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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)/aug-cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.970 ± 0.026 78 248 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4402 4161 0.945 1 1
LiH Lithium Hydride 1 Σ 1386 1360 0.981 2 2
Li2 Lithium diatomic 1 Σg 345 346 1.004 3 3
NaH sodium hydride 1 Σ 1129 1133 1.004 4 4
Na2 Sodium diatomic 1 Σg 151 158 1.041 5 5
BeH beryllium monohydride 1 Σ 2037 1987 0.975 6 6
BH Boron monohydride 1 Σ 2349 2269 0.966 7 7
CH Methylidyne 1 Σ 2847 2733 0.960 8 8
    1 Σ 3102     8 9
C2 Carbon diatomic 1 Σg 1841 1827 0.993 9 10
SiH Silylidyne 1 Σ 2028 1971 0.972 10 11
CN Cyano radical 1 Σ 2110 2042 0.968 11 12
N2 Nitrogen diatomic 1 Σg 2340 2330 0.996 12 13
    1 Σg 1720 1733 1.008 12 14
PH phosphorus monohydride 1 Σ 2351 2276 0.968 13 15
    1 Σ 2372 2319 0.978 13 16
P2 Phosphorus diatomic 1 Σg 768 775 1.009 14 17
OH Hydroxyl radical 1 Σ 3713 3570 0.961 15 18
LiO lithium oxide 1 Σ 792 799 1.009 16 19
BeO beryllium oxide 1 Σ 1451 1435 0.989 17 20
CO Carbon monoxide 1 Σ 2144 2143 1.000 18 21
    1 Σ 1773     18 22
NaO sodium monoxide 1 Σ 472     19 23
HS Mercapto radical 1 Σ 2691 2599 0.966 20 24
BeS beryllium sulfide 1 Σ 976 986 1.010 21 25
SO Sulfur monoxide 1 Σ 1136 1138 1.002 22 26
    1 Σ 1081 1054 0.975 22 27
MgS magnesium sulfide 1 Σ 518 523 1.010 23 28
SiS silicon monosulfide 1 Σ 734 744 1.014 24 29
S2 Sulfur diatomic 1 Σg 709 720 1.015 25 30
HF Hydrogen fluoride 1 Σ 4128 3961 0.960 26 31
LiF lithium fluoride 1 Σ 885 896 1.012 27 32
BeF Beryllium monofluoride 1 Σ 1242     28 33
NF nitrogen fluoride 1 Σ 1131 1123 0.994 29 34
F2 Fluorine diatomic 1 Σg 916 894 0.976 30 35
NaF sodium fluoride 1 Σ 532 529 0.994 31 36
SiF silicon monofluoride 1 Σ 834 848 1.016 32 37
SF Monosulfur monofluoride 1 Σ 827 829 1.002 33 38
HCl Hydrogen chloride 1 Σ 2992 2886 0.965 34 39
LiCl lithium chloride 1 Σ 628 634 1.010 35 40
BeCl beryllium monochloride 1 Σ 833 847 1.016 36 41
BCl boron monochloride 1 Σ 829 829 1.000 37 42
ClF Chlorine monofluoride 1 Σ 772 773 1.002 38 43
NaCl Sodium Chloride 1 Σ 347 361 1.042 39 44
AlCl Aluminum monochloride 1 Σ 473 478 1.010 40 45
SCl sulfur monochloride 1 Σ 562 577 1.027 41 46
Cl2 Chlorine diatomic 1 Σg 542 554 1.023 42 47
BeH2 beryllium dihydride 2 Σu 2231 2159 0.968 43 48
    3 Πu 709 698 0.984 43 49
MgH2 magnesium dihydride 2 Σu 1620 1572 0.970 44 50
    3 Πu 440 440 1.000 44 51
SiH2 silicon dihydride 1 A1 2058 1996 0.970 45 52
    2 A1 1015 999 0.984 45 53
    3 B2 2058 1993 0.968 45 54
HCN Hydrogen cyanide 1 Σ 3434 3312 0.965 46 55
    2 Σ 2108 2089 0.991 46 56
    3 Π 717 712 0.993 46 57
H2O Water 1 A1 3812 3657 0.959 47 58
    2 A1 1645 1595 0.969 47 59
    3 B2 3921 3756 0.958 47 60
LiOH lithium hydroxide 1 Σ 3999 3688 0.922 48 61
    2 Σ 928 871 0.938 48 62
    3 Π 345 257 0.743 48 63
HCO Formyl radical 1 A' 2706 2434 0.900 49 64
    2 A' 1882 1868 0.993 49 65
    3 A' 1109 1081 0.974 49 66
HO2 Hydroperoxy radical 1 A' 3641 3436 0.944 50 67
    2 A' 1429 1392 0.974 50 68
    3 A' 1125 1098 0.975 50 69
CO2 Carbon dioxide 1 Σg 1340 1333 0.994 51 70
    2 Σu 2373 2349 0.990 51 71
    3 Πu 663 667 1.005 51 72
N2O Nitrous oxide 1 Σ 2268 2224 0.981 52 73
    2 Σ 1287 1285 0.998 52 74
    3 Π 593 589 0.993 52 75
H2S Hydrogen sulfide 1 A1 2711 2615 0.965 53 76
    2 A1 1206 1183 0.981 53 77
    3 B2 2727 2626 0.963 53 78
SO2 Sulfur dioxide 1 A1 1136 1151 1.013 54 79
    2 A1 506 518 1.023 54 80
    3 B2 1332 1362 1.022 54 81
HOF Hypofluorous acid 1 A' 3751 3578 0.954 55 82
    2 A' 1389 1362 0.981 55 83
    3 A' 913 893 0.978 55 84
BH3 boron trihydride 2 A2" 1158 1148 0.991 56 85
    3 E' 2695 2602 0.965 56 86
    4 E' 1217 1197 0.983 56 87
AlH3 aluminum trihydride 1 A1' 1932 1900 0.983 57 88
    2 A2" 714 698 0.977 57 89
    3 E' 1938 1883 0.972 57 90
    4 E' 789 783 0.993 57 91
C2H2 Acetylene 1 Σg 3504 3374 0.963 58 92
    2 Σg 1995 1974 0.990 58 93
    3 Σu 3396 3289 0.969 58 94
    4 Πg 592 612 1.033 58 95
    5 Πu 748 730 0.976 58 96
SiH3 Silyl radical 1 A1 2213 2136 0.965 59 97
    2 A1 763 728 0.954 59 98
    3 E 2250 2185 0.971 59 99
    4 E 934 922 0.987 59 100
P4 Phosphorus tetramer 1 A1 607 601 0.990 60 101
    2 E 364 361 0.991 60 102
    3 T2 459 467 1.018 60 103
H2CO Formaldehyde 1 A1 2933 2782 0.949 61 104
    2 A1 1766 1746 0.989 61 105
    3 A1 1530 1500 0.981 61 106
    4 B1 1181 1167 0.988 61 107
    5 B2 3001 2843 0.947 61 108
    6 B2 1261 1249 0.990 61 109
H2O2 Hydrogen peroxide 1 A 3777 3599 0.953 62 110
    2 A 1422 1402 0.986 62 111
    3 A 898 877 0.976 62 112
    4 A 376 371 0.986 62 113
    5 B 3777 3608 0.955 62 114
    6 B 1317 1266 0.961 62 115
H2CS Thioformaldehyde 1 A1 3081 2971 0.964 63 116
    2 A1 1488 1456 0.978 63 117
    3 A1 1063 1059 0.997 63 118
    4 B1 987 990 1.003 63 119
    5 B2 3171 3025 0.954 63 120
    6 B2 996 991 0.995 63 121
H2S2 Disulfane 1 A 2670 2556 0.957 64 122
    2 A 894 882 0.986 64 123
    3 A 512 515 1.004 64 124
    4 A 421 417 0.993 64 125
    5 B 2672 2559 0.957 64 126
    6 B 892 878 0.985 64 127
AlF3 Aluminum trifluoride 1 A1' 688 690 1.002 65 128
    2 A2" 297 297 0.999 65 129
    3 E' 951 935 0.983 65 130
    4 E' 243 263 1.081 65 131
BCl3 Borane, trichloro- 1 A1' 474 471 0.993 66 132
    2 A2" 455 460 1.011 66 133
    3 E' 965 956 0.991 66 134
    4 E' 253 243 0.960 66 135
CH4 Methane 1 A1 3029 2917 0.963 67 136
    2 E 1573 1534 0.975 67 137
    3 T2 3148 3019 0.959 67 138
    4 T2 1350 1306 0.967 67 139
HCOOH Formic acid 1 A' 3743 3570 0.954 68 140
    2 A' 3089 2943 0.953 68 141
    3 A' 1804 1770 0.981 68 142
    4 A' 1406 1387 0.987 68 143
    5 A' 1311 1229 0.938 68 144
    6 A' 1131 1105 0.977 68 145
    7 A' 627 625 0.997 68 146
    8 A" 1052 1033 0.982 68 147
    9 A" 667 638 0.957 68 148
C2H4 Ethylene 1 Ag 3154 3026 0.960 69 149
    2 Ag 1665 1623 0.974 69 150
    3 Ag 1364 1342 0.984 69 151
    4 Au 1020 1023 1.003 69 152
    5 B1u 3135 2989 0.953 69 153
    6 B1u 1472 1444 0.981 69 154
    7 B2g 930 940 1.011 69 155
    8 B2u 3242 3105 0.958 69 156
    9 B2u 817 826 1.011 69 157
    10 B3g 3215 3086 0.960 69 158
    11 B3g 1240 1217 0.981 69 159
    12 B3u 959 949 0.990 69 160
CH3OH Methyl alcohol 1 A' 3843 3681 0.958 70 161
    2 A' 3128 3000 0.959 70 162
    3 A' 3011 2844 0.945 70 163
    4 A' 1522 1477 0.971 70 164
    5 A' 1484 1455 0.980 70 165
    6 A' 1379 1345 0.975 70 166
    7 A' 1082 1060 0.979 70 167
    8 A' 1054 1033 0.980 70 168
    9 A" 3069 2960 0.965 70 169
    10 A" 1512 1477 0.977 70 170
    11 A" 1176 1165 0.991 70 171
    12 A" 289 200 0.691 70 172
CHONH2 formamide 1 A' 3742 3564 0.952 71 173
    2 A' 3599 3439 0.956 71 174
    3 A' 2990 2854 0.954 71 175
    4 A' 1782 1754 0.984 71 176
    5 A' 1620 1577 0.973 71 177
    6 A' 1414 1390 0.983 71 178
    7 A' 1270 1258 0.991 71 179
    8 A' 1049 1046 0.997 71 180
    9 A' 560 581 1.037 71 181
    10 A" 1043 1021 0.979 71 182
    11 A" 626 603 0.963 71 183
    12 A" 91i 289 -3.184 71 184
C2H6 Ethane 1 A1g 3032 2954 0.974 72 185
    2 A1g 1429 1388 0.971 72 186
    3 A1g 1013 995 0.982 72 187
    4 A1u 309 289 0.936 72 188
    5 A2u 3031 2896 0.955 72 189
    6 A2u 1413 1379 0.976 72 190
    7 Eg 3090 2969 0.961 72 191
    8 Eg 1515 1468 0.969 72 192
    9 Eg 1227 1190 0.970 72 193
    10 Eu 3113 2985 0.959 72 194
    11 Eu 1516 1469 0.969 72 195
    12 Eu 823 822 0.998 72 196
C3H5 Allyl radical 1 A1 3250 3114 0.958 73 197
    2 A1 3153 3048 0.967 73 198
    4 A1 1522 1488 0.977 73 199
    5 A1 1272 1245 0.979 73 200
    6 A1 1035 1066 1.030 73 201
    7 A1 420 427 1.016 73 202
    9 A2 543 549 1.012 73 203
    10 B1 995 968 0.973 73 204
    11 B1 798 802 1.005 73 205
    12 B1 519 518 0.998 73 206
    13 B2 3247 3105 0.956 73 207
    14 B2 3146 3016 0.959 73 208
    15 B2 1511 1463 0.968 73 209
    16 B2 1417 1389 0.980 73 210
    17 B2 1183 1182 0.999 73 211
C3H6 Cyclopropane 1 A1' 3151 3038 0.964 74 212
    2 A1' 1525 1479 0.970 74 213
    3 A1' 1209 1188 0.982 74 214
    4 A1" 1152 1126 0.977 74 215
    5 A2' 1077 1070 0.993 74 216
    6 A2" 3243 3103 0.957 74 217
    7 A2" 846 854 1.009 74 218
    8 E' 3141 3025 0.963 74 219
    9 E' 1474 1438 0.976 74 220
    10 E' 1047 1029 0.982 74 221
    11 E' 887 866 0.976 74 222
    12 E" 3223 3082 0.956 74 223
    13 E" 1209 1188 0.983 74 224
    14 E" 731 739 1.011 74 225

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