Fe(II) complex: DFT-calculated hyperfine tensors#

This tutorial works through susceptibility fitting and spin-Hamiltonian extraction on an iron(II) complex, using hyperfine coupling (HFC) tensors from a DFT calculation.

For a transition metal such as Fe(II), the unpaired electrons occupy valence d-orbitals that delocalise significantly onto the ligands. This covalency produces a sizeable Fermi-contact hyperfine contribution that depends on the electronic structure, not just the geometry — so the point-dipole approximation used for lanthanides (see Dy(III) complex: the point-dipole approximation) is not sufficient. Instead, SimpNMR reads the full hyperfine tensors from a quantum-chemistry output (hyperfine: method: dft), and here also takes the ab-initio susceptibility from an ORCA calculation.

Prerequisites#

Install simpnmr by following the Installation guide, then check it is available:

simpnmr --version

Command line or the desktop app#

The workflows below can be run from the terminal (the simpnmr command) or from the desktop GUI, which presents the same options as a form and can open and save the run.yml shown here. To use the GUI, install the optional GUI dependencies and launch it:

pip install "simpnmr[gui]"
simpnmr-gui

The window has a toolbar (New, Open YAML…, Save YAML, Save As…, ▶ Run, ■ Stop); a form on the left whose sections mirror the run.yml blocks, with a Workflow selector (Predict / Fit susceptibility) at the top; and a 3D viewer with a live log panel on the right. The general pattern is: Open YAML… → choose your run.yml → set the Workflow mode → click ▶ Run.

The complex and its input files#

Create a working directory with the data/ sub-folders:

mkdir fe-tutorial
cd fe-tutorial
mkdir -p data/chi data/hfc data/labels data/dia data/para

Ab-initio inputs (downloads). The hyperfine tensors and the susceptibility come from quantum-chemistry calculations whose output files are large. Download each and save it under the path shown:

hyperfine.out → data/hfc/hyperfine.out (DFT hyperfine tensors)
susceptibility.out → data/chi/susceptibility.out (ORCA NEVPT2 susceptibility)

The diamagnetic reference shifts (ppm):

data/dia/diamagnetic_shifts.csv#

chem_label,shift
H1,1.87
H2_u,1.26
H2_d,1.35
H3,1.09
H4,7.46
H5,7.26
H6,7.26
C1,10.81
C2_up,19.30
C2_down,21.01
C3,33.07
C4,133.6
C5,128.46
C6,129.47
C7,134.48

The chemical-label map — note the extra chem_math_label column, which gives a LaTeX label used in figures:

data/labels/chemical_labels.csv

data/labels/chemical_labels.csv#

atom_label,chem_label,chem_math_label
H1,H3,$\mathbf{H}_{\mathit{3}}$
H2,H3,$\mathbf{H}_{\mathit{3}}$
H3,H3,$\mathbf{H}_{\mathit{3}}$
H4,H3,$\mathbf{H}_{\mathit{3}}$
H5,H3,$\mathbf{H}_{\mathit{3}}$
H6,H3,$\mathbf{H}_{\mathit{3}}$
H7,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H8,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H9,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H10,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H11,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H12,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H13,H1,$\mathbf{H}_{\mathit{1}}$
H14,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H15,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H16,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H17,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H18,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H19,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H20,H1,$\mathbf{H}_{\mathit{1}}$
H21,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H22,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H23,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H24,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H25,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H26,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H27,H1,$\mathbf{H}_{\mathit{1}}$
H28,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H29,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H30,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H31,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H32,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H33,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H34,H1,$\mathbf{H}_{\mathit{1}}$
H35,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H36,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H37,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H38,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H39,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H40,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H41,H1,$\mathbf{H}_{\mathit{1}}$
H42,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H43,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H44,H2_d,$\mathbf{H}_{\mathit{2}}^{\mathit{D}}$
H45,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H46,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H47,H2_u,$\mathbf{H}_{\mathit{2}}^{\mathit{U}}$
H48,H4,$\mathbf{H}_{\mathit{4}}$
H49,H5,$\mathbf{H}_{\mathit{5}}$
H50,H6,$\mathbf{H}_{\mathit{6}}$
H51,H5,$\mathbf{H}_{\mathit{5}}$
H52,H4,$\mathbf{H}_{\mathit{4}}$
H53,H1,$\mathbf{H}_{\mathit{1}}$
C1,C3,$\mathbf{C}_{\mathit{3}}$
C2,C3,$\mathbf{C}_{\mathit{3}}$
C3,C3,$\mathbf{C}_{\mathit{3}}$
C4,C1,$\mathbf{C}_{\mathit{1}}$
C5,C2_up,$\mathbf{C}_{\mathit{2}}^{\mathit{U}}$
C6,C2_down,$\mathbf{C}_{\mathit{2}}^{\mathit{D}}$
C7,C1,$\mathbf{C}_{\mathit{1}}$
C8,C2_up,$\mathbf{C}_{\mathit{2}}^{\mathit{U}}$
C9,C2_down,$\mathbf{C}_{\mathit{2}}^{\mathit{D}}$
C10,C1,$\mathbf{C}_{\mathit{1}}$
C11,C2_up,$\mathbf{C}_{\mathit{2}}^{\mathit{U}}$
C12,C2_down,$\mathbf{C}_{\mathit{2}}^{\mathit{D}}$
C13,C1,$\mathbf{C}_{\mathit{1}}$
C14,C2_up,$\mathbf{C}_{\mathit{2}}^{\mathit{U}}$
C15,C2_down,$\mathbf{C}_{\mathit{2}}^{\mathit{D}}$
C16,C1,$\mathbf{C}_{\mathit{1}}$
C17,C2_down,$\mathbf{C}_{\mathit{2}}^{\mathit{D}}$
C18,C2_up,$\mathbf{C}_{\mathit{2}}^{\mathit{U}}$
C19,C1,$\mathbf{C}_{\mathit{1}}$
C20,C2_down,$\mathbf{C}_{\mathit{2}}^{\mathit{D}}$
C21,C2_up,$\mathbf{C}_{\mathit{2}}^{\mathit{U}}$
C22,C7,$\mathbf{C}_{\mathit{7}}$
C23,C4,$\mathbf{C}_{\mathit{4}}$
C24,C5,$\mathbf{C}_{\mathit{5}}$
C25,C6,$\mathbf{C}_{\mathit{6}}$
C26,C5,$\mathbf{C}_{\mathit{5}}$
C27,C4,$\mathbf{C}_{\mathit{4}}$

The variable-temperature peak lists — twelve measured spectra, one per temperature. Save each block under data/para/ with the file name in its caption:

1. Variable-temperature susceptibility fitting#

This workflow fits the temperature dependence of the susceptibility across the twelve measured spectra. The configuration reads hyperfine tensors from the DFT output (hyperfine: method: dft) and the ab-initio susceptibility from the ORCA output (susc_vt: ab_initio_file):

run.yml#

project:
  name: fe_vt_fit

hyperfine:
  method: dft
  file: data/hfc/hyperfine.out
  paramagnetic_centre: [9.122358, 5.108520, 11.946464]
  spin: 2.0

nuclei:
  include_groups: ['H4', 'H5', 'H6', 'C4', 'C5', 'C6', 'C7']

assignment:
  method: fixed

diamagnetic:
  method: csv
  file: data/dia/diamagnetic_shifts.csv

experiment:
  files: [data/para/*K.csv]

chem_labels:
  file: data/labels/chemical_labels.csv

susc_vt:
  method: vt_2nd_order
  tip_type: fix_tip_from_ab_initio
  ab_initio_file: data/chi/susceptibility.out
  ab_initio_format: orca_nev
  variables:
    iso:
      intercept: [fit, 0.01]
      slope: [fit, 0.01]
    ax:
      intercept: [fit, 0.01]
      slope: [fit, 0.01]
    rh:
      intercept: [fix, 0.0]
      slope: [fix, 0.0]

susc_fit:
  type: isoaxrh
  variables:
    iso: [fit, 0.01]
    ax: [fit, 0.01]
    rh_over_ax: [fix, 0.00]
  average_shifts: 'all'

Key points of this configuration:

hyperfine: method: dft: Reads the full hyperfine tensors from hyperfine.out instead of computing them from geometry. spin: 2.0 is the total spin S = 2 of high-spin Fe(II).
susc_vt: Models the temperature dependence of the susceptibility to second order (vt_2nd_order), fixing the temperature-independent paramagnetism (TIP) from the ab-initio susceptibility in susceptibility.out (ab_initio_format: orca_nev).

Run the variable-temperature fit:

Command line

simpnmr --hide fit_susc --susc_units 'cm3 mol-1' run.yml

--hide saves the figures without displaying them interactively; --susc_units states the units of the susceptibility input explicitly.

Desktop app

Launch simpnmr-gui, Open YAML… this run.yml, and set the Workflow to Fit susceptibility. The susc_vt block populates the variable-temperature section of the form. Choose the susceptibility units in that section (equivalent to --susc_units), then click ▶ Run.

Among the outputs is an isoaxrh-type fit file summarising the fitted tensor as a function of temperature — used as the input to the next workflow.

2. Extracting a spin Hamiltonian#

The fitted susceptibility can be converted into spin-Hamiltonian parameters. Take the iso/ax/rh fit produced above (an example is shown below; save it as isoaxrh_fit.csv):

isoaxrh_fit.csv#

# Data reported in Curie-normalised chiT (dimensionless) Units
# spin 2.0
type,intercept,slope,intercept_err,slope_err,adj_r2
iso,4.314820,383.105186,0.498071,138.244569,0.970155
ax,1.743901,323.957098,0.150237,41.699677,0.976824
rh,0.000000,0.000000,0.000000,0.000000,

Then run:

simpnmr get_sh --spin 2.0 isoaxrh_fit.csv

Note

get_sh is a command-line utility and has no equivalent in the desktop GUI, which covers the Predict and Fit susceptibility workflows.

Next steps#

See Dy(III) complex: the point-dipole approximation for the lanthanide workflow, where hyperfine tensors are approximated from geometry rather than DFT.
Read Workflows for an overview of all workflows.
Consult Input YAML Files when adapting run.yml to your own system.