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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)=FULL/aug-cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.971 ± 0.032 54 244 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1478 1360 0.920 1 1
Li2 Lithium diatomic 1 Σg 333 346 1.041 2 2
NaH sodium hydride 1 Σ 1140 1133 0.994 3 3
Na2 Sodium diatomic 1 Σg 151 158 1.044 4 4
BeH beryllium monohydride 1 Σ 2024 1987 0.982 5 5
C2 Carbon diatomic 1 Σg 1818 1827 1.005 6 6
CN Cyano radical 1 Σ 2080 2042 0.982 7 7
N2 Nitrogen diatomic 1 Σg 2322 2330 1.003 8 8
P2 Phosphorus diatomic 1 Σg 749 775 1.035 9 9
BeO beryllium oxide 1 Σ 1391 1435 1.031 10 10
CO Carbon monoxide 1 Σ 2108 2143 1.017 11 11
HS Mercapto radical 1 Σ 2678 2599 0.970 12 12
SO Sulfur monoxide 1 Σ 1076 1138 1.058 13 13
SiS silicon monosulfide 1 Σ 715 744 1.041 14 14
HF Hydrogen fluoride 1 Σ 4085 3961 0.970 15 15
F2 Fluorine diatomic 1 Σg 824 894 1.084 16 16
SF Monosulfur monofluoride 1 Σ 806 829 1.028 17 17
HCl Hydrogen chloride 1 Σ 2974 2886 0.970 18 18
BeCl beryllium monochloride 1 Σ 818 847 1.035 19 19
ClF Chlorine monofluoride 1 Σ 755 773 1.025 20 20
NaCl Sodium Chloride 1 Σ 341 361 1.058 21 21
AlCl Aluminum monochloride 1 Σ 448 478 1.065 22 22
SCl sulfur monochloride 1 Σ 531 577 1.087 23 23
Cl2 Chlorine diatomic 1 Σg 502 554 1.104 24 24
BeH2 beryllium dihydride 2 Σu 2227 2159 0.969 25 25
    3 Πu 722 698 0.966 25 26
SiH2 silicon dihydride 1 A1 2051 1996 0.973 26 27
    2 A1 1023 999 0.976 26 28
    3 B2 2050 1993 0.972 26 29
HCN Hydrogen cyanide 1 Σ 3423 3312 0.968 27 30
    2 Σ 2082 2089 1.003 27 31
    3 Π 701 712 1.015 27 32
H2O Water 1 A1 3790 3657 0.965 28 33
    2 A1 1638 1595 0.974 28 34
    3 B2 3909 3756 0.961 28 35
CO2 Carbon dioxide 1 Σg 1318 1333 1.011 29 36
    2 Σu 2342 2349 1.003 29 37
    3 Πu 660 667 1.011 29 38
N2O Nitrous oxide 1 Σ 2712 2224 0.820 30 39
    2 Σ 1437 1285 0.894 30 40
    3 Π 389 589 1.514 30 41
H2S Hydrogen sulfide 1 A1 2702 2615 0.968 31 42
    2 A1 1193 1183 0.991 31 43
    3 B2 2725 2626 0.964 31 44
SO2 Sulfur dioxide 1 A1 1053 1151 1.093 32 45
    2 A1 476 518 1.088 32 46
    3 B2 1221 1362 1.115 32 47
BH3 boron trihydride 2 A2" 1143 1148 1.004 33 48
    3 E' 2682 2602 0.970 33 49
    4 E' 1204 1197 0.994 33 50
AlH3 aluminum trihydride 1 A1' 1923 1900 0.988 34 51
    2 A2" 718 698 0.972 34 52
    3 E' 1931 1883 0.975 34 53
    4 E' 789 783 0.993 34 54
C2H2 Acetylene 1 Σg 3486 3374 0.968 35 55
    2 Σg 1973 1974 1.001 35 56
    3 Σu 3389 3289 0.970 35 57
    4 Πg 376 612 1.630 35 58
    5 Πu 697 730 1.048 35 59
NH3 Ammonia 1 A1 3439 3337 0.970 36 60
    2 A1 1067 950 0.890 36 61
    3 E 3578 3444 0.963 36 62
    4 E 1652 1627 0.985 36 63
P4 Phosphorus tetramer 1 A1 578 601 1.038 37 64
    2 E 343 361 1.051 37 65
    3 T2 433 467 1.079 37 66
H2CO Formaldehyde 1 A1 2937 2782 0.947 38 67
    2 A1 1741 1746 1.003 38 68
    3 A1 1517 1500 0.989 38 69
    4 B1 1168 1167 0.999 38 70
    5 B2 3014 2843 0.943 38 71
    6 B2 1246 1249 1.002 38 72
H2S2 Disulfane 1 A 2667 2556 0.958 39 73
    2 A 881 882 1.001 39 74
    3 A 488 515 1.054 39 75
    4 A 419 417 0.995 39 76
    5 B 2669 2559 0.959 39 77
    6 B 875 878 1.003 39 78
BF3 Borane, trifluoro- 1 A1' 842 888 1.055 40 79
    2 A2" 711 691 0.972 40 80
    3 E' 1405 1449 1.031 40 81
    4 E' 458 480 1.048 40 82
AlF3 Aluminum trifluoride 1 A1' 665 690 1.038 41 83
    2 A2" 292 297 1.016 41 84
    3 E' 924 935 1.012 41 85
    4 E' 244 263 1.077 41 86
BCl3 Borane, trichloro- 1 A1' 469 471 1.003 42 87
    2 A2" 452 460 1.017 42 88
    3 E' 962 956 0.994 42 89
    4 E' 252 243 0.963 42 90
CH4 Methane 1 A1 3022 2917 0.965 43 91
    2 E 1537 1534 0.998 43 92
    3 T2 3151 3019 0.958 43 93
    4 T2 1321 1306 0.989 43 94
HCOOH Formic acid 1 A' 3724 3570 0.959 44 95
    2 A' 3101 2943 0.949 44 96
    3 A' 1779 1770 0.995 44 97
    4 A' 1393 1387 0.996 44 98
    5 A' 1304 1229 0.942 44 99
    6 A' 1113 1105 0.993 44 100
    7 A' 618 625 1.012 44 101
    8 A" 1036 1033 0.997 44 102
    9 A" 663 638 0.962 44 103
C2H4 Ethylene 1 Ag 3154 3026 0.960 45 104
    2 Ag 1656 1623 0.980 45 105
    3 Ag 1354 1342 0.991 45 106
    4 Au 1017 1023 1.006 45 107
    5 B1u 3136 2989 0.953 45 108
    6 B1u 1460 1444 0.989 45 109
    7 B2g 930 940 1.011 45 110
    8 B2u 3251 3105 0.955 45 111
    9 B2u 813 826 1.016 45 112
    10 B3g 3223 3086 0.958 45 113
    11 B3g 1223 1217 0.995 45 114
    12 B3u 959 949 0.990 45 115
CH3OH Methyl alcohol 1 A' 3822 3681 0.963 46 116
    2 A' 3133 3000 0.958 46 117
    3 A' 3007 2844 0.946 46 118
    4 A' 1494 1477 0.989 46 119
    5 A' 1461 1455 0.996 46 120
    6 A' 1374 1345 0.979 46 121
    7 A' 1070 1060 0.991 46 122
    8 A' 1041 1033 0.992 46 123
    9 A" 3072 2960 0.964 46 124
    10 A" 1482 1477 0.996 46 125
    11 A" 1163 1165 1.002 46 126
    12 A" 312 200 0.640 46 127
CHONH2 formamide 1 A' 3734 3564 0.954 47 128
    2 A' 3583 3439 0.960 47 129
    3 A' 2998 2854 0.952 47 130
    4 A' 1761 1754 0.996 47 131
    5 A' 1619 1577 0.974 47 132
    6 A' 1398 1390 0.994 47 133
    7 A' 1265 1258 0.995 47 134
    8 A' 1045 1046 1.001 47 135
    9 A' 554 581 1.048 47 136
    10 A" 1023 1021 0.998 47 137
    11 A" 624 603 0.967 47 138
    12 A" 33 289 8.723 47 139
C2H6 Ethane 1 A1g 3028 2954 0.975 48 140
    2 A1g 1410 1388 0.984 48 141
    3 A1g 1013 995 0.982 48 142
    4 A1u 313 289 0.924 48 143
    5 A2u 3024 2896 0.958 48 144
    6 A2u 1382 1379 0.998 48 145
    7 Eg 3091 2969 0.961 48 146
    8 Eg 1485 1468 0.989 48 147
    9 Eg 1207 1190 0.986 48 148
    10 Eu 3112 2985 0.959 48 149
    11 Eu 1487 1469 0.988 48 150
    12 Eu 810 822 1.015 48 151
C3H5 Allyl radical 1 A1 3255 3114 0.957 49 152
    2 A1 3161 3048 0.964 49 153
    4 A1 1514 1488 0.983 49 154
    5 A1 1261 1245 0.987 49 155
    6 A1 1027 1066 1.038 49 156
    7 A1 420 427 1.017 49 157
    9 A2 548 549 1.002 49 158
    10 B1 985 968 0.982 49 159
    11 B1 794 802 1.009 49 160
    12 B1 526 518 0.985 49 161
    13 B2 3252 3105 0.955 49 162
    14 B2 3145 3016 0.959 49 163
    15 B2 1506 1463 0.971 49 164
    16 B2 1406 1389 0.988 49 165
    17 B2 1186 1182 0.997 49 166
C3H6 Cyclopropane 1 A1' 3146 3038 0.966 50 167
    2 A1' 1508 1479 0.981 50 168
    3 A1' 1204 1188 0.986 50 169
    4 A1" 1138 1126 0.990 50 170
    5 A2' 1054 1070 1.015 50 171
    6 A2" 3242 3103 0.957 50 172
    7 A2" 838 854 1.019 50 173
    8 E' 3133 3025 0.965 50 174
    9 E' 1454 1438 0.989 50 175
    10 E' 1034 1029 0.995 50 176
    11 E' 879 866 0.985 50 177
    12 E" 3222 3082 0.957 50 178
    13 E" 1195 1188 0.994 50 179
    14 E" 723 739 1.022 50 180
CH2CHCH3 Propene 1 A' 3231 3090 0.956 51 181
    2 A' 3149 3013 0.957 51 182
    3 A' 3133 2991 0.955 51 183
    4 A' 3105 2954 0.951 51 184
    5 A' 3015 2871 0.952 51 185
    6 A' 1683 1650 0.980 51 186
    7 A' 1478 1470 0.995 51 187
    8 A' 1439 1420 0.987 51 188
    9 A' 1386 1378 0.994 51 189
    10 A' 1307 1297 0.993 51 190
    11 A' 1180 1171 0.993 51 191
    12 A' 929 963 1.036 51 192
    13 A' 926 920 0.993 51 193
    14 A' 414 428 1.034 51 194
    15 A" 3083 2954 0.958 51 195
    16 A" 1461 1443 0.988 51 196
    17 A" 1048 1045 0.997 51 197
    18 A" 989 991 1.002 51 198
    19 A" 912 912 1.000 51 199
    20 A" 571 578 1.012 51 200
    21 A" 199 174 0.873 51 201
CHCCH2CH3 1-Butyne 1 A' 3453 3332 0.965 52 202
    2 A' 3116 2988 0.959 52 203
    3 A' 3035     52 204
    4 A' 3032     52 205
    5 A' 2143 2116 0.988 52 206
    6 A' 1485 1470 0.990 52 207
    7 A' 1460 1446 0.990 52 208
    8 A' 1393 1385 0.994 52 209
    9 A' 1331 1322 0.994 52 210
    10 A' 1081 1070 0.990 52 211
    11 A' 1027 1008 0.981 52 212
    12 A' 840 840 1.000 52 213
    13 A' 572 634 1.108 52 214
    14 A' 472 509 1.078 52 215
    15 A' 169 197 1.163 52 216
    16 A" 3121 2988 0.957 52 217
    17 A" 3076 2939 0.956 52 218
    18 A" 1479 1462 0.989 52 219
    19 A" 1273 1261 0.991 52 220
    20 A" 1093 1090 0.997 52 221
    21 A" 773 782 1.011 52 222
    22 A" 555 630 1.135 52 223
    23 A" 302 344 1.139 52 224
    24 A" 201 213 1.060 52 225

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.

40 120 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