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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-pVTZ
Scale factor How many Source
Molecules Vibrations
0.957 ± 0.017 39 208 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2967 2782 0.938 1 1
    2 A1 1840 1746 0.949 1 2
    3 A1 1554 1500 0.965 1 3
    4 B1 1212 1167 0.963 1 4
    5 B2 3039 2843 0.935 1 5
    6 B2 1284 1249 0.973 1 6
CH4 Methane 1 A1 3049 2917 0.957 2 7
    2 E 1586 1534 0.967 2 8
    3 T2 3170 3019 0.952 2 9
    4 T2 1365 1306 0.957 2 10
C2H6 Ethane 1 A1g 3058 2896 0.947 3 11
    2 A1g 1448 1388 0.959 3 12
    3 A1g 1023 995 0.972 3 13
    4 A1u 311 289 0.930 3 14
    5 A2u 3058 2915 0.953 3 15
    6 A2u 1430 1370 0.958 3 16
    7 Eg 3119 2969 0.952 3 17
    8 Eg 1529 1468 0.960 3 18
    9 Eg 1241 1190 0.959 3 19
    10 Eu 3141 2974 0.947 3 20
    11 Eu 1531 1460 0.954 3 21
    12 Eu 832 822 0.988 3 22
C2H4 Ethylene 1 Ag 3180 3026 0.952 4 23
    2 Ag 1708 1623 0.950 4 24
    3 Ag 1389 1342 0.966 4 25
    4 Au 1041 1023 0.982 4 26
    5 B1u 3159 2989 0.946 4 27
    6 B1u 1490 1444 0.969 4 28
    7 B2g 967 940 0.972 4 29
    8 B2u 3267 3105 0.951 4 30
    9 B2u 831 826 0.994 4 31
    10 B3g 3239 3086 0.953 4 32
    11 B3g 1256 1217 0.969 4 33
    12 B3u 985 949 0.964 4 34
C2H2 Acetylene 1 Σg 3536 3374 0.954 5 35
    2 Σg 2058 1974 0.959 5 36
    3 Σu 3420 3289 0.962 5 37
    4 Πg 646 612 0.947 5 38
    5 Πu 774 730 0.943 5 39
CH3Cl Methyl chloride 1 A1 3102 2966 0.956 6 40
    2 A1 1413 1355 0.959 6 41
    3 A1 762 732 0.960 6 42
    4 E 3204 3042 0.950 6 43
    5 E 1515 1455 0.960 6 44
    6 E 1054 1015 0.963 6 45
HCN Hydrogen cyanide 1 Σ 3472 3312 0.954 7 46
    2 Σ 2192 2089 0.953 7 47
    3 Π 751 712 0.948 7 48
CH2F2 Methane, difluoro- 1 A1 3105 2948 0.949 8 49
    2 A1 1574 1508 0.958 8 50
    3 A1 1158 1111 0.959 8 51
    4 A1 543 529 0.973 8 52
    5 A2 1303 1262 0.969 8 53
    6 B1 3177 3014 0.949 8 54
    7 B1 1210 1178 0.973 8 55
    8 B2 1493 1435 0.961 8 56
    9 B2 1156 1090 0.943 8 57
C3H6 Cyclopropane 1 A1' 3179 3038 0.956 9 58
    2 A1' 1549 1479 0.955 9 59
    3 A1' 1231 1188 0.965 9 60
    4 A1" 1168 1126 0.964 9 61
    5 A2' 1102 1070 0.971 9 62
    6 A2" 3270 3103 0.949 9 63
    7 A2" 859 854 0.994 9 64
    8 E' 3168 3025 0.955 9 65
    9 E' 1493 1438 0.963 9 66
    10 E' 1071 1029 0.961 9 67
    11 E' 907 866 0.955 9 68
    12 E" 3250 3082 0.948 9 69
    13 E" 1226 1188 0.969 9 70
    14 E" 745 739 0.992 9 71
CH3CHClCH3 Propane, 2-chloro- 1 A' 3159 3005 0.951 10 72
    2 A' 3140 2955 0.941 10 73
    3 A' 3117 2927 0.939 10 74
    4 A' 3060 2878 0.940 10 75
    5 A' 1532 1472 0.961 10 76
    6 A' 1518 1454 0.958 10 77
    7 A' 1445 1390 0.962 10 78
    8 A' 1319 1270 0.963 10 79
    9 A' 1211 1163 0.960 10 80
    10 A' 1105 1065 0.964 10 81
    11 A' 922 888 0.963 10 82
    12 A' 659 633 0.961 10 83
    13 A' 426 418 0.981 10 84
    14 A' 340 336 0.989 10 85
    15 A' 274 253 0.923 10 86
    16 A" 3154 2997 0.950 10 87
    17 A" 3133 2985 0.953 10 88
    18 A" 3057 2947 0.964 10 89
    19 A" 1511 1472 0.974 10 90
    20 A" 1507 1454 0.965 10 91
    21 A" 1433 1377 0.961 10 92
    22 A" 1386 1334 0.963 10 93
    23 A" 1174 1123 0.957 10 94
    24 A" 974 972 0.997 10 95
    25 A" 955 936 0.980 10 96
    26 A" 328 317 0.968 10 97
    27 A" 243 276 1.135 10 98
CH2CF2 Ethene, 1,1-difluoro- 1 A1 3230 3070 0.950 11 99
    2 A1 1822 1728 0.949 11 100
    3 A1 1433 1360 0.949 11 101
    4 A1 960 926 0.964 11 102
    5 A1 561 550 0.980 11 103
    6 A2 735 714 0.972 11 104
    7 B1 851 803 0.943 11 105
    8 B1 639 611 0.956 11 106
    9 B2 3335 3154 0.946 11 107
    10 B2 1368 1302 0.952 11 108
    11 B2 985 955 0.970 11 109
    12 B2 443 438 0.989 11 110
CF2Cl2 difluorodichloromethane 1 A1 1165 1101 0.945 12 111
    2 A1 688 667 0.970 12 112
    3 A1 471 458 0.973 12 113
    4 A1 268 262 0.976 12 114
    5 A2 330 322 0.975 12 115
    6 B1 952 902 0.948 12 116
    7 B1 449 437 0.973 12 117
    8 B2 1231 1159 0.941 12 118
    9 B2 446 446 1.001 12 119
CH2CHCH3 Propene 1 A' 3250 3090 0.951 13 120
    2 A' 3172 3013 0.950 13 121
    3 A' 3159 2991 0.947 13 122
    4 A' 3135 2954 0.942 13 123
    5 A' 3051 2871 0.941 13 124
    6 A' 1738 1650 0.950 13 125
    7 A' 1521 1470 0.966 13 126
    8 A' 1473 1420 0.964 13 127
    9 A' 1431 1378 0.963 13 128
    10 A' 1339 1297 0.969 13 129
    11 A' 1207 1171 0.970 13 130
    12 A' 954 963 1.009 13 131
    13 A' 941 920 0.978 13 132
    14 A' 423 428 1.011 13 133
    15 A" 3113 2954 0.949 13 134
    16 A" 1508 1443 0.957 13 135
    17 A" 1088 1045 0.961 13 136
    18 A" 1032 991 0.960 13 137
    19 A" 955 912 0.955 13 138
    20 A" 593 578 0.974 13 139
    21 A" 204 174 0.854 13 140
CO2 Carbon dioxide 1 Σg 1403 1333 0.950 14 141
    2 Σu 2438 2349 0.963 14 142
    3 Πu 696 667 0.958 14 143
OCS Carbonyl sulfide 1 Σ 2155 2062 0.957 15 144
    2 Σ 887 859 0.968 15 145
    3 Π 544 520 0.956 15 146
CO Carbon monoxide 1 Σ 2245 2170 0.967 16 147
H2CS Thioformaldehyde 1 A1 3114 2971 0.954 17 148
    2 A1 1517 1456 0.960 17 149
    3 A1 1122 1059 0.944 17 150
    4 B1 1024 990 0.967 17 151
    5 B2 3203 3025 0.944 17 152
    6 B2 1015 991 0.977 17 153
H2 Hydrogen diatomic 1 Σg 4413 4401 0.997 18 154
C3H5 Allyl radical 1 A1 3285 3114 0.948 19 155
    2 A1 3190 3048 0.956 19 156
    4 A1 1550 1488 0.960 19 157
    5 A1 1303 1245 0.955 19 158
    6 A1 1060 1066 1.005 19 159
    7 A1 429 427 0.994 19 160
    9 A2 574 549 0.957 19 161
    10 B1 1043 968 0.928 19 162
    11 B1 848 802 0.945 19 163
    12 B1 548 518 0.945 19 164
    13 B2 3282 3105 0.946 19 165
    14 B2 3178 3016 0.949 19 166
    15 B2 1518 1463 0.964 19 167
    16 B2 1431 1389 0.970 19 168
    17 B2 1146 1182 1.031 19 169
CH Methylidyne 1 Σ 3146 3145 1.000 20 170
OH Hydroxyl radical 1 Σ 3783 3738 0.988 21 171
SO2 Sulfur dioxide 1 A1 1229 1151 0.937 22 172
    2 A1 537 518 0.964 22 173
    3 B2 1426 1362 0.955 22 174
LiH Lithium Hydride 1 Σ 1391 1405 1.010 23 175
BF3 Borane, trifluoro- 1 A1' 908 888 0.978 24 176
    2 A2" 705 691 0.981 24 177
    3 E' 1498 1449 0.967 24 178
    4 E' 485 480 0.990 24 179
HCl Hydrogen chloride 1 Σ 3024 2991 0.989 25 180
HF Hydrogen fluoride 1 Σ 4188 4138 0.988 26 181
NH3 Ammonia 1 A1 3507 3337 0.951 27 182
    2 A1 1065 950 0.892 27 183
    3 E 3637 3444 0.947 27 184
    4 E 1688 1627 0.964 27 185
H2O Water 1 A1 3869 3657 0.945 28 186
    2 A1 1662 1595 0.960 28 187
    3 B2 3976 3756 0.945 28 188
F2 Fluorine diatomic 1 Σg 1047 917 0.876 29 189
H2S Hydrogen sulfide 1 A1 2741 2615 0.954 30 190
    2 A1 1222 1183 0.968 30 191
    3 B2 2756 2626 0.953 30 192
NF3 Nitrogen trifluoride 1 A1 1103 1032 0.936 31 193
    2 A1 694 647 0.933 31 194
    3 E 1021 907 0.888 31 195
    4 E 529 492 0.931 31 196
AlF3 Aluminum trifluoride 1 A1' 701 690 0.985 32 197
    2 A2" 302 297 0.982 32 198
    3 E' 966 935 0.968 32 199
    4 E' 247 263 1.064 32 200
BeH2 beryllium dihydride 2 Σu 2239 2159 0.965 33 201
    3 Πu 711 698 0.981 33 202
AlCl Aluminum monochloride 1 Σ 475 482 1.014 34 203
NH Imidogen 1 Σ 3366 3314 0.985 35 204
SO Sulfur monoxide 1 Σ 1212 1151 0.949 36 205
    1 Σ 1167 1069 0.916 36 206
PH phosphorus monohydride 1 Σ 2400 2415 1.006 37 207
Li2 Lithium diatomic 1 Σg 346 351 1.016 38 208
Na2 Sodium diatomic 1 Σg 153 159 1.043 39 209

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.

180
160
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