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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/6-311G**
Scale factor How many Source
Molecules Vibrations
0.955 ± 0.017 32 169 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2961 2782 0.939 1 1
    2 A1 1852 1746 0.943 1 2
    3 A1 1577 1500 0.951 1 3
    4 B1 1215 1167 0.961 1 4
    5 B2 3028 2843 0.939 1 5
    6 B2 1300 1249 0.961 1 6
CH4 Methane 1 A1 3056 2917 0.955 2 7
    2 E 1576 1534 0.973 2 8
    3 T2 3180 3019 0.949 2 9
    4 T2 1370 1306 0.954 2 10
C2H6 Ethane 1 A1g 3065 2896 0.945 3 11
    2 A1g 1460 1388 0.951 3 12
    3 A1g 1029 995 0.967 3 13
    4 A1u 326 289 0.886 3 14
    5 A2u 3063 2915 0.952 3 15
    6 A2u 1431 1370 0.958 3 16
    7 Eg 3127 2969 0.950 3 17
    8 Eg 1525 1468 0.963 3 18
    9 Eg 1246 1190 0.955 3 19
    10 Eu 3149 2974 0.944 3 20
    11 Eu 1529 1460 0.955 3 21
    12 Eu 834 822 0.985 3 22
C2H4 Ethylene 1 Ag 3180 3026 0.952 4 23
    2 Ag 1705 1623 0.952 4 24
    3 Ag 1389 1342 0.967 4 25
    4 Au 1059 1023 0.966 4 26
    5 B1u 3161 2989 0.946 4 27
    6 B1u 1489 1444 0.969 4 28
    7 B2g 932 940 1.009 4 29
    8 B2u 3269 3105 0.950 4 30
    9 B2u 832 826 0.992 4 31
    10 B3g 3243 3086 0.952 4 32
    11 B3g 1243 1217 0.979 4 33
    12 B3u 974 949 0.975 4 34
C2H2 Acetylene 1 Σg 3544 3374 0.952 5 35
    2 Σg 2049 1974 0.964 5 36
    3 Σu 3443 3289 0.955 5 37
    4 Πg 603 612 1.015 5 38
    5 Πu 785 730 0.930 5 39
C3H6 Cyclopropane 1 A1' 3177 3038 0.956 6 40
    2 A1' 1558 1479 0.949 6 41
    3 A1' 1240 1188 0.958 6 42
    4 A1" 1183 1126 0.951 6 43
    5 A2' 1116 1070 0.959 6 44
    6 A2" 3271 3103 0.949 6 45
    7 A2" 873 854 0.978 6 46
    8 E' 3166 3025 0.955 6 47
    9 E' 1499 1438 0.959 6 48
    10 E' 1103 1029 0.933 6 49
    11 E' 915 866 0.946 6 50
    12 E" 3251 3082 0.948 6 51
    13 E" 1240 1188 0.958 6 52
    14 E" 763 739 0.968 6 53
CH3CHClCH3 Propane, 2-chloro- 1 A' 3165 3005 0.950 7 54
    2 A' 3149 2955 0.938 7 55
    3 A' 3122 2927 0.937 7 56
    4 A' 3067 2878 0.938 7 57
    5 A' 1526 1472 0.964 7 58
    6 A' 1519 1454 0.957 7 59
    7 A' 1455 1390 0.955 7 60
    8 A' 1352 1270 0.940 7 61
    9 A' 1216 1163 0.956 7 62
    10 A' 1116 1065 0.954 7 63
    11 A' 932 888 0.953 7 64
    12 A' 676 633 0.936 7 65
    13 A' 432 418 0.969 7 66
    14 A' 347 336 0.968 7 67
    15 A' 290 253 0.873 7 68
    16 A" 3160 2997 0.948 7 69
    17 A" 3141 2985 0.950 7 70
    18 A" 3063 2947 0.962 7 71
    19 A" 1508 1472 0.976 7 72
    20 A" 1506 1454 0.965 7 73
    21 A" 1443 1377 0.954 7 74
    22 A" 1382 1334 0.965 7 75
    23 A" 1178 1123 0.953 7 76
    24 A" 977 972 0.994 7 77
    25 A" 957 936 0.978 7 78
    26 A" 335 317 0.947 7 79
    27 A" 253 276 1.093 7 80
C3H2N2 Malononitrile 1 A1 3103 2935 0.946 8 81
    2 A1 2382 2275 0.955 8 82
    3 A1 1485 1395 0.939 8 83
    4 A1 915 890 0.973 8 84
    5 A1 588 582 0.990 8 85
    6 A1 148 167 1.127 8 86
    7 A2 1268 1220 0.962 8 87
    8 A2 368 367 0.999 8 88
    9 B1 3150 2968 0.942 8 89
    10 B1 958 933 0.973 8 90
    11 B1 340 337 0.992 8 91
    12 B2 2384 2275 0.954 8 92
    13 B2 1374 1318 0.960 8 93
    14 B2 1006 982 0.976 8 94
    15 B2 371 366 0.987 8 95
CH2CHCH3 Propene 1 A' 3253 3090 0.950 9 96
    2 A' 3173 3013 0.950 9 97
    3 A' 3161 2991 0.946 9 98
    4 A' 3141 2954 0.941 9 99
    5 A' 3054 2871 0.940 9 100
    6 A' 1737 1650 0.950 9 101
    7 A' 1520 1470 0.967 9 102
    8 A' 1474 1420 0.963 9 103
    9 A' 1434 1378 0.961 9 104
    10 A' 1334 1297 0.973 9 105
    11 A' 1205 1171 0.972 9 106
    12 A' 955 963 1.008 9 107
    13 A' 941 920 0.977 9 108
    14 A' 425 428 1.008 9 109
    15 A" 3119 2954 0.947 9 110
    16 A" 1504 1443 0.959 9 111
    17 A" 1084 1045 0.964 9 112
    18 A" 1025 991 0.967 9 113
    19 A" 927 912 0.984 9 114
    20 A" 584 578 0.990 9 115
    21 A" 194 174 0.899 9 116
CO2 Carbon dioxide 1 Σg 1415 1333 0.942 10 117
    2 Σu 2484 2349 0.946 10 118
    3 Πu 691 667 0.966 10 119
CO Carbon monoxide 1 Σ 2267 2170 0.957 11 120
H2 Hydrogen diatomic 1 Σg 4436 4401 0.992 12 121
C3H5 Allyl radical 1 A1 3286 3114 0.948 13 122
    2 A1 3189 3048 0.956 13 123
    4 A1 1550 1488 0.960 13 124
    5 A1 1299 1245 0.959 13 125
    6 A1 1057 1066 1.009 13 126
    7 A1 433 427 0.985 13 127
    9 A2 575 549 0.954 13 128
    10 B1 1032 968 0.938 13 129
    11 B1 797 802 1.006 13 130
    12 B1 544 518 0.952 13 131
    13 B2 3283 3105 0.946 13 132
    14 B2 3178 3016 0.949 13 133
    15 B2 1515 1463 0.965 13 134
    16 B2 1428 1389 0.973 13 135
    17 B2 1144 1182 1.033 13 136
CH Methylidyne 1 Σ 3159 3145 0.995 14 137
OH Hydroxyl radical 1 Σ 3820 3738 0.978 15 138
SO2 Sulfur dioxide 1 A1 1218 1151 0.945 16 139
    2 A1 537 518 0.964 16 140
    3 B2 1428 1362 0.954 16 141
LiH Lithium Hydride 1 Σ 1418 1405 0.991 17 142
BF3 Borane, trifluoro- 1 A1' 897 888 0.990 18 143
    2 A2" 719 691 0.961 18 144
    3 E' 1486 1449 0.975 18 145
    4 E' 491 480 0.977 18 146
HCl Hydrogen chloride 1 Σ 3060 2991 0.977 19 147
HF Hydrogen fluoride 1 Σ 4277 4138 0.968 20 148
NH3 Ammonia 1 A1 3516 3337 0.949 21 149
    2 A1 1145 950 0.829 21 150
    3 E 3645 3444 0.945 21 151
    4 E 1687 1627 0.964 21 152
N2 Nitrogen diatomic 1 Σg 2435 2359 0.969 22 153
H2O Water 1 A1 3922 3657 0.933 23 154
    2 A1 1693 1595 0.942 23 155
    3 B2 4015 3756 0.936 23 156
F2 Fluorine diatomic 1 Σg 935 917 0.980 24 157
AlF3 Aluminum trifluoride 1 A1' 709 690 0.973 25 158
    2 A2" 307 297 0.968 25 159
    3 E' 993 935 0.941 25 160
    4 E' 250 263 1.054 25 161
BeH2 beryllium dihydride 2 Σu 2264 2159 0.954 26 162
    3 Πu 693 698 1.008 26 163
AlCl Aluminum monochloride 1 Σ 493 482 0.977 27 164
NH Imidogen 1 Σ 3361 3314 0.986 28 165
SO Sulfur monoxide 1 Σ 1178 1151 0.977 29 166
    1 Σ 1119 1069 0.955 29 167
PH phosphorus monohydride 1 Σ 2426 2415 0.996 30 168
Li2 Lithium diatomic 1 Σg 350 351 1.003 31 169
Na2 Sodium diatomic 1 Σg 156 159 1.022 32 170

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.

140
120
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