Recommendations

This page contains a summary of the methods we recommend for good performance and cost when calculating chemical shifts and coupling constants. If you are experienced in running these sorts of calculations, you may simply refer to the information below for each method. For further information and help running calculations and processing data, please see the instructions page. For a complete list of empirical scaling factors, see the scaling factors page.

Contents:

Recommendations from Tantillo, et al. for ¹H and ¹³C computed chemical shifts

Recommendations from Bally & Rablen for ¹H computed chemical shifts

Recommendations from Bally & Rablen for ¹H-¹H computed coupling constants

Recommendations from Benassi for ¹H and ¹³C computed chemical shifts

Recommendations from Tantillo, et al. for ¹H and ¹³C computed chemical shifts:

The following information applies to calculations run using G03^G03a or G09.^G09a

Solvent modeling: We strongly recommend utilizing an implicit solvent model in the NMR single-point portion of your calculations. Doing so consistently provides significant gains in accuracy compared to gas-phase NMR calculations and does so at negligible cost in terms of effort and CPU time.

High accuracy methods: Among the scaling factors we've determined, those from the mPW1PW91 and PBE0 functionals paired with the 6-311+G(2d,p) basis set for NMR single-point calculations generally provided the lowest RMSD values for both nuclei. Both of these functionals perform well, with no significant difference between them. There is also not a significant difference between the two basis sets used for the geometry optimizations (6-31+G(d,p) and 6-311+G(2d,p) with the B3LYP or M062X functionals). Depending on the computational resources available, these methods may likely be quite affordable and we recommend their use where possible.

G03 Methods		Scaling Factors		Performance (RMSD = root mean square deviation (ppm))
Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹³C	¹H Test Set	¹H Probe Set	¹³C Test Set	¹³C Probe Set
B3LYP/6-31+G(d,p) (gas phase)	mPW1PW91/6-311+G(2d,p) (giao, scrf)	slope: -1.0823 intercept: 31.8486	slope: -1.0448 intercept: 186.0596	RMSD: 0.1128 R²: 0.9979	RMSD: 0.1446	RMSD: 1.8038 R²: 0.9990	RMSD: 2.4528
B3LYP/6-311+G(2d,p) (gas phase)	mPW1PW91/6-311+G(2d,p) (giao, scrf)	slope: -1.0821 intercept: 31.9551	slope: -1.0365 intercept: 186.6383	RMSD: 0.1146 R²: 0.9979	RMSD: 0.1455	RMSD: 1.6818 R²: 0.9991	RMSD: 2.6074
B3LYP/6-31+G(d,p) (gas phase)	PBE0/6-311+G(2d,p) (giao, scrf)	slope: -1.0844 intercept: 31.8006	slope: -1.0447 intercept: 186.8438	RMSD: 0.1159 R²: 0.9978	RMSD: 0.1476	RMSD: 1.8206 R²: 0.9990	RMSD: 2.4497
B3LYP/6-311+G(2d,p) (gas phase)	PBE0/6-311+G(2d,p) (giao, scrf)	slope: -1.0844 intercept: 31.9073	slope: -1.0365 intercept: 187.4187	RMSD: 0.1180 R²: 0.9977	RMSD: 0.1485	RMSD: 1.7008 R²: 0.9991	RMSD: 2.5991

G09 Methods		Scaling Factors		Performance (RMSD = root mean square deviation (ppm))
B3LYP/6-31+G(d,p) (gas phase)	mPW1PW91/6-311+G(2d,p) (giao, scrf)	slope: -1.0936 intercept: 31.8018	slope: -1.0533 intercept: 186.5242	RMSD: 0.1180 R²: 0.9977	RMSD: 0.1610	RMSD: 2.0561 R²: 0.9987	RMSD: 2.4900
B3LYP/6-311+G(2d,p) (gas phase)	mPW1PW91/6-311+G(2d,p) (giao, scrf)	slope: -1.0933 intercept: 31.9088	slope: -1.0449 intercept: 187.1018	RMSD: 0.1169 R²: 0.9978	RMSD: 0.1597	RMSD: 1.9114 R²: 0.9989	RMSD: 2.5949
B3LYP/6-31+G(d,p) (gas phase)	PBE0/6-311+G(2d,p) (giao, scrf)	slope: -1.0958 intercept: 31.7532	slope: -1.0533 intercept: 187.3123	RMSD: 0.1204 R²: 0.9976	RMSD: 0.1640	RMSD: 2.0768 R²: 0.9987	RMSD: 2.4913
B3LYP/6-311+G(2d,p) (gas phase)	PBE0/6-311+G(2d,p) (giao, scrf)	slope: -1.0956 intercept: 31.8603	slope: -1.0450 intercept: 187.8859	RMSD: 0.1196 R²: 0.9977	RMSD: 0.1628	RMSD: 1.9347 R²: 0.9989	RMSD: 2.5905
#M062X/6-31+G(d,p) (gas phase)	mPW1PW91/6-311+G(2d,p) (giao, scrf)	slope: -1.0938 intercept: 31.8723	slope: -1.0446 intercept: 186.7246	RMSD: 0.1233 R²: 0.9975	RMSD: 0.1604	RMSD: 1.9544 R²: 0.9989	RMSD: 2.4674
#M062X/6-311+G(2d,p) (gas phase)	mPW1PW91/6-311+G(2d,p) (giao, scrf)	slope: -1.0951 intercept: 31.9773	slope: -1.0379 intercept: 187.2065	RMSD: 0.1227 R²: 0.9975	RMSD: 0.1639	RMSD: 1.8311 R²: 0.9990	RMSD: 2.3399

Good accuracy at low cost: For a lower-cost method that still provides very good results, we recommend the B3LYP/6-31+G(d,p)//B3LYP/6-31G(d) level of theory (including implicit solvent in the NMR single-point calculation).

Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹³C	¹H Test Set	¹H Probe Set	¹³C Test Set	¹³C Probe Set
B3LYP/6-31G(d) (gas phase)	B3LYP/6-31+G(d,p) (giao, scrf)	slope: -1.0472 intercept: 31.6874	slope: -0.9600 intercept: 190.0155	RMSD: 0.1190 R²: 0.9977	RMSD: 0.1398	RMSD: 2.2640 R²: 0.9985	RMSD: 2.8937

Specific for ¹H NMR: For proton chemical shifts, the WP04/aug-cc-pVDZ//B3LYP/6-31+G(d,p) method (which was specifically-parameterized to reproduce proton chemical shifts in chloroform solvent) performs exceptionally well.

Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹³C	¹H Test Set	¹H Probe Set	¹³C Test Set	¹³C Probe Set
B3LYP/6-31+G(d,p) (gas phase)	WP04/aug-cc-pVDZ (giao, scrf)	slope: -1.0410 intercept: 31.9173	--	RMSD: 0.0959 R²: 0.9985	RMSD: 0.1137	--	--

*G03 keyword is nmr=giao (default NMR method) or nmr=csgt as indicated.

SCRF for G03 methods refers to CPCM implicit solvent model with chloroform and uaks radii.
G03 keyword: scrf=(solvent=chcl3,cpcm,read) with the specifications: radii=uaks and nosymcav read in at the end of the file.

SCRF for G09 methods refers to smd implicit solvent model with chloroform.
G09 keyword: scrf=(solvent=chloroform,smd).

WP04 is invoked using an iop statement and the BLYP functional in G03.
G03 keywords: BLYP/BasisSet and iop(3/76=1000001189,3/77=0961409999,3/78=0000109999).

#int=ultrafine was included in all calculations involving M06 functionals.

Recommendations from Bally & Rablen for ¹H computed chemical shifts:

Good accuracy at low cost:

G03 Methods		Scaling Factors	Performance (RMSD = root mean square deviation (ppm))
Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹H Test Set
B3LYP/6-31G(d) (gas phase)	WP04/6-31G(d,p) (giao, scrf)	slope: -1.0332 intercept: 32.018	RMSD: 0.119

Slightly better accuracy at somewhat greater cost:

Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹H Test Set
B3LYP/6-31G(d) (gas phase)	WP04/cc-pVDZ (giao, scrf)	slope: -1.0205 intercept: 31.844	RMSD: 0.115

Money (CPU time) is no object...:

Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹H Test Set
B3LYP/6-31G(d) (gas phase)	WP04/aug-cc-pVDZ (giao, scrf)	slope: -1.0544 intercept: 31.905	RMSD: 0.103

If you don't want to use the WP04 functional:

Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹H Test Set
B3LYP/6-31G(d) (gas phase)	B3LYP/6-31G(d,p) (giao, scrf)	slope: -1.0552 intercept: 31.840	RMSD: 0.129

If you don't want to include a simulated solvent: (This can be useful because sometimes SCRF causes convergence problems)

Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹H Test Set
B3LYP/6-31G(d) (gas phase)	WP04/6-31++G(d,p) (giao, gas phase)	slope: -1.0140 intercept: 31.988	RMSD: 0.129

If you don't want to use WP04 or SCRF:

Geometry (opt & freq)	NMR (nmr=method)*	¹H	¹H Test Set
B3LYP/6-31G(d) (gas phase)	B3LYP/aug-cc-pVDZ (giao, gas phase)	slope: -1.0554 intercept: 31.719	RMSD: 0.133
B3LYP/6-31G(d) (gas phase)	B3LYP/6-31++G(d,p) (giao, gas phase)	slope: -1.0407 intercept: 31.754	RMSD: 0.153

*G03 keyword is nmr=giao (default NMR method) or nmr=csgt as indicated.

SCRF refers to PCM implicit solvent model with chloroform.
G03 keyword: scrf(solvent=chloroform)

WP04 is invoked using an iop statement and the BLYP functional in G03.
G03 keywords: BLYP/BasisSet and iop(3/76=1000001189,3/77=0961409999,3/78=0000109999).

Recommendations from Bally & Rablen for ¹H-¹H computed coupling constants:

The simplest recommended procedure below for computing proton-proton coupling constants with gas-phase calculations has been shown to produce results with an RMS error of 0.5 Hz for a large set of organic molecules and at a relatively affordable computational cost.^Rab11a

Optimize the geometry with B3LYP/6-31G(d)
Run an NMR single-point calculation with the following route section in GAUSSIAN^G03a,^G09a

#n B3LYP/6-31G(d,p) nmr=(fconly,readatoms) iop(3/10=1100000)

At the end of the molecule specification (separated by a blank line) read in: atoms=H

A sample input file for chloroethane can be viewed by clicking here.
From the resulting log file, extract the desired Fermi contact J values, and scale them by a factor of 0.9117

Note that the iop statement in the above route section is equivalent to the NMR=mixed command in GAUSSIAN. However, this command does not inherently work with the fconly specification for the NMR calculation. Using fconly allows for calculation of just the Fermi contact terms, which are the dominant factor for proton-proton coupling constants (the other factors are spin-dipole and spin-orbit terms). As described in our paper,^Rab11a this procedure not only significantly reduces the computational cost (by a factor of approximately 0.5), but the results obtained this way are in fact superior to those obtained by consideration of all terms.

It is possible to further reduce the computational cost for this type of calculation by restricting the basis set enhancement (invoked by iop statement above) to only the hydrogen atoms. However, this requires manual specification of the modified basis set directly in the input file. Detailed instructions for this procedure can be found on the instructions page.

A recent parameterization approach for computing ¹H-¹H coupling constants with dramatically reduced computational expense has been reported.^Kut14a

Recommendations from Benassi for ¹H and ¹³C computed chemical shifts:

When paired with a triple-ζ basis set, the WP04 DFT functional represents a good compromise for both ¹H and ¹³C NMR predictions. mPW1LYP performs well for ¹H chemical shifts, while APF performs well for ¹³C chemical shifts.