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