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III.G.1.a.

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 PM6 6.4604
4
composite G2 2.6897
4
G3 2.6897
4
G3B3 2.5510
4
G4 2.2603
3
CBS-Q 2.6897
4

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
hartree fock HF 1.1794
2
2.7062
4
2.5062
4
2.6862
4
2.9378
6
2.6897
4
2.6785
4
2.6948
4
2.6948
4
2.7054
4
3.1936
1
3.1937
1
2.7468
4
2.7105
4
2.5361
3
2.7004
4
2.7055
4
2.7002
4
2.3024
3
3.1953
1
3.1946
1
density functional LSDA 1.1871
2
2.5228
4
2.3044
4
2.4843
4
2.4804
4
2.4804
4
2.4673
4
2.4710
4
2.4710
4
2.4408
4
2.9672
1
2.9672
1
1.5074
2
2.4753
4
2.4668
4
3.2671
3
2.4629
4
2.4619
4
3.2288
2
2.9911
1
2.9826
1
SVWN 2.3742
1
2.5224
4
2.1775
1
2.9797
1
2.4804
4
1.4850
2
2.4674
4
1.4913
2
1.4913
2
1.4496
2
2.9672
1
2.9672
1
3.0147
1
1.4890
2
1.4857
2
2.9666
1
1.4852
2
1.4836
2
2.9640
1
2.9911
1
2.9826
1
BLYP 1.2032
2
2.5560
4
2.3495
4
2.5688
4
2.5669
4
2.5669
4
2.5390
4
2.5509
4
2.5510
4
2.5486
4
3.0473
1
3.0473
1
1.5431
2
2.5470
4
2.5451
4
3.0482
1
3.0468
1
3.0465
1
3.0436
1
3.0656
1
3.0637
1
B1B95 1.1897
2
2.5900
4
2.3873
4
2.5568
4
2.5564
4
2.5564
4
2.1799
3
3.2908
2
3.2908
2
2.1912
3
3.0618
1
3.0618
1
1.5483
2
2.5585
4
2.5535
4
3.2716
2
2.1854
3
2.5483
4
3.0557
1
3.0739
1
3.0712
1
B3LYP 1.1940
2
2.5527
4
2.3529
4
2.5524
4
2.5512
4
2.5512
4
2.5329
4
2.5387
4
2.3678
3
2.5366
4
3.0394
1
3.0391
1
2.6034
4
2.5402
4
2.3665
3
2.5221
4
2.5275
4
2.5309
4
2.1984
3
3.0530
1
3.0507
1
B3LYPultrafine 2.3880
1
3.0717
1
2.2697
1
3.0427
1
2.5511
4
3.0381
1
3.0377
1
3.0514
1
3.0514
1
3.0150
1
3.0393
1
3.0393
1
3.0710
1
3.0435
1
3.0426
1
3.0400
1
3.0407
1
2.6252
4
3.0372
1
3.0523
1
3.0503
1
B3PW91   2.6134
4
2.4006
4
2.5808
4
2.5802
4
2.5802
4
2.5701
4
2.5782
4
2.4015
3
2.5691
4
3.0987
1
3.0987
1
1.5657
2
2.5818
4
2.5774
4
3.0989
1
3.1068
1
3.1033
1
3.0942
1
3.1119
1
3.1085
1
mPW1PW91   2.6069
4
2.4220
3
2.5795
4
2.5784
4
2.5784
4
2.5690
4
2.5778
4
2.5782
4
2.5698
4
3.1008
1
3.1008
1
1.5658
2
2.5818
4
2.4005
3
3.1003
1
1.5536
2
1.5521
2
3.0963
1
3.1115
1
3.1091
1
M06-2X 1.1791
2
1.5474
2
1.1516
2
1.4766
2
2.4987
4
1.4740
2
1.4739
2
1.4759
2
1.4759
2
1.4631
2
2.9437
1
2.9437
1
1.4941
2
1.4819
2
1.4756
2
2.9428
1
1.4800
2
1.4741
2
2.9434
1
2.9642
1
2.9558
1
PBEPBE   2.5733
4
2.3924
3
2.3939
3
2.5631
4
2.5631
4
2.5497
4
2.5604
4
2.5604
4
2.5484
4
3.0775
1
3.0774
1
1.5561
2
2.5578
4
2.5559
4
3.3893
3
  1.5398
2
3.3726
3
3.0917
1
3.0902
1
PBEPBEultrafine 2.3997
1
3.1155
1
2.2754
1
3.0783
1
3.0746
1
3.0747
1
3.0743
1
3.0893
1
3.0893
1
3.0438
1
3.0761
1
3.0761
1
3.1116
1
3.0838
1
3.0813
1
3.0783
1
3.0800
1
3.0780
1
3.0740
1
3.0898
1
3.0886
1
PBE1PBE 1.1905
2
1.5641
2
1.1575
2
1.5430
2
2.5682
4
1.5420
2
1.5419
2
1.5479
2
1.5479
2
1.5308
2
3.0871
1
3.0871
1
1.5578
2
1.5467
2
1.5452
2
3.0877
1
1.5459
2
1.5446
2
3.0851
1
3.0965
1
3.0951
1
HSEh1PBE 1.1907
2
1.5645
2
1.1548
2
1.5457
2
2.5698
4
1.5446
2
1.5445
2
1.5501
2
1.5501
2
1.5328
2
3.0912
1
3.0912
1
1.5604
2
1.5493
2
1.5477
2
3.0923
1
1.5483
2
1.5470
2
3.0895
1
3.1012
1
3.0988
1
TPSSh         2.6680
4
  2.6662
4
              2.6685
4
           
Moller Plesset perturbation MP2   2.6743
4
2.4644
4
2.6508
4
2.6413
4
2.6413
4
2.6308
4
2.6351
4
2.6351
4
2.6463
4
3.1769
1
3.1769
1
2.7069
4
2.6631
4
2.4581
3
2.6395
4
2.6572
4
2.6407
4
1.5885
2
3.1887
1
3.1777
1
MP2=FULL 1.1802
2
2.6710
4
2.6414
4
2.6446
4
2.6170
4
2.6168
4
2.6058
4
2.5973
4
2.4235
3
2.5103
4
3.0541
1
3.0541
1
1.6021
2
2.6515
4
2.5368
4
1.4827
2
1.5942
2
1.5318
2
1.1183
2
3.1510
1
3.0830
1
MP3 15.7875
1
3.2269
1
3.1831
1
3.1777
1
2.2705
3
3.1591
1
2.3289
3
3.1591
1
3.1591
1
3.1632
1
3.1738
1
3.1738
1
3.2256
1
3.1978
1
3.1714
1
3.1717
1
3.1950
1
3.1715
1
3.1719
1
3.1816
1
3.1723
1
MP3=FULL         2.6624
4
  2.6610
4
                           
MP4   2.6504
4
3.1822
1
3.1760
1
2.6146
4
3.1586
1
3.1601
1
3.1596
1
2.6070
4
3.1652
1
3.1774
1
3.1774
1
3.2263
1
3.1990
1
2.6136
4
3.1747
1
3.1971
1
3.1746
1
3.1749
1
3.1825
1
3.1755
1
MP4=FULL 6.0067
1
3.2246
1
3.1704
1
3.1737
1
3.1425
1
3.1425
1
3.1432
1
3.1091
1
3.1091
1
2.9703
1
3.0531
1
3.0531
1
3.2084
1
3.2043
1
3.0710
1
2.9584
1
3.1859
1
3.0526
1
1.9538
1
3.1515
1
3.0882
1
B2PLYP         3.4248
3
                  3.7294
2
           
Configuration interaction CID 2.3787
1
2.6515
4
2.6329
4
2.6257
4
2.6179
4
3.1586
1
3.1602
1
2.6131
4
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
CISD 2.3805
1
1.8562
2
2.6389
4
2.6325
4
2.6217
4
  3.1659
1
2.2864
3
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
Quadratic configuration interaction QCISD 2.3805
1
2.6605
4
2.6393
4
2.6327
4
2.6220
4
2.4412
3
2.6145
4
2.6203
4
2.6202
4
2.6302
4
3.1811
1
3.1811
1
1.6212
2
2.6470
4
2.6272
4
3.1772
1
1.6017
2
1.5889
2
3.1774
1
3.1887
1
3.1782
1
QCISD(T) 2.3805
1
3.2386
1
3.1901
1
3.1893
1
2.6199
4
3.1640
1
3.1663
1
3.1647
1
3.1647
1
3.1678
1
3.1810
1
3.1810
1
1.6212
2
2.6443
4
2.6230
4
3.1773
1
2.6418
4
2.2610
3
3.1775
1
3.1872
1
3.1776
1
Coupled Cluster CCD 2.3787
1
2.6515
4
2.6329
4
2.6257
4
2.6179
4
2.6179
4
2.6112
4
2.6130
4
2.6130
4
2.6262
4
3.1793
1
3.1793
1
1.6128
2
2.6421
4
2.6218
4
3.1766
1
2.6403
4
2.6263
4
3.1768
1
3.1836
1
3.1776
1
CCSD 2.3805
1
3.2386
1
3.1902
1
3.1892
1
2.6234
4
3.1642
1
3.1659
1
3.1641
1
3.1646
1
3.1676
1
3.1811
1
3.1811
1
3.2424
1
1.6024
2
1.5889
2
3.1772
1
3.2034
1
3.1778
1
3.1774
1
3.1887
1
3.1782
1
CCSD=FULL 2.3662
1
3.2381
1
3.1807
1
3.1876
1
3.1493
1
3.1495
1
3.1503
1
3.1230
1
3.1230
1
2.9808
1
3.0699
1
3.0699
1
3.2287
1
3.2110
1
3.0779
1
2.9646
1
3.1935
1
3.0598
1
2.2339
1
3.1615
1
 
CCSD(T) 2.3805
1
3.2385
1
3.1901
1
3.1894
1
1.5821
2
3.1642
1
3.1658
1
3.1643
1
3.1642
1
3.1678
1
3.1809
1
3.1810
1
1.6212
2
2.6452
4
2.6236
4
2.6256
4
2.6425
4
2.2631
3
1.5887
2
3.1872
1
3.1776
1
CCSD(T)=FULL 2.3671
1
3.2381
1
3.1809
1
3.1877
1
2.5974
4
3.1495
1
3.1503
1
3.1194
1
3.1194
1
2.9753
1
3.0655
1
3.0655
1
1.6151
2
1.6057
2
1.5375
2
2.3049
4
1.5967
2
1.5281
2
0.9768
2
3.1614
1
3.0991
1

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 2.8526
4
2.8479
4
2.7314
4
2.5593
3
2.5485
3
2.3626
3
density functional LSDA 3.3949
1
3.4023
1
3.1924
1
3.1925
1
3.2951
1
2.9797
1
SVWN 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 2.8060
4
2.7951
4
2.6627
4
2.6416
4
2.4953
3
2.4559
4
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
Moller Plesset perturbation MP2 2.5003
3
2.4691
3
1.8872
2
1.8620
2
1.9131
2
2.5249
4
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
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.