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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at MP4/6-311G*
Scale factor How many Source
Molecules Vibrations
0.959 ± 0.115 110 321 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2904 2782 0.958 1 1
    2 A1 1752 1746 0.997 1 2
    3 A1 1542 1500 0.973 1 3
    4 B1 1175 1167 0.993 1 4
    5 B2 2966 2843 0.958 1 5
    6 B2 1273 1249 0.981 1 6
CH3OH Methyl alcohol 1 A' 3825 3681 0.962 2 7
    2 A' 3136 3000 0.957 2 8
    3 A' 2993 2844 0.950 2 9
    4 A' 1536 1477 0.962 2 10
    5 A' 1511 1455 0.963 2 11
    6 A' 1417 1345 0.950 2 12
    7 A' 1095 1060 0.968 2 13
    8 A' 1077 1033 0.959 2 14
    9 A" 3051 2960 0.970 2 15
    10 A" 1521 1477 0.971 2 16
    11 A" 1183 1165 0.984 2 17
    12 A" 365 200 0.547 2 18
CH4 Methane 1 A1 3028 2917 0.963 3 19
    2 E 1583 1534 0.969 3 20
    3 T2 3153 3019 0.957 3 21
    4 T2 1373 1306 0.951 3 22
C2H6 Ethane 1 A1g 3031 2896 0.956 4 23
    2 A1g 1452 1388 0.956 4 24
    3 A1g 1021 995 0.974 4 25
    4 A1u 317 289 0.911 4 26
    5 A2u 3029 2915 0.962 4 27
    6 A2u 1431 1370 0.958 4 28
    7 Eg 3095 2969 0.959 4 29
    8 Eg 1527 1468 0.961 4 30
    9 Eg 1238 1190 0.961 4 31
    10 Eu 3117 2974 0.954 4 32
    11 Eu 1530 1460 0.954 4 33
    12 Eu 826 822 0.995 4 34
C2H4 Ethylene 1 Ag 3145 3026 0.962 5 35
    2 Ag 1667 1623 0.974 5 36
    3 Ag 1368 1342 0.981 5 37
    4 Au 1046 1023 0.978 5 38
    5 B1u 3127 2989 0.956 5 39
    6 B1u 1480 1444 0.976 5 40
    7 B2g 889 940 1.057 5 41
    8 B2u 3236 3105 0.959 5 42
    9 B2u 832 826 0.993 5 43
    10 B3g 3211 3086 0.961 5 44
    11 B3g 1241 1217 0.981 5 45
    12 B3u 948 949 1.001 5 46
C2H2 Acetylene 1 Σg 3494 3374 0.966 6 47
    2 Σg 1947 1974 1.014 6 48
    3 Σu 3402 3289 0.967 6 49
    4 Πg 324 612 1.890 6 50
    5 Πu 722 730 1.011 6 51
CH3Cl Methyl chloride 1 A1 3072 2966 0.966 7 52
    2 A1 1435 1355 0.944 7 53
    3 A1 753 732 0.973 7 54
    4 E 3176 3042 0.958 7 55
    5 E 1503 1455 0.968 7 56
    6 E 1061 1015 0.957 7 57
CH3NH2 methyl amine 1 A' 3498 3361 0.961 8 58
    2 A' 3078 2961 0.962 8 59
    3 A' 2981 2820 0.946 8 60
    4 A' 1741 1623 0.932 8 61
    5 A' 1522 1473 0.968 8 62
    6 A' 1482 1430 0.965 8 63
    7 A' 1207 1130 0.936 8 64
    8 A' 1073 1044 0.973 8 65
    9 A' 917 780 0.850 8 66
    10 A" 3585 3427 0.956 8 67
    11 A" 3119 2985 0.957 8 68
    12 A" 1541 1485 0.963 8 69
    13 A" 1386 1335 0.963 8 70
    14 A" 987     8 71
    15 A" 335 268 0.800 8 72
HCN Hydrogen cyanide 1 Σ 3428 3312 0.966 9 73
    2 Σ 2011 2089 1.039 9 74
    3 Π 712 712 1.001 9 75
CH3SH Methanethiol 1 A' 3146 3000 0.954 10 76
    2 A' 3051 2931 0.961 10 77
    3 A' 2614 2597 0.994 10 78
    4 A' 1509 1475 0.977 10 79
    5 A' 1416 1335 0.943 10 80
    6 A' 1124 1074 0.956 10 81
    7 A' 812 803 0.989 10 82
    8 A' 730 708 0.970 10 83
    9 A" 3143 3000 0.955 10 84
    10 A" 1498 1430 0.954 10 85
    11 A" 1008 976 0.968 10 86
N2H4 Hydrazine 1 A 3586 3398 0.948 11 87
    2 A 3475 3329 0.958 11 88
    3 A 1765 1642 0.930 11 89
    4 A 1389 1275 0.918 11 90
    5 A 1158 1076 0.929 11 91
    6 A 903 780 0.863 11 92
    7 A 441 377 0.853 11 93
    8 B 3592 3350 0.933 11 94
    9 B 3463 3314 0.957 11 95
    10 B 1749 1628 0.931 11 96
    11 B 1341 1275 0.951 11 97
    12 B 1089 966 0.887 11 98
CH3F Methyl fluoride 1 A1 3038 2930 0.965 12 99
    2 A1 1525 1464 0.960 12 100
    3 A1 1079 1049 0.973 12 101
    4 E 3131 3006 0.960 12 102
    5 E 1522 1467 0.964 12 103
    6 E 1212 1182 0.975 12 104
CH3PH2 Methyl phosphine 1 A 3133 3000 0.958 13 105
    2 A 3041 2938 0.966 13 106
    3 A 2347 2297 0.979 13 107
    4 A 1499 1450 0.967 13 108
    5 A 1383 1238 0.895 13 109
    6 A 1135 1086 0.957 13 110
    7 A 1022 977 0.956 13 111
    8 A 754 740 0.981 13 112
    9 A 697 677 0.972 13 113
    10 A 3124 2992 0.958 13 114
    11 A 2353 2312 0.982 13 115
    12 A 1504 1450 0.964 13 116
    13 A 1057 1017 0.962 13 117
    15 A 230 207 0.899 13 118
CO Carbon monoxide 1 Σ 2010 2170 1.079 14 119
H2CS Thioformaldehyde 1 A1 3063 2971 0.970 15 120
    2 A1 1523 1456 0.956 15 121
    3 A1 1066 1059 0.994 15 122
    4 B1 1007 990 0.983 15 123
    5 B2 3155 3025 0.959 15 124
    6 B2 1033 991 0.959 15 125
CH3SiH3 methyl silane 1 A1 3028 2898 0.957 16 126
    2 A1 2217 2166 0.977 16 127
    3 A1 1345 1260 0.937 16 128
    4 A1 952 940 0.987 16 129
    5 A1 709 700 0.987 16 130
    6 A2 183 187 1.020 16 131
    7 E 3113 2982 0.958 16 132
    8 E 2218 2169 0.978 16 133
    9 E 1493 1403 0.940 16 134
    10 E 964 980 1.016 16 135
    11 E 911 868 0.952 16 136
    12 E 526 540 1.027 16 137
BeO beryllium oxide 1 Σ 812 1457 1.795 17 138
MgO magnesium oxide 1 Σ 1183 785 0.663 18 139
NaOH sodium hydroxide 1 Σ 3900 3637 0.933 19 140
    2 Σ 602 540 0.897 19 141
    3 Π 192 300 1.564 19 142
H2 Hydrogen diatomic 1 Σg 4315 4401 1.020 20 143
Si2H6 disilane 1 A1g 2211 2152 0.973 21 144
    2 A1g 939 909 0.969 21 145
    3 A1g 443 434 0.981 21 146
    4 A1u 145 131 0.906 21 147
    5 A2u 2202 2154 0.978 21 148
    6 A2u 864 844 0.976 21 149
    7 Eg 2212 2155 0.974 21 150
    8 Eg 942 929 0.987 21 151
    9 Eg 651 625 0.960 21 152
    10 Eu 2220 2179 0.981 21 153
    11 Eu 957 940 0.981 21 154
    12 Eu 389 379 0.974 21 155
CH2NH Methanimine 1 A' 3428 3263 0.952 22 156
    2 A' 3148 3024 0.961 22 157
    3 A' 3034 2914 0.961 22 158
    4 A' 1666 1638 0.984 22 159
    5 A' 1487 1452 0.977 22 160
    6 A' 1410 1344 0.954 22 161
    7 A' 1091 1058 0.970 22 162
    8 A" 1177 1127 0.958 22 163
    9 A" 1067 1061 0.994 22 164
CN Cyano radical 1 Σ 2686 2069 0.770 23 165
HCO Formyl radical 1 A' 2606 2434 0.934 24 166
    2 A' 1876 1868 0.996 24 167
    3 A' 1124 1081 0.962 24 168
CS carbon monosulfide 1 Σ 1164 1285 1.104 25 169
HO2 Hydroperoxy radical 1 A' 3643 3436 0.943 26 170
    2 A' 1505 1392 0.925 26 171
    3 A' 1204 1098 0.912 26 172
OH Hydroxyl radical 1 Σ 3709 3738 1.008 27 173
CF Fluoromethylidyne 1 Σ 1297 1308 1.008 28 174
CCl carbon monochloride 1 Σ 870 877 1.007 29 175
HCP HCP 1 Σ 3315 3217 0.970 30 176
    2 Σ 1230 1278 1.040 30 177
    3 Π 648 674 1.041 30 178
LiCl lithium chloride 1 Σ 654 643 0.984 31 179
LiH Lithium Hydride 1 Σ 1392 1405 1.009 32 180
NaH sodium hydride 1 Σ 1147 1172 1.021 33 181
HCl Hydrogen chloride 1 Σ 2880 2991 1.039 34 182
NaCl Sodium Chloride 1 Σ 364 365 1.002 35 183
HF Hydrogen fluoride 1 Σ 4067 4138 1.018 36 184
NH3 Ammonia 1 A1 3481 3337 0.959 37 185
    2 A1 1183 950 0.803 37 186
    3 E 3620 3444 0.951 37 187
    4 E 1764 1627 0.922 37 188
NaF sodium fluoride 1 Σ 572 536 0.937 38 189
MgH2 magnesium dihydride 2 Σu 1615 1572 0.973 39 190
    3 Πu 455 440 0.967 39 191
H2O2 Hydrogen peroxide 1 A 3786 3599 0.951 40 192
    2 A 1505 1402 0.932 40 193
    3 A 895 877 0.980 40 194
    4 A 310 371 1.197 40 195
    5 B 3788 3608 0.952 40 196
    6 B 1330 1266 0.952 40 197
N2 Nitrogen diatomic 1 Σg 2186 2359 1.079 41 198
H2O Water 1 A1 3814 3657 0.959 42 199
    2 A1 1746 1595 0.914 42 200
    3 B2 3941 3756 0.953 42 201
F2 Fluorine diatomic 1 Σg 794 917 1.155 43 202
Cl2 Chlorine diatomic 1 Σg 508 560 1.102 44 203
H2S Hydrogen sulfide 1 A1 2621 2615 0.998 45 204
    2 A1 1251 1183 0.945 45 205
    3 B2 2642 2626 0.994 45 206
AlH3 aluminum trihydride 1 A1' 1942 1900 0.979 46 207
    2 A2" 716 698 0.975 46 208
    3 E' 1953 1883 0.964 46 209
    4 E' 790 783 0.992 46 210
BeH2 beryllium dihydride 2 Σu 2236 2159 0.966 47 211
    3 Πu 719 698 0.971 47 212
LiF lithium fluoride 1 Σ 954 911 0.955 48 213
ClF Chlorine monofluoride 1 Σ 691 783 1.133 49 214
HOCl hypochlorous acid 1 A' 3757 3609 0.961 50 215
    2 A' 1308 1239 0.947 50 216
    3 A' 671 724 1.079 50 217
PH3 Phosphine 1 A1 2366 2323 0.982 51 218
    2 A1 1054 992 0.941 51 219
    3 E 2376 2328 0.980 51 220
    4 E 1160 1118 0.964 51 221
SiH4 Silane 1 A1 2232 2187 0.980 52 222
    2 E 977 975 0.998 52 223
    3 T2 2239 2191 0.978 52 224
    4 T2 926 914 0.987 52 225
SiO Silicon monoxide 1 Σ 1012 1242 1.226 53 226
SiF silicon monofluoride 1 Σ 844 857 1.016 54 227
MgS magnesium sulfide 1 Σ 539 529 0.981 55 228
SiN Silicon nitride 1 Σ 1386 1151 0.831 56 229
C2 Carbon diatomic 1 Σg 1731 1855 1.071 57 230
LiO lithium oxide 1 Σ 903 815 0.902 58 231
P2 Phosphorus diatomic 1 Σg 722 781 1.081 59 232
BS boron sulfide 1 Σ 1169 1180 1.009 60 233
AlS Aluminum sulfide 1 Σ 665 617 0.927 61 234
CP Carbon monophosphide 1 Σ 1285 1240 0.965 62 235
NaO sodium monoxide 1 Σ 557 492 0.884 63 236
SiS silicon monosulfide 1 Σ 699 750 1.073 64 237
BO boron monoxide 1 Σ 1871 1885 1.007 65 238
Si2 Silicon diatomic 1 Σg 536 511 0.954 66 239
BH3 boron trihydride 2 A2" 1149 1148 0.999 67 240
    3 E' 2674 2602 0.973 67 241
    4 E' 1192 1197 1.004 67 242
HCF Fluoromethylene 1 A' 2783 2643 0.950 68 243
    2 A' 1471 1403 0.954 68 244
    3 A' 1212 1189 0.981 68 245
H2S2 HSSH 1 A 2586 2556 0.988 69 246
    2 A 916 882 0.963 69 247
    3 A 492 515 1.045 69 248
    4 A 432 417 0.967 69 249
    5 B 2587 2559 0.989 69 250
    6 B 913 878 0.961 69 251
SiH3Cl chlorosilane 1 A1 2258 2201 0.975 70 252
    2 A1 973 949 0.976 70 253
    3 A1 548 551 1.005 70 254
    4 E 2271 2195 0.967 70 255
    5 E 962 954 0.992 70 256
    6 E 683 664 0.973 70 257
SiH3F monofluorosilane 1 A1 2260 2206 0.976 71 258
    2 A1 1035 990 0.956 71 259
    3 A1 869 872 1.004 71 260
    4 E 2265 2196 0.969 71 261
    5 E 967 956 0.989 71 262
    6 E 749 728 0.972 71 263
AlF Aluminum monofluoride 1 Σ 809 802 0.991 72 264
BeF Beryllium monofluoride 1 Σ 1226 1247 1.017 73 265
BeH beryllium monohydride 1 Σ 2028 2061 1.016 74 266
BeS beryllium sulfide 1 Σ 951 998 1.049 75 267
PH2 Phosphino radical 1 A1 2334 2310 0.990 76 268
    2 A1 1153 1102 0.956 76 269
SiH3 Silyl radical 1 A1 2203 2136 0.970 77 270
    2 A1 771 728 0.944 77 271
    3 E 2237 2185 0.977 77 272
    4 E 941 922 0.980 77 273
BH Boron monohydride 1 Σ 2328 2367 1.016 78 274
NH2 Amino radical 1 A1 3368 3219 0.956 79 275
    2 A1 1619 1497 0.925 79 276
    3 B2 3471 3301 0.951 79 277
NH Imidogen 1 Σ 3280 3283 1.001 80 278
BeCl beryllium chloride 1 Σ 859 847 0.986 81 279
HPO HPO 1 A' 2057 2095 1.018 82 280
    2 A' 1095 1188 1.085 82 281
    3 A' 1012 986 0.974 82 282
SiH2 silicon dihydride 1 A1 2032 1996 0.982 83 283
    2 A1 1032 999 0.968 83 284
    3 B2 2029 1993 0.982 83 285
SO Sulfur monoxide 1 Σ 1069 1151 1.077 84 286
SH Mercapto radical 1 Σ 2585 2696 1.043 85 287
SiCl Clorosilylidyne 1 Σ 520 536 1.029 86 288
NF nitrogen fluoride 1 Σ 1151 1141 0.991 87 289
PH phosphorus monohydride 1 Σ 2289 2364 1.032 88 290
AlH aluminum monohydride 1 Σ 1682 1682 1.000 89 291
HOF Hypofluorous acid 1 A' 3738 3537 0.946 90 292
    2 A' 1417 1393 0.983 90 293
    3 A' 858 886 1.033 90 294
HNO Nitrosyl hydride 1 A' 2902 2684 0.925 91 295
    2 A' 1592 1565 0.983 91 296
    3 A' 1494 1501 1.004 91 297
MgH magnesium monohydride 1 Σ 1470 1493 1.015 92 298
Li2 Lithium diatomic 1 Σg 348 351 1.011 93 299
BH2 boron dihydride 2 A1 1007 954 0.947 94 300
AlH2 aluminum dihydride 1 A1 1859 1770 0.952 95 301
    2 A1 765 760 0.994 95 302
    3 B2 1897 1807 0.953 95 303
HBS hydrogen boron sulfide 1 Σ 2798 2736 0.978 96 304
    2 Σ 1162 1172 1.009 96 305
MgF Magnesium monofluoride 1 Σ 717 712 0.993 97 306
MgCl magnesium monochloride 1 Σ 464 462 0.997 98 307
ClO Monochlorine monoxide 1 Σ 808 854 1.057 99 308
SCl sulfur monochloride 1 Σ 526 575 1.092 100 309
PF phosphorus monofluoride 1 Σ 806 847 1.050 101 310
SF Monosulfur monofluoride 1 Σ 767 838 1.092 102 311
PCl phosphorus chloride 1 Σ 514 577 1.123 103 312
PN Phosphorus mononitride 1 Σ 1142 1337 1.170 104 313
BCl boron monochloride 1 Σ 862 840 0.975 105 314
HBO Boron hydride oxide 1 Σ 2864 2850 0.995 106 315
    2 Σ 1740 1826 1.049 106 316
    3 Π 757 756 0.999 106 317
BeOH beryllium hydroxide 2 A' 1283 1246 0.971 107 318
S2 Sulfur diatomic 1 Σg 664 726 1.093 108 319
Na2 Sodium diatomic 1 Σg 157 159 1.016 109 320

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.

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