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Comparison of levels of theory for H-Ge


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 1.5341
14
PM3 1.5085
16
PM6 1.5177
22
composite G2 1.5516
22
G3 1.5519
22
G3B3 1.5642
22
G4 1.5462
20
CBS-Q 1.5533
22

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 daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.4452
19
1.5562
19
1.5626
19
1.5476
19
1.5537
19
1.5427
19
1.5418
19
1.5516
19
1.5473
19
1.5372
19
1.5392
13
1.5513
16
1.5510
19
1.5492
19
1.5479
19
1.5509
19
1.5487
19
1.5477
19
1.5334
11
1.5486
19
ROHF   1.5758
8
1.5799
8
1.5675
8
1.5725
8
1.5578
8
1.5730
8
1.5697
8
1.5647
8
  1.5317
4
1.5628
6
1.5694
8
1.5662
8
1.5644
8
1.5679
8
1.5651
8
1.5638
8
1.5347
4
1.5318
4
density functional LSDA 1.3901
15
1.5654
9
1.5746
19
1.5637
19
1.5640
19
1.5516
19
1.5513
19
1.5603
19
1.5562
19
1.5437
19
1.5511
6
1.5595
15
1.5655
19
1.5549
19
  1.5605
18
1.5544
19
     
BLYP 1.4032
17
1.5794
19
1.5881
19
1.5756
19
1.5761
19
1.5626
19
1.5622
19
1.5730
19
1.5688
19
1.5581
19
1.5566
13
1.5753
16
1.5795
19
1.5680
19
  1.5696
14
1.5608
14
  1.5555
11
1.5472
11
B1B95 1.4170
19
1.5484
11
1.5672
19
1.5553
19
1.5567
19
1.5567
19
1.5449
19
1.5545
19
1.5504
19
1.5395
19
1.5401
13
1.5551
16
1.5574
19
1.5499
19
  1.5558
19
1.5493
19
  1.5418
8
1.5308
11
B3LYP 1.4095
19
1.5672
19
1.5745
19
1.5624
19
1.5641
19
1.5515
19
1.5509
19
1.5604
19
1.5564
19
1.5459
19
1.5454
13
1.5621
16
1.5653
19
1.5560
19
1.5541
19
1.5626
19
1.5554
19
1.5536
19
1.5434
11
1.5365
11
B3LYPultrafine   1.5597
14
    1.5641
19
1.5462
14
1.5456
14
1.5538
14
  1.5373
13
1.5454
13
1.5514
14
1.5687
16
1.5592
16
  1.5660
16
1.5554
19
  1.5434
11
1.5365
11
B3PW91 1.4159
19
1.5676
19
1.5733
19
1.5592
19
1.5611
19
1.5492
19
1.5485
19
1.5585
19
1.5542
19
1.5427
19
1.5441
13
1.5592
16
1.5613
19
1.5541
19
  1.5535
14
1.5458
17
  1.5408
11
1.5352
11
mPW1PW91 1.4174
19
1.5651
19
1.5704
19
1.5562
19
1.5581
19
1.5468
19
1.5461
19
1.5561
19
1.5518
19
1.5401
19
1.5421
13
1.5566
16
1.5583
19
1.5519
19
  1.5569
19
1.5515
19
  1.5384
11
1.5334
11
M06-2X 1.4123
19
1.5605
19
1.5707
19
1.5584
19
1.5615
19
1.5495
19
1.5489
19
1.5612
19
1.5571
19
1.5459
19
1.5548
22
1.5621
16
1.5616
19
1.5583
19
  1.5612
19
1.5578
19
  1.5437
11
1.5404
11
PBEPBE 1.4093
17
1.5806
19
1.5869
19
1.5722
19
1.5741
19
1.5598
19
1.5592
19
1.5708
19
1.5663
19
1.5541
19
1.5555
13
1.5722
16
1.5748
19
1.5661
19
  1.5722
19
1.5654
19
  1.5527
11
1.5463
11
PBEPBEultrafine   1.5730
14
    1.5776
16
1.5549
14
1.5542
14
1.5645
14
  1.5456
13
1.5555
13
1.5616
14
1.5784
16
1.5696
16
  1.5757
16
1.5688
16
  1.5527
11
1.5463
11
PBE1PBE 1.4187
16
1.5543
11
1.5758
16
1.5614
16
1.5633
16
1.5633
16
1.5503
16
1.5611
16
1.5566
16
1.5442
16
1.5441
13
1.5586
16
1.5633
16
1.5569
16
  1.5617
16
1.5563
16
  1.5403
11
1.5354
11
HSEh1PBE 1.4161
19
1.5667
19
1.5725
19
1.5588
19
1.5608
19
1.5489
19
1.5482
19
1.5581
19
1.5538
19
1.5424
19
1.5440
13
1.5591
16
1.5609
19
1.5540
19
  1.5592
19
1.5536
19
  1.5406
11
1.5353
11
TPSSh 1.4138
14
1.5564
14
1.5639
14
1.5477
14
1.5583
19
1.5420
14
1.5464
19
1.5508
14
1.5468
14
1.5406
19
1.5434
13
1.5467
14
1.5529
14
1.5529
19
1.5448
14
1.5521
14
1.5463
14
1.5446
14
1.5397
11
1.5342
11
wB97X-D 1.4202
14
1.5540
14
1.5689
19
1.5467
14
1.5571
19
1.5407
14
1.5450
19
1.5480
14
1.5504
19
1.5341
14
1.5402
13
1.5526
19
1.5508
19
1.5506
19
1.5429
14
1.5496
14
1.5503
19
1.5426
14
1.5374
11
1.5321
11
B97D3 1.4334
13
1.5769
18
1.5723
13
1.5576
13
1.5680
18
1.5478
13
1.5541
18
1.5572
13
1.5616
18
1.5422
13
1.5618
19
1.5637
18
1.5610
13
1.5600
18
1.5494
13
1.5589
13
1.5593
18
1.5491
13
1.5486
11
1.5591
22
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 daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.4564
19
1.5692
19
1.5697
19
1.5617
19
1.5658
19
1.5439
19
1.5432
19
1.5602
19
1.5485
19
1.5377
19
1.5437
13
1.5383
16
1.5490
19
1.5330
19
1.5260
16
1.5488
19
1.5299
19
1.5229
16
1.5315
11
1.5145
11
MP2=FULL 1.4552
19
1.5688
19
1.5694
19
1.5598
19
1.5630
19
1.5385
19
1.5377
19
1.5523
19
1.5357
19
1.5231
19
1.5305
13
1.5382
16
1.5485
19
1.5264
19
1.5069
16
1.5454
19
1.5175
19
1.4976
16
1.5283
11
1.5046
11
ROMP2 1.4678
8
1.5559
4
1.5865
8
1.5825
8
1.5846
8
1.5591
8
1.5579
8
1.5786
8
1.5668
8
1.5518
8
1.5379
4
1.5489
6
1.5674
8
1.5502
8
  1.5671
8
    1.5349
4
1.5185
4
MP3         1.5729
19
  1.5862
19
      1.5572
6
1.5492
8
1.5606
8
1.5476
8
           
MP3=FULL   1.5879
8
1.5848
8
1.5778
8
1.6062
19
1.5496
8
1.5815
19
1.5724
8
1.5515
8
1.5354
8
1.5483
6
1.5510
8
1.5603
8
1.5432
8
  1.5593
8
1.5361
8
     
MP4   1.5801
19
    1.5770
19
      1.5544
19
  1.5601
6
1.5498
13
1.5623
13
1.5398
19
  1.5631
13
1.5445
13
     
MP4=FULL   1.5889
13
    1.5818
13
      1.5493
13
  1.5466
6
  1.5615
13
1.5406
13
  1.5594
13
1.5324
13
     
B2PLYP 1.4306
14
1.5576
14
1.5639
14
1.5514
14
1.5534
17
1.5415
14
1.5409
14
1.5511
14
1.5448
14
1.5339
17
1.5429
13
1.5415
14
1.5501
14
1.5382
17
  1.5493
14
1.5373
17
  1.5371
11
1.5277
11
B2PLYP=FULL 1.4302
14
1.5569
14
1.5638
14
1.5506
14
1.5536
14
1.5397
14
1.5390
14
1.5487
14
1.5408
14
1.5308
14
1.5385
13
1.5415
14
1.5499
14
1.5378
14
  1.5482
14
1.5353
14
  1.5361
11
1.5246
11
B2PLYP=FULLultrafine 1.4302
14
1.5575
14
1.5639
14
1.5507
14
1.5586
22
1.5398
14
1.5392
14
1.5488
14
1.5409
14
1.5309
14
1.5386
13
1.5416
14
1.5547
22
1.5421
22
  1.5483
14
1.5369
25
  1.5361
11
1.5246
11
Configuration interaction CID   1.5773
19
1.5760
19
1.5691
19
1.5722
19
    1.5662
19
    1.5458
13
  1.5418
13
1.5287
13
        1.5336
7
1.5191
7
CISD   1.5754
22
1.5747
22
1.5677
22
1.5710
22
    1.5652
22
    1.5465
13
  1.5423
13
1.5288
13
        1.5340
7
1.5191
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 daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.5792
22
1.5788
22
1.5713
22
1.5755
22
1.5475
22
1.5468
22
1.5696
22
1.5521
22
1.5406
22
1.5505
13
1.5432
19
1.5530
22
1.5387
22
  1.5534
22
1.5362
22
  1.5378
7
1.5228
7
QCISD(T)         1.5770
22
    1.5665
14
    1.5520
13
1.5445
19
1.5542
22
1.5398
22
  1.5566
19
1.5393
19
  1.5391
7
1.5239
7
QCISD(T)=FULL         1.5694
14
  1.5387
14
      1.5416
13
  1.5447
13
1.5306
14
1.5157
10
1.5468
14
1.5231
14
1.5033
14
1.5359
7
1.5153
7
QCISD(TQ)         1.5901
8
  1.5589
8
      1.5621
6
  1.5658
8
1.5516
8
1.5704
4
1.5673
8
1.5494
8
1.5668
2
   
QCISD(TQ)=FULL         1.6211
4
  1.5797
4
      1.5896
2
  1.5935
4
1.5764
3
1.5519
2
1.5929
4
1.5673
4
     
Coupled Cluster CCD   1.5778
22
1.5775
22
1.5700
22
1.5739
22
1.5463
22
1.5455
22
1.5682
22
1.5507
22
1.5394
22
1.5495
13
1.5423
19
1.5519
22
1.5385
22
  1.5525
22
1.5362
22
  1.5372
7
1.5226
7
CCSD         1.5753
22
1.5338
7
1.5332
7
1.5538
7
1.5365
7
1.5356
17
1.5504
13
1.5464
16
1.5531
22
1.5389
22
1.5352
16
1.5585
16
1.5386
19
1.5386
12
1.5379
7
1.5231
7
CCSD=FULL         1.5750
19
        1.5227
17
1.5401
13
1.5472
16
1.5575
16
1.5356
19
1.5181
16
1.5550
16
1.5281
19
1.5143
12
1.5349
7
1.5144
7
CCSD(T)         1.5795
19
1.5447
14
1.5415
13
1.5665
14
1.5459
13
1.5355
13
1.5519
13
1.5476
16
1.5564
19
1.5421
19
1.5336
19
1.5569
19
1.5397
19
1.5255
13
1.5392
7
1.5240
7
CCSD(T)=FULL         1.5549
22
          1.5417
13
1.5455
19
1.5514
21
1.5346
22
1.5123
17
1.5513
22
1.5289
19
1.5017
16
1.5360
7
1.5154
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 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 1.5562
19
  1.5548
19
  1.5544
19
1.5622
19
1.5257
4
  1.5507
19
ROHF             1.5257
4
  1.5329
4
density functional LSDA             1.5448
4
  1.5528
6
BLYP             1.5548
4
  1.5586
13
B1B95             1.5351
4
  1.5413
13
B3LYP 1.5699
19
  1.5717
19
  1.5695
19
1.5774
19
1.5410
4
  1.5574
19
B3LYPultrafine             1.5410
4
  1.5472
13
B3PW91             1.5393
4
  1.5455
13
mPW1PW91             1.5368
4
  1.5434
13
M06-2X             1.5420
4
  1.5494
13
PBEPBE             1.5532
4
  1.5670
19
PBEPBEultrafine             1.5532
4
  1.5573
13
PBE1PBE             1.5387
4
  1.5455
13
HSEh1PBE             1.5391
4
  1.5456
13
TPSSh             1.5385
4
  1.5437
13
wB97X-D 1.5603
14
  1.5599
14
  1.5611
14
1.5642
14
1.5346
4
  1.5423
13
B97D3             1.5490
4
  1.5529
13
Moller Plesset perturbation MP2 1.5731
19
  1.5721
19
  1.5685
19
1.5797
19
1.5155
4
  1.5371
19
MP2=FULL             1.5064
4
  1.5268
13
ROMP2             1.5154
4
  1.5227
4
MP3             1.5206
4
  1.5435
6
MP3=FULL             1.5133
4
  1.5444
6
MP4             1.5213
4
  1.5438
6
MP4=FULL             1.5121
4
  1.5427
6
B2PLYP             1.5299
4
  1.5389
13
B2PLYP=FULL             1.5268
4
  1.5386
13
B2PLYP=FULLultrafine             1.5268
4
  1.5387
13
Configuration interaction CID             1.5200
4
  1.5316
13
CISD             1.5201
4
  1.5316
13
Quadratic configuration interaction QCISD             1.5231
4
  1.5364
13
QCISD(T)             1.5241
4
  1.5377
13
QCISD(T)=FULL             1.5158
4
  1.5378
13
QCISD(TQ)                 1.5854
2
QCISD(TQ)=FULL                 1.5861
2
Coupled Cluster CCD             1.5227
4
  1.5359
13
CCSD             1.5234
4
  1.5366
13
CCSD=FULL             1.5150
4
  1.5365
13
CCSD(T)             1.5243
4
  1.5378
13
CCSD(T)=FULL             1.5159
4
  1.5378
13
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.