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 G03G03a 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.
G03 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

  1. Optimize the geometry with B3LYP/6-31G(d)
  2. Run an NMR single-point calculation with the following route section in GAUSSIANG03a,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.
  3. 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.