return to home page

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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at CCD/6-31G(2df,p)
Scale factor How many Source
Molecules Vibrations
0.947 ± 0.018 32 169 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2989 2782 0.931 1 1
    2 A1 1864 1746 0.937 1 2
    3 A1 1576 1500 0.952 1 3
    4 B1 1220 1167 0.956 1 4
    5 B2 3058 2843 0.930 1 5
    6 B2 1302 1249 0.959 1 6
CH4 Methane 1 A1 3092 2917 0.943 2 7
    2 E 1597 1534 0.960 2 8
    3 T2 3222 3019 0.937 2 9
    4 T2 1377 1306 0.948 2 10
C2H6 Ethane 1 A1g 3099 2896 0.934 3 11
    2 A1g 1461 1388 0.950 3 12
    3 A1g 1029 995 0.967 3 13
    4 A1u 314 289 0.922 3 14
    5 A2u 3100 2915 0.940 3 15
    6 A2u 1439 1370 0.952 3 16
    7 Eg 3167 2969 0.937 3 17
    8 Eg 1539 1468 0.954 3 18
    9 Eg 1246 1190 0.955 3 19
    10 Eu 3189 2974 0.933 3 20
    11 Eu 1543 1460 0.946 3 21
    12 Eu 834 822 0.986 3 22
C2H4 Ethylene 1 Ag 3215 3026 0.941 4 23
    2 Ag 1716 1623 0.946 4 24
    3 Ag 1401 1342 0.958 4 25
    4 Au 1077 1023 0.949 4 26
    5 B1u 3196 2989 0.935 4 27
    6 B1u 1497 1444 0.965 4 28
    7 B2g 980 940 0.959 4 29
    8 B2u 3303 3105 0.940 4 30
    9 B2u 834 826 0.990 4 31
    10 B3g 3279 3086 0.941 4 32
    11 B3g 1258 1217 0.967 4 33
    12 B3u 997 949 0.952 4 34
C2H2 Acetylene 1 Σg 3587 3374 0.941 5 35
    2 Σg 2078 1974 0.950 5 36
    3 Σu 3485 3289 0.944 5 37
    4 Πg 566 612 1.082 5 38
    5 Πu 795 730 0.918 5 39
C3H6 Cyclopropane 1 A1' 3209 3038 0.947 6 40
    2 A1' 1555 1479 0.951 6 41
    3 A1' 1243 1188 0.955 6 42
    4 A1" 1184 1126 0.951 6 43
    5 A2' 1118 1070 0.957 6 44
    6 A2" 3303 3103 0.939 6 45
    7 A2" 866 854 0.986 6 46
    8 E' 3199 3025 0.946 6 47
    9 E' 1500 1438 0.959 6 48
    10 E' 1093 1029 0.941 6 49
    11 E' 925 866 0.936 6 50
    12 E" 3285 3082 0.938 6 51
    13 E" 1237 1188 0.961 6 52
    14 E" 751 739 0.984 6 53
CH3CHClCH3 Propane, 2-chloro- 1 A' 3202 3005 0.939 7 54
    2 A' 3184 2955 0.928 7 55
    3 A' 3151 2927 0.929 7 56
    4 A' 3099 2878 0.929 7 57
    5 A' 1540 1472 0.956 7 58
    6 A' 1527 1454 0.952 7 59
    7 A' 1454 1390 0.956 7 60
    8 A' 1326 1270 0.958 7 61
    9 A' 1213 1163 0.959 7 62
    10 A' 1106 1065 0.963 7 63
    11 A' 927 888 0.958 7 64
    12 A' 669 633 0.946 7 65
    13 A' 427 418 0.979 7 66
    14 A' 342 336 0.984 7 67
    15 A' 279 253 0.908 7 68
    16 A" 3198 2997 0.937 7 69
    17 A" 3178 2985 0.939 7 70
    18 A" 3096 2947 0.952 7 71
    19 A" 1519 1472 0.969 7 72
    20 A" 1515 1454 0.960 7 73
    21 A" 1441 1377 0.956 7 74
    22 A" 1388 1334 0.961 7 75
    23 A" 1176 1123 0.955 7 76
    24 A" 974 972 0.998 7 77
    25 A" 954 936 0.981 7 78
    26 A" 329 317 0.962 7 79
    27 A" 248 276 1.114 7 80
C3H2N2 Malononitrile 1 A1 3124 2935 0.940 8 81
    2 A1 2403 2275 0.947 8 82
    3 A1 1483 1395 0.940 8 83
    4 A1 915 890 0.973 8 84
    5 A1 589 582 0.988 8 85
    6 A1 149 167 1.121 8 86
    7 A2 1270 1220 0.961 8 87
    8 A2 376 367 0.975 8 88
    9 B1 3173 2968 0.935 8 89
    10 B1 961 933 0.971 8 90
    11 B1 347 337 0.971 8 91
    12 B2 2402 2275 0.947 8 92
    13 B2 1375 1318 0.958 8 93
    14 B2 1008 982 0.974 8 94
    15 B2 376 366 0.974 8 95
CH2CHCH3 Propene 1 A' 3287 3090 0.940 9 96
    2 A' 3209 3013 0.939 9 97
    3 A' 3196 2991 0.936 9 98
    4 A' 3178 2954 0.929 9 99
    5 A' 3087 2871 0.930 9 100
    6 A' 1749 1650 0.943 9 101
    7 A' 1530 1470 0.961 9 102
    8 A' 1481 1420 0.959 9 103
    9 A' 1439 1378 0.957 9 104
    10 A' 1348 1297 0.962 9 105
    11 A' 1212 1171 0.966 9 106
    12 A' 958 963 1.005 9 107
    13 A' 945 920 0.974 9 108
    14 A' 424 428 1.009 9 109
    15 A" 3155 2954 0.936 9 110
    16 A" 1517 1443 0.951 9 111
    17 A" 1090 1045 0.959 9 112
    18 A" 1047 991 0.947 9 113
    19 A" 965 912 0.945 9 114
    20 A" 596 578 0.969 9 115
    21 A" 202 174 0.862 9 116
CO2 Carbon dioxide 1 Σg 1418 1333 0.940 10 117
    2 Σu 2490 2349 0.943 10 118
    3 Πu 716 667 0.932 10 119
CO Carbon monoxide 1 Σ 2253 2170 0.963 11 120
H2 Hydrogen diatomic 1 Σg 4519 4401 0.974 12 121
C3H5 Allyl radical 1 A1 3320 3114 0.938 13 122
    2 A1 3223 3048 0.946 13 123
    4 A1 1555 1488 0.957 13 124
    5 A1 1308 1245 0.952 13 125
    6 A1 1067 1066 0.999 13 126
    7 A1 431 427 0.991 13 127
    9 A2 592 549 0.928 13 128
    10 B1 1069 968 0.906 13 129
    11 B1 847 802 0.946 13 130
    12 B1 563 518 0.920 13 131
    13 B2 3317 3105 0.936 13 132
    14 B2 3213 3016 0.939 13 133
    15 B2 1518 1463 0.964 13 134
    16 B2 1437 1389 0.967 13 135
    17 B2 1157 1182 1.021 13 136
CH Methylidyne 1 Σ 3201 3145 0.982 14 137
OH Hydroxyl radical 1 Σ 3809 3738 0.981 15 138
SO2 Sulfur dioxide 1 A1 1240 1151 0.928 16 139
    2 A1 542 518 0.955 16 140
    3 B2 1463 1362 0.931 16 141
LiH Lithium Hydride 1 Σ 1425 1405 0.986 17 142
BF3 Borane, trifluoro- 1 A1' 920 888 0.965 18 143
    2 A2" 725 691 0.953 18 144
    3 E' 1534 1449 0.945 18 145
    4 E' 503 480 0.955 18 146
HCl Hydrogen chloride 1 Σ 3043 2991 0.983 19 147
HF Hydrogen fluoride 1 Σ 4242 4138 0.976 20 148
NH3 Ammonia 1 A1 3533 3337 0.944 21 149
    2 A1 1148 950 0.828 21 150
    3 E 3664 3444 0.940 21 151
    4 E 1720 1627 0.946 21 152
N2 Nitrogen diatomic 1 Σg 2433 2359 0.970 22 153
H2O Water 1 A1 3904 3657 0.937 23 154
    2 A1 1717 1595 0.929 23 155
    3 B2 4015 3756 0.936 23 156
F2 Fluorine diatomic 1 Σg 1043 917 0.879 24 157
AlF3 Aluminum trifluoride 1 A1' 723 690 0.955 25 158
    2 A2" 311 297 0.954 25 159
    3 E' 1005 935 0.931 25 160
    4 E' 248 263 1.062 25 161
BeH2 beryllium dihydride 2 Σu 2304 2159 0.937 26 162
    3 Πu 737 698 0.947 26 163
AlCl Aluminum monochloride 1 Σ 488 482 0.988 27 164
NH Imidogen 1 Σ 3387 3314 0.978 28 165
SO Sulfur monoxide 1 Σ 1204 1151 0.956 29 166
    1 Σ 1154 1069 0.926 29 167
PH phosphorus monohydride 1 Σ 2429 2415 0.994 30 168
Li2 Lithium diatomic 1 Σg 347 351 1.014 31 169
Na2 Sodium diatomic 1 Σg 152 159 1.046 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