NMR calculations are available at both the Hartree-Fock and DFT levels of theory.
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Q-Chem computes NMR chemical shielding tensors using gauge-including atomic
orbitals (GIAOs),
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an approach that has proven to reliable and accurate for many applications.
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The shielding tensor
is a second-order property that depends upon the external magnetic field,
, and the spin angular momentum for a given nucleus:
| (10.116) |
Using analytical derivative techniques to evaluate , the components of this tensor are computed as
| (10.117) |
where indicate Cartesian components. Note that there is a
separate chemical shielding tensor for each , that is, for each
nucleus. To compute it is necessary to solve coupled-perturbed
SCF (CPSCF) equations to obtain the perturbed densities , which can be accomplished using the MO-based “MOProp” module whose use
is described below. (Use of the MOProp module to compute optical properties of
molecules was discussed in Section 10.10.) Alternatively, a
linear-scaling, density matrix-based CPSCF (D-CPSCF) formulation is
available,
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which is described in
Section 10.11.3.
In addition to chemical shifts, indirect nuclear spin-spin coupling constants, also known as scalar couplings or -couplings, can be computed at the SCF level. The coupling tensor between atoms and is evaluated as the second derivative of the electronic energy with respect to the nuclear magnetic moments :
| (10.118) |
The indirect coupling tensor has five distinct contributions. The diamagnetic spin-orbit (DSO) contribution is calculated as an expectation value with the ground state wave function. The other contributions are the paramagnetic spin-orbit (PSO), spin-dipole (SD), Fermi contact (FC), and mixed SD/FC contributions. These terms require the electronic response of the systems to the perturbation due to the magnetic nuclei. Ten distinct CPSCF equations must be solved for each perturbing nucleus, which makes the calculation of -coupling constants more time-consuming than that of chemical shifts.
Some authors have recommended calculating only the Fermi contact
contribution,
71
J. Org. Chem
(2011),
76,
pp. 4818.
Link
and skipping the other contributions, for
H–H coupling constants. For that purpose, Q-Chem allows the user
to skip calculation of any of the four contributions: (FC, SD, PSO, or DSO.
(The mixed SD/FC contributions is automatically calculated at no
additional cost whenever both the SD and FC contributions are computed.) See
Section 10.10.3 for details. Note that omitting any of the
contributions cannot be rationalized from a theoretical point of view. Results
from such calculations should be interpreted extremely cautiously.
Note:
1.
Specialized basis sets are highly recommended in any -coupling
calculation, such as the pcJ- basis set family.
634
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(2006),
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Link
2.
The Hartree-Fock level of theory is not suitable to obtain
-coupling constants of any degree of reliability. Use GGA or
hybrid density functionals instead.
Q-Chem’s new FD-NMR feature calculates the NMR shielding tensor by applying finite differentiation on an analytic property, such as the total energy (when IDERIV = 0), or the atom-wise induced magnetic field (when IDERIV = 1) the first derivative of the energy with respect to the nuclear magentic moments. FD1 based shielding calculation is much more efficient than that of FD2, and is avaliable at restricted SCF level (i.e. up to rung 4 hybrid / range-separated hybrid functionals). FD2 also has limited support for correlated methods such as (regularized) RI-MP2.
Example 10.55 FD2-based NMR calculation for water at RI-MP2/pcSseg-2 level.
$molecule 0 1 O 0.00000 0.00000 0.11779 H 0.00000 0.75545 -0.47116 H 0.00000 -0.75545 -0.47116 $end $rem JOBTYPE SP ! Required: zero-field job to prepare the initial guess for field-on job METHOD HF SYM_IGNORE 1 SYMMETRY FALSE BASIS pcSseg-2 AUX_BASIS_J RIJK-def2-TZVP AUX_BASIS_K RIJK-def2-TZVP RI_J TRUE RI_K TRUE SCF_ALGORITHM DIIS SCF_CONVERGENCE 10 MAX_SCF_CYCLES 100 NMR_SAVE 1 ! Required: zero-field job to prepare the initial guess for field-on job MEM_TOTAL 4000 $end @@@ $molecule READ $end $rem JOBTYPE NMRSHIELD METHOD RIMP2 IDERIV 0 ! Required for FD2 logic SYM_IGNORE 1 SYMMETRY FALSE BASIS pcSseg-2 AUX_BASIS_J RIJK-def2-TZVP AUX_BASIS_K RIJK-def2-TZVP AUX_BASIS_CORR RIMP2-def2-TZVP RI_J TRUE RI_K TRUE SCF_ALGORITHM DIIS SCF_CONVERGENCE 10 DO_FINITE_B_OR_M 1 FDIFF_STEPSIZE_B 100 ! B field finite Difference step size in 1E-5 A.U. TENSOR_DIAG_ONLY TRUE ! Calculates diagonal elements only COMPLEX TRUE ! Required USE_LIBQINTS TRUE ! Required MEM_TOTAL 4000 $end $shielding ! select atom for shielding computation, index starts from 0 0 1 2 $end
Example 10.56 FD1-based NMR calculation for benzene at HF/pcSseg-3 level.
$molecule 0 1 H -8.15907 2.62281 1.60092 C -8.66658 2.57679 0.63197 C -10.05547 2.62953 0.57123 H -10.64089 2.71700 1.49206 C -10.70043 2.57096 -0.65988 H -11.79336 2.61234 -0.70769 C -9.95678 2.45974 -1.83037 H -10.46440 2.41365 -2.79910 C -8.56799 2.40692 -1.76952 H -7.98287 2.31923 -2.69053 C -7.92294 2.46549 -0.53841 H -6.83011 2.42401 -0.49049 $end $rem JOBTYPE SP ! Required: zero-field job to prepare the initial guess for field-on job METHOD HF SYM_IGNORE 1 SYMMETRY FALSE BASIS pcSseg-3 AUX_BASIS_J RIJK-def2-QZVP AUX_BASIS_K RIJK-def2-QZVP RI_J TRUE OCC_RI_K TRUE SCF_ALGORITHM DIIS SCF_CONVERGENCE 10 NMR_SAVE 1 ! Required: zero-field job to prepare the initial guess for field-on job MEM_TOTAL 8000 $end @@@ $molecule READ $end $rem JOBTYPE NMRSHIELD METHOD HF IDERIV 1 ! Required for FD1 logic SYM_IGNORE 1 SYMMETRY FALSE BASIS pcSseg-3 AUX_BASIS_J RIJK-def2-QZVP AUX_BASIS_K RIJK-def2-QZVP RI_J TRUE OCC_RI_K TRUE SCF_ALGORITHM DIIS SCF_CONVERGENCE 10 DO_FINITE_B_OR_M 1 FDIFF_STEPSIZE_B 100 ! B field finite Difference step size in 1E-5 A.U. COMPLEX TRUE USE_LIBQINTS TRUE ! Required NMR_FORWARD_DIFF TRUE ! Calculates NMR properties with forward difference instead of central difference MEM_TOTAL 8000 $end
This section describes the use of Q-Chem’s MO-based CPSCF code, which is contained in the “MOProp” module that is also responsible for computing electric properties. NMR chemical shifts are requested by setting MOPROP = 1, and -couplings by setting JOBTYPE = ISSC. The reader is referred to to Section 10.10.3 for additional job control variables associated with the MOProp module, as well as explanations of the ones that are invoked in the samples below. An alternative, density matrix-based implementation of NMR chemical shifts is also available and is described in Section 10.11.3. Setting JOBTYPE = NMR invokes the density-based code, not the MO-based code.
Example 10.57 MO-based NMR calculation.
$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 METHOD B3LYP BASIS 6-31G* MOPROP 1 MOPROP_PERTNUM 0 ! do all perturbations at once MOPROP_CONV_1ST 7 ! sets the CPSCF convergence threshold MOPROP_DIIS_DIM_SS 4 ! no. of DIIS subspace vectors MOPROP_MAXITER_1ST 100 ! max iterations MOPROP_DIIS 5 ! turns on DIIS (=0 to turn off) MOPROP_DIIS_THRESH 1 MOPROP_DIIS_SAVE 0 $end
In the following compound job, we show how to restart an NMR calculation should it exceed the maximum number of CPSCF iterations (specified with MOPROP_MAXITER_1ST, or should the calculation run out of time on a shared computer resource. Note that the first job is intentionally set up to exceed the maximum number of iterations, so will crash. However, the calculation is restarted and completed in the second job.
Example 10.58 Illustrates how to restart an NMR calculation. In this first job, we intentionally set the max number of iterations too small, to force premature end so that we can demonstrate restart capability in the 2nd job.
$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 METHOD B3LYP BASIS 6-31G* SCF_ALGORITHM DIIS MOPROP 1 MOPROP_MAXITER_1ST 10 ! too small, for demonstration only GUESS_PX 1 MOPROP_DIIS_SAVE 0 ! don’t hang onto the subspace vectors $end @@@ $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 METHOD B3LYP BASIS 6-31G* SCF_GUESS READ SKIP_SCFMAN TRUE ! no need to redo the SCF MOPROP 1 MOPROP_RESTART 1 MOPROP_MAXITER_1ST 100 ! more reasonable choice GUESS_PX 1 MOPROP_DIIS_SAVE 0 $end
Example 10.59 -coupling calculation: water molecule with B3LYP/cc-pVDZ
$molecule 0 1 O H1 O OH H2 O OH H1 HOH OH = 0.947 HOH = 105.5 $end $rem JOBTYPE ISSC EXCHANGE B3LYP BASIS cc-pVDZ LIN_K FALSE MOPROP_CONV_1ST 6 INTEGRAL_SYMMETRY TRUE $end
In the event that spin-spin couplings of only certain atom pairs are of interest, it is possible to limit the atom pairs for which the couplings are computed. Selection is done via the $spin-spin input section, which is zero-indexed. For example, the section
$spin-spin 0 1 5 $end
would compute couplings between all possible pairings of the first, second, and sixth atoms in the respective $molecule section: (1, 2), (1, 6), and (2,6). If the $spin-spin section is not specified, couplings between all possible pairs of atoms in $molecule will be computed.
Unambiguous theoretical estimates of degree of aromaticity are still on high
demand. The NMR chemical shift methodology offers one unique probe of
aromaticity based on one defining characteristics of an aromatic system: its
ability to sustain a diatropic ring current. This leads to a response to an
imposed external magnetic field with a strong (negative) shielding at the
center of the ring. Von Schleyer et al. have employed this phenomenon to justify
a new unique probe of aromaticity.
1383
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(1996),
118,
pp. 6317.
Link
They proposed the
computed absolute magnetic shielding at ring centers (unweighted mean of the
heavy-atoms ring coordinates) as a new aromaticity criterion, called
nucleus-independent chemical shift (NICS). Aromatic rings show strong negative
shielding at the ring center (negative NICS), while anti-aromatic systems
reveal positive NICS at the ring center. As an example, a typical NICS value
for benzene is about ppm as estimated with Q-Chem at the
Hartree-Fock/6-31G* level. The same NICS value for benzene was also
reported in Ref.
1383
J. Am. Chem. Soc.
(1996),
118,
pp. 6317.
Link
. The calculated NICS value for
furan of ppm with Q-Chem is about the same as the value reported for
furan in Ref.
1383
J. Am. Chem. Soc.
(1996),
118,
pp. 6317.
Link
. Below is one input example of how
to the NICS of furan with Q-Chem, using the ghost atom option. The ghost
atom is placed at the center of the furan ring, and the basis set assigned to
it within the basis mix option must be the basis used for hydrogen atom.
Example 10.60 Calculation of the NMR NICS probe of furan, HF/6-31G* level. Note the ghost atom at the center of the ring.
$molecule 0 1 C -0.69480 -0.62270 -0.00550 C 0.72110 -0.63490 0.00300 C 1.11490 0.68300 0.00750 O 0.03140 1.50200 0.00230 C -1.06600 0.70180 -0.00560 H 2.07530 1.17930 0.01410 H 1.37470 -1.49560 0.00550 H -1.36310 -1.47200 -0.01090 H -2.01770 1.21450 -0.01040 @H 0.02132 0.32584 0.00034 $end $rem JOBTYPE NMR METHOD HF BASIS 6-31G* PURCAR 111 SCF_CONVERGENCE 7 NO_REORIENT 1 POINT_GROUP_SYMMETRY FALSE $end