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

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