III.G.1.a.

Comparison of levels of theory for S-O

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	1.4424 17
	PM3	1.4850 45
	PM6	1.4865 52
composite	G2	1.4639 43
	G3	1.4624 54
	G3B3	1.5033 54
	CBS-Q	1.4561 46

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	cc-pV(D+d)Z	cc-pV(T+d)Z	aug-cc-pV(T+d)Z	cc-pCVDZ	cc-pCVTZ	Sadlej_pVTZ
hartree fock	HF	1.7016 54	1.5887 54	1.4677 54	1.6345 51	1.4623 54	1.4622 54	1.4622 54	1.4548 54	1.4549 54	1.4366 54	1.4307 28	1.4767 55	1.4762 54	1.4459 54	1.4276 20	1.4801 54	1.4403 51	1.4244 17	1.4231 3	1.4166 14	1.4430 1			1.4262 2
hartree fock	ROHF	1.6373 13	1.5903 17	1.4738 17	1.6402 16	1.4666 16	1.4664 16	1.4663 17	1.4589 16	1.4589 16	1.4187 13			1.4800 17	1.4413 17	1.4170 13	1.4849 16	1.4208 13	1.4038 10	1.4600 1
density functional	LSDA	1.6570 54	1.6006 54	1.5030 54	1.6469 54	1.5007 54	1.5013 54	1.5021 54	1.4949 54	1.4951 54	1.4782 54		1.4374 2	1.5173 54	1.4853 51	1.4767 15	1.5179 50	1.4771 18	1.4651 14	1.4679 3
	SVWN		1.6103 48			1.4963 45	1.4350 2	1.5150 48	1.4250 2	1.4250 2	1.4148 2			1.4488 2	1.4215 2		1.4523 2	1.4221 2
	BLYP	1.6997 54	1.6447 51	1.5301 46	1.6866 51	1.5305 54	1.5304 54	1.5339 52	1.5201 46	1.5249 54	1.5047 54		1.4604 2	1.5477 54	1.5147 54		1.5482 27			1.4886 3
	B1B95	1.6488 50	1.5625 50	1.4938 50	1.6413 50	1.4894 49	1.4902 50	1.4909 50	1.4838 50	1.4839 50	1.4691 49		1.4257 2	1.5050 50	1.4751 50	1.4674 17	1.5042 45	1.4665 19	1.4634 17	1.4559 3	1.4469 3	1.4810 1	1.5156 1	1.4823 1
	B3LYP	1.6745 54	1.6223 54	1.5062 54	1.6615 54	1.5038 54	1.5028 54	1.5049 52	1.4967 54	1.5002 27	1.4790 54	1.4712 27	1.5184 55	1.5196 54	1.4878 54	1.4793 17	1.5181 35	1.4787 32	1.4755 17	1.4662 3	1.4556 14	1.4890 1			1.4746 2
	B3LYPultrafine					1.5036 53		1.4929 17
	B3PW91	1.6632 24	1.6157 54	1.5007 54	1.6536 54	1.4971 54	1.4971 54	1.4939 46	1.4906 54	1.4938 27	1.4759 54		1.4331 2	1.5128 54	1.4830 54		1.5141 27			1.4621 3
	mPW1PW91	1.6548 27	1.6074 54	1.5033 27	1.6436 54	1.4932 54	1.4931 54	1.4942 54	1.4868 54	1.4869 54	1.4719 54		1.4288 2	1.5081 54	1.4768 35		1.5094 32	1.4149 2		1.4576 3
	M06-2X	1.6182 5	1.5852 5	1.5006 5	1.6045 5	1.4995 55	1.4978 5	1.4984 5	1.4926 5	1.4923 5	1.4825 5		1.4242 2	1.5083 5	1.4877 5		1.5110 5	1.4122 2
	PBEPBE	1.6887 27	1.6397 54	1.5291 27	1.6825 27	1.5197 54	1.5197 54	1.5205 54	1.5136 54	1.5138 54	1.4967 54	1.4876 27	1.4532 2	1.5390 51	1.5050 54	1.4977 16	1.5375 7	1.4775 13	1.4871 14	1.4821 3	1.4719 3				1.4943 2
	PBEPBEultrafine					1.5162 28		1.4846 2
	HSEh1PBE	1.6194 5	1.5843 5	1.5028 5	1.6041 5	1.5028 47	1.5005 5	1.5011 5	1.4954 5	1.4951 5	1.4860 5		1.4299 2	1.5109 5	1.4907 5		1.5134 5	1.4157 2
Moller Plesset perturbation	MP2FC	1.6669 27	1.6177 54	1.5011 51	1.6543 54	1.5031 54	1.5029 54	1.5080 52	1.4930 51	1.4905 54	1.4755 40		1.5160 55	1.5159 54	1.4797 35	1.4828 11	1.5246 35	1.4802 21	1.4791 8	1.4760 3	1.4575 14	1.4919 1	1.5050 3	1.4622 3	1.4954 2
	MP2FU	1.6667 27	1.6196 35	1.5124 27	1.6550 27	1.5013 54	1.4976 46	1.5013 46	1.4897 54	1.4927 27	1.4764 27		1.4337 2	1.5126 35	1.4788 29	1.4878 9	1.5083 14	1.4715 18	1.4812 8	1.4751 3	1.4539 14	1.4871 1	1.5045 3	1.4601 3
	ROMP2	1.6805 12	1.6196 16	1.5319 16	1.6688 11	1.5129 13	1.5129 13	1.5223 16	1.5005 13	1.5052 16	1.4898 16			1.5314 16	1.4942 13	1.4842 10	1.5385 13	1.4995 11	1.4809 10	1.5408 1
	MP3					1.4877 53
	MP4		1.6536 24			1.5128 33			1.5193 1	1.5118 23					1.4844 21					1.4935 3
	B2PLYP	1.6221 5	1.5910 5	1.5095 5	1.6103 5	1.5131 48	1.5065 5	1.5154 48	1.5004 5	1.5001 5	1.4904 5		1.4375 2	1.5165 5	1.4951 5		1.5200 5	1.4225 2
Configuration interaction	CID	1.5407 1	1.6074 27	1.4936 27	1.6460 27	1.4728 46			1.4669 27
Configuration interaction	CISD	1.5648 1	1.6157 26	1.4918 27	1.6534 27	1.4748 46			1.4686 26
Quadratic configuration interaction	QCISD	1.6523 1	1.6218 39	1.5093 24	1.6926 18	1.4903 34	1.4997 24	1.4996 28	1.4803 32	1.4790 42	1.4754 22		1.4297 2	1.5074 24	1.4659 26		1.4681 4	1.4449 2		1.4635 3	1.4479 3
Quadratic configuration interaction	QCISD(T)					1.5079 25			1.4822 2				1.4368 2	1.5156 21	1.4857 18		1.5340 16	1.4870 12
Coupled Cluster	CCD	1.6163 2	1.6199 26	1.4982 27	1.6560 27	1.4854 46	1.4914 27	1.4875 26	1.4763 25	1.4788 27	1.4606 25		1.4226 2	1.4979 27	1.4618 24		1.5055 23	1.4569 20		1.4560 3	1.4406 3	1.4752 1
	CCSD					1.4811 27			1.5007 1					1.4377 2	1.4108 2
	CCSD(T)		1.6283 3			1.4942 27	1.4904 4	1.4891 3	1.4822 2	1.4753 3		1.4890 1	1.4354 2	1.5189 25	1.4785 23	1.5029 1	1.5296 24	1.4800 12	1.5026 1	1.4582 2	1.4569 3	1.4925 1	1.4991 3	1.4574 3
	CCSD(T)=FULL					1.5321 19							1.4347 2	1.5063 8	1.4450 5	1.5005 1	1.5217 6	1.4664 3	1.4996 1	1.4758 3	1.4533 3	1.4875 1	1.4983 3	1.4554 3

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	1.6621 50	1.4745 53	1.6591 53	1.4739 53	1.6283 53	1.6220 53
density functional	B1B95	1.6654 29	1.5007 28	1.6852 1	1.5147 1	1.6774 1	1.6670 1
density functional	B3LYP	1.6819 50	1.5159 53	1.6725 53	1.5153 52	1.6540 53	1.6432 51
Moller Plesset perturbation	MP2FC	1.6740 50	1.5176 52	1.6656 53	1.5173 53	1.6524 50	1.6386 50

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.