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Comparison of levels of theory for Na-S


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 2.6287
5
PM6 1.6782
5
composite G2 2.5266
1
G3 2.5266
1
G3B3 2.4387
5
G4 2.4210
5
CBS-Q 2.5266
1

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 aug-cc-pV(T+d)Z aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 2.1741
5
2.4519
5
2.4222
5
2.4592
5
2.4451
5
2.4450
5
2.4521
5
2.4512
5
2.4512
5
2.4407
5
2.4246
4
2.4480
5
2.4507
5
2.4494
5
2.4488
5
2.4630
5
2.4500
5
2.4490
5
2.4457
5
2.4265
4
2.4449
4
2.4502
5
ROHF   2.5575
1
2.5148
1
2.5626
1
2.5212
1
2.5212
1
2.5293
1
2.5263
1
2.5263
1
    2.5330
1
2.5233
1
2.5211
1
2.5205
1
2.5330
1
2.5240
1
2.5212
1
2.4584
3
2.4261
4
   
density functional LSDA 2.2123
1
  2.4512
1
2.4992
1
2.4641
1
2.4641
1
2.4747
1
2.4691
1
2.4691
1
2.4433
1
  2.4757
1
2.4666
1
2.4645
1
  2.4649
1
2.4625
1
  2.3969
5
2.3830
4
   
BLYP 2.1951
5
2.4623
5
2.4230
5
2.4717
5
2.4560
5
2.4560
5
2.4620
5
2.4668
5
2.4668
5
2.4461
5
2.4396
4
2.4654
5
2.4606
5
2.4634
5
  2.4500
4
2.4610
5
  2.4397
4
2.4444
4
2.4468
4
2.4443
4
B1B95 2.1752
5
2.3742
4
2.3964
5
2.4390
5
2.4283
5
2.4283
5
2.4233
5
2.4351
5
2.4351
5
2.4201
5
2.4086
4
2.4350
5
2.4356
5
2.4335
5
  2.4264
4
2.4148
4
  2.4344
5
2.4119
4
2.4243
4
2.4145
4
B3LYP 2.1828
5
2.4404
5
2.4038
5
2.4494
5
2.4358
5
2.4358
5
2.4419
5
2.4453
5
2.4453
5
2.4270
5
2.4184
4
2.4442
5
2.4405
5
2.4427
5
2.4375
5
2.4470
5
2.4409
5
2.4391
5
2.4362
5
2.4226
4
2.4293
4
2.4244
4
B3LYPultrafine   2.4403
5
    2.4356
5
2.4356
5
2.4285
5
2.4451
5
  2.4122
4
2.4184
4
2.4440
5
2.4403
5
2.4426
5
  2.4468
5
2.4408
5
  2.4361
5
2.4226
4
2.4293
4
2.4244
4
B3PW91 2.1797
5
2.4398
5
2.4153
5
2.4474
5
2.4356
5
2.4356
5
2.4404
5
2.4427
5
2.4427
5
2.4267
5
2.4155
4
2.4434
5
2.4420
5
2.4417
5
  2.4315
4
2.4231
4
  2.4348
5
2.4195
4
2.4293
4
2.4226
4
mPW1PW91 2.1765
5
2.4341
5
2.3998
5
2.4395
5
2.4310
5
2.4310
5
2.4257
5
2.4375
5
2.4375
5
2.4226
5
2.4108
4
2.4377
5
2.4375
5
2.4368
5
  2.4432
5
2.4350
5
  2.4300
5
2.4145
4
2.4254
4
2.4178
4
M06-2X 2.1712
5
2.4158
5
2.3831
5
2.4203
5
2.4172
5
2.4172
5
2.4141
5
2.4212
5
2.4212
5
2.4089
5
2.4139
5
2.4206
5
2.4236
5
2.4223
5
  2.4298
5
2.4211
5
  2.4173
5
2.4016
4
2.4120
4
2.4047
4
PBEPBE 2.1858
5
2.4581
5
2.4195
5
2.4618
5
2.4452
5
2.4452
5
2.4501
5
2.4533
5
2.4533
5
2.4354
5
2.4263
4
2.4536
5
2.4520
5
2.4513
5
  2.4546
5
2.4490
5
  2.4440
5
2.4304
4
2.4370
4
2.4326
4
PBEPBEultrafine   2.4580
5
    2.4450
5
2.4450
5
2.4500
5
2.4532
5
  2.4208
4
2.4263
4
2.4535
5
2.4518
5
2.4512
5
  2.4544
5
2.4489
5
  2.4439
5
2.4304
4
2.4370
4
2.4326
4
PBE1PBE 2.1748
5
2.3710
4
2.3943
5
2.4396
5
2.4285
5
2.4285
5
2.4225
5
2.4352
5
2.4352
5
2.4201
5
2.4085
4
2.4347
5
2.4350
5
2.4338
5
  2.4405
5
2.4323
5
  2.4275
5
2.4121
4
2.4230
4
2.4157
4
HSEh1PBE 2.1751
5
2.4298
5
2.3952
5
2.4432
5
2.4307
5
2.4307
5
2.4357
5
2.4374
5
2.4374
5
2.4220
5
2.4107
4
2.4376
5
2.4366
5
2.4362
5
  2.4425
5
2.4346
5
  2.4298
5
2.4143
4
2.4249
4
2.4180
4
TPSSh 2.1686
4
2.4532
5
2.4071
5
2.4545
5
2.4413
5
2.4413
5
2.4350
5
2.4475
5
2.4308
4
2.4180
4
2.4208
4
2.4485
5
2.4482
5
2.4466
5
2.4262
4
2.4537
5
2.4451
5
2.4271
4
2.4402
5
2.4249
4
2.4363
4
2.4284
4
wB97X-D 2.1618
4
2.4329
4
2.4244
5
2.4170
4
2.4345
5
2.4175
4
2.4359
5
2.4241
4
2.4408
5
2.4106
4
2.4173
4
2.4411
5
2.4406
5
2.4411
5
2.4207
4
2.4357
4
2.4401
5
2.4220
4
2.4176
4
2.4185
4
2.4340
4
2.4231
4
B97D3 2.1859
4
2.4843
5
2.4378
4
2.4677
4
2.4683
5
2.4567
4
2.4728
5
2.4671
4
2.4779
5
2.4486
4
2.4683
5
2.4862
5
2.4623
4
2.4758
5
2.4588
4
2.4692
4
2.4786
5
2.4592
4
2.4557
4
2.4604
4
2.4672
4
2.4778
5
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 aug-cc-pV(T+d)Z aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 2.1741
5
2.4783
5
2.4416
5
2.4957
5
2.4572
5
2.4572
5
2.4652
5
2.4336
4
2.4487
5
2.4554
5
2.4466
4
2.4636
5
2.4714
5
2.4684
5
2.4671
5
2.4917
5
2.4744
5
2.4696
5
2.4700
5
2.4523
4
2.4750
4
2.4585
4
MP2=FULL 2.1727
5
2.4777
5
2.4372
5
2.4937
5
2.4502
5
2.4502
5
2.4519
5
2.4419
5
2.4419
5
2.4302
5
2.4192
4
2.4579
5
2.4686
5
2.4621
5
2.3451
5
2.4594
5
2.4051
5
2.1929
5
2.3939
5
2.4224
4
2.4204
4
2.3797
4
ROMP2 2.2272
1
  2.5111
1
2.5795
1
2.5113
1
2.5113
1
2.5218
1
2.5076
1
2.5076
1
2.5139
1
  2.5330
1
2.5306
1
2.5283
1
  2.5516
1
    2.4861
3
2.4521
4
   
MP3         2.4497
5
  2.4581
5
      2.4357
4
2.4563
5
2.4634
5
2.4593
5
        2.4605
5
2.4413
4
2.4662
4
2.4466
4
MP3=FULL   2.4457
4
2.4078
4
2.4532
4
2.4434
5
2.4273
4
2.4435
3
2.4190
4
2.4190
4
2.4043
4
2.4119
4
2.4519
5
2.4608
5
2.4542
5
  2.4322
4
2.3747
4
  2.3909
5
2.4235
2
2.4118
4
2.3731
4
MP4   2.5128
5
    2.4639
5
      2.4515
5
  2.4481
4
2.4719
5
2.4801
5
2.4702
5
  2.4981
5
2.4763
5
  2.4717
5
2.4542
4
2.4823
4
2.4610
4
MP4=FULL   2.5131
5
    2.4573
5
      2.4453
5
  2.4222
4
  2.4776
5
2.4646
5
  2.4660
5
2.4025
5
  2.3647
4
2.4270
4
2.4182
4
2.3762
4
B2PLYP 2.1771
5
2.4551
5
2.4141
5
2.4640
5
2.4418
5
2.4418
5
2.4484
5
2.4437
5
2.4437
5
2.4345
5
2.4260
4
2.4486
5
2.4486
5
2.4487
5
  2.4603
5
2.4498
5
  2.4455
5
2.4305
4
2.4438
4
2.4343
4
B2PLYP=FULL 2.1768
5
2.4550
5
2.4124
5
2.4636
5
2.4392
5
2.4392
5
2.4286
5
2.4413
5
2.4413
5
2.4262
5
2.4171
4
2.4468
5
2.4475
5
2.4467
5
  2.4501
5
2.4192
5
  2.4215
5
2.4210
4
2.4242
4
2.4108
4
B2PLYP=FULLultrafine 2.1638
4
2.4341
4
2.3938
4
2.4427
4
2.4391
5
2.4241
4
2.4082
4
2.4259
4
2.4259
4
2.4113
4
2.4171
4
2.4297
4
2.4473
5
2.4466
5
  2.4344
4
2.4191
5
  2.4020
4
2.4210
4
2.4242
4
2.4108
4
Configuration interaction CID   2.4721
5
2.4203
5
2.4815
5
2.4492
5
    2.4414
5
    2.4302
4
  2.4437
4
2.4378
4
        2.4349
4
2.4344
4
2.4608
4
2.4404
4
CISD   2.4760
5
2.4226
5
2.4913
5
2.4517
5
    2.4437
5
    2.4312
4
  2.4464
4
2.4388
4
        2.4543
5
2.4348
4
2.4621
4
2.4412
4
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 aug-cc-pV(T+d)Z aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   2.5063
5
2.4426
5
2.5121
5
2.4588
5
2.4588
5
2.4662
5
2.4487
5
2.4487
5
2.4499
5
2.4386
4
2.4662
5
2.4716
5
2.4621
5
  2.4888
5
2.4665
5
  2.4624
5
2.4439
4
2.4711
4
2.4493
4
QCISD(T)         2.4638
5
    2.4380
4
    2.4457
4
2.4738
5
2.4794
5
2.4683
5
  2.4965
5
2.4738
5
  2.4693
5
2.4513
4
2.4799
4
2.4579
4
QCISD(T)=FULL         2.4572
5
  2.4579
5
      2.4212
4
  2.4768
5
2.4663
3
2.3366
5
2.4646
5
2.4016
5
2.1926
5
2.3916
5
2.4366
2
2.4167
4
2.3749
4
QCISD(TQ)         2.5161
1
  2.5263
1
          2.5363
1
2.5291
1
2.5276
1
2.5579
1
2.5381
1
2.5310
1
2.5374
1
     
QCISD(TQ)=FULL         2.5136
1
  2.5229
1
          2.5352
1
2.5175
1
2.4986
1
2.5426
1
2.5040
1
  2.5024
1
     
Coupled Cluster CCD   2.4746
5
2.4332
5
2.4869
5
2.4514
5
2.4514
5
2.4597
5
2.4425
5
2.4425
5
2.4467
5
2.4353
4
2.4578
5
2.4645
5
2.4590
5
  2.4847
5
2.4638
5
  2.4596
5
2.4460
2
2.4664
4
2.4459
4
CCSD         2.4551
5
2.4404
4
2.4479
4
2.4305
4
2.4305
4
2.4485
5
2.4371
4
2.4626
5
2.4681
5
2.4608
5
2.4574
5
2.4866
5
2.4651
5
2.4588
5
2.4609
5
2.4426
4
2.4683
4
2.4476
4
CCSD=FULL         2.4486
5
        2.4241
5
2.4094
4
2.4584
5
2.4655
5
2.4557
5
2.3361
5
2.4548
5
2.3992
5
2.1929
5
2.3894
5
2.4259
2
2.4087
2
2.3721
4
CCSD(T)         2.4617
5
2.4481
4
2.4551
4
2.4360
4
2.4360
4
2.4389
4
2.4447
4
2.4714
5
2.4770
5
2.4674
5
2.4639
5
2.4951
5
2.4730
5
2.4660
5
2.4685
5
2.4503
4
2.4781
4
2.4568
4
CCSD(T)=FULL         2.4550
5
          2.4202
4
2.4671
5
2.4744
5
2.4620
5
2.3366
5
2.4629
5
2.4015
5
2.1928
5
2.3638
4
2.4242
4
2.4159
4
2.3747
4
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 aug-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 2.4913
5
2.4649
5
2.4588
5
2.4434
5
2.4903
5
2.4503
5
    2.4378
5
density functional BLYP                 2.4330
4
B1B95                 2.4053
4
B3LYP 2.4967
5
2.4796
5
2.4728
5
2.4610
5
2.5118
5
2.4475
5
    2.4285
5
B3LYPultrafine                 2.4132
4
B3PW91                 2.4127
4
mPW1PW91                 2.4078
4
M06-2X                 2.3946
4
PBEPBE                 2.4357
5
PBEPBEultrafine                 2.4214
4
PBE1PBE                 2.4049
4
HSEh1PBE                 2.4072
4
TPSSh                 2.4180
4
wB97X-D 2.4566
4
2.4487
4
2.4338
4
2.4347
4
2.4705
4
2.4136
4
    2.4150
4
B97D3                 2.4536
4
Moller Plesset perturbation MP2 2.5151
5
2.4785
5
2.4893
5
2.4488
5
2.5236
5
2.4926
5
    2.4518
5
MP2=FULL                 2.4055
4
MP3                 2.4287
4
MP3=FULL                 2.4003
4
MP4                 2.4400
4
MP4=FULL                 2.4095
4
B2PLYP                 2.4201
4
B2PLYP=FULL                 2.4095
4
B2PLYP=FULLultrafine                 2.4095
4
Configuration interaction CID                 2.4246
4
CISD                 2.4257
4
Quadratic configuration interaction QCISD                 2.4320
4
QCISD(T)                 2.4382
4
QCISD(T)=FULL                 2.4088
4
Coupled Cluster CCD                 2.4287
4
CCSD                 2.4307
4
CCSD=FULL                 2.4027
4
CCSD(T)                 2.4372
4
CCSD(T)=FULL                 2.4078
4
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.