# NMR Chemical Shifts¶

NMR Chemical shifts have been implemented [113-117] in a separate property program NMR. It requires the TAPE21 result file from an ADF calculation. The NMR module can be combined with the ZORA treatment for relativistic effects and with Spin-Orbit effects, making it suitable for treatment of heavy elements. See also the general review on relativistic computations of NMR parameters [331].

## Important notes¶

TAPE21 and TAPE10

NMR requires an ASCII input file and TAPE21 and TAPE10 result files from an ADF calculation on the molecule to be analyzed. The ADF result files TAPE21 and TAPE10 must be present with names TAPE21 and TAPE10 in the directory where you execute NMR. Use the keywords SAVE TAPE10 in the adf calculation in order to obtain a TAPE10 result file.

Recalculation of TAPE10 by NMR

Warning: the NMR property program will not always give the correct result for every SCF potential in the ADF calculation, like for example the SAOP potential, or if one uses COSMO in the ADF calculation, if one lets the NMR recalculate TAPE10. This is due to the GIAO method used in this program, which requires the calculation of the SCF potential, which is not done correctly for potentials, other than the standard LDA and GGA potentials. To obtain correct results one should, in addition to the use of TAPE21, also use TAPE10 that ADF generates, using the keywords SAVE TAPE10, and use it as input for the NMR property program. On TAPE10 the SCF potential is written, which is read in by the NMR program.

Atomic calculation

NMR calculations on 1 atom must have symmetry NOSYM.

Spin-orbit coupling

NMR calculations on systems computed by ADF with Spin Orbit relativistic effects included must have used NOSYM symmetry in the ADF calculation. NMR can also be combined with ADF ZORA calculations. The NMR program reads from TAPE21 the relativistic option that is used in the ADF calculation, and will use the same relativistic option in the NMR calculations.

Kernel used in spin-orbit coupling

One can include an improved exchange-correlation kernel, as was implemented by J. Autschbach [427], but this is not used by default, see subkey USE. This is an important option that should be seriously considered and has been advocated in Ref. [427].

In the ADF2008.01 a bug was introduced in the spin-orbit part of the calculated chemical shielding, which caused the calculated chemical shielding to be gauge dependent. This bug is relevant for spin-orbit coupled calculations for ADF versions ADF2008-ADF2013. In ADF2014 this bug has been fixed.

There is gauge dependence if the scaled ZORA method is used in the calculation of NMR chemical shieldings. Therefore the default method for NMR chemical shielding calculations is changed in ADF2014 to use the unscaled ZORA method.

SAOP

The use of the model SAOP potential leads to isotropic chemical shifts which are substantially improved over both LDA and GGA functionals, and of similar accuracy as results with a self-interaction-corrected functional (SIC), see [421]. SAOP is computationally expedient and routinely applicable to all systems, requiring virtually the same computational effort as LDA and GGA calculations.

NICS

The Nucleus-Independent Chemical Shift (NICS) can be calculated at any point in the molecule.

Hybrids

Starting from ADF2009.01 Hartree-Fock and the hybrid potentials can used in combination with NMR chemical shielding calculations. see Refs. [422, 423]. Use SAVE TAPE10 in the ADF calculation. The use of frozen cores and hybrids gives gauge dependent results for the NMR chemical shieldings, therefore the NMR program will stop in this case.

Meta-GGA’s and meta-hybrids

Meta-GGA’s and meta-hybrids should not be used in combination with NMR chemical shielding calculations. The results are wrong due to an incorrect inclusion of GIAO terms.

Bug fix ADF2005.01 off-diagonal part shielding tensor

Bug fix off-diagonal part shielding tensor: In the ADF2005.01 the bugs in the NMR module are fixed that gave problems in the ADF2004.01 and older versions.

## Input options¶

The input file for NMR uses the block key NMR, with several (optional) subkeys, each having a series of options. For analysis a separate block key can be used.

ADFBIN/nmr << eor ZSOAO2007 RECALCULATETAPE10 NMR End Analysis End eor  ZSOAO2007 keyword In the ADF2008.01 a bug was introduced in the spin-orbit part of the calculated chemical shielding, which caused the calculated chemical shielding to be gauge dependent. This bug is relevant for spin-orbit coupled calculations for ADF versions ADF2008-ADF2013. Workaround in ADF versions ADF2008-ADF2013 is to include the keyword ZSOAO2007 in the NMR part of the input, which causes a one-center approximation to be used. The bug has been fixed in ADF2014 by introducing an extra gauge-correction term for the spin-orbit coupled part. One can still get the (slightly) incorrect results in ADF2014 by using the keyword WRONGSOGAUGE, and not including ZSOAO2007. REACALCULATETAPE10 keyword If there is no TAPE10 present the NMR program will stop. One can use the key REACALCULATETAPE10 such that TAPE10 will be recalculated by the NMR module. Not recommended to be used. Better use ‘SAVE TAPE10’ in the ADF calculation, and use this TAPE10 as input for NMR. NMR block key NMR Out OutOptions Calc CalcOptions Use UseOptions U1K U1KOptions Nuc NucOptions Atoms AtomsOptions Ghosts GhostsOptions Analysis AnalysisOptions End  Out OutOptions The subkey Out controls printed output. Its options specify the details by their (optional) presence. The following OutOptions are recognized (Default ISO TENS): All Implies all the other options ISO Isotropic shielding constants Tens Shielding tensors Eig Eigenvectors U1 The U1 matrix F1 The first order change in the Fock matrix S1 The first order change in the Overlap matrix AOP The paramagnetic AO matrix (= the matrix in the representation of elementary atomic basis functions) AOD The diamagnetic AO matrix AOF The Fermi-contact AO matrix REFS Literature references INFO General information Calc CalcOptions The subkey Calc controls what is actually calculated. The following options are available (Default ALL): All Implies all of the other options to this key Para The paramagnetic part Dia The diamagnetic part FC The Fermi-contact part in case of the Pauli Hamiltonian SO The Fermi-contact part in case of the ZORA Hamiltonian Use UseOptions The subkey Use controls some optional options (default none) FXC Improves the exchange-correlation kernel used, as was implemented by J. Autschbach [427]. Important only in case of spin-orbit coupled calculations. This may give some (small) gauge dependent results when using this. Important option that should be seriously considered and has been advocated in Ref. [427]. SCALED Implies the scaled ZORA method, which gives (slightly) gauge dependent results, as was shown in Ref. [427]. Note that in case of the ZORA Hamiltonian default the unscaled ZORA method is used. For chemical shifts, only compare results with the same options. SO1C Before ADF2008.01 in the the spin-orbit term a 1-center approximation was used, which does not suffer from gauge dependence. This 1-center approximation can be used with USE SO1C. U1K U1KOptions The subkey U1K determines which terms are included in the calculation of the U1 matrix (first order changes in MO coefficients). Options (Default Best): Best The best (recommended) options for each relativistic option are included for this subkey. Implies ‘None’ for non-relativistic and scalar relativistic ZORA, ‘SO’ + ‘SOFULL’ for spin-orbit coupled ZORA, and ‘MV + ‘Dar’ for the Pauli Hamiltonian. None Implies none of the other options to this key. All Implies all the other options to this key. MV The mass-velocity term . Dar The Darwin term. ZMAN The Spin-Zeeman term. Can be included only in case of spin-orbit coupled Pauli Hamiltonian. SO ZORA spin-orbit part. SOFULL ZORA spin-orbit part. Note: for chemical shifts, only compare results with the same options. If the subkey U1K is used with the option ALL in the ZORA calculation, then the scaled ZORA orbital energies are used in the making of the U1 matrix, which is not recommended. Recommended is to use ‘U1K Best’ in all cases, which uses plain ZORA orbital energies in the making of the U1 matrix. NUC NucOptions This subkey NUC specifies for which nuclei the NMR shielding is calculated. Default all nuclei are calculated, i.e. as for omitting the subkeys ATOMS and NUC. Else you may use this options by simply typing Nuc in the NMR block (without any further data); this means: for no nuclei at all. Alternatively you may type the index of the atom(s) you want to see analyzed. Default all nuclei are calculated, i.e. as for omitting this subkey. Example: NUC 2 1  The numbers refer to the internal numbering of the nuclei as it appears somewhere early in the general ADF output. This internal numbering is also the internal NMR numbering, but it is not necessarily the same as the input ordering. Use the subkey ATOMS to specify the nuclei according to this input ordering in the ADF calculation. Note that the number of nuclei has a significant consequence for the total CPU time. Atoms AtomsOptions This subkey ATOMS specifies for which nuclei the NMR shielding is calculated. Default all nuclei are calculated, i.e. as for omitting the subkeys ATOMS and NUC. Example: ATOMS 2 1  The numbers refer to the input ordering in the ADF calculation. Use the subkey NUC to specify the nuclei according to the internal NMR numbers of the atoms. GHOSTS The subkey GHOSTS is a block type subkey. The format is: Ghosts xx1 yy1 zz1 xx2 yy2 zz2 ... SubEnd  With this key, the user can specify ANY point(s) within the molecule at which the shielding is to be calculated (whatever the physical meaning of this shielding is). One can think of those points as neutrons within the molecule. There is a publication by P. Schleyer et al. using a similar feature (J. Am. Chem. Soc. 118, 6317, 1996). They call it NICS, Nucleus-Independent Chemical Shift. Note that the NICS value is minus 1 times the isotropic part of the shielding tensor that is calculated at these points: xx1 yy1 zz1  real numbers that specify the Cartesian coordinates of ‘ghost’ 1, etc. The coordinates have to be specified in the same units as any other input (ADF subkey Units). That is, you use Angstrom for the ghosts if you did so for the atomic coordinates, or bohr otherwise. The same set of coordinates has to be specified as ‘point charges with charge zero’ using the key EFIELD. This is necessary in order to allow the appropriate distribution of integration points around the ghosts. E.g., if you want to have two ‘ghosts’ with the coordinates xx1 yy1 zz1 and xx2 yy2 zz2 then you must also have in the input the key EFIELD as follows: EFIELD xx1 yy1 zz1 0.0 xx2 yy2 zz2 0.0 END  (the last number is the charge at these coordinates - zero). Eventually, this step should be programmed internally but for now the procedure outlined above works. No check is done to verify whether those ‘point charges’ are taken care of or not, but their omission leads to unpredictable results. Only Cartesian coordinates are possible for ghosts, even if the atoms were originally specified using internal coordinates. This shouldn’t be a problem, though (e.g., one could start an ADF run of the molecule of interest, and get very soon the Cartesian coordinates of the atoms in the output. This run would then be aborted, and restarted with the ghosts specified as desired.) The ghosts are numbered in the output as NNUC+1, NNUC+2 ... where NNUC is the total number of nuclei in this molecule. Default: no ghosts. Analysis AnalysisOptions The subkey Analysis controls the MO analysis. After the word (subkey) Analysis you type an integer, which then specifies that the first so many MOs are to be analyzed. Default no Analysis. The value of this analysis subkey in the block key NMR is somewhat limited. The separate ANALYSIS block key can give more analysis of the NMR chemical shielding. Analysis block key The NMR shielding tensor, can be analyzed in detail, see Refs. [329-331]. For the analysis option with the ANALYSIS block key there are some restrictions. In the ADF calculation all electron basis sets should have been used, and SYMMETRY NOSYM. Can not be used in case of non-relativistic calculations. The ADF calculation should use relativistic scalar ZORA or relativistic spinorbit ZORA. In case of scalar relativistic ZORA the keyword FAKESO should be added to the NMR input (outside of the NMR or Analysis block keys). The analysis utilizes the ZORA spin-orbit branch of the NMR code. For scalar ZORA, the NMR analysis contributions will appear in equivalent pairs for spin-orbitals even if the ADF calculation is closed-shell spin restricted. The MO numbering then also reflects this doubling of MOs. In the analysis, canonical MOs number 1 and 2 are the alpha and beta spin ADF MO 1, canonical MOs number 3 and 4 correspond to the alpha and beta spin ADF MO 2, and so on. In case of spinorbit relativistic ZORA the keyword FAKESO should not be included. For an NBO analysis of NMR, see the section on NBO analysis. Analysis print threshold canonical {components} End {FakeSO}  print threshold The print keyword selects printout of contributions relative to the total diamagnetic, paramagnetic. For example in case of ‘print 0.01’ only contributions greater than 1% are printed. Set to zero to print ALL contributions. canonical It enables an analysis of the shielding in terms of the canonical MOs. components The components keyword is optional and enables an analysis not only of the isotropic shielding but also of the diagonal Cartesian components of the tensor XX, YY, and ZZ). In order to analyze the principal shielding tensor components with canonical MOs you can calculate the shielding tensor first with the NMR code, rotate the molecule such that the principal axes system aligns with the Cartesian coordinate system, and then repeat the NMR calculation with the analysis features switched on. # Paramagnetic NMR Chemical Shifts¶ Knowledge of the g-tensor and hyperfine A-tensor can be used in the prediction and analysis of paramagnetic NMR shifts, see Refs. [340-342]. Because of the dependence on the g-tensor, prediction of paramagnetic NMR (pNMR) shifts is not straightforward, as the dependence of the pNMR shift on excess $$\alpha$$ or $$\beta$$ electron spin density at a nucleus is to be combined with the sign and magnitude of the isotropic g-value. Ref. [340] describes in detail how to calculate pNMR contact chemical shifts and pNMR pseudo-contact chemical shifts, using the ADF program. Of course, like for NMR chemical shielding of closed shell molecules, one also needs to calculate of the so called orbital dependent part of the NMR chemical shielding of the open shell molecule. For open shell molecules in ADF this can only be calculated without taken into account spin-orbit coupling: ADFBIN/adf << eor
CHARGE charge spinpolarization
unrestricted
Relativistic scalar ZORA
Basis
Core None
End
SAVE TAPE10
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