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Comparison of levels of theory for N-Si


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 1.6731
5
PM3 1.6641
7
PM6 1.6886
7
composite G2 1.7022
6
G3 1.7022
6
G3B3 1.6930
7
G4 1.6705
7
CBS-Q 1.7026
6

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-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.7771
6
1.8530
7
1.7736
7
1.9066
7
1.6861
7
1.6857
7
1.6880
7
1.6821
7
1.6989
6
1.6727
7
1.6944
5
1.7477
7
1.8078
7
1.6794
7
1.6896
6
1.7850
7
1.6957
6
1.6899
6
  1.5767
1
1.7567
4
1.6800
7
ROHF   1.5889
1
1.5438
1
  1.5400
1
1.5400
1
1.5425
1
1.5370
1
        1.5537
1
1.5403
1
          1.5360
1
   
density functional LSDA 1.6175
3
1.6362
3
1.6215
3
1.6766
3
1.6138
3
1.6138
3
1.6143
3
1.6092
3
1.6092
3
1.6035
3
    1.6263
3
1.6074
3
1.6205
2
1.6284
3
1.6273
2
1.6205
2
  1.5640
1
   
BLYP 1.7373
6
1.7478
7
1.7091
7
1.7583
7
1.7036
7
1.7088
7
1.7110
7
1.7061
7
1.7264
6
1.7160
6
1.7541
4
1.7717
4
1.7264
7
1.7043
7
  1.7863
4
1.7610
4
    1.5841
1
1.7854
4
1.7610
4
B1B95 1.6886
7
1.7365
4
1.6864
7
1.7343
7
1.6844
7
1.6847
7
1.6863
7
1.6812
7
1.6819
7
1.6746
7
1.7287
4
1.7456
4
1.7025
7
1.6803
7
1.6214
2
1.7043
6
1.7046
5
1.6217
2
  1.5630
1
1.7523
1
1.7349
4
B3LYP 1.7194
6
1.7329
7
1.6943
7
1.7428
7
1.6932
7
1.6929
7
1.6951
7
1.6902
7
1.7104
6
1.6818
7
1.7384
4
1.6991
7
1.7105
7
1.6886
7
1.7020
6
1.7119
7
1.7084
6
1.7021
6
  1.5687
1
1.7696
4
1.7454
4
B3LYPultrafine   1.7764
4
    1.7124
6
1.7493
4
1.7521
4
1.7472
4
  1.7371
4
1.7384
4
1.7563
4
1.7706
4
1.7454
4
  1.7706
4
1.6922
6
    1.5688
1
1.7696
4
1.7454
4
B3PW91 1.7176
6
1.7311
7
1.6925
7
1.7401
7
1.6902
7
1.6900
7
1.6917
7
1.6869
7
1.7071
6
1.6797
7
1.7347
4
1.7523
4
1.7079
7
1.6858
7
  1.7316
5
1.7416
4
    1.5666
1
1.7660
4
1.7415
4
mPW1PW91 1.7137
6
1.7281
7
1.7080
6
1.7553
6
1.6870
7
1.6868
7
1.6885
7
1.6837
7
1.7038
6
1.6956
6
1.7315
4
1.7491
4
1.7048
7
1.6827
7
  1.7637
4
1.7383
4
    1.5639
1
1.7628
4
1.7382
4
M06-2X 1.7446
4
1.7637
4
1.6830
7
1.7761
4
1.6842
7
1.7411
4
1.7437
4
1.7389
4
1.7400
4
1.7303
4
1.6751
7
1.7475
4
1.7611
4
1.7369
4
  1.7611
4
1.7368
4
    1.5628
1
1.7601
4
1.7367
4
PBEPBE 1.7317
6
1.7606
6
1.7231
6
1.7705
6
1.7223
6
1.7221
6
1.7240
6
1.7192
6
1.7200
6
1.7113
6
1.7133
5
1.7641
4
1.7413
6
1.7179
6
1.6396
2
1.7795
4
1.7541
4
1.6398
2
  1.5808
1
1.7786
4
1.7541
4
PBEPBEultrafine   1.7853
4
    1.7579
4
1.7576
4
1.7603
4
1.7550
4
  1.7463
4
1.7471
4
1.7641
4
1.7795
4
1.7541
4
  1.7795
4
1.7541
4
    1.5809
1
1.7786
4
1.7541
4
PBE1PBE 1.7518
4
1.7408
4
1.7408
4
1.7799
4
1.6877
7
1.7436
4
1.7454
4
1.7400
4
1.7413
4
1.7320
4
1.7318
4
1.7494
4
1.7644
4
1.7387
4
  1.7642
4
1.7387
4
    1.5648
1
1.7632
4
1.7386
4
HSEh1PBE 1.7524
4
1.7292
7
1.7410
4
1.7806
4
1.6882
7
1.7433
4
1.6896
7
1.7406
4
1.7418
4
1.7320
4
1.7321
4
1.7499
4
1.7649
4
1.6837
7
  1.7647
4
1.7390
4
    1.5650
1
1.7637
4
1.7389
4
TPSSh 1.7611
4
1.7774
4
1.7470
4
1.7863
4
1.6908
7
1.7497
4
1.6921
7
1.7466
4
1.7479
4
1.6810
7
1.7381
4
1.7555
4
1.7708
4
1.6864
7
1.7393
4
1.7706
4
1.7449
4
1.7393
4
  1.5713
1
1.7697
4
1.7448
4
wB97X-D 1.7518
4
1.7685
4
1.6838
7
1.7783
4
1.6818
7
1.7418
4
1.6835
7
1.7387
4
1.6792
7
1.7300
4
1.7304
4
1.6873
7
1.6942
7
1.6777
7
1.7312
4
1.7630
4
1.6780
7
1.7189
1
  1.5606
1
1.7620
4
1.7369
4
B97D3 1.7692
4
1.7439
7
1.7533
4
1.7935
4
1.7022
7
1.7557
4
1.7037
7
1.7532
4
1.6998
7
1.7442
4
1.6902
7
1.7078
7
1.7777
4
1.6974
7
1.7460
4
1.7776
4
1.6977
7
1.7374
1
  1.5796
1
1.7767
4
1.6976
7
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-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.7201
6
1.7333
7
1.6926
7
1.7442
7
1.6886
7
1.6911
7
1.6933
7
1.6819
7
1.6854
7
1.6812
7
1.7369
4
1.6949
7
1.7096
7
1.6850
7
1.6784
7
1.7145
7
1.6869
7
1.6794
7
1.5274
1
1.5289
1
1.7755
4
1.7451
4
MP2=FULL 1.7197
6
1.7331
7
1.7163
6
1.7697
6
1.6898
7
1.6886
7
1.6908
7
1.6837
7
1.7094
6
1.6995
6
1.7314
4
1.7523
4
1.7071
7
1.7041
6
1.6690
7
1.7274
5
1.7340
4
1.6908
6
1.5235
1
1.5262
1
1.7699
4
1.7338
4
ROMP2                                       1.5959
1
   
MP3         1.7064
6
  1.6829
7
      1.7318
4
1.7499
4
1.7688
4
1.7384
4
          1.5349
1
1.7712
4
1.7305
1
MP3=FULL   1.7755
4
1.7402
4
1.7901
4
1.6801
7
1.7424
4
1.6808
7
1.7379
4
1.7380
4
1.7266
4
1.7269
4
1.7480
4
1.7652
4
1.7310
4
  1.7678
4
1.7292
4
    1.5326
1
1.7618
1
1.7192
1
MP4   1.7612
6
    1.6982
7
    1.5439
1
1.7160
6
  1.7394
4
1.7579
4
1.7766
4
1.6922
7
  1.7814
4
1.7478
4
    1.5425
1
1.7749
1
1.7393
1
MP4=FULL   1.7836
4
    1.7510
4
      1.7451
4
  1.7224
1
  1.7727
4
1.7289
1
  1.7759
4
1.7369
4
    1.5397
1
1.7704
1
1.7275
1
B2PLYP 1.7531
4
1.7758
4
1.7443
4
1.7874
4
1.6950
7
1.7476
4
1.7509
4
1.7442
4
1.7452
4
1.7364
4
1.7366
4
1.7543
4
1.7697
4
1.6867
7
  1.7714
4
1.7441
4
    1.5719
1
1.7702
4
1.7441
4
B2PLYP=FULL 1.7530
4
1.7756
4
1.7436
4
1.7872
4
1.7474
4
1.7465
4
1.7498
4
1.7437
4
1.7447
4
1.7336
4
1.7350
4
1.7536
4
1.7686
4
1.7410
4
  1.7698
4
1.7407
4
    1.5709
1
1.7684
4
1.7406
4
B2PLYP=FULLultrafine 1.7530
4
1.7756
4
1.7436
4
1.7872
4
1.6943
7
1.7465
4
1.7498
4
1.7437
4
1.7447
4
1.7336
4
1.7350
4
1.7536
4
1.7121
7
1.6885
7
  1.7698
4
1.6888
7
    1.5709
1
1.7685
4
1.7406
4
Configuration interaction CID   1.7424
6
1.7044
6
1.7579
6
1.6823
7
    1.6752
7
    1.7262
4
  1.7640
4
1.7326
4
          1.5361
1
1.7643
4
1.7243
1
CISD   1.7523
6
1.7076
6
1.7679
6
1.6868
7
    1.7002
6
    1.7267
4
  1.7647
4
1.7331
4
          1.5501
1
1.7648
4
1.7251
1
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-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.7481
7
1.7168
6
1.7787
6
1.6981
7
1.7154
6
1.6991
7
1.6905
7
1.6906
7
1.7035
6
1.7347
4
1.7536
4
1.7176
7
1.6891
7
  1.7764
4
1.7336
1
  1.5720
1
1.5747
1
1.7747
4
1.7335
1
QCISD(T)         1.7025
7
    1.7135
5
    1.7381
4
1.7494
1
1.7425
6
1.7130
6
  1.7479
6
1.7149
6
    1.5834
1
1.7787
4
1.7384
1
QCISD(T)=FULL         1.7508
4
  1.7520
4
      1.7215
1
  1.7722
4
1.7370
4
1.7153
1
1.7750
4
1.7285
1
    1.5792
1
1.7701
1
1.7265
1
Coupled Cluster CCD   1.7479
6
1.7093
6
1.7614
6
1.7107
6
1.7092
6
1.7114
6
1.6795
7
1.7029
6
1.6984
6
1.7333
4
1.7521
4
1.7288
6
1.7017
6
  1.7333
6
1.6623
3
    1.5348
1
1.7729
4
1.7317
1
CCSD         1.7160
6
1.7492
4
1.7524
4
1.7431
4
1.7431
4
1.7369
4
1.7343
4
1.7531
4
1.7723
4
1.7411
4
1.7220
1
1.7758
4
1.7333
1
    1.5727
1
1.7742
4
 
CCSD=FULL         1.7482
4
        1.7286
4
1.7292
4
1.7513
4
1.7686
4
1.7333
4
1.7107
1
1.7706
4
1.7235
1
    1.5686
1
1.7648
1
1.7214
1
CCSD(T)         1.7538
4
1.7188
5
1.7554
4
1.7124
5
1.7459
4
1.7400
4
1.7378
4
1.7567
4
1.7414
6
1.7119
6
1.7265
1
1.7469
6
1.7138
6
    1.5783
1
1.7784
4
1.7464
4
CCSD(T)=FULL         1.7175
6
          1.7328
4
1.7546
4
1.7719
4
1.7367
4
1.7150
1
1.7747
4
1.7282
1
    1.5744
1
1.7698
1
1.7262
1
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-pCVTZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 1.9347
6
1.7195
6
1.9320
6
1.7716
6
1.8978
6
1.9354
6
    1.6688
7
density functional BLYP                 1.7538
4
B1B95 1.6298
1
1.5868
1
            1.7289
4
B3LYP 1.7619
6
1.7216
6
1.7619
6
1.7225
6
1.7379
6
1.7499
6
    1.6794
7
B3LYPultrafine                 1.7385
4
B3PW91                 1.7349
4
mPW1PW91                 1.7318
4
M06-2X                 1.7313
4
PBEPBE                 1.6890
7
PBEPBEultrafine                 1.7471
4
PBE1PBE                 1.7322
4
HSEh1PBE                 1.7325
4
TPSSh                 1.7382
4
wB97X-D 1.7836
4
1.7564
4
1.7835
4
1.7554
4
1.7637
4
1.7694
4
    1.7308
4
B97D3                 1.7452
4
Moller Plesset perturbation MP2 1.7803
6
1.7258
6
1.7720
6
1.7255
6
1.7526
6
1.7594
6
    1.6770
7
MP2=FULL                 1.7337
4
MP3                 1.7337
4
MP3=FULL                 1.7295
4
MP4=FULL                 1.7368
4
B2PLYP                 1.7373
4
B2PLYP=FULL                 1.7358
4
B2PLYP=FULLultrafine                 1.7358
4
Configuration interaction CID                 1.7278
4
CISD                 1.7283
4
Quadratic configuration interaction QCISD                 1.7365
4
QCISD(T)                 1.7402
4
QCISD(T)=FULL                 1.7357
4
Coupled Cluster CCD                 1.7352
4
CCSD                 1.7361
4
CCSD=FULL                 1.7207
1
CCSD(T)                 1.7400
4
CCSD(T)=FULL                 1.7253
1
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.