return to home page Computational Chemistry Comparison and Benchmark DataBase Release 19 (April 2018) Standard Reference Database 101 National Institute of Standards and Technology
You are here: Calculated > Geometry > Calculated geometry > One type of bond

Comparison of levels of theory for Na-Na


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 PM3 3.1656
1
PM6 8.6138
3
composite G2 3.5862
3
G3 3.5862
3
G3B3 3.4201
3
G3MP2 3.6800
1
G4 3.3904
2
CBS-Q 3.5862
3

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) 6-311+G(3df,2pd) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ
hartree fock HF 2.4091
2
3.6083
3
3.3416
3
3.5816
3
3.5863
3
3.5862
3
3.5713
3
3.5931
3
3.5931
3
3.6072
3
3.1936
1
3.1937
1
3.6624
3
3.5986
3
3.6140
3
3.8041
2
3.6005
3
3.6073
3
3.6004
3
3.1936
1
3.1953
1
3.1946
1
3.1953
1
ROHF   3.7128
1
3.7092
1
3.6654
1
3.6800
1
3.6800
1
3.6815
1
3.6958
1
3.6958
1
      3.8150
1
  3.7224
1
3.7099
1
3.7135
1
3.7241
1
3.7123
1
3.7144
1
    3.1953
1
density functional LSDA 2.4321
2
3.3638
3
3.0725
3
3.3125
3
3.3072
3
3.3072
3
3.2898
3
3.2947
3
3.2947
3
3.2545
3
2.9672
1
2.9672
1
3.3440
2
  3.3003
3
3.2891
3
3.2673
3
3.2839
3
3.2825
3
3.2289
2
2.9911
1
2.9826
1
2.9819
1
BLYP 2.4647
2
3.4080
3
3.1327
3
3.4250
3
3.5476
3
3.4226
3
3.3853
3
3.4012
3
3.4013
3
3.3981
3
3.0473
1
3.0473
1
3.4295
2
  3.3959
3
3.3935
3
3.0482
1
3.3282
2
3.3404
2
3.0436
1
3.0656
1
3.0637
1
3.0625
1
B1B95 2.4352
2
  3.1823
3
3.4091
3
3.4086
3
3.4086
3
3.2699
2
3.2908
2
3.2908
2
3.2868
2
3.0618
1
3.0618
1
3.4308
2
  3.4117
3
3.4046
3
3.2716
2
3.2781
2
3.3975
3
3.0557
1
3.0739
1
3.0712
1
3.0709
1
B3LYP 2.4441
2
3.4036
3
3.1371
3
3.4031
3
3.4017
3
3.4017
3
3.3772
3
3.3850
3
3.5516
2
3.3821
3
3.0394
1
3.0391
1
3.4712
3
3.5413
3
3.3869
3
3.5498
2
3.3628
3
3.3700
3
3.3746
3
3.2975
2
3.0530
1
3.0507
1
3.0502
1
B3LYPultrafine 2.3880
1
3.3404
2
2.2697
1
3.0427
1
3.4014
3
3.3175
2
3.3180
2
3.3296
2
3.0514
1
3.0150
1
3.0393
1
3.0393
1
3.4014
2
  3.3188
2
3.3239
2
3.0400
1
3.3153
2
3.5002
3
3.0372
1
3.0523
1
3.0503
1
3.0502
1
B3PW91 2.4989
1
3.4845
3
3.2008
3
3.4411
3
3.4402
3
3.4402
3
3.4268
3
3.4375
3
3.6023
2
3.4255
3
3.0987
1
3.0987
1
3.4528
2
  3.4425
3
3.4366
3
3.0989
1
3.3715
2
3.3713
2
3.0942
1
3.1119
1
3.1085
1
3.1079
1
mPW1PW91 2.4923
1
3.4759
3
3.6330
2
3.4393
3
3.4378
3
3.4378
3
3.4253
3
3.4371
3
3.4376
3
3.4264
3
3.1008
1
3.1008
1
3.4526
2
  3.4424
3
3.6008
2
3.1003
1
3.3717
2
3.3702
2
3.0963
1
3.1115
1
3.1091
1
3.1085
1
M06-2X 2.3939
2
3.3936
2
3.1737
3
3.2347
2
3.3317
3
3.2352
2
3.2355
2
3.2297
2
3.2297
2
3.2107
2
2.9437
1
2.9437
1
3.3415
2
  3.2487
2
3.2391
2
2.9428
1
3.2451
2
3.2372
2
2.9434
1
2.9642
1
2.9558
1
2.9540
1
PBEPBE 2.5126
1
3.4311
3
3.5886
2
3.5908
2
3.4175
3
3.4175
3
3.3995
3
3.4138
3
3.4138
3
3.3978
3
3.0775
1
3.0774
1
3.4485
2
3.5459
3
3.4104
3
3.4079
3
3.3893
3
3.6292
1
3.3620
2
3.3725
3
3.0917
1
3.0902
1
3.0894
1
PBEPBEultrafine 2.3997
1
3.3859
2
2.2754
1
3.0783
1
3.3556
2
3.3557
2
3.3562
2
3.3742
2
3.0893
1
3.0438
1
3.0761
1
3.0761
1
3.4478
2
  3.3601
2
3.3673
2
3.0783
1
3.3554
2
3.3625
2
3.0740
1
3.0898
1
3.0886
1
3.0894
1
PBE1PBE 2.4355
2
  2.9799
2
3.3501
2
3.4243
3
3.3507
2
3.3513
2
3.3662
2
3.3662
2
3.3375
2
3.0871
1
3.0871
1
3.4398
2
  3.3618
2
3.3624
2
3.0877
1
3.3605
2
3.3601
2
3.0851
1
3.0965
1
3.0951
1
3.0948
1
HSEh1PBE 2.4363
2
3.4488
3
2.9782
2
3.3563
2
3.4264
3
3.3561
2
3.4099
3
3.3705
2
3.3705
2
3.3419
2
3.0912
1
3.0912
1
3.4454
2
  3.3666
2
3.4194
3
3.0923
1
3.3650
2
3.3650
2
3.0895
1
3.1012
1
3.0988
1
3.0985
1
TPSSh 2.5009
1
3.6800
1
3.6723
1
3.6381
1
3.5573
3
3.6385
1
3.5549
3
3.6723
1
3.6723
1
3.5567
3
    3.8021
1
  3.6588
1
3.5579
3
3.6534
1
3.6585
1
3.6632
1
3.6446
1
    3.1469
1
wB97X-D 2.4973
1
3.7706
1
3.5783
3
3.6348
1
3.5401
3
3.6556
1
3.5374
3
3.6588
1
3.5397
3
3.6643
1
    3.6057
3
  3.5442
3
3.5430
3
3.6680
1
3.6955
1
3.5440
3
3.6579
1
     
B97D3 2.4977
1
3.7704
3
4.0528
1
4.0608
1
3.6893
3
4.0567
1
3.7621
3
4.0857
1
3.7729
3
4.0669
1
3.6896
3
  4.1208
1
  4.0731
1
3.7710
3
  4.0746
1
3.7706
3
4.0683
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) 6-311+G(3df,2pd) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ
Moller Plesset perturbation MP2 2.4594
1
3.5658
3
3.2859
3
3.5344
3
3.5680
3
3.5217
3
3.5077
3
3.5673
3
3.5135
3
3.5284
3
3.1769
1
3.1769
1
3.6092
3
3.5789
3
3.5508
3
3.5170
3
3.5193
3
3.5430
3
3.5212
3
3.4452
2
3.1887
1
3.1777
1
3.1776
1
MP2=FULL 2.4056
2
3.5614
3
3.5218
3
3.5261
3
3.4022
2
3.4891
3
3.4743
3
3.4631
3
3.6352
2
3.3470
3
3.0541
1
3.0541
1
3.5014
2
  3.5353
3
3.3824
3
3.0793
2
3.4414
2
3.3986
3
2.5652
2
3.1510
1
3.0830
1
3.0768
1
ROMP2 2.4599
1
  3.7091
1
3.6653
1
3.6800
1
3.6800
1
3.6815
1
3.6956
1
3.6956
1
3.7001
1
    3.8149
1
  3.7223
1
3.7099
1
  3.7240
1
        3.1782
1
MP3 15.7875
1
3.2269
1
3.1831
1
3.1777
1
3.4972
3
3.1591
1
3.5555
3
3.1591
1
3.1591
1
3.1632
1
3.1738
1
3.1738
1
3.5201
2
  3.4598
2
3.4402
2
3.1717
1
3.1950
1
3.1715
1
3.1719
1
3.1816
1
3.1723
1
3.1723
1
MP3=FULL   3.7091
1
3.6946
1
3.6580
1
3.5499
3
3.6502
1
3.5479
3
3.6590
1
3.6590
1
3.5509
1
    3.8018
1
  3.7033
1
3.5914
1
  3.6942
1
3.5820
1
      3.0817
1
MP4   3.5338
3
3.1822
1
3.1760
1
3.4861
3
3.1586
1
3.1601
1
3.1596
1
3.4760
3
3.1652
1
3.1774
1
3.1774
1
3.5203
2
  3.4604
2
3.4848
3
3.1747
1
3.4602
2
3.4429
2
3.1749
1
3.1825
1
3.1755
1
3.1758
1
MP4=FULL 6.0067
1
3.4667
2
3.1704
1
3.1737
1
3.3955
2
3.1425
1
3.1432
1
3.1091
1
3.3810
2
2.9703
1
3.0531
1
3.0531
1
3.2084
1
  3.4533
2
3.3266
2
2.9584
1
3.4391
2
3.3117
2
1.9538
1
3.1515
1
3.0882
1
3.0812
1
B2PLYP 2.4279
2
3.3732
2
2.9720
2
3.3468
2
3.4248
3
3.3452
2
3.6115
1
3.3526
2
3.3526
2
3.3353
2
3.0820
1
3.0820
1
3.4299
2
  3.3597
2
3.5146
3
3.0829
1
3.3585
2
3.3518
2
3.0824
1
    3.0884
1
B2PLYP=FULL 2.4253
2
3.4280
2
2.9553
2
3.3453
2
3.4058
2
3.3380
2
3.4060
2
3.3375
2
3.3375
2
3.2809
2
    3.4241
2
  3.3578
2
3.3176
2
  3.3510
2
3.3104
2
    3.0576
1
3.0552
1
B2PLYP=FULLultrafine 2.4756
1
3.6271
1
3.6186
1
3.6028
1
3.6001
1
3.6001
1
3.6010
1
3.6054
1
3.6054
1
3.5510
1
    3.7357
1
  3.6193
1
3.5813
1
  3.6137
1
3.5741
1
       
Configuration interaction CID 2.3787
1
3.5353
3
3.5106
3
3.5010
3
3.4905
3
3.1586
1
3.1602
1
3.4841
3
3.1583
1
3.1665
1
3.1797
1
3.1797
1
3.2255
1
  3.2009
1
3.1770
1
3.1766
1
3.2002
1
3.1770
1
3.1768
1
3.1836
1
3.1776
1
3.1774
1
CISD 2.3805
1
3.7124
1
3.5185
3
3.5099
3
3.4956
3
  3.1659
1
3.4297
2
3.1646
1
3.1676
1
3.1811
1
3.1811
1
3.2424
1
  3.2048
1
3.1779
1
3.1772
1
3.2034
1
3.1778
1
3.1774
1
3.1887
1
3.1782
1
3.1779
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) 6-311+G(3df,2pd) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ
Quadratic configuration interaction QCISD 2.3805
1
3.5473
3
3.5190
3
3.5103
3
3.4960
3
3.6618
2
3.4860
3
3.4937
3
3.4936
3
3.5069
3
3.1811
1
3.1811
1
3.5285
2
  3.5293
3
3.5029
3
3.1772
1
3.4634
2
3.4445
2
3.1774
1
3.1887
1
3.1782
1
3.1779
1
QCISD(T) 2.3805
1
3.2386
1
3.1901
1
3.1893
1
3.4932
3
3.1640
1
3.1663
1
3.4296
2
3.1647
1
3.1678
1
3.1810
1
3.1810
1
3.5284
2
  3.5258
3
3.4973
3
3.1773
1
3.5224
3
3.4981
3
3.1775
1
3.1872
1
3.1776
1
3.1781
1
QCISD(T)=FULL         3.6482
1
  3.6488
1
              3.7021
1
3.5814
1
3.1796
1
3.6923
1
3.5700
1
2.8873
1
    3.0917
1
QCISD(TQ)=FULL         3.6484
1
  3.6489
1
              3.7022
1
3.5824
1
3.1819
1
3.6925
1
3.5713
1
2.8895
1
     
Coupled Cluster CCD 2.3787
1
3.5353
3
3.5106
3
3.5010
3
3.4905
3
3.4905
3
3.4817
3
3.4841
3
3.4840
3
3.5016
3
3.1793
1
3.1793
1
3.5200
2
  3.5228
3
3.4957
3
3.1766
1
3.5205
3
3.5019
3
3.1768
1
3.1836
1
3.1776
1
3.1774
1
CCSD 2.3805
1
3.2386
1
3.1902
1
3.1892
1
3.4979
3
3.1642
1
3.1659
1
3.1641
1
3.1646
1
3.4336
2
3.1811
1
3.1811
1
3.5285
2
  3.4633
2
3.4434
2
3.4448
2
3.4634
2
3.4445
2
3.4454
2
3.1887
1
3.1782
1
3.1779
1
CCSD=FULL 2.3662
1
3.2381
1
3.1807
1
3.1876
1
3.3991
2
3.1495
1
3.1503
1
3.1230
1
3.1230
1
3.2629
2
3.0699
1
3.0699
1
3.5149
2
  3.4568
2
3.3318
2
3.0762
2
3.4433
2
3.3174
2
2.5644
2
3.1615
1
  3.0958
1
CCSD(T) 2.3805
1
3.2385
1
3.1901
1
3.1894
1
3.4221
2
3.4221
2
3.4233
2
3.4294
2
3.4294
2
3.4335
2
3.1809
1
3.1810
1
3.5284
2
  3.5269
3
3.4981
3
3.5007
3
3.5234
3
3.5002
3
3.4454
2
3.1872
1
3.1776
1
3.1781
1
CCSD(T)=FULL 2.3671
1
3.2381
1
3.1809
1
3.1877
1
2.7996
2
3.1495
1
3.1503
1
3.1194
1
3.1194
1
2.9753
1
3.0655
1
3.0655
1
3.5154
2
  3.4567
2
3.3284
2
3.0732
3
3.4428
2
3.3132
2
2.4207
2
3.1614
1
3.0991
1
3.0922
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) 6-311+G(3df,2pd) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF         3.8035
3
3.7972
3
3.6419
3
3.8389
2
3.8227
2
3.5899
2
density functional LSDA         3.3949
1
3.4023
1
3.1924
1
3.1925
1
3.2951
1
2.9797
1
BLYP         3.3935
1
3.3926
1
3.1797
1
3.1738
1
3.2862
1
3.0539
1
B1B95         3.3819
1
3.3867
1
3.1739
1
3.1701
1
3.2767
1
3.0567
1
B3LYP         3.7413
3
3.7268
3
3.5503
3
3.5221
3
3.7429
2
3.2946
3
B3LYPultrafine         3.3767
1
3.3800
1
3.1681
1
3.1639
1
3.2720
1
3.0427
1
B3PW91         3.3692
1
3.3780
1
3.1706
1
3.1701
1
3.2665
1
3.0994
1
mPW1PW91         3.3741
1
3.3846
1
3.1752
1
3.1748
1
3.2721
1
3.0996
1
M06-2X         3.3870
1
3.4010
1
3.1915
1
3.1908
1
3.2882
1
2.9532
1
PBEPBE         3.3915
1
3.3977
1
3.1884
1
3.1863
1
3.2890
1
3.0793
1
PBEPBEultrafine         3.3915
1
3.3977
1
3.1884
1
3.1863
1
3.2890
1
3.0783
1
PBE1PBE         3.3798
1
3.3905
1
3.1813
1
3.1815
1
3.2793
1
3.0861
1
HSEh1PBE         3.3843
1
3.3938
1
3.1835
1
3.1833
1
3.2830
1
3.0913
1
wB97X-D         3.8170
1
3.7879
1
3.7337
1
3.6833
1
3.6538
1
3.6348
1
Moller Plesset perturbation MP2         3.7894
3
3.7500
3
3.7877
2
3.7422
2
3.7800
2
3.3972
3
MP2=FULL         3.4384
1
3.4042
1
3.2134
1
3.1849
1
3.3137
1
3.1840
1
MP3         3.4518
1
3.3961
1
3.2120
1
3.1752
1
3.3096
1
3.1777
1
MP4         3.4632
1
3.3984
1
3.2128
1
3.1749
1
3.3106
1
3.1760
1
MP4=FULL         3.4632
1
3.3984
1
3.2128
1
3.1749
1
3.3106
1
3.1737
1
B2PLYP         3.4106
1
3.3961
1
3.1903
1
3.1770
1
3.2930
1
3.0884
1
Configuration interaction CID         3.4842
1
3.3996
1
3.2139
1
3.1746
1
3.3177
1
3.1757
1
CISD         3.5028
1
3.4132
1
3.2296
1
3.1823
1
3.3334
1
3.1892
1
Quadratic configuration interaction QCISD         3.5029
1
3.4133
1
3.2296
1
3.1823
1
3.3334
1
3.1892
1
QCISD(T)         3.5033
1
3.4134
1
3.2296
1
3.1824
1
3.3334
1
3.1893
1
Coupled Cluster CCD         3.4838
1
3.3996
1
3.2139
1
3.1746
1
3.3177
1
3.1757
1
CCSD         3.5029
1
3.4133
1
3.2296
1
3.1823
1
3.3334
1
3.1892
1
CCSD=FULL         3.5029
1
3.4133
1
3.2296
1
3.1823
1
3.3334
1
3.1876
1
CCSD(T)         3.5033
1
3.4134
1
3.2296
1
3.1824
1
3.3334
1
3.1894
1
CCSD(T)=FULL         3.5033
1
3.4134
1
3.2296
1
3.1824
1
3.3334
1
3.1877
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.