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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

### Abstract

Two finite-field implementations for the calculation of chemical shieldings of molecular systems using a plane-wave basis set and the Gauge-Including Projector-Augmented-Wave method are presented. The direct approach mimics the nuclear magnetic resonance experiment in that it puts the molecule in a uniform magnetic field and obtains shieldings from the current response. The other is based on the recently introduced “converse method” [T. Thonhauser, D. Ceresoli, A. A. Mostofi et al. , J. Chem. Phys.131, 101101 (Year: 2009)]10.1063/1.3216028. In both methods two-center contributions to the shieldings can be included via a numerically simple augmentation construction. Results obtained with both methods are discussed as well as (dis)similarities in their behaviors.

© 2013 AIP Publishing LLC

Received 15 April 2013
Accepted 24 May 2013
Published online 03 July 2013

Acknowledgments: We thank Dr. D. Ceresoli, Dr. T. Thonhauser, and Professor D. Vanderbilt for useful discussion and providing Ref. 18 long before publication. The work of F.V. and G.A.W. is part of the research programme of the “Stichting voor Fundamenteel Onderzoek der Materie (FOM),” which is financially supported by the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).” R.W.A.H. acknowledges the Zernike Institute for Advanced Materials for financial support (“Dieptestrategie” program). Two of the authors (M.M. and G.K.) acknowledge support by the Austrian Science Fund, FWF, within the SFB ViCoM (F41).

Article outline:

I. INTRODUCTION

II. THEORY

A. Hamiltonian and current operator

1. Hamiltonian

2. Current density and current operator

3. Vector potential

B. Direct approach

1. Hamiltonian

2. Induced field

C. Converse approach

1. Hamiltonian

2. Induced moment

D. PAW and GIPAW methodologies

1. Basics of PAW

2. Basics of GIPAW

III. MOLECULAR GIPAW METHODS

A. Direct approach

1. GIPAW Hamiltonian

2. Total induced field

3. Current augmentation

B. Converse approach

1. Total induced moment

2. PAW Hamiltonian

3. Completing the Hamiltonian: *D* _{ ij } augmentation

IV. NUMERICAL CONSIDERATIONS AND TESTS

A. General computational details

B. Convergence issues

1. Plane wave basis set and super-cell convergence

2. The linear regime and orbital convergence

C. Two-center contributions

D. Small molecules

E. Large molecules: Venlafaxine

V. CONCLUSION

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2013-07-03

2014-04-16

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