11.13 NMR and Other Magnetic Properties

11.13.3 Additional Magnetic Field-Related Properties

It is now possible to calculate certain open-shell magnetic field-related properties in Q-Chem. One is the hyperfine interaction (HFI) tensor, describing the interaction of unpaired electron spin with an atom’s nuclear spin levels:

Aabtot(N)=AabFC(N)δab+AabSD(N), (11.72)

where the Fermi contact (FC) contribution is

AFC(N)=α21S8π3gegNμNμνPμνα-βχμ|δ(𝐫N)|χν (11.73)

and the spin-dipole (SD) contribution is

AabSD(N)=α21SgegNμNμνPμνα-βχμ|3rN,arN,b-δabrN2rN5|χν (11.74)

for a nucleus N.

Another sensitive probe of the individual nuclear environments in a molecule is the nuclear quadrupolar interaction (NQI), arising from the interaction of a nuclei’s quadrupole moment with an applied electric field gradient (EFG), calculated as

Qab(N) =2VeNXN,aXN,b+2VNNXN,aXN,b (11.75)
=-μνPμνα+βχμ|3rN,arN,b-δabrN2rN5|χν+ANZA3RAN,aRAN,b-δabRAN2RAN5

for a nucleus N. Diagonalizing the tensor gives three principal values, ordered |Q1||Q2||Q3|, which are components of the asymmetry parameter eta:

η=Q1-Q2Q3 (11.76)

Both the hyperfine and EFG tensors are automatically calculated for all possible nuclei. All SCF-based methods (HF and DFT) are available with restricted and unrestricted references. Restricted open-shell references and post-HF methods are unavailable.

11.13.3.1 Job Control and Examples

Only one keyword is necessary in the $rem section to activate the magnetic property module.

MAGNET
       Activate the magnetic property module.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE (or 0) Don’t activate the magnetic property module. TRUE (or 1) Activate the magnetic property module.
RECOMMENDATION:
       None.

All other options are controlled through the $magnet input section, which has the same key-value format as the $rem section (see section 3.4). Current options are:

HYPERFINE
       Activate the calculation of hyperfine interaction tensors.
INPUT SECTION: $magnet
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE (or 0) Don’t calculate hyperfine interaction tensors. TRUE (or 1) Calculate hyperfine interaction tensors.
RECOMMENDATION:
       None. Due to the nature of the property, which requires the spin density ρα-β(𝐫)ρα(𝐫)-ρβ(𝐫), this is not meaningful for restricted (RHF) references. Only UHF (not ROHF) is available.

ELECTRIC
       Activate the calculation of electric field gradient tensors.
INPUT SECTION: $magnet
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE (or 0) Don’t calculate EFG tensors and nuclear quadrupole parameters. TRUE (or 1) Calculate EFG tensors and nuclear quadrupole parameters.
RECOMMENDATION:
       None.

Example 11.28  Calculating hyperfine and EFG tensors for the glycine cation.

$rem
  method = hf
  basis = def2-sv(p)
  scf_convergence = 11
  thresh = 14
  symmetry = false
  sym_ignore = true
  magnet = true
$end

$magnet
  hyperfine = true
  electric = true
$end

$molecule
1 2
N        0.0000000000      0.0000000000      0.0000000000
C        1.4467530000      0.0000000000      0.0000000000
C        1.9682482963      0.0000000000      1.4334965024
O        1.2385450522      0.0000000000      2.4218667010
H        1.7988742211     -0.8959881458     -0.5223754133
H        1.7997303368      0.8930070757     -0.5235632630
H       -0.4722340827     -0.0025218132      0.8996536532
H       -0.5080000000      0.0766867527     -0.8765335943
O        3.3107284257     -0.0000000000      1.5849828121
H        3.9426948542     -0.0000000000      0.7289954096
$end