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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at QCISD/aug-cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.969 ± 0.024 30 164 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2952 2782 0.942 1 1
    2 A1 1769 1746 0.987 1 2
    3 A1 1527 1500 0.982 1 3
    4 B1 1187 1167 0.983 1 4
    5 B2 3027 2843 0.939 1 5
    6 B2 1255 1249 0.995 1 6
CH4 Methane 1 A1 3030 2917 0.963 2 7
    2 E 1544 1534 0.994 2 8
    3 T2 3156 3019 0.957 2 9
    4 T2 1330 1306 0.982 2 10
C2H6 Ethane 1 A1g 3041 2896 0.952 3 11
    2 A1g 1423 1388 0.975 3 12
    3 A1g 1021 995 0.974 3 13
    4 A1u 315 289 0.917 3 14
    5 A2u 3036 2915 0.960 3 15
    6 A2u 1393 1370 0.983 3 16
    7 Eg 3100 2969 0.958 3 17
    8 Eg 1493 1468 0.983 3 18
    9 Eg 1217 1190 0.978 3 19
    10 Eu 3122 2974 0.953 3 20
    11 Eu 1495 1460 0.977 3 21
    12 Eu 816 822 1.007 3 22
C2H4 Ethylene 1 Ag 3167 3026 0.955 4 23
    2 Ag 1681 1623 0.966 4 24
    3 Ag 1370 1342 0.980 4 25
    4 Au 1032 1023 0.992 4 26
    5 B1u 3148 2989 0.949 4 27
    6 B1u 1473 1444 0.980 4 28
    7 B2g 953 940 0.986 4 29
    8 B2u 3262 3105 0.952 4 30
    9 B2u 824 826 1.003 4 31
    10 B3g 3234 3086 0.954 4 32
    11 B3g 1235 1217 0.986 4 33
    12 B3u 975 949 0.974 4 34
C2H2 Acetylene 1 Σg 3499 3374 0.964 5 35
    2 Σg 2007 1974 0.983 5 36
    3 Σu 3403 3289 0.967 5 37
    4 Πg 434 612 1.411 5 38
    5 Πu 712 730 1.025 5 39
C3H6 Cyclopropane 1 A1' 3160 3038 0.962 6 40
    2 A1' 1525 1479 0.970 6 41
    3 A1' 1218 1188 0.976 6 42
    4 A1" 1148 1126 0.981 6 43
    5 A2' 1070 1070 1.000 6 44
    6 A2" 3253 3103 0.954 6 45
    7 A2" 846 854 1.009 6 46
    8 E' 3146 3025 0.961 6 47
    9 E' 1468 1438 0.980 6 48
    10 E' 1049 1029 0.981 6 49
    11 E' 890 866 0.972 6 50
    12 E" 3233 3082 0.953 6 51
    13 E" 1206 1188 0.985 6 52
    14 E" 731 739 1.011 6 53
CH3CHClCH3 Propane, 2-chloro- 1 A' 3142 3005 0.956 7 54
    2 A' 3122 2955 0.947 7 55
    3 A' 3100 2927 0.944 7 56
    4 A' 3040 2878 0.947 7 57
    5 A' 1498 1472 0.982 7 58
    6 A' 1485 1454 0.979 7 59
    7 A' 1416 1390 0.982 7 60
    8 A' 1290 1270 0.985 7 61
    9 A' 1189 1163 0.978 7 62
    10 A' 1079 1065 0.987 7 63
    11 A' 912 888 0.973 7 64
    12 A' 632 633 1.001 7 65
    13 A' 423 418 0.988 7 66
    14 A' 339 336 0.992 7 67
    15 A' 271 253 0.933 7 68
    16 A" 3137 2997 0.955 7 69
    17 A" 3113 2985 0.959 7 70
    18 A" 3036 2947 0.971 7 71
    19 A" 1478 1472 0.996 7 72
    20 A" 1473 1454 0.987 7 73
    21 A" 1407 1377 0.979 7 74
    22 A" 1357 1334 0.983 7 75
    23 A" 1163 1123 0.965 7 76
    24 A" 955 972 1.018 7 77
    25 A" 934 936 1.003 7 78
    26 A" 327 317 0.969 7 79
    27 A" 238 276 1.160 7 80
CF2Cl2 difluorodichloromethane 1 A1 1110 1101 0.992 8 81
    2 A1 657 667 1.015 8 82
    3 A1 457 458 1.002 8 83
    4 A1 267 262 0.981 8 84
    5 A2 324 322 0.992 8 85
    6 B1 934 902 0.966 8 86
    7 B1 441 437 0.991 8 87
    8 B2 1162 1159 0.997 8 88
    9 B2 440 446 1.014 8 89
CH2CHCH3 Propene 1 A' 3244 3090 0.953 9 90
    2 A' 3164 3013 0.952 9 91
    3 A' 3148 2991 0.950 9 92
    4 A' 3118 2954 0.948 9 93
    5 A' 3030 2871 0.948 9 94
    6 A' 1711 1650 0.964 9 95
    7 A' 1488 1470 0.988 9 96
    8 A' 1453 1420 0.978 9 97
    9 A' 1399 1378 0.985 9 98
    10 A' 1321 1297 0.982 9 99
    11 A' 1190 1171 0.984 9 100
    12 A' 939 963 1.026 9 101
    13 A' 935 920 0.984 9 102
    14 A' 420 428 1.020 9 103
    15 A" 3094 2954 0.955 9 104
    16 A" 1471 1443 0.981 9 105
    17 A" 1061 1045 0.985 9 106
    18 A" 1004 991 0.987 9 107
    19 A" 935 912 0.976 9 108
    20 A" 580 578 0.997 9 109
    21 A" 199 174 0.876 9 110
CO2 Carbon dioxide 1 Σg 1338 1333 0.996 10 111
    2 Σu 2353 2349 0.998 10 112
    3 Πu 675 667 0.988 10 113
CO Carbon monoxide 1 Σ 2130 2170 1.019 11 114
H2 Hydrogen diatomic 1 Σg 4349 4401 1.012 12 115
C3H5 Allyl radical 1 A1 3266 3114 0.953 13 116
    2 A1 3176 3048 0.960 13 117
    4 A1 1522 1488 0.978 13 118
    5 A1 1268 1245 0.982 13 119
    6 A1 1032 1066 1.033 13 120
    7 A1 422 427 1.011 13 121
    9 A2 547 549 1.004 13 122
    10 B1 989 968 0.979 13 123
    11 B1 798 802 1.004 13 124
    12 B1 527 518 0.983 13 125
    13 B2 3263 3105 0.952 13 126
    14 B2 3156 3016 0.956 13 127
    15 B2 1513 1463 0.967 13 128
    16 B2 1415 1389 0.981 13 129
    17 B2 1188 1182 0.995 13 130
OH Hydroxyl radical 1 Σ 3707 3738 1.008 14 131
SO2 Sulfur dioxide 1 A1 1092 1151 1.054 15 132
    2 A1 489 518 1.059 15 133
    3 B2 1252 1362 1.088 15 134
LiH Lithium Hydride 1 Σ 1343 1405 1.046 16 135
BF3 Borane, trifluoro- 1 A1' 845 888 1.051 17 136
    2 A2" 712 691 0.971 17 137
    3 E' 1412 1449 1.026 17 138
    4 E' 460 480 1.044 17 139
HCl Hydrogen chloride 1 Σ 2988 2991 1.001 18 140
HF Hydrogen fluoride 1 Σ 4103 4138 1.009 19 141
NH3 Ammonia 1 A1 3461 3337 0.964 20 142
    2 A1 1071 950 0.887 20 143
    3 E 3596 3444 0.958 20 144
    4 E 1661 1627 0.979 20 145
N2 Nitrogen diatomic 1 Σg 2378 2359 0.992 21 146
H2O Water 1 A1 3814 3657 0.959 22 147
    2 A1 1647 1595 0.969 22 148
    3 B2 3929 3756 0.956 22 149
F2 Fluorine diatomic 1 Σg 919 917 0.998 23 150
NF3 Nitrogen trifluoride 1 A1 1037 1032 0.995 24 151
    2 A1 647 647 1.000 24 152
    3 E 937 907 0.968 24 153
    4 E 492 492 1.000 24 154
AlF3 Aluminum trifluoride 1 A1' 670 690 1.030 25 155
    2 A2" 294 297 1.009 25 156
    3 E' 929 935 1.006 25 157
    4 E' 246 263 1.068 25 158
BeH2 beryllium dihydride 2 Σu 2232 2159 0.968 26 159
    3 Πu 725 698 0.962 26 160
Si2 Silicon diatomic 1 Σg 508 511 1.005 27 161
AlCl Aluminum monochloride 1 Σ 445 482 1.082 28 162
Li2 Lithium diatomic 1 Σg 339 351 1.037 29 163
Na2 Sodium diatomic 1 Σg 149 159 1.067 30 164

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.

90
80
70
60
50
40
30
20
10
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