Molecular properties

Calculations of molecular properties in ORCA are performed using either the %elprop or the %eprnmr block if computed with an SCF-type method (HF, DFT) or MP2. Most electric properties are performed using the %elprop block while magnetic properties (as well as ρ₀ values and quadrupole coupling constants) are generally performed using the %eprnmr block.

Electric properties

The molecular dipole moment is calculated automatically and the result is shown at the end of the outputfile. To calculate the quadrupole moment:

%elprop
Quadrupole True
end

Calculating the polarizability is more expensive as it requires solving the coupled-perturbed equations (CP-SCF):

%elprop
Polar 1
end

EPR parameters: g-tensor, hyperfine coupling tensor (HFC) and zero-field splitting (ZFS)

In HF/DFT calculations, EPR parameters such as the g-tensor, hyperfine coupling and zero-field splitting, are calculated by specifying the %eprnmr block ( for CASSCF/MRCI type calculations, the %eprnmr module is not used, see manual for more information). Note that the %eprnmr block has usually to be placed below the coordinate block (otherwise ORCA does not understand the "all H" keyword for example).

! UKS BP86 EPR-III TIGHTSCF Grid5 Finalgrid6

# Example here for methyl radical.

*xyz 0 2
C -0.738805 0.000011 -1.267493
H -1.825843 -0.009509 -1.266372
H -0.187344 -0.936654 -1.267954
H -0.203740 0.946152 -1.267952
*
%eprnmr
gtensor true printlevel 3 # this computes the g-tensor
nuclei = all H {aiso, adip} # this compute the hyperfine coupling for all hydrogens.
nuclei = all C {aiso, adip} # this compute the hyperfine coupling for all carbons.
end

The input above computes the isotropic (aiso) and the dipolar (adip) part of the hyperfine coupling tensor (HFC) that is sufficient for light elements. Note that accurate hyperfine coupling calculations of heavy elements often require computation of the 2nd order contribution of the HFC from spin orbit coupling (SOC) as well, which is given by the aorb term. The input for a calculation of the full HFC tensor of molybdenum might then look like:

nuclei = all Mo {aiso, adip, aorb}

The aorb term is quite expensive to compute, and as it makes a negligible contribution to the HFC for light elements it is only recommended for heavy elements. The manual has a discussion of this in chapter 6.21.3.1.

If the CPSCF equations fail to converge one can increase the number of iterations or perhaps change solvers:

%eprnmr
maxiter 124
end

⁵⁷Fe Mössbauer isomer shift calculations

The isomer shift is not directly calculated but rather the electron density at the Fe nucleus which can then be used to compute semi-empirical isomer shifts. Requires careful calibration.

Useful papers:

Calibration of modern density functional theory methods for the prediction of 57Fe Mössbauer isomer shifts: meta-GGA and double-hybrid functionals

M. Römelt, S. Ye, F. Neese, Inorg. Chem. 2009, 48, 784-785.

Revisiting the Mössbauer Isomer Shifts of the FeMoco cluster of Nitrogenase and the Cofactor Charge

R. Bjornsson, F. Neese and S. DeBeer, Inorg. Chem. 2017, 46, 1470-1477.

! UKS B3LYP Def2-TZVP TightSCF SlowConv
%basis NewGTO 26 "CP(PPP)" end
end

* xyz 0 1
coordinates
*
# Note that the EPR block needs to below the coordinate block for the “all Fe” command (all irons) to be recognized.
%eprnmr nuclei = all Fe {rho, fgrad}
end

Nuclear quadrupole coupling calculations

The electric field gradient is a molecular property that is very sensitive to the basis set composition, the integration grid, electronic structrure method, SCF convergence and relativistic effects (for heavier nuclei). If a standard basis set is used, the basis set can easily dominate the calculation error (never desirable), particularly for a transition metal complex EFG. A large decontracted basis set on the quadrupolar atom is usually required or possibly a specialized core-property basis set. The integration grid on the quadrupolar atom should almost always be increased and the numerical accuracy monitored. The SCF should be reliably converged and one might want to reduce numerical noise by checking the accuracy of RIJCOSX approximation. Relativistic corrections are probably not required unless going below the K-Kr row in the periodic table but are easily included (DKH2 with picture-change correction is recommended). The achieved accuracy will then depend on the electronic structure method. DFT methods have limited accuracy.

Useful papers:

Electric field gradients of transition metal complexes: Basis set uncontraction and scalar relativistic effects

R. Bjornsson and M. Bühl, Chem. Phys. Lett., 2013, 559, 112-116.

Electric Field Gradients of Transition Metal Complexes from Density Functional Theory: Assessment of Functionals, Geometries and Basis sets.

R. Bjornsson and M. Bühl, Dalton. T., 2010, 39, 5319-5324.

Input below shows the inputfile for a fairly reliable EFG calculation using DKH2:

! RKS NORI TPSS DKH2 def2-TZVP Decontract VERYTIGHTSCF SlowConv

%basis
newgto Mn "DKH-def2-QZVPP" end
end
%rel PictureChange true # Turns on the picturechange correction for the DKH2 method.

* xyz 0 1

coordinates

*
# Note that the EPR block needs to be below the coordinate block for the “all Mn” command (all manganese atoms) to be recognized.

%eprnmr nuclei = all Mn {fgrad} end

Good results (and less expensive) can usually also be obtained by using a partially contracted core-property basis set on the quadrupolar atom:

! RKS NORI TPSS def2-TZVP VERYTIGHTSCF SlowConv
%basis
newgto Mn "CP(PPP)" end
end
* xyz 0 1

coordinates

*
# Note that the EPR block needs to be below the coordinate block for the “all Mn” command (all manganese atoms) to be recognized.

%eprnmr nuclei = all Mn {fgrad} end

Visualizing g-tensor, D- tensor, EFG tensor and A tensors

The orca_euler program can be used for this. See manual

NMR Chemical Shifts

GIAO-NMR chemical shifts are available in ORCA. In computational NMR spectroscopy the shielding tensor is calculated that can be related to the chemical shift by taking the shielding difference with respect to a standard (e.g. TMS). As there is an origin dependence in shielding equations, the final shielding value actually depends on the chosen origin for finite basis sets which creates problems.

The best method to account for origin-dependence, GIAO, is now implemented in ORCA. It is the only origin recommended for NMR chemical shifts (don't use OwnNuc, IGLO or anything else) and is used by default if the NMR keyword is enabled in the simple-input line: ! NMR

Note: if the ! NMR keyword is not specified then the gauge origin needs to be set manually:

%eprnmr Ori = GIAO end

See ORCA manual for more details on the implementation. Note that the time-consuming 2-electron GIAO integrals make by default use of the RIJK approximation in ORCA (even though you may not use RIJK for the SCF). See manual for more information and for other options for calculating the 1-electron and 2-electron integrals (NORI, RIJONX, RIJCOSX etc.).

See the paper by Stoychev et al. for details on the implementation.

The simplest way of calculating the NMR chemical shifts is to just use the ! NMR keyword. This would calculate the shielding for all nuclei that can be an unnecessarily expensive calculation. If only certain nuclei are wanted, this can be requested in the %eprnmr block.

Recommended functional:

PBE0 has been popular in the literature for organic systems. The paper by Stoychev et al. found TPSS and M06-L to work better, however, and since they are non-hybrid functionals the computational cost is less.

A recent paper described a double-hybrid DFT implementation for NMR chemical shifts that suggests that double-hybrid density functionals may be the most accurate affordable methods for chemical shifts.

Recommended basis sets:

Special basis sets for NMR chemical shifts have been created by Jensen, the pcS-n basis sets (S stands for shielding).

The pcSseg-2 is a triple-zeta basis set for NMR calculations that I (RB) have used quite a lot. Sauer's core-property basis set (aug-cc-pVTZ-J) may also work well.

! PBE0 def2-TZVP def2/JK tightscf NMR

%eprnmr
Nuclei = All H { shift }
end