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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at LSDA/TZVP
Scale factor How many Source
Molecules Vibrations
0.988 ± 0.024 48 298 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1379 1360 0.986 1 1
Li2 Lithium diatomic 1 Σg 341 346 1.016 2 2
NaH sodium hydride 1 Σ 1147 1133 0.988 3 3
Na2 Sodium diatomic 1 Σg 161 158 0.981 4 4
BeH beryllium monohydride 1 Σ 2017 1987 0.985 5 5
CN Cyano radical 1 Σ 2157 2042 0.947 6 6
N2 Nitrogen diatomic 1 Σg 2419 2330 0.963 7 7
P2 Phosphorus diatomic 1 Σg 789 775 0.982 8 8
OH Hydroxyl radical 1 Σ 3603 3570 0.991 9 9
BeO beryllium oxide 1 Σ 1485 1435 0.966 10 10
CO Carbon monoxide 1 Σ 2192 2143 0.978 11 11
HS Mercapto radical 1 Σ 2607 2599 0.997 12 12
SO Sulfur monoxide 1 Σ 1118 1138 1.018 13 13
HF Hydrogen fluoride 1 Σ 3992 3961 0.992 14 14
F2 Fluorine diatomic 1 Σg 1047 894 0.854 15 15
SF Monosulfur monofluoride 1 Σ 824 829 1.006 16 16
HCl Hydrogen chloride 1 Σ 2868 2886 1.006 17 17
NaCl Sodium Chloride 1 Σ 361 361 1.000 18 18
AlCl Aluminum monochloride 1 Σ 468 478 1.021 19 19
SCl sulfur monochloride 1 Σ 569 577 1.014 20 20
Cl2 Chlorine diatomic 1 Σg 539 554 1.028 21 21
BeH2 beryllium dihydride 2 Σu 2217 2159 0.974 22 22
    3 Πu 726 698 0.962 22 23
SiH2 silicon dihydride 1 A1 1984 1996 1.006 23 24
    2 A1 961 999 1.040 23 25
    3 B2 1993 1993 1.000 23 26
HCN Hydrogen cyanide 1 Σ 3366 3312 0.984 24 27
    2 Σ 2172 2089 0.962 24 28
    3 Π 739 712 0.963 24 29
CO2 Carbon dioxide 1 Σg 1366 1333 0.976 25 30
    2 Σu 2445 2349 0.961 25 31
    3 Πu 657 667 1.016 25 32
N2O Nitrous oxide 1 Σ 2375 2224 0.936 26 33
    2 Σ 1359 1285 0.946 26 34
    3 Π 592 589 0.995 26 35
SO2 Sulfur dioxide 1 A1 1114 1151 1.034 27 36
    2 A1 482 518 1.075 27 37
    3 B2 1279 1362 1.064 27 38
BH3 boron trihydride 2 A2" 1097 1148 1.046 28 39
    3 E' 2647 2602 0.983 28 40
    4 E' 1130 1197 1.059 28 41
C2H2 Acetylene 1 Σg 3445 3374 0.979 29 42
    2 Σg 2041 1974 0.967 29 43
    3 Σu 3342 3289 0.984 29 44
    4 Πg 601 612 1.018 29 45
    5 Πu 725 730 1.007 29 46
NH3 Ammonia 1 A1 3424 3337 0.974 30 47
    2 A1 910 950 1.044 30 48
    3 E 3571 3444 0.965 30 49
    4 E 1588 1627 1.024 30 50
H2CO Formaldehyde 1 A1 2787 2782 0.998 31 51
    2 A1 1820 1746 0.960 31 52
    3 A1 1483 1500 1.012 31 53
    4 B1 1160 1167 1.006 31 54
    5 B2 2839 2843 1.001 31 55
    6 B2 1228 1249 1.017 31 56
BF3 Borane, trifluoro- 1 A1' 891 888 0.996 32 57
    2 A2" 664 691 1.041 32 58
    3 E' 1479 1449 0.980 32 59
    4 E' 461 480 1.042 32 60
AlF3 Aluminum trifluoride 1 A1' 675 690 1.022 33 61
    2 A2" 280 297 1.062 33 62
    3 E' 945 935 0.990 33 63
    4 E' 230 263 1.145 33 64
CH4 Methane 1 A1 2977 2917 0.980 34 65
    2 E 1493 1534 1.028 34 66
    3 T2 3109 3019 0.971 34 67
    4 T2 1265 1306 1.032 34 68
B2Cl4 Diboron tetrachloride 1 A1 1148 1122 0.977 35 69
    2 A1 407 401 0.985 35 70
    3 A1 170 176 1.035 35 71
    5 B2 736 728 0.989 35 72
    6 B2 287 289 1.005 35 73
    7 E 926 917 0.990 35 74
    8 E 475 512 1.078 35 75
    9 E 88 104 1.178 35 76
CH2N4 1H-Tetrazole 1 A' 3550 3447 0.971 36 77
    2 A' 3210 3102 0.966 36 78
    3 A' 1472 1441 0.979 36 79
    4 A' 1428 1384 0.969 36 80
    5 A' 1278 1259 0.985 36 81
    6 A' 1233 1159 0.940 36 82
    7 A' 1129 1084 0.960 36 83
    8 A' 1071 1015 0.948 36 84
    9 A' 1047 1002 0.957 36 85
    10 A' 1000 969 0.969 36 86
    11 A' 961 925 0.962 36 87
    12 A" 801 906 1.132 36 88
    13 A" 733 663 0.905 36 89
    14 A" 690 658 0.953 36 90
    15 A" 607 578 0.953 36 91
C2H6 Ethane 1 A1g 2973 2954 0.994 37 92
    2 A1g 1364 1388 1.017 37 93
    3 A1g 1029 995 0.967 37 94
    4 A1u 311 289 0.928 37 95
    5 A2u 2977 2896 0.973 37 96
    6 A2u 1341 1379 1.028 37 97
    7 Eg 3037 2969 0.978 37 98
    8 Eg 1435 1468 1.023 37 99
    9 Eg 1167 1190 1.020 37 100
    10 Eu 3061 2985 0.975 37 101
    11 Eu 1434 1469 1.024 37 102
    12 Eu 796 822 1.033 37 103
C3H5 Allyl radical 1 A1 3182 3114 0.979 38 104
    2 A1 3078 3048 0.990 38 105
    4 A1 1459 1488 1.020 38 106
    5 A1 1245 1245 1.000 38 107
    6 A1 1018 1066 1.047 38 108
    7 A1 414 427 1.031 38 109
    9 A2 528 549 1.039 38 110
    10 B1 982 968 0.986 38 111
    11 B1 808 802 0.993 38 112
    12 B1 513 518 1.010 38 113
    13 B2 3180 3105 0.976 38 114
    14 B2 3075 3016 0.981 38 115
    15 B2 1508 1463 0.970 38 116
    16 B2 1366 1389 1.017 38 117
    17 B2 1220 1182 0.969 38 118
C3H3NO Oxazole 1 A' 3226 3170 0.983 39 119
    2 A' 3200 3144 0.982 39 120
    3 A' 3188 3141 0.985 39 121
    4 A' 1553 1537 0.990 39 122
    5 A' 1510 1504 0.996 39 123
    6 A' 1345 1324 0.984 39 124
    7 A' 1228 1252 1.020 39 125
    8 A' 1157 1139 0.984 39 126
    9 A' 1153 1086 0.942 39 127
    10 A' 1084 1078 0.994 39 128
    11 A' 1074 1046 0.974 39 129
    12 A' 918 899 0.979 39 130
    13 A' 903 854 0.946 39 131
    14 A" 837 907 1.084 39 132
    15 A" 795 830 1.044 39 133
    16 A" 733 750 1.023 39 134
    17 A" 660 647 0.980 39 135
    18 A" 622 607 0.975 39 136
C3H6 Cyclopropane 1 A1' 3078 3038 0.987 40 137
    2 A1' 1462 1479 1.011 40 138
    3 A1' 1226 1188 0.969 40 139
    4 A1" 1104 1126 1.020 40 140
    5 A2' 1041 1070 1.027 40 141
    6 A2" 3171 3103 0.979 40 142
    7 A2" 838 854 1.020 40 143
    8 E' 3072 3025 0.985 40 144
    9 E' 1404 1438 1.024 40 145
    10 E' 1008 1029 1.021 40 146
    11 E' 907 866 0.955 40 147
    12 E" 3151 3082 0.978 40 148
    13 E" 1165 1188 1.019 40 149
    14 E" 721 739 1.025 40 150
CH2CHCH3 Propene 1 A' 3158 3090 0.978 41 151
    2 A' 3068 3013 0.982 41 152
    3 A' 3062 2991 0.977 41 153
    4 A' 3046 2954 0.970 41 154
    5 A' 2959 2871 0.970 41 155
    6 A' 1696 1650 0.973 41 156
    7 A' 1420 1470 1.035 41 157
    8 A' 1382 1420 1.028 41 158
    9 A' 1337 1378 1.031 41 159
    10 A' 1276 1297 1.016 41 160
    11 A' 1156 1171 1.013 41 161
    12 A' 934 963 1.031 41 162
    13 A' 907 920 1.014 41 163
    14 A' 415 428 1.030 41 164
    15 A" 3020 2954 0.978 41 165
    16 A" 1403 1443 1.028 41 166
    17 A" 1023 1045 1.022 41 167
    18 A" 989 991 1.002 41 168
    19 A" 900 912 1.014 41 169
    20 A" 578 578 1.000 41 170
    21 A" 213 174 0.818 41 171
CHCCH2CH3 1-Butyne 1 A' 3402 3332 0.979 42 172
    2 A' 3069 2988 0.974 42 173
    3 A' 2985     42 174
    4 A' 2959     42 175
    5 A' 2197 2116 0.963 42 176
    6 A' 1435 1470 1.025 42 177
    7 A' 1400 1446 1.033 42 178
    8 A' 1348 1385 1.027 42 179
    9 A' 1297 1322 1.019 42 180
    10 A' 1064 1070 1.006 42 181
    11 A' 1036 1008 0.973 42 182
    12 A' 858 840 0.979 42 183
    13 A' 625 634 1.015 42 184
    14 A' 514 509 0.990 42 185
    15 A' 194 197 1.014 42 186
    16 A" 3070 2988 0.973 42 187
    17 A" 2991 2939 0.983 42 188
    18 A" 1423 1462 1.027 42 189
    19 A" 1234 1261 1.022 42 190
    20 A" 1057 1090 1.031 42 191
    21 A" 759 782 1.030 42 192
    22 A" 612 630 1.030 42 193
    23 A" 360 344 0.956 42 194
    24 A" 215 213 0.989 42 195
C4H6 Bicyclo[1.1.0]butane 1 A1 3188 3131 0.982 43 196
    2 A1 3107 3044 0.980 43 197
    3 A1 2986 2935 0.983 43 198
    4 A1 1472 1501 1.020 43 199
    5 A1 1291 1266 0.981 43 200
    6 A1 1081 1081 0.999 43 201
    7 A1 894 839 0.938 43 202
    8 A1 682 657 0.963 43 203
    9 A1 427 423 0.989 43 204
    10 A2 1132 1172 1.035 43 205
    11 A2 1042 1063 1.020 43 206
    12 A2 912 909 0.997 43 207
    13 A2 846 838 0.991 43 208
    14 B1 3175 3120 0.982 43 209
    15 B1 1141 1110 0.973 43 210
    16 B1 1092 1092 1.000 43 211
    17 B1 964 980 1.017 43 212
    18 B1 760 737 0.969 43 213
    19 B2 3110 3044 0.979 43 214
    20 B2 2995 2969 0.991 43 215
    21 B2 1421 1485 1.045 43 216
    22 B2 1298 1261 0.972 43 217
    23 B2 1077 1081 1.004 43 218
    24 B2 920 935 1.017 43 219

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.

40 140 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 120 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 80 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 60 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 40 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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