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

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