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

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