計算原子序1到10之原子的電子游離能,列出平均誤差與標準差,並將結果與實驗值比較

 

游離能(Ionization energy)   X → X+ + e-     I.E. = E(X+) - E(X)

X(Charge=0) H He Li Be B C N O F Ne
Multiplicity 2 1 2 1 2 3 4 3 2 1
X+(Charge = +1) H+ He+ Li+ Be+ B+ C+ N+ O+ F+ Ne+
Multiplicity 1 2 1 2 1 2 3 4 3 2

 

X
HF/6-31G(d,p) -312.65 -1791.64 -4663.26 -9140.90 -15387.81 -23645.10 -34127.38 -46927.63 -61992.96 -80618.91
HF/6-31++G(d,p) -313.00 -1791.95 -4663.38 -9142.65 -15390.40 -23646.91 -34128.08 -46929.40 -61993.33 -80624.87
HF/ cc-pVTZ -313.64 -1795.40 -4664.09 -9144.62 -15394.11 -23651.82 -34136.95 -46945.09 -62016.92 -80654.96
HF/aug-cc-pVTZ -313.64 -1795.42 -4664.09 -9144.62 -15394.17 -23651.97 -34137.25 -46945.86 -62017.31 -80655.85
MP2/6-31G(d,p) -312.65 -1791.64 -4663.26 -9157.41 -15410.83 -23645.10 -34172.29 -46987.93 -62041.63 -80713.24
MP2/6-31++G(d,p) -313.00 -1791.95 -4663.38 -9158.87 -15413.58 -23680.08 -34173.67 -46991.23 -62042.54 -80723.38
MP2/ cc-pVTZ -313.64 -1795.40 -4664.09 -9162.29 -15421.77 -23693.81 -34197.14 -47034.91 -62106.80 -80654.96
MP2/aug-cc-pVTZ -313.64 -1795.42 -4664.09 -9162.38 -15422.04 -23694.48 -34198.42 -47037.67 -62108.31 -80655.85
B3LYP/6-31G(d,p) -313.93 -1824.20 -4700.66 -9204.59 -15470.84 -23748.90 -34252.29 -47101.25 -62171.60 -80882.44
B3LYP/6-31++G(d,p) -314.80 -1825.48 -4700.80 -9206.03 -15474.11 -23752.07 -34254.35 -47105.64 -62171.81 -80896.11
B3LYP/ cc-pVTZ -315.11 -1828.88 -4701.31 -9207.10 -15476.74 -23756.62 -34263.14 -47120.86 -62194.94 -80924.79
B3LYP/aug-cc-pVTZ -315.17 -1829.00 -4701.34 -9207.10 -15476.83 -23756.92 -34263.83 -47122.31 -62195.10 -80927.57
M06-2X/6-31G(d,p) -311.66 -1819.25 -4693.65 -9199.56 -15461.66 -23738.03 -34241.80 -47083.36 -62154.05 -80859.95
M06-2X /6-31++G(d,p) -312.69 -1820.26 -4693.93 -9201.09 -15464.97 -23740.92 -34243.32 -47086.75 -62154.22 -80870.25
M06-2X / cc-pVTZ -312.58 -1822.28 -4694.20 -9202.55 -15468.25 -23746.51 -34253.72 -47103.52 -62177.65 -80902.64
M06-2X /aug-cc-pVTZ -312.63 -1822.35 -4694.29 -9202.55 -15468.37 -23746.75 -34254.15 -47104.59 -62177.93 -80904.33
  H He Li Be B C N O F Ne

X+
HF/6-31G(d,p) 0 -1251.0141 -4540.368 -8958.03 -15207.102 -23397.994 -33805.316 -46650.71078 -61993 -61992.959
HF/6-31++G(d,p) 0 -1251.5768 -4540.368 -8958.03 -15207.117 -23398.145 -33806.226 -46651.81388 -61993.3 -61993.333
HF/ cc-pVTZ 0 -1254.3419 -4540.897 -8959.1 -15208.748 -23402.808 -33816.596 -46668.11652 -62016.9 -62016.925
HF/aug-cc-pVTZ 0 -1254.342 -4540.897 -8959.11 -15208.832 -23402.942 -33816.766 -46668.35227 -62017.3 -62017.315
MP2/6-31G(d,p) 0 -1251.0141 -4540.368 -8958.03 -15207.102 -23425.599 -33839.696 -46689.46991 -62041.6 -62041.631
MP2/6-31++G(d,p) 0 -1251.5768 -4540.368 -8958.03 -15228.49 -23425.857 -33840.862 -46690.99576 -62042.5 -62042.535
MP2/ cc-pVTZ 0 -1254.3419 -4540.897 -8959.1 -15231.271 -23434.62 -33861.467 -46729.3836 -62106.8 -62106.805
MP2/aug-cc-pVTZ 0 -1254.342 -4540.897 -8959.11 -15231.425 -23434.934 -33861.959 -46730.12939 -62108.3 -62108.31
B3LYP/6-31G(d,p) 0 -1250.7253 -4571.121 -8995.92 -15273.853 -23485.994 -33914.292 -46778.69574 -62171.6 -62171.604
B3LYP/6-31++G(d,p) 0 -1251.0187 -4571.151 -8995.96 -15273.881 -23486.149 -33914.953 -46779.27983 -62171.8 -62171.809
B3LYP/ cc-pVTZ 0 -1253.7392 -4571.648 -8997.01 -15275.299 -23490.685 -33925.587 -46795.99831 -62194.9 -62194.936
B3LYP/aug-cc-pVTZ 0 -1253.7405 -4571.659 -8997.01 -15275.391 -23490.802 -33925.699 -46796.13385 -62195.1 -62195.102
M06-2X/6-31G(d,p) 0 -1249.8714 -4568.908 -8992.03 -15274.563 -23480.108 -33905.878 -46769.93615 -62154 -62154.046
M06-2X /6-31++G(d,p) 0 -1250.2013 -4568.927 -8992.07 -15274.587 -23480.269 -33906.613 -46770.65822 -62154.2 -62154.22
M06-2X / cc-pVTZ 0 -1252.8619 -4569.642 -8993.51 -15276.712 -23485.54 -33918.105 -46788.26708 -62177.6 -62177.646
M06-2X /aug-cc-pVTZ 0 -1252.8646 -4569.648 -8993.55 -15276.771 -23485.658 -33918.261 -46788.49217 -62177.9 -62177.932
  H+ He+ Li+ Be+ B+ C+ N+ O+ F+ Ne+

游離能(Ionization energy)
HF/6-31G(d,p) 312.65 540.63 122.89 182.87 180.71 247.10 322.07 276.92 359.50 453.50
HF/6-31++G(d,p) 313.00 540.37 123.01 184.61 183.28 248.76 321.86 277.59 363.32 458.69
HF/ cc-pVTZ 313.64 541.06 123.19 185.51 185.36 249.01 320.35 276.97 360.99 453.68
HF/aug-cc-pVTZ 313.64 541.08 123.20 185.51 185.34 249.03 320.48 277.50 361.45 454.13
MP2/6-31G(d,p) 312.65 540.63 122.89 199.38 203.73 219.50 332.59 298.46 387.58 487.36
MP2/6-31++G(d,p) 313.00 540.37 123.01 200.84 185.09 254.23 332.80 300.24 393.92 496.49
MP2/ cc-pVTZ 313.64 541.06 123.19 203.19 190.50 259.19 335.68 305.53 396.50 330.17
MP2/aug-cc-pVTZ 313.64 541.08 123.20 203.27 190.61 259.55 336.46 307.54 399.23 328.58
B3LYP/6-31G(d,p) 313.93 573.48 129.54 208.67 196.99 262.91 337.99 322.56 400.84 490.96
B3LYP/6-31++G(d,p) 314.80 574.46 129.65 210.07 200.23 265.92 339.39 326.36 410.09 503.72
B3LYP/ cc-pVTZ 315.11 575.14 129.66 210.09 201.44 265.93 337.55 324.86 407.21 498.50
B3LYP/aug-cc-pVTZ 315.17 575.26 129.68 210.09 201.44 266.12 338.13 326.18 409.10 501.14
M06-2X/6-31G(d,p) 311.66 569.37 124.75 207.53 187.10 257.92 335.92 313.42 397.65 488.87
M06-2X /6-31++G(d,p) 312.69 570.06 125.00 209.02 190.38 260.65 336.70 316.09 404.71 498.44
M06-2X / cc-pVTZ 312.58 569.42 124.56 209.03 191.54 260.97 335.62 315.26 404.01 496.80
M06-2X /aug-cc-pVTZ 312.63 569.48 124.64 209.00 191.59 261.09 335.89 316.09 405.05 498.21
  H He Li Be B C N O F Ne

 

實驗值 HF/6-31G(d,p) HF/6-31++G(d,p) HF/ cc-pVTZ HF/aug-cc-pVTZ
H 313.6 312.645878 313.0024289 313.635398 313.6425513
He 567.1 540.6261662 540.3710208 541.058959 541.0777847
Li 124.3 122.8888249 123.0085538 123.19392 123.1957398
Be 214.9 182.8701363 184.6144244 185.514775 185.5081862
Be 191.4 180.7095583 183.281908 185.357207 185.3385704
C 259.7 247.103452 248.7639048 249.010014 249.0280236
N 335.1 322.0657996 321.8552701 320.351067 320.4801458
O 314.1 276.9179971 277.5909383 276.971461 277.5047812
F 401.7 359.4958627 363.3229177 360.986574 361.4466643
Ne 497.2 453.4974761 458.690431 453.679077 454.1310097

 

實驗值 MP2/6-31G(d,p) MP2/6-31++G(d,p) MP2/ cc-pVTZ MP2/aug-cc-pVTZ
H 313.6 312.645878 313.0024289 313.6353977 313.6425513
He 567.1 540.6261662 540.3710208 541.0589595 541.0777847
Li 124.3 122.8888249 123.0085538 123.1939201 123.1957398
Be 214.9 199.3836135 200.835545 203.1927844 203.2730429
Be 191.4 203.7274853 185.0927122 190.4958827 190.6099012
C 259.7 219.4989953 254.2260613 259.1899124 259.5487851
N 335.1 332.593903 332.8027381 335.6775474 336.4596752
O 314.1 298.464477 300.2357481 305.5296692 307.5397704
F 401.7 387.5763481 393.9195279 396.504867 399.2325881
Ne 497.2 487.359834 496.4863949 330.1659432 328.5783442

 

實驗值 B3LYP/6-31G(d,p) B3LYP/6-31++G(d,p) B3LYP/ cc-pVTZ B3LYP/aug-cc-pVTZ
H 313.6 313.9259346 314.8001181 315.1078487 315.1727332
He 567.1 573.4754727 574.4595331 575.1413849 575.2575369
Li 124.3 129.5432494 129.6487965 129.663041 129.6767207
Be 214.9 208.6656085 210.0746184 210.0899923 210.0867293
Be 191.4 196.988849 200.2301238 201.4439155 201.4360088
C 259.7 262.9062747 265.9227129 265.9305567 266.1190606
N 335.1 337.9936222 339.3935959 337.5495965 338.1334941
O 314.1 322.5583318 326.3564585 324.8599111 326.1772418
F 401.7 400.8422127 410.0869964 407.2109321 409.0993592
Ne 497.2 490.9624915 503.7192577 498.504089 501.1392524

 

實驗值 M06-2X/6-31G(d,p) M06-2X /6-31++G(d,p) M06-2X / cc-pVTZ M06-2X /aug-cc-pVTZ
H 313.6 311.6624451 312.6891761 312.5843193 312.6293117
He 567.1 569.3742589 570.0556714 569.4191258 569.483069
Li 124.3 124.7469433 125.0005199 124.5591925 124.6380077
Be 214.9 207.5300046 209.0214064 209.0332036 209.0004476
Be 191.4 187.1014328 190.380923 191.5352267 191.5942753
C 259.7 257.9247905 260.6479935 260.9681489 261.0878149
N 335.1 335.9174443 336.7023959 335.6178712 335.8893319
O 314.1 313.4197854 316.0891481 315.257698 316.0928504
F 401.7 397.6477501 404.7086125 404.0058018 405.0511072
Ne 497.2 488.8656058 498.4447893 496.7958198 498.2073397

 

平均值 HF/6-31G(d,p) 22.0278849 MP2/6-31G(d,p) 13.89894453 B3LYP/6-31G(d,p) 4.542142167 M06-2X/6-31G(d,p) 3.198683217
  HF/6-31++G(d,p) 20.45982023 MP2/6-31++G(d,p) 7.911926916 B3LYP/6-31++G(d,p) 6.524297453 M06-2X /6-31++G(d,p) 2.025762514
  HF/ cc-pVTZ 20.9412342 MP2/ cc-pVTZ 22.16810066 B3LYP/ cc-pVTZ 5.602128318 M06-2X / cc-pVTZ 1.524972218
  HF/aug-cc-pVTZ 20.78316456 MP2/aug-cc-pVTZ 21.87462701 B3LYP/aug-cc-pVTZ 6.282467842 M06-2X /aug-cc-pVTZ 1.831403675

 

標準差 HF/6-31G(d,p) 14.75204384 MP2/6-31G(d,p) 10.98702327 B3LYP/6-31G(d,p) 2.37172358 M06-2X/6-31G(d,p) 2.518477747
  HF/6-31++G(d,p) 13.80796974 MP2/6-31++G(d,p) 7.486788549 B3LYP/6-31++G(d,p) 2.697200288 M06-2X /6-31++G(d,p) 1.43463295
  HF/ cc-pVTZ 14.94232344 MP2/ cc-pVTZ 46.61681298 B3LYP/ cc-pVTZ 2.993094336 M06-2X / cc-pVTZ 1.54790347
  HF/aug-cc-pVTZ 14.77623234 MP2/aug-cc-pVTZ 47.20694608 B3LYP/aug-cc-pVTZ 2.917930012 M06-2X /aug-cc-pVTZ 1.560965618