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.703, 521 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.706, 700, 108, 702, 703 GIAO-HF/6-31G* calculations with 1,003 atoms and 8,593 basis functions, without symmetry, have been reported.703 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”) method704, 705 for the formation of exchange contributions.703 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 method1040 is used.703 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.
$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