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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-pVTZ
Scale factor How many Source
Molecules Vibrations
0.962 ± 0.017 27 127 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2955 2782 0.942 1 1
    2 A1 1803 1746 0.968 1 2
    3 A1 1545 1500 0.971 1 3
    4 B1 1204 1167 0.969 1 4
    5 B2 3021 2843 0.941 1 5
    6 B2 1275 1249 0.980 1 6
CH4 Methane 1 A1 3042 2917 0.959 2 7
    2 E 1584 1534 0.969 2 8
    3 T2 3158 3019 0.956 2 9
    4 T2 1363 1306 0.958 2 10
C2H6 Ethane 1 A1g 3049 2896 0.950 3 11
    2 A1g 1445 1388 0.960 3 12
    3 A1g 1021 995 0.975 3 13
    4 A1u 310 289 0.931 3 14
    5 A2u 3048 2915 0.956 3 15
    6 A2u 1427 1370 0.960 3 16
    7 Eg 3105 2969 0.956 3 17
    8 Eg 1527 1468 0.962 3 18
    9 Eg 1239 1190 0.960 3 19
    10 Eu 3128 2974 0.951 3 20
    11 Eu 1528 1460 0.955 3 21
    12 Eu 831 822 0.990 3 22
C2H4 Ethylene 1 Ag 3172 3026 0.954 4 23
    2 Ag 1694 1623 0.958 4 24
    3 Ag 1382 1342 0.971 4 25
    4 Au 1037 1023 0.987 4 26
    5 B1u 3152 2989 0.948 4 27
    6 B1u 1487 1444 0.971 4 28
    7 B2g 956 940 0.982 4 29
    8 B2u 3258 3105 0.953 4 30
    9 B2u 829 826 0.997 4 31
    10 B3g 3231 3086 0.955 4 32
    11 B3g 1253 1217 0.971 4 33
    12 B3u 979 949 0.970 4 34
C2H2 Acetylene 1 Σg 3525 3374 0.957 5 35
    2 Σg 2035 1974 0.970 5 36
    3 Σu 3413 3289 0.964 5 37
    4 Πg 632 612 0.969 5 38
    5 Πu 769 730 0.949 5 39
C3H6 Cyclopropane 1 A1' 3170 3038 0.958 6 40
    2 A1' 1545 1479 0.958 6 41
    3 A1' 1226 1188 0.969 6 42
    4 A1" 1166 1126 0.966 6 43
    5 A2' 1099 1070 0.974 6 44
    6 A2" 3259 3103 0.952 6 45
    7 A2" 857 854 0.997 6 46
    8 E' 3158 3025 0.958 6 47
    9 E' 1490 1438 0.965 6 48
    10 E' 1067 1029 0.964 6 49
    11 E' 902 866 0.960 6 50
    12 E" 3239 3082 0.952 6 51
    13 E" 1223 1188 0.971 6 52
    14 E" 743 739 0.995 6 53
CH2CHCH3 Propene 1 A' 3240 3090 0.954 7 54
    2 A' 3164 3013 0.952 7 55
    3 A' 3151 2991 0.949 7 56
    4 A' 3124 2954 0.946 7 57
    5 A' 3042 2871 0.944 7 58
    6 A' 1723 1650 0.957 7 59
    7 A' 1518 1470 0.968 7 60
    8 A' 1469 1420 0.966 7 61
    9 A' 1428 1378 0.965 7 62
    10 A' 1334 1297 0.972 7 63
    11 A' 1205 1171 0.972 7 64
    12 A' 952 963 1.011 7 65
    13 A' 938 920 0.981 7 66
    14 A' 422 428 1.015 7 67
    15 A" 3101 2954 0.952 7 68
    16 A" 1505 1443 0.959 7 69
    17 A" 1084 1045 0.964 7 70
    18 A" 1028 991 0.964 7 71
    19 A" 945 912 0.965 7 72
    20 A" 591 578 0.978 7 73
    21 A" 204 174 0.853 7 74
CO2 Carbon dioxide 1 Σg 1368 1333 0.974 8 75
    2 Σu 2393 2349 0.981 8 76
    3 Πu 682 667 0.978 8 77
CO Carbon monoxide 1 Σ 2180 2170 0.996 9 78
H2 Hydrogen diatomic 1 Σg 4403 4401 1.000 10 79
C3H5 Allyl radical 1 A1 3267 3114 0.953 11 80
    2 A1 3175 3048 0.960 11 81
    4 A1 1535 1488 0.969 11 82
    5 A1 1282 1245 0.971 11 83
    6 A1 1042 1066 1.023 11 84
    7 A1 423 427 1.010 11 85
    9 A2 547 549 1.003 11 86
    10 B1 999 968 0.969 11 87
    11 B1 802 802 1.000 11 88
    12 B1 526 518 0.984 11 89
    13 B2 3264 3105 0.951 11 90
    14 B2 3162 3016 0.954 11 91
    15 B2 1523 1463 0.961 11 92
    16 B2 1428 1389 0.973 11 93
    17 B2 1186 1182 0.997 11 94
OH Hydroxyl radical 1 Σ 3750 3738 0.997 12 95
SO2 Sulfur dioxide 1 A1 1185 1151 0.971 13 96
    2 A1 524 518 0.989 13 97
    3 B2 1375 1362 0.991 13 98
LiH Lithium Hydride 1 Σ 1386 1405 1.014 14 99
BF3 Borane, trifluoro- 1 A1' 899 888 0.988 15 100
    2 A2" 698 691 0.991 15 101
    3 E' 1485 1449 0.976 15 102
    4 E' 481 480 0.999 15 103
HCl Hydrogen chloride 1 Σ 3014 2991 0.992 16 104
HF Hydrogen fluoride 1 Σ 4156 4138 0.996 17 105
NH3 Ammonia 1 A1 3495 3337 0.955 18 106
    2 A1 1067 950 0.890 18 107
    3 E 3621 3444 0.951 18 108
    4 E 1686 1627 0.965 18 109
N2 Nitrogen diatomic 1 Σg 2404 2359 0.981 19 110
H2O Water 1 A1 3845 3657 0.951 20 111
    2 A1 1658 1595 0.962 20 112
    3 B2 3951 3756 0.951 20 113
F2 Fluorine diatomic 1 Σg 1007 917 0.911 21 114
NF3 Nitrogen trifluoride 1 A1 1078 1032 0.957 22 115
    2 A1 677 647 0.956 22 116
    3 E 982 907 0.924 22 117
    4 E 515 492 0.954 22 118
AlF3 Aluminum trifluoride 1 A1' 694 690 0.994 23 119
    2 A2" 300 297 0.991 23 120
    3 E' 958 935 0.976 23 121
    4 E' 245 263 1.074 23 122
BeH2 beryllium dihydride 2 Σu 2234 2159 0.966 24 123
    3 Πu 710 698 0.983 24 124
AlCl Aluminum monochloride 1 Σ 473 482 1.018 25 125
Li2 Lithium diatomic 1 Σg 345 351 1.019 26 126
Na2 Sodium diatomic 1 Σg 151 159 1.050 27 127

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