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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(T)/aug-cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.973 ± 0.021 30 129 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2927 2782 0.950 1 1
    2 A1 1762 1746 0.991 1 2
    3 A1 1528 1500 0.982 1 3
    4 B1 1181 1167 0.989 1 4
    5 B2 2994 2843 0.950 1 5
    6 B2 1260 1249 0.991 1 6
CH4 Methane 1 A1 3027 2917 0.964 2 7
    2 E 1573 1534 0.975 2 8
    3 T2 3147 3019 0.959 2 9
    4 T2 1350 1306 0.967 2 10
C2H6 Ethane 1 A1g 3032 2896 0.955 3 11
    2 A1g 1428 1388 0.972 3 12
    3 A1g 1009 995 0.986 3 13
    4 A1u 307 289 0.941 3 14
    5 A2u 3030 2915 0.962 3 15
    6 A2u 1412 1370 0.970 3 16
    7 Eg 3090 2969 0.961 3 17
    8 Eg 1515 1468 0.969 3 18
    9 Eg 1226 1190 0.971 3 19
    10 Eu 3113 2974 0.955 3 20
    11 Eu 1516 1460 0.963 3 21
    12 Eu 822 822 1.000 3 22
C2H4 Ethylene 1 Ag 3153 3026 0.960 4 23
    2 Ag 1664 1623 0.975 4 24
    3 Ag 1364 1342 0.984 4 25
    4 Au 1020 1023 1.003 4 26
    5 B1u 3134 2989 0.954 4 27
    6 B1u 1471 1444 0.981 4 28
    7 B2g 929 940 1.012 4 29
    8 B2u 3241 3105 0.958 4 30
    9 B2u 817 826 1.011 4 31
    10 B3g 3214 3086 0.960 4 32
    11 B3g 1240 1217 0.982 4 33
    12 B3u 959 949 0.990 4 34
C2H2 Acetylene 1 Σg 3503 3374 0.963 5 35
    2 Σg 1992 1974 0.991 5 36
    3 Σu 3395 3289 0.969 5 37
    4 Πg 591 612 1.036 5 38
    5 Πu 747 730 0.977 5 39
C3H6 Cyclopropane 1 A1' 3151 3038 0.964 6 40
    2 A1' 1524 1479 0.970 6 41
    3 A1' 1208 1188 0.983 6 42
    4 A1" 1152 1126 0.977 6 43
    5 A2' 1077 1070 0.994 6 44
    6 A2" 3242 3103 0.957 6 45
    7 A2" 846 854 1.009 6 46
    8 E' 3140 3025 0.963 6 47
    9 E' 1474 1438 0.976 6 48
    10 E' 1047 1029 0.983 6 49
    11 E' 887 866 0.977 6 50
    12 E" 3222 3082 0.957 6 51
    13 E" 1208 1188 0.983 6 52
    14 E" 731 739 1.011 6 53
CH2CHCH3 Propene 1 A' 3222 3090 0.959 7 54
    2 A' 3142 3013 0.959 7 55
    3 A' 3130 2991 0.956 7 56
    4 A' 3107 2954 0.951 7 57
    5 A' 3023 2871 0.950 7 58
    6 A' 1688 1650 0.977 7 59
    7 A' 1504 1470 0.977 7 60
    8 A' 1451 1420 0.979 7 61
    9 A' 1411 1378 0.977 7 62
    10 A' 1317 1297 0.985 7 63
    11 A' 1190 1171 0.984 7 64
    12 A' 940 963 1.025 7 65
    13 A' 927 920 0.992 7 66
    14 A' 415 428 1.031 7 67
    15 A" 3084 2954 0.958 7 68
    16 A" 1491 1443 0.968 7 69
    17 A" 1068 1045 0.979 7 70
    18 A" 1008 991 0.983 7 71
    19 A" 920 912 0.992 7 72
    20 A" 579 578 0.997 7 73
    21 A" 199 174 0.873 7 74
CO2 Carbon dioxide 1 Σg 1332 1333 1.000 8 75
    2 Σu 2363 2349 0.994 8 76
    3 Πu 660 667 1.010 8 77
OCS Carbonyl sulfide 1 Σ 2068 2062 0.997 9 78
    2 Σ 861 859 0.998 9 79
    3 Π 518 520 1.003 9 80
CO Carbon monoxide 1 Σ 2131 2170 1.018 10 81
H2 Hydrogen diatomic 1 Σg 4402 4401 1.000 11 82
C3H5 Allyl radical 1 A1 3249 3114 0.958 12 83
    2 A1 3152 3048 0.967 12 84
    4 A1 1521 1488 0.978 12 85
    5 A1 1270 1245 0.980 12 86
    6 A1 1034 1066 1.031 12 87
    7 A1 420 427 1.017 12 88
    9 A2 542 549 1.014 12 89
    10 B1 993 968 0.975 12 90
    11 B1 794 802 1.009 12 91
    12 B1 518 518 1.000 12 92
    13 B2 3246 3105 0.957 12 93
    14 B2 3145 3016 0.959 12 94
    15 B2 1512 1463 0.968 12 95
    16 B2 1417 1389 0.980 12 96
    17 B2 1185 1182 0.998 12 97
CH Methylidyne 1 Σ 3098 3145 1.015 13 98
OH Hydroxyl radical 1 Σ 3710 3738 1.008 14 99
SO2 Sulfur dioxide 1 A1 1124 1151 1.025 15 100
    2 A1 504 518 1.028 15 101
    3 B2 1320 1362 1.032 15 102
LiH Lithium Hydride 1 Σ 1387 1405 1.013 16 103
BF3 Borane, trifluoro- 1 A1' 889 888 0.999 17 104
    2 A2" 691 691 1.000 17 105
    3 E' 1470 1449 0.986 17 106
    4 E' 476 480 1.009 17 107
HCl Hydrogen chloride 1 Σ 2990 2991 1.000 18 108
HF Hydrogen fluoride 1 Σ 4122 4138 1.004 19 109
NH3 Ammonia 1 A1 3463 3337 0.964 20 110
    2 A1 1063 950 0.893 20 111
    3 E 3592 3444 0.959 20 112
    4 E 1672 1627 0.973 20 113
N2 Nitrogen diatomic 1 Σg 2333 2359 1.011 21 114
H2O Water 1 A1 3808 3657 0.960 22 115
    2 A1 1645 1595 0.970 22 116
    3 B2 3917 3756 0.959 22 117
F2 Fluorine diatomic 1 Σg 917 917 1.000 23 118
AlF3 Aluminum trifluoride 1 A1' 687 690 1.005 24 119
    2 A2" 297 297 1.000 24 120
    3 E' 949 935 0.985 24 121
    4 E' 243 263 1.083 24 122
BeH2 beryllium dihydride 2 Σu 2231 2159 0.968 25 123
    3 Πu 709 698 0.985 25 124
NH Imidogen 1 Σ 3316 3314 0.999 26 125
SO Sulfur monoxide 1 Σ 1130 1151 1.018 27 126
    1 Σ 1074 1069 0.995 27 127
PH phosphorus monohydride 1 Σ 2374 2415 1.017 28 128
Li2 Lithium diatomic 1 Σg 345 351 1.019 29 129
Na2 Sodium diatomic 1 Σg 151 159 1.050 30 130

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.

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