In conventional implementations, the cost for computation of NMR chemical
shifts within even the simplest quantum chemical methods such as Hartree-Fock
of DFT increases cubically with molecular size $M$, $\mathcal{O}({M}^{3})$. As such,
NMR chemical shift calculations have largely been limited to molecular systems
on the order of 100 atoms, assuming no symmetry. For larger systems it is
crucial to reduce the increase of the computational effort to linear, which is
possible for systems with a nonzero HOMO/LUMO gaps and was reported for
the first time by Kussmann and Ochsenfeld.^{Ochsenfeld:2004, Kussmann:2007a}
This approach incurs no loss of accuracy with respect to traditional
cubic-scaling implementations, and makes feasible NMR chemical shift
calculations using Hartree-Fock or DFT approaches in molecular systems with
1,000+ atoms. For many molecular systems the Hartree-Fock (GIAO-HF) approach
provides typically an accuracy of 0.2–0.4 ppm for the computation of ${}^{1}$H NMR
chemical shifts, for example.^{Ochsenfeld:2000b, Ochsenfeld:2001, Brown:2001, Ochsenfeld:2002, Ochsenfeld:2004} GIAO-HF/6-31G* calculations
with 1,003 atoms and 8,593 basis functions, without symmetry, have been
reported.^{Ochsenfeld:2004} GIAO-DFT calculations are even simpler and
faster for density functionals that do not contain Hartree-Fock exchange.

The present implementation of NMR shieldings employs the LinK (linear exchange,
“K”) method^{Ochsenfeld:1998, Ochsenfeld:2000a} for the formation of
exchange contributions.^{Ochsenfeld:2004} Since the derivative of the
density matrix with respect to the magnetic field is skew-symmetric, its
Coulomb-type contractions vanish. For the remaining Coulomb-type matrices the
CFMM method^{White:1994a} is used.^{Ochsenfeld:2004} In addition, a
multitude of different approaches for the solution of the CPSCF equations can
be selected within Q-Chem.

To request a NMR chemical shift calculation using the density matrix approach,
set JOBTYPE to NMR in the *$rem* section.
Additional job-control variables can be found below.

D_CPSCF_PERTNUM

Specifies whether to do the perturbations one at a time, or all together.

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

0
Perturbed densities to be calculated all together.
1
Perturbed densities to be calculated one at a time.

RECOMMENDATION:

None

D_SCF_CONV_1

Sets the convergence criterion for the level-1 iterations. This preconditions
the density for the level-2 calculation, and does not include any
two-electron integrals.

TYPE:

INTEGER

DEFAULT:

4
corresponding to a threshold of ${10}^{-4}$.

OPTIONS:

$$
Sets convergence threshold to ${10}^{-n}$.

RECOMMENDATION:

The criterion for level-1 convergence must be less than or equal to the
level-2 criterion, otherwise the D-CPSCF will not converge.

D_SCF_CONV_2

Sets the convergence criterion for the level-2 iterations.

TYPE:

INTEGER

DEFAULT:

4
Corresponding to a threshold of ${10}^{-4}$.

OPTIONS:

$$
Sets convergence threshold to ${10}^{-n}$.

RECOMMENDATION:

None

D_SCF_MAX_1

Sets the maximum number of level-1 iterations.

TYPE:

INTEGER

DEFAULT:

100

OPTIONS:

$n$
User defined.

RECOMMENDATION:

Use the default.

D_SCF_MAX_2

Sets the maximum number of level-2 iterations.

TYPE:

INTEGER

DEFAULT:

30

OPTIONS:

$n$ User defined.

RECOMMENDATION:

Use the default.

D_SCF_DIIS

Specifies the number of matrices to use in the DIIS extrapolation in the
D-CPSCF.

TYPE:

INTEGER

DEFAULT:

11

OPTIONS:

$n$
$n$ = 0 specifies no DIIS extrapolation is to be used.

RECOMMENDATION:

Use the default.

$molecule 0 1 H 0.00000 0.00000 0.00000 C 1.10000 0.00000 0.00000 F 1.52324 1.22917 0.00000 F 1.52324 -0.61459 1.06450 F 1.52324 -0.61459 -1.06450 $end $rem JOBTYPE NMR EXCHANGE B3LYP BASIS 6-31G* D_CPSCF_PERTNUM 0 D-CPSCF number of perturbations at once D_SCF_SOLVER 430 D-SCF leqs_solver D_SCF_CONV_1 4 D-SCF leqs_conv1 D_SCF_CONV_2 4 D-SCF leqs_conv2 D_SCF_MAX_1 200 D-SCF maxiter level 1 D_SCF_MAX_2 50 D-SCF maxiter level 2 D_SCF_DIIS 11 D-SCF DIIS D_SCF_ITOL 2 D-SCF conv. criterion $end