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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at MP4/cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.967 ± 0.031 27 150 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2914 2782 0.955 1 1
    2 A1 1763 1746 0.990 1 2
    3 A1 1527 1500 0.983 1 3
    4 B1 1177 1167 0.992 1 4
    5 B2 2971 2843 0.957 1 5
    6 B2 1260 1249 0.991 1 6
CH4 Methane 1 A1 3050 2917 0.956 2 7
    2 E 1553 1534 0.988 2 8
    3 T2 3189 3019 0.947 2 9
    4 T2 1335 1306 0.978 2 10
C2H6 Ethane 1 A1g 3055 2896 0.948 3 11
    2 A1g 1427 1388 0.973 3 12
    3 A1g 1027 995 0.968 3 13
    4 A1u 326 289 0.886 3 14
    5 A2u 3050 2915 0.956 3 15
    6 A2u 1395 1370 0.982 3 16
    7 Eg 3127 2969 0.950 3 17
    8 Eg 1495 1468 0.982 3 18
    9 Eg 1218 1190 0.977 3 19
    10 Eu 3148 2974 0.945 3 20
    11 Eu 1498 1460 0.975 3 21
    12 Eu 817 822 1.006 3 22
C2H4 Ethylene 1 Ag 3172 3026 0.954 4 23
    2 Ag 1671 1623 0.971 4 24
    3 Ag 1360 1342 0.987 4 25
    4 Au 1042 1023 0.982 4 26
    5 B1u 3153 2989 0.948 4 27
    6 B1u 1461 1444 0.988 4 28
    7 B2g 914 940 1.028 4 29
    8 B2u 3270 3105 0.949 4 30
    9 B2u 818 826 1.010 4 31
    10 B3g 3244 3086 0.951 4 32
    11 B3g 1229 1217 0.990 4 33
    12 B3u 955 949 0.994 4 34
C2H2 Acetylene 1 Σg 3507 3374 0.962 5 35
    2 Σg 1956 1974 1.009 5 36
    3 Σu 3419 3289 0.962 5 37
    4 Πg 523 612 1.171 5 38
    5 Πu 737 730 0.990 5 39
C3H6 Cyclopropane 1 A1' 3163 3038 0.960 6 40
    2 A1' 1520 1479 0.973 6 41
    3 A1' 1219 1188 0.974 6 42
    4 A1" 1151 1126 0.978 6 43
    5 A2' 1072 1070 0.998 6 44
    6 A2" 3262 3103 0.951 6 45
    7 A2" 849 854 1.006 6 46
    8 E' 3151 3025 0.960 6 47
    9 E' 1459 1438 0.986 6 48
    10 E' 1060 1029 0.971 6 49
    11 E' 897 866 0.965 6 50
    12 E" 3242 3082 0.951 6 51
    13 E" 1205 1188 0.986 6 52
    14 E" 730 739 1.012 6 53
CH3CHClCH3 Propane, 2-chloro- 1 A' 3162 3005 0.950 7 54
    2 A' 3144 2955 0.940 7 55
    3 A' 3095 2927 0.946 7 56
    4 A' 3053 2878 0.943 7 57
    5 A' 1496 1472 0.984 7 58
    6 A' 1483 1454 0.981 7 59
    7 A' 1411 1390 0.985 7 60
    8 A' 1289 1270 0.986 7 61
    9 A' 1186 1163 0.980 7 62
    10 A' 1078 1065 0.988 7 63
    11 A' 915 888 0.971 7 64
    12 A' 645 633 0.982 7 65
    13 A' 420 418 0.995 7 66
    14 A' 337 336 0.996 7 67
    15 A' 279 253 0.907 7 68
    16 A" 3159 2997 0.949 7 69
    17 A" 3138 2985 0.951 7 70
    18 A" 3050 2947 0.966 7 71
    19 A" 1476 1472 0.997 7 72
    20 A" 1472 1454 0.988 7 73
    21 A" 1402 1377 0.982 7 74
    22 A" 1354 1334 0.985 7 75
    23 A" 1161 1123 0.968 7 76
    24 A" 953 972 1.019 7 77
    25 A" 931 936 1.006 7 78
    26 A" 323 317 0.981 7 79
    27 A" 247 276 1.117 7 80
CH2CHCH3 Propene 1 A' 3253 3090 0.950 8 81
    2 A' 3164 3013 0.952 8 82
    3 A' 3151 2991 0.949 8 83
    4 A' 3138 2954 0.941 8 84
    5 A' 3042 2871 0.944 8 85
    6 A' 1698 1650 0.972 8 86
    7 A' 1485 1470 0.990 8 87
    8 A' 1445 1420 0.983 8 88
    9 A' 1397 1378 0.986 8 89
    10 A' 1308 1297 0.992 8 90
    11 A' 1185 1171 0.988 8 91
    12 A' 937 963 1.028 8 92
    13 A' 933 920 0.986 8 93
    14 A' 416 428 1.030 8 94
    15 A" 3117 2954 0.948 8 95
    16 A" 1472 1443 0.981 8 96
    17 A" 1057 1045 0.989 8 97
    18 A" 1008 991 0.983 8 98
    19 A" 906 912 1.006 8 99
    20 A" 575 578 1.005 8 100
    21 A" 200 174 0.868 8 101
CO2 Carbon dioxide 1 Σg 1259 1333 1.059 9 102
    2 Σu 2352 2349 0.999 9 103
    3 Πu 626 667 1.065 9 104
CO Carbon monoxide 1 Σ 1992 2170 1.089 10 105
H2 Hydrogen diatomic 1 Σg 4417 4401 0.996 11 106
C3H5 Allyl radical 1 A1 3285 3114 0.948 12 107
    2 A1 3183 3048 0.958 12 108
    4 A1 1533 1488 0.971 12 109
    5 A1 1289 1245 0.966 12 110
    6 A1 1052 1066 1.013 12 111
    7 A1 427 427 0.999 12 112
    9 A2 583 549 0.942 12 113
    10 B1 1043 968 0.929 12 114
    11 B1 808 802 0.992 12 115
    12 B1 551 518 0.941 12 116
    13 B2 3282 3105 0.946 12 117
    14 B2 3170 3016 0.951 12 118
    15 B2 1500 1463 0.975 12 119
    16 B2 1409 1389 0.986 12 120
    17 B2 1154 1182 1.025 12 121
CS carbon monosulfide 1 Σ 1143 1285 1.124 13 122
OH Hydroxyl radical 1 Σ 3736 3738 1.000 14 123
SO2 Sulfur dioxide 1 A1 938 1151 1.227 15 124
    2 A1 458 518 1.130 15 125
    3 B2 1145 1362 1.189 15 126
LiH Lithium Hydride 1 Σ 1385 1405 1.015 16 127
BF3 Borane, trifluoro- 1 A1' 858 888 1.035 17 128
    2 A2" 706 691 0.979 17 129
    3 E' 1459 1449 0.993 17 130
    4 E' 479 480 1.003 17 131
HCl Hydrogen chloride 1 Σ 3036 2991 0.985 18 132
HF Hydrogen fluoride 1 Σ 4161 4138 0.995 19 133
NH3 Ammonia 1 A1 3446 3337 0.968 20 134
    2 A1 1179 950 0.806 20 135
    3 E 3576 3444 0.963 20 136
    4 E 1688 1627 0.964 20 137
N2 Nitrogen diatomic 1 Σg 2198 2359 1.073 21 138
H2O Water 1 A1 3832 3657 0.954 22 139
    2 A1 1689 1595 0.944 22 140
    3 B2 3939 3756 0.953 22 141
F2 Fluorine diatomic 1 Σg 817 917 1.123 23 142
AlF3 Aluminum trifluoride 1 A1' 665 690 1.038 24 143
    2 A2" 292 297 1.016 24 144
    3 E' 938 935 0.996 24 145
    4 E' 233 263 1.128 24 146
BeH2 beryllium dihydride 2 Σu 2261 2159 0.955 25 147
    3 Πu 727 698 0.960 25 148
Li2 Lithium diatomic 1 Σg 341 351 1.031 26 149
Na2 Sodium diatomic 1 Σg 153 159 1.039 27 150

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.

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