
    6 A2" 3263 3103 0.951 9 63
    7 A2" 849 854 1.006 9 64
    8 E' 3155 3025 0.959 9 65
    9 E' 1471 1438 0.978 9 66
    10 E' 1052 1029 0.978 9 67
    11 E' 896 866 0.967 9 68
    12 E" 3243 3082 0.950 9 69
    13 E" 1208 1188 0.983 9 70
    14 E" 733 739 1.008 9 71
CH3CHClCH3 Propane, 2-chloro- 1 A' 3151 3005 0.954 10 72
    2 A' 3131 2955 0.944 10 73
    3 A' 3107 2927 0.942 10 74
    4 A' 3048 2878 0.944 10 75
    5 A' 1501 1472 0.981 10 76
    6 A' 1487 1454 0.978 10 77
    7 A' 1419 1390 0.980 10 78
    8 A' 1299 1270 0.978 10 79
    9 A' 1192 1163 0.976 10 80
    10 A' 1084 1065 0.983 10 81
    11 A' 917 888 0.968 10 82
    12 A' 647 633 0.979 10 83
    13 A' 425 418 0.983 10 84
    14 A' 341 336 0.986 10 85
    15 A' 273 253 0.928 10 86
    16 A" 3146 2997 0.953 10 87
    17 A" 3123 2985 0.956 10 88
    18 A" 3044 2947 0.968 10 89
    19 A" 1480 1472 0.994 10 90
    20 A" 1476 1454 0.985 10 91
    21 A" 1410 1377 0.976 10 92
    22 A" 1360 1334 0.981 10 93
    23 A" 1166 1123 0.963 10 94
    24 A" 958 972 1.015 10 95
    25 A" 936 936 1.000 10 96
    26 A" 329 317 0.963 10 97
    27 A" 239 276 1.153 10 98
CH2CF2 Ethene, 1,1-difluoro- 1 A1 3225 3070 0.952 11 99
    2 A1 1808 1728 0.956 11 100
    3 A1 1417 1360 0.960 11 101
    4 A1 927 926 0.999 11 102
    5 A1 538 550 1.022 11 103
    6 A2 726 714 0.984 11 104
    7 B1 847 803 0.948 11 105
    8 B1 616 611 0.992 11 106
    9 B2 3338 3154 0.945 11 107
    10 B2 1328 1302 0.981 11 108
    11 B2 965 955 0.989 11 109
    12 B2 437 438 1.003 11 110
CF2Cl2 difluorodichloromethane 1 A1 1129 1101 0.976 12 111
    2 A1 665 667 1.003 12 112
    3 A1 462 458 0.992 12 113
    4 A1 269 262 0.974 12 114
    5 A2 328 322 0.983 12 115
    6 B1 943 902 0.956 12 116
    7 B1 445 437 0.982 12 117
    8 B2 1184 1159 0.979 12 118
    9 B2 443 446 1.006 12 119
CH2CHCH3 Propene 1 A' 3250 3090 0.951 13 120
    2 A' 3171 3013 0.950 13 121
    3 A' 3155 2991 0.948 13 122
    4 A' 3127 2954 0.945 13 123
    5 A' 3038 2871 0.945 13 124
    6 A' 1726 1650 0.956 13 125
    7 A' 1490 1470 0.986 13 126
    8 A' 1456 1420 0.975 13 127
    9 A' 1403 1378 0.982 13 128
    10 A' 1326 1297 0.978 13 129
    11 A' 1193 1171 0.981 13 130
    12 A' 941 963 1.023 13 131
    13 A' 938 920 0.981 13 132
    14 A' 421 428 1.017 13 133
    15 A" 3105 2954 0.952 13 134
    16 A" 1473 1443 0.980 13 135
    17 A" 1065 1045 0.981 13 136
    18 A" 1009 991 0.982 13 137
    19 A" 947 912 0.963 13 138
    20 A" 582 578 0.993 13 139
    21 A" 199 174 0.874 13 140
CO2 Carbon dioxide 1 Σg 1378 1333 0.967 14 141
    2 Σu 2405 2349 0.977 14 142
    3 Πu 692 667 0.964 14 143
OCS Carbonyl sulfide 1 Σ 2122 2062 0.972 15 144
    2 Σ 876 859 0.980 15 145
    3 Π 532 520 0.977 15 146
CO Carbon monoxide 1 Σ 2203 2170 0.985 16 147
H2 Hydrogen diatomic 1 Σg 4360 4401 1.009 17 148
C3H5 Allyl radical 1 A1 3284 3114 0.948 18 149
    2 A1 3190 3048 0.956 18 150
    4 A1 1537 1488 0.968 18 151
    5 A1 1290 1245 0.965 18 152
    6 A1 1050 1066 1.015 18 153
    7 A1 430 427 0.994 18 154
    9 A2 574 549 0.957 18 155
    10 B1 1034 968 0.936 18 156
    11 B1 844 802 0.950 18 157
    12 B1 550 518 0.942 18 158
    13 B2 3281 3105 0.946 18 159
    14 B2 3172 3016 0.951 18 160
    15 B2 1507 1463 0.971 18 161
    16 B2 1419 1389 0.979 18 162
    17 B2 1151 1182 1.027 18 163
CH Methylidyne 1 Σ 3110 3145 1.011 19 164
OH Hydroxyl radical 1 Σ 3744 3738 0.998 20 165
SO2 Sulfur dioxide 1 A1 1147 1151 1.004 21 166
    2 A1 505 518 1.026 21 167
    3 B2 1319 1362 1.032 21 168
LiH Lithium Hydride 1 Σ 1349 1405 1.042 22 169
BF3 Borane, trifluoro- 1 A1' 856 888 1.037 23 170
    2 A2" 721 691 0.958 23 171
    3 E' 1427 1449 1.015 23 172
    4 E' 464 480 1.033 23 173
HCl Hydrogen chloride 1 Σ 3000 2991 0.997 24 174
HF Hydrogen fluoride 1 Σ 4140 4138 1.000 25 175
NH3 Ammonia 1 A1 3475 3337 0.960 26 176
    2 A1 1069 950 0.888 26 177
    3 E 3614 3444 0.953 26 178
    4 E 1664 1627 0.978 26 179
H2O Water 1 A1 3841 3657 0.952 27 180
    2 A1 1651 1595 0.966 27 181
    3 B2 3956 3756 0.949 27 182
F2 Fluorine diatomic 1 Σg 963 917 0.952 28 183
H2S Hydrogen sulfide 1 A1 2722 2615 0.961 29 184
    2 A1 1203 1183 0.984 29 185
    3 B2 2742 2626 0.958 29 186
NF3 Nitrogen trifluoride 1 A1 1064 1032 0.970 30 187
    2 A1 666 647 0.971 30 188
    3 E 978 907 0.928 30 189
    4 E 506 492 0.972 30 190
AlF3 Aluminum trifluoride 1 A1' 678 690 1.017 31 191
    2 A2" 298 297 0.997 31 192
    3 E' 940 935 0.995 31 193
    4 E' 249 263 1.057 31 194
BeH2 beryllium dihydride 2 Σu 2236 2159 0.966 32 195
    3 Πu 727 698 0.960 32 196
Si2 Silicon diatomic 1 Σg 514 511 0.994 33 197
AlCl Aluminum monochloride 1 Σ 447 482 1.077 34 198
NH Imidogen 1 Σ 3324 3314 0.997 35 199
SO Sulfur monoxide 1 Σ 1148 1151 1.002 36 200
    1 Σ 1095 1069 0.976 36 201
PH phosphorus monohydride 1 Σ 2386 2415 1.012 37 202
Li2 Lithium diatomic 1 Σg 341 351 1.032 38 203
Na2 Sodium diatomic 1 Σg 151 159 1.057 39 204

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.

100
80
60
40
20
0
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