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 , . 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.683, 513 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 H NMR chemical shifts, for example.686, 680, 123, 682, 683 GIAO-HF/6-31G* calculations with 1,003 atoms and 8,593 basis functions, without symmetry, have been reported.683 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”) method684, 685 for the formation of exchange contributions.683 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 method991 is used.683 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 .
OPTIONS:
Sets convergence threshold to .
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 .
OPTIONS:
Sets convergence threshold to .
RECOMMENDATION:
None
D_SCF_MAX_1
Sets the maximum number of level-1 iterations.
TYPE:
INTEGER
DEFAULT:
100
OPTIONS:
User defined.
RECOMMENDATION:
Use the default.
D_SCF_MAX_2
Sets the maximum number of level-2 iterations.
TYPE:
INTEGER
DEFAULT:
30
OPTIONS:
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:
= 0 specifies no DIIS extrapolation is to be used.
RECOMMENDATION:
Use the default.
Example 11.30 NMR chemical shifts via the D-CPSCF method, showing all input options.
$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