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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-pVDZ
Scale factor How many Source
Molecules Vibrations
0.978 ± 0.028 32 157 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2928 2782 0.950 1 1
    2 A1 1734 1746 1.007 1 2
    3 A1 1514 1500 0.991 1 3
    4 B1 1166 1167 1.001 1 4
    5 B2 3004 2843 0.946 1 5
    6 B2 1243 1249 1.005 1 6
CH4 Methane 1 A1 3017 2917 0.967 2 7
    2 E 1535 1534 1.000 2 8
    3 T2 3144 3019 0.960 2 9
    4 T2 1319 1306 0.990 2 10
C2H6 Ethane 1 A1g 3023 2896 0.958 3 11
    2 A1g 1408 1388 0.986 3 12
    3 A1g 1011 995 0.984 3 13
    4 A1u 312 289 0.926 3 14
    5 A2u 3018 2915 0.966 3 15
    6 A2u 1380 1370 0.993 3 16
    7 Eg 3085 2969 0.963 3 17
    8 Eg 1483 1468 0.990 3 18
    9 Eg 1206 1190 0.987 3 19
    10 Eu 3106 2974 0.958 3 20
    11 Eu 1484 1460 0.984 3 21
    12 Eu 809 822 1.016 3 22
C2H4 Ethylene 1 Ag 3148 3026 0.961 4 23
    2 Ag 1653 1623 0.982 4 24
    3 Ag 1352 1342 0.993 4 25
    4 Au 1016 1023 1.007 4 26
    5 B1u 3130 2989 0.955 4 27
    6 B1u 1459 1444 0.989 4 28
    7 B2g 927 940 1.014 4 29
    8 B2u 3245 3105 0.957 4 30
    9 B2u 813 826 1.016 4 31
    10 B3g 3217 3086 0.959 4 32
    11 B3g 1223 1217 0.995 4 33
    12 B3u 957 949 0.992 4 34
C2H2 Acetylene 1 Σg 3479 3374 0.970 5 35
    2 Σg 1967 1974 1.004 5 36
    3 Σu 3385 3289 0.972 5 37
    4 Πg 364 612 1.684 5 38
    5 Πu 690 730 1.058 5 39
C3H6 Cyclopropane 1 A1' 3140 3038 0.967 6 40
    2 A1' 1506 1479 0.982 6 41
    3 A1' 1201 1188 0.989 6 42
    4 A1" 1136 1126 0.991 6 43
    5 A2' 1050 1070 1.019 6 44
    6 A2" 3236 3103 0.959 6 45
    7 A2" 837 854 1.020 6 46
    8 E' 3128 3025 0.967 6 47
    9 E' 1453 1438 0.990 6 48
    10 E' 1031 1029 0.998 6 49
    11 E' 876 866 0.989 6 50
    12 E" 3216 3082 0.958 6 51
    13 E" 1193 1188 0.995 6 52
    14 E" 722 739 1.024 6 53
CH3CHClCH3 Propane, 2-chloro- 1 A' 3124 3005 0.962 7 54
    2 A' 3102 2955 0.953 7 55
    3 A' 3078 2927 0.951 7 56
    4 A' 3019 2878 0.953 7 57
    5 A' 1486 1472 0.991 7 58
    6 A' 1472 1454 0.988 7 59
    7 A' 1399 1390 0.994 7 60
    8 A' 1272 1270 0.999 7 61
    9 A' 1176 1163 0.989 7 62
    10 A' 1065 1065 1.000 7 63
    11 A' 901 888 0.985 7 64
    12 A' 621 633 1.019 7 65
    13 A' 417 418 1.001 7 66
    14 A' 334 336 1.006 7 67
    15 A' 266 253 0.950 7 68
    16 A" 3120 2997 0.961 7 69
    17 A" 3094 2985 0.965 7 70
    18 A" 3015 2947 0.977 7 71
    19 A" 1465 1472 1.004 7 72
    20 A" 1460 1454 0.996 7 73
    21 A" 1390 1377 0.991 7 74
    22 A" 1342 1334 0.994 7 75
    23 A" 1152 1123 0.975 7 76
    24 A" 943 972 1.030 7 77
    25 A" 923 936 1.014 7 78
    26 A" 321 317 0.987 7 79
    27 A" 233 276 1.184 7 80
CH2CHCH3 Propene 1 A' 3225 3090 0.958 8 81
    2 A' 3143 3013 0.959 8 82
    3 A' 3127 2991 0.956 8 83
    4 A' 3100 2954 0.953 8 84
    5 A' 3010 2871 0.954 8 85
    6 A' 1679 1650 0.983 8 86
    7 A' 1476 1470 0.996 8 87
    8 A' 1437 1420 0.988 8 88
    9 A' 1384 1378 0.996 8 89
    10 A' 1305 1297 0.994 8 90
    11 A' 1178 1171 0.994 8 91
    12 A' 928 963 1.037 8 92
    13 A' 925 920 0.995 8 93
    14 A' 414 428 1.034 8 94
    15 A" 3076 2954 0.960 8 95
    16 A" 1458 1443 0.989 8 96
    17 A" 1046 1045 0.999 8 97
    18 A" 987 991 1.004 8 98
    19 A" 911 912 1.001 8 99
    20 A" 570 578 1.015 8 100
    21 A" 198 174 0.878 8 101
CO2 Carbon dioxide 1 Σg 1307 1333 1.020 9 102
    2 Σu 2328 2349 1.009 9 103
    3 Πu 656 667 1.017 9 104
OCS Carbonyl sulfide 1 Σ 2037 2062 1.012 10 105
    2 Σ 847 859 1.014 10 106
    3 Π 508 520 1.023 10 107
CO Carbon monoxide 1 Σ 2091 2170 1.037 11 108
H2 Hydrogen diatomic 1 Σg 4344 4401 1.013 12 109
C3H5 Allyl radical 1 A1 3249 3114 0.958 13 110
    2 A1 3156 3048 0.966 13 111
    4 A1 1512 1488 0.984 13 112
    5 A1 1259 1245 0.989 13 113
    6 A1 1025 1066 1.040 13 114
    7 A1 420 427 1.017 13 115
    9 A2 546 549 1.005 13 116
    10 B1 982 968 0.986 13 117
    11 B1 790 802 1.015 13 118
    12 B1 524 518 0.988 13 119
    13 B2 3246 3105 0.957 13 120
    14 B2 3139 3016 0.961 13 121
    15 B2 1504 1463 0.972 13 122
    16 B2 1405 1389 0.989 13 123
    17 B2 1185 1182 0.997 13 124
CH Methylidyne 1 Σ 3078 3145 1.022 14 125
OH Hydroxyl radical 1 Σ 3678 3738 1.016 15 126
SO2 Sulfur dioxide 1 A1 1032 1151 1.115 16 127
    2 A1 470 518 1.101 16 128
    3 B2 1201 1362 1.134 16 129
LiH Lithium Hydride 1 Σ 1344 1405 1.046 17 130
BF3 Borane, trifluoro- 1 A1' 838 888 1.060 18 131
    2 A2" 707 691 0.977 18 132
    3 E' 1400 1449 1.035 18 133
    4 E' 456 480 1.052 18 134
HCl Hydrogen chloride 1 Σ 2970 2991 1.007 19 135
HF Hydrogen fluoride 1 Σ 4079 4138 1.015 20 136
NH3 Ammonia 1 A1 3432 3337 0.972 21 137
    2 A1 1070 950 0.888 21 138
    3 E 3570 3444 0.965 21 139
    4 E 1650 1627 0.986 21 140
N2 Nitrogen diatomic 1 Σg 2313 2359 1.020 22 141
H2O Water 1 A1 3784 3657 0.966 23 142
    2 A1 1637 1595 0.974 23 143
    3 B2 3904 3756 0.962 23 144
F2 Fluorine diatomic 1 Σg 831 917 1.104 24 145
AlF3 Aluminum trifluoride 1 A1' 665 690 1.037 25 146
    2 A2" 293 297 1.014 25 147
    3 E' 924 935 1.012 25 148
    4 E' 245 263 1.075 25 149
BeH2 beryllium dihydride 2 Σu 2229 2159 0.968 26 150
    3 Πu 724 698 0.964 26 151
Si2 Silicon diatomic 1 Σg 522 511 0.978 27 152
NH Imidogen 1 Σ 3302 3314 1.004 28 153
SO Sulfur monoxide 1 Σ 1065 1151 1.081 29 154
    1 Σ 1003 1069 1.065 29 155
PH phosphorus monohydride 1 Σ 2354 2415 1.026 30 156
Li2 Lithium diatomic 1 Σg 339 351 1.037 31 157
Na2 Sodium diatomic 1 Σg 149 159 1.067 32 158

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