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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at QCISD/cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.956 ± 0.023 62 258 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2953 2782 0.942 1 1
    2 A1 1817 1746 0.961 1 2
    3 A1 1557 1500 0.963 1 3
    4 B1 1213 1167 0.962 1 4
    5 B2 3018 2843 0.942 1 5
    6 B2 1287 1249 0.971 1 6
CCl4 Carbon tetrachloride 1 A1 470 459 0.976 2 7
    2 E 222 217 0.979 2 8
    3 T2 825 776 0.940 2 9
    4 T2 321 314 0.979 2 10
HCOOH Formic acid 1 A' 3808 3570 0.938 3 11
    2 A' 3113 2943 0.945 3 12
    3 A' 1851 1770 0.956 3 13
    4 A' 1431 1387 0.969 3 14
    5 A' 1341 1229 0.917 3 15
    6 A' 1156 1105 0.956 3 16
    7 A' 639 625 0.978 3 17
    8 A" 1081 1033 0.956 3 18
    9 A" 676 638 0.944 3 19
CH3OH Methyl alcohol 1 A' 3901 3681 0.944 4 20
    2 A' 3142 3000 0.955 4 21
    3 A' 3027 2844 0.940 4 22
    4 A' 1536 1477 0.962 4 23
    5 A' 1503 1455 0.968 4 24
    6 A' 1405 1345 0.958 4 25
    7 A' 1109 1060 0.956 4 26
    8 A' 1080 1033 0.956 4 27
    9 A" 3080 2960 0.961 4 28
    10 A" 1520 1477 0.971 4 29
    11 A" 1193 1165 0.977 4 30
    12 A" 306 200 0.653 4 31
CH4 Methane 1 A1 3047 2917 0.957 5 32
    2 E 1581 1534 0.971 5 33
    3 T2 3164 3019 0.954 5 34
    4 T2 1356 1306 0.963 5 35
C2H4 Ethylene 1 Ag 3176 3026 0.953 6 36
    2 Ag 1700 1623 0.955 6 37
    3 Ag 1386 1342 0.968 6 38
    4 Au 1063 1023 0.962 6 39
    5 B1u 3156 2989 0.947 6 40
    6 B1u 1493 1444 0.967 6 41
    7 B2g 969 940 0.969 6 42
    8 B2u 3262 3105 0.952 6 43
    9 B2u 832 826 0.992 6 44
    10 B3g 3236 3086 0.954 6 45
    11 B3g 1255 1217 0.970 6 46
    12 B3u 986 949 0.963 6 47
C2H2 Acetylene 1 Σg 3533 3374 0.955 7 48
    2 Σg 2040 1974 0.968 7 49
    3 Σu 3429 3289 0.959 7 50
    4 Πg 617 612 0.991 7 51
    5 Πu 766 730 0.954 7 52
CH3Cl Methyl chloride 1 A1 3097 2966 0.958 8 53
    2 A1 1401 1355 0.967 8 54
    3 A1 755 732 0.970 8 55
    4 E 3197 3042 0.952 8 56
    5 E 1506 1455 0.966 8 57
    6 E 1043 1015 0.973 8 58
CH3NH2 methyl amine 1 A' 3530 3361 0.952 9 59
    2 A' 3094 2961 0.957 9 60
    3 A' 3013 2820 0.936 9 61
    4 A' 1684 1623 0.964 9 62
    5 A' 1521 1473 0.968 9 63
    6 A' 1474 1430 0.970 9 64
    7 A' 1198 1130 0.943 9 65
    8 A' 1081 1044 0.966 9 66
    9 A' 883 780 0.884 9 67
    10 A" 3609 3427 0.950 9 68
    11 A" 3129 2985 0.954 9 69
    12 A" 1540 1485 0.964 9 70
    13 A" 1371 1335 0.974 9 71
    14 A" 985     9 72
    15 A" 307 268 0.872 9 73
HCN Hydrogen cyanide 1 Σ 3467 3312 0.955 10 74
    2 Σ 2162 2089 0.966 10 75
    3 Π 741 712 0.960 10 76
HNCO Isocyanic acid 1 A' 3721 3538 0.951 11 77
    2 A' 2328 2269 0.975 11 78
    3 A' 1329 1327 0.999 11 79
    4 A' 832 777 0.933 11 80
    5 A' 569 577 1.014 11 81
    6 A" 641 656 1.024 11 82
CS2 Carbon disulfide 1 Σg 676 658 0.974 12 83
    2 Σu 1552 1535 0.989 12 84
    3 Πu 410 397 0.969 12 85
C3H6 Cyclopropane 1 A1' 3175 3038 0.957 13 86
    2 A1' 1547 1479 0.956 13 87
    3 A1' 1230 1188 0.966 13 88
    4 A1" 1174 1126 0.959 13 89
    5 A2' 1109 1070 0.965 13 90
    6 A2" 3264 3103 0.951 13 91
    7 A2" 865 854 0.987 13 92
    8 E' 3163 3025 0.956 13 93
    9 E' 1493 1438 0.963 13 94
    10 E' 1078 1029 0.954 13 95
    11 E' 906 866 0.956 13 96
    12 E" 3244 3082 0.950 13 97
    13 E" 1231 1188 0.965 13 98
    14 E" 750 739 0.986 13 99
CCl2O Phosgene 1 A1 1883 1827 0.970 14 100
    2 A1 584 567 0.971 14 101
    3 A1 306 285 0.932 14 102
    4 B1 598 580 0.969 14 103
    5 B2 883 849 0.962 14 104
    6 B2 453 440 0.970 14 105
CF2Cl2 difluorodichloromethane 1 A1 1162 1101 0.947 15 106
    2 A1 684 667 0.975 15 107
    3 A1 468 458 0.979 15 108
    4 A1 266 262 0.985 15 109
    5 A2 328 322 0.980 15 110
    6 B1 944 902 0.955 15 111
    7 B1 447 437 0.978 15 112
    8 B2 1234 1159 0.939 15 113
    9 B2 444 446 1.003 15 114
CH2CHCH3 Propene 1 A' 3248 3090 0.951 16 115
    2 A' 3171 3013 0.950 16 116
    3 A' 3157 2991 0.947 16 117
    4 A' 3129 2954 0.944 16 118
    5 A' 3047 2871 0.942 16 119
    6 A' 1728 1650 0.955 16 120
    7 A' 1515 1470 0.970 16 121
    8 A' 1472 1420 0.965 16 122
    9 A' 1425 1378 0.967 16 123
    10 A' 1337 1297 0.970 16 124
    11 A' 1205 1171 0.972 16 125
    12 A' 953 963 1.010 16 126
    13 A' 940 920 0.979 16 127
    14 A' 424 428 1.011 16 128
    15 A" 3105 2954 0.951 16 129
    16 A" 1502 1443 0.961 16 130
    17 A" 1084 1045 0.964 16 131
    18 A" 1032 991 0.960 16 132
    19 A" 950 912 0.960 16 133
    20 A" 594 578 0.974 16 134
    21 A" 202 174 0.863 16 135
CO2 Carbon dioxide 1 Σg 1372 1333 0.971 17 136
    2 Σu 2414 2349 0.973 17 137
    3 Πu 678 667 0.984 17 138
CF2O Carbonic difluoride 1 A1 2007 1928 0.961 18 139
    2 A1 1000 965 0.965 18 140
    3 A1 596 584 0.980 18 141
    4 B1 801 774 0.966 18 142
    5 B2 1318 1249 0.948 18 143
    6 B2 635 626 0.985 18 144
CH2CCH2 allene 1 A1 3166 3015 0.952 19 145
    2 A1 1507 1443 0.958 19 146
    3 A1 1100 1073 0.975 19 147
    4 B1 884 865 0.978 19 148
    5 B2 3165 3007 0.950 19 149
    6 B2 2050 1957 0.954 19 150
    7 B2 1453 1398 0.962 19 151
    8 E 3247 3086 0.950 19 152
    9 E 1031 999 0.969 19 153
    10 E 882 841 0.954 19 154
    11 E 361 355 0.985 19 155
OCS Carbonyl sulfide 1 Σ 2117 2062 0.974 20 156
    2 Σ 870 859 0.988 20 157
    3 Π 534 520 0.975 20 158
ClCN chlorocyanogen 1 Σ 2304 2216 0.962 21 159
    2 Σ 747 744 0.996 21 160
    3 Π 395 378 0.956 21 161
CO Carbon monoxide 1 Σ 2187 2170 0.992 22 162
H2CS Thioformaldehyde 1 A1 3107 2971 0.956 23 163
    2 A1 1517 1456 0.959 23 164
    3 A1 1089 1059 0.973 23 165
    4 B1 1030 990 0.961 23 166
    5 B2 3196 3025 0.946 23 167
    6 B2 1014 991 0.977 23 168
BeO beryllium oxide 1 Σ 1434 1457 1.016 24 169
MgO magnesium oxide 1 Σ 719 785 1.092 25 170
LiOH lithium hydroxide 1 Σ 4050 3688 0.910 26 171
    2 Σ 959 871 0.907 26 172
    3 Π 323 257 0.793 26 173
NaOH sodium hydroxide 1 Σ 3995 3637 0.910 27 174
    2 Σ 572 540 0.945 27 175
    3 Π 227 300 1.319 27 176
H2 Hydrogen diatomic 1 Σg 4409 4401 0.998 28 177
CN Cyano radical 1 Σ 2177 2069 0.950 29 178
CF2 Difluoromethylene 1 A1 1271 1225 0.964 30 179
    2 A1 682 667 0.978 30 180
    3 B2 1181 1114 0.944 30 181
HCO Formyl radical 1 A' 2725 2434 0.893 31 182
    2 A' 1911 1868 0.978 31 183
    3 A' 1141 1081 0.947 31 184
ClNO Nitrosyl chloride 1 A' 1845 1800 0.975 32 185
    2 A' 630 596 0.946 32 186
    3 A' 356 332 0.932 32 187
CS carbon monosulfide 1 Σ 1288 1285 0.998 33 188
HO2 Hydroperoxy radical 1 A' 3719 3436 0.924 34 189
    2 A' 1451 1392 0.959 34 190
    3 A' 1130 1098 0.971 34 191
CH Methylidyne 1 Σ 2852 2861 1.003 35 192
    1 Σ 3134 3145 1.004 35 193
OH Hydroxyl radical 1 Σ 3772 3738 0.991 36 194
CF Fluoromethylidyne 1 Σ 1328 1308 0.985 37 195
CCl carbon monochloride 1 Σ 869 877 1.009 38 196
HNC hydrogen isocyanide 1 Σ 3857 3653 0.947 39 197
    2 Σ 2087 2029 0.972 39 198
    3 Π 484 477 0.985 39 199
SO2 Sulfur dioxide 1 A1 1195 1151 0.963 40 200
    2 A1 530 518 0.978 40 201
    3 B2 1394 1362 0.977 40 202
SO3 Sulfur trioxide 1 A1' 1096 1065 0.972 41 203
    2 A2" 506 498 0.984 41 204
    3 E' 1428 1391 0.974 41 205
    4 E' 532 530 0.995 41 206
LiCl lithium chloride 1 Σ 639 643 1.006 42 207
C2Cl2 dichloroacetylene 1 Σg 2341 2234 0.954 43 208
    2 Σg 478 477 0.998 43 209
    3 Σu 1004 988 0.984 43 210
    4 Πg 369 333 0.904 43 211
    5 Πu 180 172 0.955 43 212
LiH Lithium Hydride 1 Σ 1395 1405 1.008 44 213
SiO2 silicon dioxide 2 Σu 1449 1416 0.977 45 214
    3 Πu 300 273 0.907 45 215
BF3 Borane, trifluoro- 1 A1' 905 888 0.981 46 216
    2 A2" 704 691 0.981 46 217
    3 E' 1503 1449 0.964 46 218
    4 E' 487 480 0.986 46 219
NaH sodium hydride 1 Σ 1132 1172 1.036 47 220
HCl Hydrogen chloride 1 Σ 3019 2991 0.991 48 221
NaCl Sodium Chloride 1 Σ 354 365 1.031 49 222
HF Hydrogen fluoride 1 Σ 4202 4138 0.985 50 223
NH3 Ammonia 1 A1 3499 3337 0.954 51 224
    2 A1 1110 950 0.856 51 225
    3 E 3623 3444 0.951 51 226
    4 E 1700 1627 0.957 51 227
NaF sodium fluoride 1 Σ 550 536 0.975 52 228
MgH2 magnesium dihydride 2 Σu 1636 1572 0.961 53 229
    3 Πu 441 440 0.998 53 230
H2O2 Hydrogen peroxide 1 A 3846 3599 0.936 54 231
    2 A 1465 1402 0.957 54 232
    3 A 968 877 0.906 54 233
    4 A 383 371 0.968 54 234
    5 B 3845 3608 0.938 54 235
    6 B 1354 1266 0.935 54 236
N2 Nitrogen diatomic 1 Σg 2409 2359 0.979 55 237
H2O Water 1 A1 3873 3657 0.944 56 238
    2 A1 1677 1595 0.951 56 239
    3 B2 3976 3756 0.945 56 240
F2 Fluorine diatomic 1 Σg 1009 917 0.909 57 241
Cl2 Chlorine diatomic 1 Σg 562 560 0.996 58 242
HNO2 Nitrous acid 1 A' 3834 3591 0.937 59 243
    2 A' 1782 1700 0.954 59 244
    3 A' 1348 1263 0.937 59 245
    4 A' 877 790 0.901 59 246
    5 A' 662 596 0.899 59 247
    6 A" 573 543 0.948 59 248
H2S Hydrogen sulfide 1 A1 2734 2615 0.957 60 249
    2 A1 1219 1183 0.970 60 250
    3 B2 2748 2626 0.956 60 251
F2O Difluorine monoxide 1 A1 1008 928 0.920 61 252
    2 A1 494 461 0.933 61 253
    3 B2 952 831 0.873 61 254
NF3 Nitrogen trifluoride 1 A1 1089 1032 0.948 62 255
    2 A1 681 647 0.951 62 256
    3 E 1003 907 0.905 62 257
    4 E 519 492 0.949 62 258

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