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III.G.1.a.

Comparison of levels of theory for Si-C


Click on an entry for a histogram of the values.
The subscript refers to how many bonds of that type have been calculated.
average calculated bond lengths (Å)
Methods with predefined basis sets
semi-empirical AM1 1.6221
9
PM3 1.6466
10
PM6 1.7955
17
composite G2 1.8241
14
G3 1.8241
14
G3B3 1.7665
18
G4 1.7747
16
CBS-Q 1.8091
14

average calculated bond lengths (Å)
Methods with standard basis sets
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pV(T+d)Z
hartree fock HF 1.7641
14
1.8579
14
1.8044
14
1.8383
13
1.8297
23
1.8232
14
1.8239
14
1.8045
14
1.8043
14
1.8016
14
1.8821
5
1.8246
18
1.8158
14
1.8055
14
1.7195
7
1.8162
14
1.8045
14
1.7196
7
1.8507
12
1.6909
2
ROHF 1.6627
2
1.8013
3
1.7411
3
1.8017
3
1.7394
3
1.7394
3
1.7433
3
1.7367
3
1.7367
3
1.7202
2
  1.7760
1
1.7528
3
1.7401
3
1.7347
3
1.7570
3
1.7418
3
1.7356
3
1.6768
1
1.6776
1
density functional LSDA 1.7790
14
1.8176
14
1.7975
14
1.8285
14
1.7979
14
1.7973
14
1.7983
14
1.7921
14
1.7924
14
1.7891
14
  1.7337
3
1.8046
14
1.7916
14
1.7482
2
1.8032
14
1.7570
8
1.7487
2
1.6720
2
1.6721
2
SVWN   1.8294
18
    1.8074
17
1.7333
3
1.7987
18
1.7280
3
1.7277
3
1.7257
3
    1.7419
3
1.7286
3
  1.7410
3
1.7283
3
     
BLYP 1.8042
14
1.8608
14
1.8265
14
1.8616
14
1.8277
14
1.8271
14
1.8287
14
1.8233
14
1.8233
14
1.8190
14
  1.7620
3
1.8228
15
1.8228
14
  1.9071
1
    1.6933
2
1.6938
2
B1B95 1.7153
11
1.7590
11
1.7474
11
1.7836
11
1.7476
11
1.7477
11
1.7950
14
1.7439
11
1.7440
11
1.7415
11
  1.7370
3
1.7557
11
1.7446
11
1.6714
5
1.7562
11
1.7455
8
1.6717
5
1.6723
2
1.6726
2
B3LYP 1.7780
14
1.8365
14
1.8023
14
1.8364
14
1.8036
14
1.8030
14
1.8043
14
1.7992
14
1.7927
13
1.7956
14
1.8771
1
1.8162
18
1.8096
14
1.7992
14
1.7091
7
1.8098
14
1.7991
14
1.7093
7
1.8491
12
1.6777
2
B3LYPultrafine         1.8035
14
            1.6889
2
1.7519
3
1.7403
3
  1.7517
3
1.8101
13
     
B3PW91 1.7663
13
1.8329
14
1.7994
14
1.8320
14
1.7998
14
1.7992
14
1.7999
14
1.7949
14
1.7886
13
1.7925
14
  1.7423
3
1.8057
14
1.7953
14
  1.8893
1
    1.6751
2
1.6753
2
mPW1PW91 1.7624
13
1.8300
14
1.7897
13
1.8291
14
1.7966
14
1.7960
14
1.7967
14
1.7918
14
1.7920
14
1.7894
14
  1.7392
3
1.8023
14
1.7923
14
  1.7805
4
1.7340
3
  1.6722
2
1.6724
2
M06-2X 1.6999
3
1.7678
3
1.7312
3
1.7703
3
1.8041
18
1.7334
3
1.7343
3
1.7304
3
1.7302
3
1.7270
3
  1.7355
3
1.7415
3
1.7316
3
  1.7420
3
1.7314
3
  1.6710
2
1.6712
2
PBEPBE 1.7892
13
1.8534
14
1.8148
13
1.8479
13
1.8204
14
1.8198
14
1.8207
14
1.8153
14
1.8155
14
1.8127
14
1.8821
1
1.7552
3
1.8260
14
1.8157
14
1.7126
5
1.7915
6
1.7960
7
1.7130
5
1.6893
2
1.6896
2
PBEPBEultrafine   1.6958
1
    1.8242
6
1.6580
1
1.6593
1
1.6547
1
      1.7005
2
1.7613
3
1.7500
3
  1.7610
3
1.7497
3
     
PBE1PBE 1.7076
3
1.7376
3
1.7376
3
1.7764
3
1.8073
18
1.7377
3
1.7379
3
1.7329
3
1.7326
3
1.7311
3
  1.7397
3
1.7454
3
1.7348
3
  1.7456
3
1.7346
3
     
HSEh1PBE 1.7086
3
1.7761
3
1.7378
3
1.7773
3
1.8174
17
1.7376
3
1.7384
3
1.7334
3
1.7331
3
1.7313
3
  1.7402
3
1.7461
3
1.7351
3
  1.7461
3
1.7349
3
  1.6734
2
1.6737
2
TPSSh   1.7359
2
1.6910
2
1.7323
2
1.7567
15
1.6872
2
1.7566
15
1.6842
2
      1.6905
2
1.6982
2
1.7538
15
  1.6992
2
1.6845
2
     
Moller Plesset perturbation MP2 1.8067
13
1.8541
14
1.8126
14
1.8554
14
1.8228
17
1.8087
14
1.8072
14
1.8039
14
1.8036
14
1.7955
13
  1.8142
18
1.8204
14
1.8095
15
1.6775
3
1.8237
14
1.7815
9
1.6792
2
1.8447
12
1.6848
2
MP2=FULL 1.8063
13
1.8537
14
1.8055
13
1.8492
13
1.8198
17
1.8057
14
1.8064
14
1.8006
14
1.7944
13
1.7885
13
  1.7494
3
1.8180
14
1.8061
16
1.6676
3
1.7423
5
1.7228
6
1.6667
2
1.8350
12
1.6722
2
ROMP2 1.7220
4
1.8002
4
1.7568
4
1.8257
4
1.7554
4
1.7550
4
1.7572
4
1.7521
4
1.7519
4
1.7110
3
  1.7303
1
1.7734
4
1.7552
4
1.7828
2
1.7797
4
1.7952
2
1.7848
2
1.7208
1
1.7224
1
MP3         1.8026
14
  1.7496
15
        1.6881
2
1.7028
2
1.6775
2
        1.6716
2
1.6724
2
MP3=FULL         1.7484
15
  1.7469
15
        1.6871
2
1.7019
2
1.6710
2
           
MP4   1.8562
12
    1.8169
13
    1.8833
1
1.7940
10
    1.7570
3
1.7696
3
1.7212
6
  1.7248
2
1.6968
2
  1.6904
2
1.6909
2
MP4=FULL   1.8112
3
    1.7506
3
      1.7450
3
      1.7677
3
1.7407
3
  1.7223
2
1.6859
2
     
B2PLYP 1.6343
2
1.7341
2
1.6867
2
1.7340
2
1.8062
17
1.6850
2
1.6869
2
1.6826
2
1.6826
2
1.6792
2
  1.6893
2
1.6978
2
1.7500
15
  1.6999
2
1.6846
2
  1.6790
2
1.6798
2
B2PLYP=FULL 1.6343
2
1.7341
2
1.6864
2
1.7340
2
1.6845
2
1.6845
2
1.6863
2
1.6822
2
1.6822
2
1.6775
2
  1.6889
2
1.6975
2
1.6821
2
  1.6993
2
1.6820
2
     
Configuration interaction CID   1.8364
13
1.7961
13
1.8373
13
1.8007
14
    1.7961
14
                       
CISD   1.8475
11
1.7963
13
1.8450
12
1.8053
13
    1.7871
13
                       
Quadratic configuration interaction QCISD 1.8855
2
1.8540
14
1.8064
13
1.8504
13
1.8063
14
1.7994
13
1.7999
13
1.8014
14
1.8078
13
1.7993
12
  1.7510
3
1.7862
10
1.7624
7
  1.7643
3
1.7437
3
  1.6853
2
1.6862
2
QCISD(T)         1.8000
12
    1.8840
1
      1.7565
3
1.7537
6
1.7258
6
  1.7452
5
1.6918
4
  1.6944
2
1.6959
2
Coupled Cluster CCD 1.8854
2
1.8451
13
1.8032
13
1.8470
13
1.8064
14
1.7995
13
1.7980
13
1.8014
14
1.8022
12
1.7996
12
  1.7485
3
1.7883
10
1.7618
8
  1.7489
6
1.7227
5
  1.6784
2
1.6792
2
CCSD         1.7915
12
    1.8820
1
      1.7512
3
1.7627
3
1.7439
3
1.6813
2
1.7647
3
1.6917
2
1.6817
2
1.6860
2
1.6869
2
CCSD=FULL         1.7446
3
            1.7498
3
1.7611
3
1.7368
3
1.6726
2
1.7138
2
1.6821
2
1.6706
2
   
CCSD(T)         1.8243
12
1.8876
1
  1.8838
1
      1.7567
3
1.7466
7
1.7256
7
1.6796
3
1.7449
6
1.7083
5
1.6905
2
1.6947
2
1.6962
2
CCSD(T)=FULL         1.7197
6
            1.7555
3
1.7670
3
1.7430
3
1.6706
4
1.7681
3
1.6910
2
1.6766
3
1.6860
2
1.6844
2

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 1.8409
13
1.8297
14
1.8412
13
1.8338
14
1.8192
13
1.8261
14
density functional B1B95 1.9153
7
1.8988
7
1.9157
2
1.8938
2
1.8941
2
1.8973
2
B3LYP 1.8425
14
1.8169
14
1.8434
14
1.8159
14
1.8319
14
1.8278
14
Moller Plesset perturbation MP2 1.8622
14
1.8258
14
1.8583
14
1.8186
14
1.8445
14
1.8474
14
For descriptions of the methods (AM1, HF, MP2, ...) and basis sets (3-21G, 3-21G*, 6-31G, ...) see the glossary in section I.C. Predefined means the basis set used is determined by the method.