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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at MP4=FULL/aug-cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.975 ± 0.041 41 200 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1490 1360 0.913 1 1
Li2 Lithium diatomic 1 Σg 334 346 1.035 2 2
NaH sodium hydride 1 Σ 1155 1133 0.981 3 3
Na2 Sodium diatomic 1 Σg 154 158 1.022 4 4
BeH beryllium monohydride 1 Σ 2049 1987 0.970 5 5
C2 Carbon diatomic 1 Σg 1726 1827 1.058 6 6
N2 Nitrogen diatomic 1 Σg 2179 2330 1.069 7 7
P2 Phosphorus diatomic 1 Σg 707 775 1.097 8 8
OH Hydroxyl radical 1 Σ 3709 3570 0.963 9 9
BeO beryllium oxide 1 Σ 867 1435 1.655 10 10
HS Mercapto radical 1 Σ 2698 2599 0.964 11 11
SO Sulfur monoxide 1 Σ 1052 1138 1.082 12 12
HF Hydrogen fluoride 1 Σ 4060 3961 0.976 13 13
SF Monosulfur monofluoride 1 Σ 789 829 1.050 14 14
HCl Hydrogen chloride 1 Σ 2989 2886 0.965 15 15
NaCl Sodium Chloride 1 Σ 341 361 1.059 16 16
AlCl Aluminum monochloride 1 Σ 447 478 1.068 17 17
SCl sulfur monochloride 1 Σ 533 577 1.083 18 18
Cl2 Chlorine diatomic 1 Σg 508 554 1.092 19 19
BeH2 beryllium dihydride 2 Σu 2238 2159 0.965 20 20
    3 Πu 725 698 0.962 20 21
SiH2 silicon dihydride 1 A1 2066 1996 0.966 21 22
    2 A1 1031 999 0.969 21 23
    3 B2 2065 1993 0.965 21 24
HCN Hydrogen cyanide 1 Σ 3420 3312 0.968 22 25
    2 Σ 1994 2089 1.048 22 26
    3 Π 697 712 1.022 22 27
CO2 Carbon dioxide 1 Σg 1242 1333 1.073 23 28
    2 Σu 2297 2349 1.022 23 29
    3 Πu 634 667 1.052 23 30
N2O Nitrous oxide 1 Σ 2147 2224 1.036 24 31
    2 Σ 1218 1285 1.055 24 32
    3 Π 543 589 1.085 24 33
SO2 Sulfur dioxide 1 A1 932 1151 1.236 25 34
    2 A1 443 518 1.169 25 35
    3 B2 1113 1362 1.223 25 36
BH3 boron trihydride 2 A2" 1147 1148 1.000 26 37
    3 E' 2694 2602 0.966 26 38
    4 E' 1207 1197 0.992 26 39
C2H2 Acetylene 1 Σg 3492 3374 0.966 27 40
    2 Σg 1941 1974 1.017 27 41
    3 Σu 3399 3289 0.968 27 42
    4 Πg 367 612 1.669 27 43
    5 Πu 697 730 1.048 27 44
NH3 Ammonia 1 A1 3441 3337 0.970 28 45
    2 A1 1067 950 0.890 28 46
    3 E 3584 3444 0.961 28 47
    4 E 1652 1627 0.985 28 48
H2CO Formaldehyde 1 A1 2929 2782 0.950 29 49
    2 A1 1705 1746 1.024 29 50
    3 A1 1506 1500 0.996 29 51
    4 B1 1164 1167 1.002 29 52
    5 B2 3003 2843 0.947 29 53
    6 B2 1238 1249 1.009 29 54
BF3 Borane, trifluoro- 1 A1' 829 888 1.071 30 55
    2 A2" 703 691 0.983 30 56
    3 E' 1388 1449 1.044 30 57
    4 E' 453 480 1.060 30 58
AlF3 Aluminum trifluoride 1 A1' 653 690 1.057 31 59
    2 A2" 289 297 1.027 31 60
    3 E' 909 935 1.028 31 61
    4 E' 242 263 1.088 31 62
CH4 Methane 1 A1 3029 2917 0.963 32 63
    2 E 1540 1534 0.996 32 64
    3 T2 3163 3019 0.955 32 65
    4 T2 1322 1306 0.988 32 66
C2H4 Ethylene 1 Ag 3162 3026 0.957 33 67
    2 Ag 1655 1623 0.980 33 68
    3 Ag 1356 1342 0.990 33 69
    4 Au 1027 1023 0.996 33 70
    5 B1u 3143 2989 0.951 33 71
    6 B1u 1460 1444 0.989 33 72
    7 B2g 934 940 1.006 33 73
    8 B2u 3260 3105 0.952 33 74
    9 B2u 813 826 1.016 33 75
    10 B3g 3232 3086 0.955 33 76
    11 B3g 1223 1217 0.995 33 77
    12 B3u 964 949 0.985 33 78
CH3OH Methyl alcohol 1 A' 3814 3681 0.965 34 79
    2 A' 3144 3000 0.954 34 80
    3 A' 3014 2844 0.944 34 81
    4 A' 1494 1477 0.988 34 82
    5 A' 1459 1455 0.997 34 83
    6 A' 1368 1345 0.983 34 84
    7 A' 1067 1060 0.993 34 85
    8 A' 1034 1033 1.000 34 86
    9 A" 3083 2960 0.960 34 87
    10 A" 1483 1477 0.996 34 88
    11 A" 1161 1165 1.003 34 89
    12 A" 313 200 0.639 34 90
CHONH2 formamide 1 A' 3732 3564 0.955 35 91
    2 A' 3578 3439 0.961 35 92
    3 A' 2986 2854 0.956 35 93
    4 A' 1729 1754 1.015 35 94
    5 A' 1612 1577 0.978 35 95
    6 A' 1385 1390 1.004 35 96
    7 A' 1260 1258 0.999 35 97
    8 A' 1036 1046 1.009 35 98
    9 A' 549 581 1.058 35 99
    10 A" 1012 1021 1.009 35 100
    11 A" 628 603 0.961 35 101
    12 A" 87 289 3.316 35 102
CH2N4 1H-Tetrazole 1 A' 3642 3447 0.946 36 103
    2 A' 3295 3102 0.941 36 104
    3 A' 1458 1441 0.988 36 105
    4 A' 1440 1384 0.961 36 106
    5 A' 1224 1259 1.028 36 107
    6 A' 1194 1159 0.971 36 108
    7 A' 1122 1084 0.966 36 109
    8 A' 1038 1015 0.977 36 110
    9 A' 1021 1002 0.982 36 111
    10 A' 981 969 0.988 36 112
    11 A' 926 925 0.999 36 113
    12 A" 813 906 1.114 36 114
    13 A" 712 663 0.932 36 115
    14 A" 674 658 0.976 36 116
    15 A" 554 578 1.043 36 117
C2H6 Ethane 1 A1g 3035 2954 0.973 37 118
    2 A1g 1411 1388 0.984 37 119
    3 A1g 1015 995 0.981 37 120
    4 A1u 314 289 0.921 37 121
    5 A2u 3031 2896 0.955 37 122
    6 A2u 1382 1379 0.998 37 123
    7 Eg 3102 2969 0.957 37 124
    8 Eg 1487 1468 0.987 37 125
    9 Eg 1208 1190 0.985 37 126
    10 Eu 3123 2985 0.956 37 127
    11 Eu 1489 1469 0.987 37 128
    12 Eu 810 822 1.014 37 129
C3H3NO Oxazole 1 A' 3312 3170 0.957 38 130
    2 A' 3291 3144 0.955 38 131
    3 A' 3277 3141 0.959 38 132
    4 A' 1539 1537 0.999 38 133
    5 A' 1499 1504 1.003 38 134
    6 A' 1328 1324 0.997 38 135
    7 A' 1247 1252 1.004 38 136
    8 A' 1142 1139 0.997 38 137
    9 A' 1102 1086 0.985 38 138
    10 A' 1072 1078 1.005 38 139
    11 A' 1042 1046 1.003 38 140
    12 A' 893 899 1.007 38 141
    13 A' 888 854 0.961 38 142
    14 A" 828 907 1.096 38 143
    15 A" 806 830 1.030 38 144
    16 A" 722 750 1.038 38 145
    17 A" 644 647 1.005 38 146
    18 A" 601 607 1.010 38 147
C3H6 Cyclopropane 1 A1' 3152 3038 0.964 39 148
    2 A1' 1507 1479 0.981 39 149
    3 A1' 1206 1188 0.985 39 150
    4 A1" 1139 1126 0.989 39 151
    5 A2' 1053 1070 1.017 39 152
    6 A2" 3251 3103 0.954 39 153
    7 A2" 839 854 1.018 39 154
    8 E' 3140 3025 0.963 39 155
    9 E' 1455 1438 0.988 39 156
    10 E' 1032 1029 0.997 39 157
    11 E' 880 866 0.984 39 158
    12 E" 3231 3082 0.954 39 159
    13 E" 1195 1188 0.994 39 160
    14 E" 723 739 1.023 39 161
CH2CHCH3 Propene 1 A' 3240 3090 0.954 40 162
    2 A' 3155 3013 0.955 40 163
    3 A' 3139 2991 0.953 40 164
    4 A' 3113 2954 0.949 40 165
    5 A' 3021 2871 0.950 40 166
    6 A' 1681 1650 0.982 40 167
    7 A' 1479 1470 0.994 40 168
    8 A' 1439 1420 0.987 40 169
    9 A' 1385 1378 0.995 40 170
    10 A' 1307 1297 0.992 40 171
    11 A' 1180 1171 0.993 40 172
    12 A' 929 963 1.036 40 173
    13 A' 927 920 0.992 40 174
    14 A' 414 428 1.034 40 175
    15 A" 3092 2954 0.955 40 176
    16 A" 1462 1443 0.987 40 177
    17 A" 1049 1045 0.996 40 178
    18 A" 995 991 0.996 40 179
    19 A" 915 912 0.997 40 180
    20 A" 573 578 1.008 40 181
    21 A" 201 174 0.864 40 182

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 90 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 70 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 50 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 30 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 10 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