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Finite-field implementation of NMR chemical shieldings for molecules: Direct and converse gauge-including projector-augmented-wave methods
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10.1063/1.4810799
/content/aip/journal/jcp/139/1/10.1063/1.4810799
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/1/10.1063/1.4810799

Figures

Image of FIG. 1.
FIG. 1.

One-dimensional representation of the vector potential in a supercell of size . Due to the vector potential discontinuity in the middle of the box, the center of mass of the target molecule should be placed at the origin.

Image of FIG. 2.
FIG. 2.

Convergence properties of the direct approach illustrated with H isotropic chemical shielding of a HO molecule. (a) Shieldings as a function of molecular position ( is the distance of the H nucleus from the origin) for supercells of various sizes using the direct approach. The molecule is translated along the () edge of the supercell. (b) and (c) Shieldings for a fixed length cell ( = 12 Å) as a function of kinetic energy cutoff for the direct (b) and converse (c) approach.

Image of FIG. 3.
FIG. 3.

Position of the HO molecule in the unit cell. It lies in the -plane. The right-hand-side H nucleus is at distance from the corner of the unit cell (the gauge origin). Unit cell boundaries are indicated with a black dashed line. The applied vector potential makes a jump half-way the unit cell at /2 (dashed-dotted green lines).

Image of FIG. 4.
FIG. 4.

Convergence of the hydrogen (top) and oxygen (bottom) chemical shielding of a water molecule as a function of the kinetic energy cut-off. For the direct approach the H (O) shielding has been calculated with the H (O) nucleus at the gauge origin. = 16 Å.

Image of FIG. 5.
FIG. 5.

H isotropic chemical shielding of a HO molecule as a function of inverse supercell volume using the direct method. The molecular position is fixed and the kinetic energy cutoff = 2000 eV. is the supercell size.

Image of FIG. 6.
FIG. 6.

Dependence of the calculated chemical shift on the strength of the external field for the two sites of a water molecule: (top) By the direct approach and (bottom) by the converse approach. All calculations are PBE. = 1000 eV, = 16 Å.

Image of FIG. 7.
FIG. 7.

Induced pseudo current density in a CH molecule calculated with the direct method. The molecule is on the -axis. The applied field is in the positive direction. The current density is represented by arrows on the plane-wave grid in the plane. Pseudo-current (a) without and (b) with current augmentation. Circles represent the PAW sphere radii, which are 1.5 a.u. and 1.1 a.u. for carbon and hydrogen, respectively.

Image of FIG. 8.
FIG. 8.

Venlafaxine molecule, containing oxygen (red), carbon (grey), nitrogen (blue), and hydrogen (white) atoms. Saturated ring: 1-2a-3a-4-3b-2b-1 and aromatic ring: 8-9a-10a-11-10b-9b-8. Figure made with Jmol.

Image of FIG. 9.
FIG. 9.

Calculated shieldings for the venlafaxine free base molecule. Abscissa: isotropic shieldings calculated with linear response (LR) and VASP (no augmentation corrections). Ordinate: isotropic shieldings calculated with the direct molecular method [(a) and (d)], with the converse molecular methods [(b) and (e)] and with using linear response [(c) and (f)]. Hydrogen shieldings calculated with the molecular methods are with (red diamonds) and without (black solid circles) augmentation corrections. All shieldings are absolute (valence only).

Image of FIG. 10.
FIG. 10.

Cutoff dependence of shieldings for the venlafaxine molecule using the direct (molecular) method. Abscissa: isotropic shieldings calculated with 900 eV kinetic energy cutoff. Ordinate: isotropic shieldings calculated with 400, 600, and 750 eV cutoffs (see legend). All shieldings are absolute (valence only).

Image of FIG. 11.
FIG. 11.

Absolute isotropic hydrogen shieldings for the venlafaxine molecule. Abscissa: VASP isotropic shieldings calculated with 900 eV kinetic energy cutoff. Ordinate: GIAO aug-cc-pCVTZ isotropic shieldings calculated with . VASP shieldings have been extrapolated to infinite cell size (0.8 ppm correction). Blue dot: VASP shielding with hard O PAW data set.

Tables

Generic image for table
Table I.

Parameters of the PAW data sets used. are the cutoff radii for the partial waves.

Generic image for table
Table II.

Oxygen and hydrogen isotropic chemical shielding calculated with various PAW data sets. Shieldings are extrapolated to infinite cell size and converged in plane wave basis set ( = 2000 eV).   calculations in vacuum are with an aug-cc-pCV5Z basis set.

Generic image for table
Table III.

Convergence of oxygen and hydrogen shielding in a water molecule for the direct and the converse approach as a function of the size of the cubic supercell. = 1000 eV.

Generic image for table
Table IV.

Hydrogen shieldings of various small molecules obtained by the direct and the converse approach with (“Yes”) and without (“No”) augmentation currents. Also shown: shieldings calculated in linear response with and VASP (VASP LR). Cubic supercells with 16 (14) Å edge length were used for the VASP finite field (linear response) calculations. Standard PAW data sets as supplied with VASP were used (for N the “N_h” data set was used, see Table I ).

Generic image for table
Table V.

Hydrogen anisotropic parameters Ω and κ of different hydrocarbon molecules obtained by the direct approach with and without augmentation current compared to results. All calculations are GGA-PBE.

Generic image for table
Table VI.

Absolute isotropic phosphorous chemical shifts for several molecules calculated with the two finite-field (FF) approaches. Linear-response (LR) results obtained with , (QE) and   are presented for comparison. All calculations are GGA-PBE. A P_d data set was used for ( = 1000 eV). No PAW and current augmentation were applied. The core contribution of 908.9 ppm has been removed from   and   results.

Generic image for table
Table VII.

Partitioning of phosphorous chemical shifts into plane-wave (PW) and one-center terms for the finite-field (FF) direct and converse approach. All calculations are GGA-PBE.

Generic image for table
Table VIII.

Carbon isotropic shieldings of venlafaxine free base. Linear response (LR) and converse VASP results were obtained with 900 eV kinetic energy cutoff. QE denotes . All columns are referenced to their average. The bottom line reports the mean absolute deviation from experiment.

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/content/aip/journal/jcp/139/1/10.1063/1.4810799
2013-07-03
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Finite-field implementation of NMR chemical shieldings for molecules: Direct and converse gauge-including projector-augmented-wave methods
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/1/10.1063/1.4810799
10.1063/1.4810799
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