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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 2.9939
3
PM6 8.6138
3
composite G2 3.5862
3
G3 3.5862
3
G3B3 3.4205
3
G3MP2 3.4343
2
G4 3.4052
3
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 2.4540
3
3.6084
3
3.5919
3
3.5812
3
3.5862
3
3.5862
3
3.5713
3
3.5931
3
3.5931
3
3.6072
3
3.5418
2
3.1937
1
3.6624
3
3.6140
3
3.6004
3
3.6021
3
3.6074
3
3.6004
3
3.5457
2
3.1953
1
3.1946
1
3.1953
1
3.5499
2
3.6006
3
ROHF   3.7096
2
3.7045
2
3.6913
2
3.6985
2
3.6985
2
3.6657
2
3.6770
2
3.6770
2
  3.6503
1
  3.8020
2
3.7091
2
3.6799
2
3.6926
2
3.6936
2
3.6869
2
3.6872
2
    3.1953
1
3.6629
1
3.6585
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 2.5126
3
3.4074
3
3.1329
3
3.4250
3
3.5155
3
3.4226
3
3.3853
3
3.4010
3
3.4010
3
3.3983
3
3.2381
2
3.0473
1
3.4937
3
3.3958
3
3.3935
3
3.0482
1
3.3611
3
3.3786
3
3.0436
1
3.0656
1
3.0637
1
3.0625
1
3.1751
2
3.1868
2
B1B95 2.4801
3
3.5922
1
3.1825
3
3.4089
3
3.4084
3
3.4084
3
3.2699
2
3.2904
2
3.2904
2
3.2877
2
3.2687
2
3.0618
1
3.4911
3
3.4111
3
3.4043
3
3.2716
2
3.2776
2
3.3971
3
3.0557
1
3.0739
1
3.0712
1
3.0709
1
3.2475
2
3.2827
2
B3LYP 2.4918
3
3.4032
3
3.1374
3
3.4032
3
3.4017
3
3.4017
3
3.3773
3
3.3847
3
3.3847
3
3.3823
3
3.2505
2
3.0391
1
3.4708
3
3.3866
3
3.3807
3
3.3626
3
3.3699
3
3.3752
3
3.3454
3
3.0530
1
3.0507
1
3.0502
1
3.2234
2
3.2552
2
B3LYPultrafine 2.3880
1
3.4029
3
2.2697
1
3.0427
1
3.4015
3
3.4015
3
3.3767
3
3.3844
3
3.0514
1
3.2831
2
3.2505
2
3.0393
1
3.4711
3
3.3862
3
3.3806
3
3.0400
1
3.3694
3
3.3934
3
3.0372
1
3.0523
1
3.0503
1
3.0502
1
3.2234
2
3.2552
2
B3PW91 2.4876
3
3.4852
3
3.4546
3
3.4408
3
3.4399
3
3.4399
3
3.4264
3
3.4371
3
3.4371
3
3.4255
3
3.3172
2
3.0987
1
3.5164
3
3.4420
3
3.4361
3
3.0989
1
3.4338
3
3.4328
3
3.0942
1
3.1119
1
3.1085
1
3.1079
1
3.3307
2
3.3290
2
mPW1PW91 2.4815
3
3.4776
3
3.4430
3
3.4390
3
3.4380
3
3.4380
3
3.4254
3
3.4371
3
3.4371
3
3.4264
3
3.3203
2
3.1008
1
3.5148
3
3.4420
3
3.4352
3
3.1003
1
3.4344
3
3.4324
3
3.0963
1
3.1115
1
3.1091
1
3.1085
1
3.3320
2
3.3299
2
M06-2X 2.4442
3
3.4578
3
3.1746
3
3.3300
3
3.3321
3
3.3320
3
3.3196
3
3.2937
3
3.2937
3
3.3050
3
3.2885
3
2.9437
1
3.4204
3
3.3344
3
3.3144
3
2.9428
1
3.3220
3
3.3181
3
2.9434
1
2.9642
1
2.9558
1
2.9540
1
3.2114
2
3.2148
2
PBEPBE 2.5009
3
3.4307
3
3.1510
3
3.4198
3
3.4169
3
3.4169
3
3.3990
3
3.4132
3
3.4132
3
3.3980
3
3.2681
2
3.0774
1
3.4928
3
3.4097
3
3.4071
3
3.3893
3
3.3942
3
3.4003
3
3.3725
3
3.0917
1
3.0902
1
3.0894
1
3.2339
2
3.2367
2
PBEPBEultrafine 2.3997
1
3.4310
3
2.2754
1
3.0783
1
3.4170
3
3.4171
3
3.3994
3
3.4135
3
3.0893
1
3.2829
2
3.2680
2
3.0761
1
3.4922
3
3.4099
3
3.4078
3
3.0783
1
3.3944
3
3.4009
3
3.0740
1
3.0898
1
3.0886
1
3.0894
1
3.2339
2
3.2367
2
PBE1PBE 2.4798
3
2.9454
2
3.1785
3
3.4250
3
3.4238
3
3.4239
3
3.4100
3
3.4220
3
3.4220
3
3.4120
3
3.2986
2
3.0871
1
3.4971
3
3.4255
3
3.4190
3
3.0877
1
3.4169
3
3.4158
3
3.0851
1
3.0965
1
3.0951
1
3.0948
1
3.3091
2
3.3073
2
HSEh1PBE 2.4814
3
3.4489
3
3.1750
3
3.4280
3
3.4263
3
3.4263
3
3.4097
3
3.4219
3
3.4219
3
3.4139
3
3.2947
2
3.0912
1
3.4998
3
3.4264
3
3.4193
3
3.0923
1
3.4157
3
3.4153
3
3.0895
1
3.1012
1
3.0988
1
3.0985
1
3.2849
2
3.3017
2
TPSSh 2.4907
3
3.4956
3
3.4711
3
3.4827
3
3.4909
3
3.4819
3
3.4798
3
3.4869
3
3.4869
3
3.5428
3
3.3790
2
  3.5669
3
3.4855
3
3.4834
3
3.4697
3
3.4797
3
3.4763
3
3.4617
3
    3.1469
1
3.3881
2
3.3842
2
wB97X-D 2.4838
3
3.5806
3
3.5782
3
3.4199
3
3.5105
3
3.4253
3
3.5077
3
3.4156
3
3.5106
3
3.4191
3
3.2787
2
  3.5837
3
3.5212
3
3.5145
3
3.4138
3
3.4401
3
3.5153
3
3.4014
3
      3.3099
2
3.3044
2
B97D3 2.5053
3
3.7699
3
3.7496
3
3.7649
3
3.7608
3
3.7608
3
3.7583
3
3.7705
3
3.7705
3
3.7567
3
3.7650
3
  3.8036
3
3.7678
3
3.7696
3
3.6027
2
3.7653
3
3.7705
3
3.7496
3
      3.1697
1
3.7551
3
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 2.4564
3
3.5660
3
3.5381
3
3.5344
3
3.5640
3
3.5219
3
3.5077
3
3.5631
3
3.5135
3
3.5284
3
3.4216
2
3.1769
1
3.6092
3
3.5508
3
3.5169
3
3.5202
3
3.5430
3
3.5211
3
3.5202
3
3.1887
1
3.1777
1
3.1776
1
3.4515
2
3.4259
2
MP2=FULL 2.4480
3
3.5616
3
3.5218
3
3.5262
3
3.4893
3
3.4893
3
3.4746
3
3.4631
3
3.4631
3
3.3469
3
3.2731
2
3.0541
1
3.5880
3
3.5353
3
3.3825
3
3.0784
3
3.5124
3
3.3986
3
2.5652
2
3.1510
1
3.0830
1
3.0768
1
3.4150
2
3.2752
2
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
3.4841
3
3.1591
1
3.1591
1
3.1632
1
3.3932
2
3.1738
1
3.5850
3
3.5266
3
3.4960
3
3.1717
1
3.1950
1
3.1715
1
3.1719
1
3.1816
1
3.1723
1
3.1723
1
3.6419
1
3.6207
1
MP3=FULL   3.6972
2
3.6643
2
3.6675
2
3.4794
3
3.6256
2
3.4654
3
3.6039
2
3.6039
2
3.4920
2
3.4499
1
  3.7488
2
3.6679
2
3.4999
2
  3.6453
2
3.4798
2
      3.0817
1
3.5866
1
3.4150
1
MP4   3.5338
3
3.1822
1
3.1760
1
3.4860
3
3.1586
1
3.1601
1
3.1596
1
3.4761
3
3.1652
1
3.3782
2
3.1774
1
3.5760
3
3.5159
3
3.4848
3
3.1747
1
3.5099
3
3.4904
3
3.1749
1
3.1825
1
3.1755
1
3.1758
1
3.6097
1
3.5833
1
MP4=FULL 6.0067
1
3.5300
3
3.1704
1
3.1737
1
3.4525
3
3.1425
1
3.1432
1
3.1091
1
3.4227
3
2.9703
1
3.2283
2
3.0531
1
3.2084
1
3.5021
3
3.3396
3
2.9584
1
3.4807
3
3.3176
3
1.9538
1
3.1515
1
3.0882
1
3.0812
1
3.5544
1
3.3706
1
B2PLYP 2.4738
3
3.4393
3
3.1705
3
3.4307
3
3.4246
3
3.4247
3
3.4033
3
3.4075
3
3.4075
3
3.4156
3
3.2892
2
3.0820
1
3.5026
3
3.4255
3
3.4201
3
3.0829
1
3.4140
3
3.4062
3
3.0824
1
    3.0884
1
3.3061
2
3.2981
2
B2PLYP=FULL 2.4712
3
3.4748
3
3.1569
3
3.4280
3
3.4590
3
3.4137
3
3.4374
3
3.3901
3
3.3901
3
3.3539
3
3.2427
2
  3.4960
3
3.4214
3
3.3628
3
  3.4037
3
3.3532
3
    3.0576
1
3.0552
1
3.2951
2
3.2488
2
B2PLYP=FULLultrafine 2.4712
3
3.4377
3
3.1568
3
3.4279
3
3.4137
3
3.4136
3
3.3920
3
3.3899
3
3.3899
3
3.3534
3
3.2426
2
  3.4964
3
3.4215
3
3.3623
3
  3.4039
3
3.3527
3
        3.2948
2
3.2483
2
Configuration interaction CID 2.3787
1
3.5353
3
3.5106
3
3.5010
3
3.4905
3
3.1586
1
3.1602
1
3.4840
3
3.1583
1
3.1665
1
3.3956
2
3.1797
1
3.2255
1
3.4235
2
3.3892
2
3.1766
1
3.2002
1
3.1770
1
3.1768
1
3.1836
1
3.1776
1
3.1774
1
3.4186
2
3.3970
2
CISD 2.3805
1
3.4755
2
3.5185
3
3.5100
3
3.4956
3
  3.1659
1
3.4297
2
3.1646
1
3.1676
1
3.1816
1
3.1811
1
3.2424
1
3.2043
1
3.3980
2
3.1772
1
3.2034
1
3.1778
1
3.1774
1
3.1887
1
3.1782
1
3.1779
1
3.2028
1
3.1782
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD 2.3805
1
3.5476
3
3.5190
3
3.5105
3
3.4960
3
3.4960
3
3.4859
3
3.4937
3
3.4937
3
3.5069
3
3.4046
2
3.1811
1
3.6011
3
3.5293
3
3.5029
3
3.1772
1
3.5265
3
3.5060
3
3.1774
1
3.1887
1
3.1782
1
3.1779
1
3.4276
2
3.4032
2
QCISD(T) 2.3805
1
3.2386
1
3.1901
1
3.1893
1
3.4222
2
3.1640
1
3.1663
1
3.4296
2
3.1647
1
3.1678
1
3.1814
1
3.1810
1
3.5288
2
3.4632
2
3.4434
2
3.1773
1
3.4634
2
3.4446
2
3.1775
1
3.1872
1
3.1776
1
3.1781
1
3.2029
1
3.1782
1
QCISD(T)=FULL         3.3989
2
  3.3995
2
      3.0646
1
    3.4569
2
3.3281
2
3.0701
2
3.4427
2
3.3129
2
2.4204
2
    3.0917
1
3.1920
1
3.0715
1
QCISD(TQ) 2.3805
1
              3.1647
1
    3.1810
1
      3.1773
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
3.5351
3
3.5106
3
3.5011
3
3.4905
3
3.4904
3
3.4816
3
3.4840
3
3.4840
3
3.5016
3
3.3955
2
3.1793
1
3.5778
3
3.5228
3
3.4957
3
3.1766
1
3.5203
3
3.5019
3
3.1768
1
3.1836
1
3.1776
1
3.1774
1
3.4186
2
3.3970
2
CCSD 2.3805
1
3.2386
1
3.1902
1
3.1892
1
3.4979
3
3.4067
2
3.3919
2
3.3959
2
3.3959
2
3.5086
3
3.4070
2
3.1811
1
3.6020
3
3.5310
3
3.5040
3
3.5083
3
3.5282
3
3.5078
3
3.5081
3
3.1887
1
3.1782
1
3.1779
1
3.4301
2
3.4058
2
CCSD=FULL 2.3662
1
3.2381
1
3.1807
1
3.1876
1
3.4677
3
3.1495
1
3.1503
1
3.1230
1
3.1230
1
3.3282
3
3.2879
2
3.0699
1
3.5897
3
3.5183
3
3.3708
3
3.0800
3
3.5006
3
3.3511
3
2.5644
2
3.1615
1
  3.0958
1
3.3994
2
3.2630
2
CCSD(T) 2.3805
1
3.2385
1
3.1901
1
3.1894
1
3.4222
2
3.4222
2
3.4237
2
3.4295
2
3.4296
2
3.4334
2
3.1810
1
3.1810
1
3.5288
2
3.4634
2
3.4434
2
3.4448
2
3.4635
2
3.4446
2
3.4456
2
3.1872
1
3.1776
1
3.1781
1
3.2029
1
3.1782
1
CCSD(T)=FULL 2.3671
1
3.2381
1
3.1809
1
3.1877
1
3.0639
3
3.1495
1
3.1503
1
3.1194
1
3.1194
1
2.9753
1
3.2713
2
3.0655
1
3.5879
3
3.5141
3
3.3601
3
3.0724
3
3.4949
3
3.3392
3
2.2662
3
3.1614
1
3.0991
1
3.0922
1
3.3917
2
3.2492
2
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ 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 3.8035
3
3.7972
3
3.6419
3
3.6273
3
3.6495
3
3.5812
3
    3.6016
3
ROHF                 3.7495
1
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
    3.3212
2
B1B95 3.3819
1
3.3867
1
3.1739
1
3.1701
1
3.2767
1
3.0567
1
    3.3280
2
B3LYP 3.7413
3
3.7268
3
3.5503
3
3.5221
3
3.5860
3
3.4032
3
    3.5121
3
B3LYPultrafine 3.3767
1
3.3800
1
3.1681
1
3.1639
1
3.2720
1
3.0427
1
    3.3112
2
B3PW91 3.3692
1
3.3780
1
3.1706
1
3.1701
1
3.2665
1
3.0994
1
    3.3632
2
mPW1PW91 3.3741
1
3.3846
1
3.1752
1
3.1748
1
3.2721
1
3.0996
1
    3.3629
2
M06-2X 3.3870
1
3.4010
1
3.1915
1
3.1908
1
3.2882
1
2.9532
1
    3.2498
2
PBEPBE 3.3915
1
3.3977
1
3.1884
1
3.1863
1
3.2890
1
3.0793
1
    3.5250
3
PBEPBEultrafine 3.3915
1
3.3977
1
3.1884
1
3.1863
1
3.2890
1
3.0783
1
    3.3214
2
PBE1PBE 3.3798
1
3.3905
1
3.1813
1
3.1815
1
3.2793
1
3.0861
1
    3.3413
2
HSEh1PBE 3.3843
1
3.3938
1
3.1835
1
3.1833
1
3.2830
1
3.0913
1
    3.3426
2
TPSSh                 3.4149
2
wB97X-D 3.6704
3
3.6693
3
3.4905
3
3.4707
3
3.5152
3
3.4199
3
    3.3372
2
B97D3                 3.6283
2
Moller Plesset perturbation MP2 3.7894
3
3.7500
3
3.5963
3
3.5562
3
3.6246
3
3.5344
3
    3.5789
3
MP2=FULL 3.4384
1
3.4042
1
3.2134
1
3.1849
1
3.3137
1
3.1840
1
    3.3359
2
MP3 3.4518
1
3.3961
1
3.2120
1
3.1752
1
3.3096
1
3.1777
1
    3.6742
1
MP3=FULL                 3.5288
1
MP4 3.4632
1
3.3984
1
3.2128
1
3.1749
1
3.3106
1
3.1760
1
    3.6374
1
MP4=FULL 3.4632
1
3.3984
1
3.2128
1
3.1749
1
3.3106
1
3.1737
1
    3.4894
1
B2PLYP 3.4106
1
3.3961
1
3.1903
1
3.1770
1
3.2930
1
3.0884
1
    3.3433
2
B2PLYP=FULL                 3.3034
2
B2PLYP=FULLultrafine                 3.3031
2
Configuration interaction CID 3.4842
1
3.3996
1
3.2139
1
3.1746
1
3.3177
1
3.1757
1
    3.4245
2
CISD 3.5028
1
3.4132
1
3.2296
1
3.1823
1
3.3334
1
3.1892
1
    3.4338
2
Quadratic configuration interaction QCISD 3.5029
1
3.4133
1
3.2296
1
3.1823
1
3.3334
1
3.1892
1
    3.4349
2
QCISD(T) 3.5033
1
3.4134
1
3.2296
1
3.1824
1
3.3334
1
3.1893
1
    3.1878
1
QCISD(T)=FULL                 3.1039
1
Coupled Cluster CCD 3.4838
1
3.3996
1
3.2139
1
3.1746
1
3.3177
1
3.1757
1
    3.4244
2
CCSD 3.5029
1
3.4133
1
3.2296
1
3.1823
1
3.3334
1
3.1892
1
    3.4368
2
CCSD=FULL 3.5029
1
3.4133
1
3.2296
1
3.1823
1
3.3334
1
3.1876
1
    3.3385
2
CCSD(T) 3.5033
1
3.4134
1
3.2296
1
3.1824
1
3.3334
1
3.1894
1
    3.1878
1
CCSD(T)=FULL 3.5033
1
3.4134
1
3.2296
1
3.1824
1
3.3334
1
3.1877
1
    3.3257
2
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.