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de Wijs GA, Kresse G, Havenith RWA, Marsman M. Comparing GIPAW with numerically exact chemical shieldings: The role of two-center contributions to the induced current. J Chem Phys 2021; 155:234101. [PMID: 34937373 DOI: 10.1063/5.0069637] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this study, we benchmark density functional theory gauge-including projector-augmented-wave (GIPAW) chemical shieldings against molecular shieldings for which basis set completeness has been achieved [Jensen et al., Phys. Chem. Chem. Phys. 18, 21145 (2016)]. We demonstrate the importance of two-center corrections for GIPAW hydrogen shieldings. For the other nuclei studied, standard GIPAW is sufficiently accurate. We find that GIPAW can be pushed to closely approach the basis set limit. The only source of small inaccuracies lies in the contribution to the shielding that is caused by surface currents, which we estimate comparing GIPAW susceptibilities to converged molecular magnetizabilities.
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Affiliation(s)
- Gilles A de Wijs
- Radboud University, Institute for Molecules and Materials, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands
| | - Georg Kresse
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Remco W A Havenith
- Stratingh Institute for Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands
| | - Martijn Marsman
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Kolingasse 14-16, A-1090 Vienna, Austria
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2
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Rérat M, Kirtman B. First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes. J Chem Theory Comput 2021; 17:4063-4076. [PMID: 34165992 DOI: 10.1021/acs.jctc.1c00243] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The self-consistent coupled-perturbed (SC-CP) method in the CRYSTAL program has been adapted to obtain electromagnetic optical rotation properties of chiral periodic systems based on the calculation of the magnetic moment induced by the electric field. Toward that end, an expression for the magnetic transition moment is developed, which involves an appropriate electronic angular momentum operator. This operator is forced to be hermitian so that the chiroptical properties are real. In our formulation, the trace of the optical rotatory power matrix is gauge-origin-invariant as long as the electric dipole transition matrix elements are obtained using the velocity (rather than position) operator. On the other hand, the component along the optic axis is invariant in general for uniaxial and biaxial crystals. Under the same conditions, these properties also do not depend on the so-called missing integers that occur in the treatment of the electric dipole moment of quasi-one-dimensional periodic systems or the analogue of missing integers for the case of higher dimensionality. Tests on a model H2O2 polymer confirm the formalism and, as desired, show that the calculated properties are independent of the size and definition of the unit cell. In addition, an empirical relation to a finite oligomer gauge-including atomic orbital (GIAO) calculation is found. Applications, with comparison to experiment, are carried for α-quartz, tartaric acid crystal, and carbon nanotubes. Future developments of this initial approach to chiroptical properties in the solid state are noted.
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Affiliation(s)
- Michel Rérat
- E2S UPPA, CNRS, IPREM, Université de Pau et des Pays de l' Adour, 2 av. président P. Angot, 64053 Pau, France
| | - Bernard Kirtman
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
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3
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Ludwig M, Hillebrecht H. First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds I: the rhombohedral boron modifications and B 12X 2 (X = P, As, O). Phys Chem Chem Phys 2021; 23:470-486. [PMID: 33320120 DOI: 10.1039/d0cp04061d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
In the present study, solid-state nuclear magnetic resonance (NMR) spectra under magic angle spinning conditions of the rhombohedral structures α-B and B12P2 are reported together with the corresponding parameter sets from first principles calculations on α-B B12X2 (X = P, As, O). With the combination of density functional theory (DFT) and the gauge-including projector-augmented wave (GIPAW) approach as the theoretical tools at hand the computed 11B parameters lead to unambiguous explanation of the measurements. Thereby, we overcome common obstacles of processing recorded NMR spectra of solid-state compounds with several crystallographic positions, in particular non-trivial signal assignments and parameter determination due to peak overlap or even unexpected intensity/area ratios. In fact, we find very good agreement between the theoretical results and measured spectra without applying fitting procedures. Using the Perdew-Burke-Ernzerhof (PBE) functional, the results of the common construction types for pseudopotentials and referencing methods for the chemical shift determination are compared. Suggestions and conclusions from experimental 11B NMR studies on parameters according to the icosahedral positions are critically discussed, for instance the early suspected correlation to chemical shifts is not confirmed. Regarding the electric field gradient (EFG) a detailed explanation for obtaining small deviations amongst all investigated structures of the icosahedral polar sites compared to the equatorial sites is given. Our results show an important link between the exohedral bonding situation of compounds with icosahedral structure elements and the main axis of the EFG and therefore, also measurable quadrupole coupling constants if certain geometrical conditions are fulfilled. Finally, this work also contributes to establishing the number of unique sites measured by solid-state NMR methods within the modification of β-B.
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Affiliation(s)
- Martin Ludwig
- Institut für Anorganische und Analytische Chemie, Albert-Ludwigs-Universität, Albertstr. 21, 79104 Freiburg, Germany.
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Abstract
With the advanced investigations into low-dimensional systems, it has become essential to find materials having interesting lattices that can be exfoliated down to monolayer. One particular important structure is a kagome lattice with its potentially diverse and vibrant physics. We report a van-der-Waals kagome lattice material, Pd3P2S8, with several unique properties such as an intriguing flat band. The flat band is shown to arise from a possible compact-localized state of all five 4d orbitals of Pd. The diamagnetic susceptibility is precisely measured to support the calculated susceptibility obtained from the band structure. We further demonstrate that Pd3P2S8 can be exfoliated down to monolayer, which ultimately will allow the possible control of the localized states in this two-dimensional kagome lattice using the electric field gating.
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Wang SS, Zhang YY, Guan JH, Yu Y, Xia Y, Li SS. Numerical study of disorder on the orbital magnetization in two dimensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:335302. [PMID: 32294636 DOI: 10.1088/1361-648x/ab8985] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Accepted: 04/15/2020] [Indexed: 06/11/2023]
Abstract
The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by using this method on the Haldane model in two dimensions, which can be tuned between a normal insulator or a Chern insulator at half filling. The effects of increasing disorder on OM for both cases are simulated. Energy renormalization shifts are observed in the weak disorder regime and topologically trivial case, which was predicted by a self-consistentT-matrix approximation. Besides this, two other phenomena can be seen. One is the localization trend of the band orbital magnetization. The other is the remarkable contribution from topological chiral states arising from nonzero Chern number or large value of integrated Berry curvature. If the fermi energy is fixed at the gap center of the clean system, there is an enhancement of |M| at the intermediate disorder, for both cases of normal and Chern insulators, which can be attributed to the disorder induced topological metal state before localization.
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Affiliation(s)
- Si-Si Wang
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, People's Republic of China
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yan-Yang Zhang
- School of Physics and Electronic Engineering, Guangzhou University, 510006 Guangzhou, People's Republic of China
| | - Ji-Huan Guan
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yan Yu
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yang Xia
- Microelectronic Instrument and Equipment Research Center, Institute of Microelectronics of Chinese Academy of Sciences, Beijing 100029, People's Republic of China
- School of Microelectronics, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Shu-Shen Li
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, People's Republic of China
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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6
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Guo R, Uddin MN, Price LS, Price SL. Calculation of Diamagnetic Susceptibility Tensors of Organic Crystals: From Coronene to Pharmaceutical Polymorphs. J Phys Chem A 2020; 124:1409-1420. [PMID: 31951408 PMCID: PMC7145345 DOI: 10.1021/acs.jpca.9b07104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
![]()
Understanding
why crystallization in strong magnetic fields can
lead to new polymorphs requires methods to calculate the diamagnetic
response of organic molecular crystals. We develop the calculation
of the macroscopic diamagnetic susceptibility tensor, χcryst, for organic molecular crystals using periodic density
functional methods. The crystal magnetic susceptibility tensor, χcryst, for all experimentally known polymorphs,
and its molecular counterpart, χmol,
are calculated for flexible pharmaceuticals such as carbamazepine,
flufenamic acid, and chalcones, and rigid molecules, such as benzene,
pyridine, acridine, anthracene, and coronene, whose molecular magnetic
properties have been traditionally studied. A tensor addition method
is developed to approximate the crystal diamagnetic susceptibility
tensor, χcryst, from the molecular one, χmol, giving good agreement with those calculated
directly using the more costly periodic density functional method
for χcryst. The response of pharmaceutical
molecules and crystals to magnetic fields, as embodied by χcryst, is largely determined by the packing in the crystal,
as well as the molecular conformation. The anisotropy of χcryst can vary considerably between polymorphs though
the isotropic terms are fairly constant. The implications for developing
a computational method for predicting whether crystallization in a
magnetic field could produce a novel or different polymorph are discussed.
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Affiliation(s)
- Rui Guo
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
| | - M Nadia Uddin
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
| | - Louise S Price
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
| | - Sarah L Price
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
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7
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Springborg M, Molayem M, Kirtman B. Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case. J Chem Phys 2018; 147:104101. [PMID: 28915743 DOI: 10.1063/1.5001261] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.
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Affiliation(s)
- Michael Springborg
- Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken, Germany
| | - Mohammad Molayem
- Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken, Germany
| | - Bernard Kirtman
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
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de Wijs GA, Laskowski R, Blaha P, Havenith RWA, Kresse G, Marsman M. NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations. J Chem Phys 2017; 146:064115. [DOI: 10.1063/1.4975122] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- G. A. de Wijs
- Radboud University, Institute for Molecules and Materials, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands
| | - R. Laskowski
- Institute of High Performance Computing, A∗STAR, 1 Fusionopolis Way, #16-16, Connexis, Singapore 138632
| | - P. Blaha
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| | - R. W. A. Havenith
- Zernike Institute for Advanced Materials, Stratingh Institute for Chemistry, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands
- Ghent Quantum Chemistry Group, Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - G. Kresse
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Sensengasse 8/12, A-1090 Vienna, Austria
| | - M. Marsman
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Sensengasse 8/12, A-1090 Vienna, Austria
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9
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Skachkov D, Krykunov M, Kadantsev E, Ziegler T. The Calculation of NMR Chemical Shifts in Periodic Systems Based on Gauge Including Atomic Orbitals and Density Functional Theory. J Chem Theory Comput 2015; 6:1650-9. [PMID: 26615697 DOI: 10.1021/ct100046a] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present here a method that can calculate NMR shielding tensors from first principles for systems with translational invariance. Our approach is based on Kohn-Sham density functional theory and gauge-including atomic orbitals. Our scheme determines the shielding tensor as the second derivative of the total electronic energy with respect to an external magnetic field and a nuclear magnetic moment. The induced current density due to a periodic perturbation from nuclear magnetic moments is obtained through numerical differentiation, whereas the influence of the responding perturbation in terms of the external magnetic field is evaluated analytically. The method is implemented into the periodic program BAND. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn-Sham potential fully without the use of effective core potentials. Results from calculations of NMR shielding constants based on the present approach are presented for isolated molecules as well as systems with one-, two- and three-dimensional periodicity. The reported values are compared to experiment and results from calculations on cluster models.
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Affiliation(s)
- Dmitry Skachkov
- Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4
| | - Mykhaylo Krykunov
- Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4
| | - Eugene Kadantsev
- Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4
| | - Tom Ziegler
- Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4
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10
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Charpentier T. The PAW/GIPAW approach for computing NMR parameters: a new dimension added to NMR study of solids. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2011; 40:1-20. [PMID: 21612895 DOI: 10.1016/j.ssnmr.2011.04.006] [Citation(s) in RCA: 235] [Impact Index Per Article: 18.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Revised: 04/24/2011] [Accepted: 04/25/2011] [Indexed: 05/18/2023]
Abstract
In 2001, Mauri and Pickard introduced the gauge including projected augmented wave (GIPAW) method that enabled for the first time the calculation of all-electron NMR parameters in solids, i.e. accounting for periodic boundary conditions. The GIPAW method roots in the plane wave pseudopotential formalism of the density functional theory (DFT), and avoids the use of the cluster approximation. This method has undoubtedly revitalized the interest in quantum chemical calculations in the solid-state NMR community. It has quickly evolved and improved so that the calculation of the key components of NMR interactions, namely the shielding and electric field gradient tensors, has now become a routine for most of the common nuclei studied in NMR. Availability of reliable implementations in several software packages (CASTEP, Quantum Espresso, PARATEC) make its usage more and more increasingly popular, maybe indispensable in near future for all material NMR studies. The majority of nuclei of the periodic table have already been investigated by GIPAW, and because of its high accuracy it is quickly becoming an essential tool for interpreting and understanding experimental NMR spectra, providing reliable assignments of the observed resonances to crystallographic sites or enabling a priori prediction of NMR data. The continuous increase of computing power makes ever larger (and thus more realistic) systems amenable to first-principles analysis. In the near future perspectives, as the incorporation of dynamical effects and/or disorder are still at their early developments, these areas will certainly be the prime target.
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Affiliation(s)
- Thibault Charpentier
- CEA, IRAMIS, SIS2M, Laboratoire de Structure et Dynamique par Résonance Magnétique, UMR CEA-CNRS 3299, F-91191 Gif-sur-Yvette cedex, France.
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11
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Resta R. Electrical polarization and orbital magnetization: the modern theories. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:123201. [PMID: 21389484 DOI: 10.1088/0953-8984/22/12/123201] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Macroscopic polarization P and magnetization M are the most fundamental concepts in any phenomenological description of condensed media. They are intensive vector quantities that intuitively carry the meaning of dipole per unit volume. But for many years both P and the orbital term in M evaded even a precise microscopic definition, and severely challenged quantum-mechanical calculations. If one reasons in terms of a finite sample, the electric (magnetic) dipole is affected in an extensive way by charges (currents) at the sample boundary, due to the presence of the unbounded position operator in the dipole definitions. Therefore P and the orbital term in M--phenomenologically known as bulk properties--apparently behave as surface properties; only spin magnetization is problemless. The field has undergone a genuine revolution since the early 1990s. Contrary to a widespread incorrect belief, P has nothing to do with the periodic charge distribution of the polarized crystal: the former is essentially a property of the phase of the electronic wavefunction, while the latter is a property of its modulus. Analogously, the orbital term in M has nothing to do with the periodic current distribution in the magnetized crystal. The modern theory of polarization, based on a Berry phase, started in the early 1990s and is now implemented in most first-principle electronic structure codes. The analogous theory for orbital magnetization started in 2005 and is partly work in progress. In the electrical case, calculations have concerned various phenomena (ferroelectricity, piezoelectricity, and lattice dynamics) in several materials, and are in spectacular agreement with experiments; they have provided thorough understanding of the behaviour of ferroelectric and piezoelectric materials. In the magnetic case the very first calculations are appearing at the time of writing (2010). Here I review both theories on a uniform ground in a density functional theory (DFT) framework, pointing out analogies and differences. Both theories are deeply rooted in geometrical concepts, elucidated in this work. The main formulae for crystalline systems express P and M in terms of Brillouin-zone integrals, discretized for numerical implementation. I also provide the corresponding formulae for disordered systems in a single k-point supercell framework. In the case of P the single-point formula has been widely used in the Car-Parrinello community to evaluate IR spectra.
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Affiliation(s)
- Raffaele Resta
- Dipartimento di Fisica, Università di Trieste, Strada Costiera 11, I-34014 Trieste, Italy
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12
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Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Dal Corso A, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:395502. [PMID: 21832390 DOI: 10.1088/0953-8984/21/39/395502] [Citation(s) in RCA: 5711] [Impact Index Per Article: 380.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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Affiliation(s)
- Paolo Giannozzi
- CNR-INFM Democritos National Simulation Center, 34100 Trieste, Italy. Dipartimento di Fisica, Università degli Studi di Udine, via delle Scienze 208, 33100 Udine, Italy
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13
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14
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Röhrig UF, Sebastiani D. NMR Chemical Shifts of the Rhodopsin Chromophore in the Dark State and in Bathorhodopsin: A Hybrid QM/MM Molecular Dynamics Study. J Phys Chem B 2008; 112:1267-74. [DOI: 10.1021/jp075662q] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ute F. Röhrig
- Ludwig Institute for Cancer Research and Swiss Institute of Bioinformatics, Molecular Modeling Group, Genopode Building CH-1015 Lausanne, Switzerland, and Max-Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Daniel Sebastiani
- Ludwig Institute for Cancer Research and Swiss Institute of Bioinformatics, Molecular Modeling Group, Genopode Building CH-1015 Lausanne, Switzerland, and Max-Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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15
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Shi J, Vignale G, Xiao D, Niu Q. Quantum theory of orbital magnetization and its generalization to interacting systems. PHYSICAL REVIEW LETTERS 2007; 99:197202. [PMID: 18233109 DOI: 10.1103/physrevlett.99.197202] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2007] [Indexed: 05/25/2023]
Abstract
Based on standard perturbation theory, we present a full quantum derivation of the formula for the orbital magnetization in periodic systems. The derivation is generally valid for insulators with or without a Chern number, for metals at zero or finite temperatures, and at weak as well as strong magnetic fields. The formula is shown to be valid in the presence of electron-electron interaction, provided the one-electron energies and wave functions are calculated self-consistently within the framework of the exact current and spin-density functional theory.
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Affiliation(s)
- Junren Shi
- Institute of Physics and ICQS, Chinese Academy of Sciences, Beijing, China
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16
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Komin S, Gossens C, Tavernelli I, Rothlisberger U, Sebastiani D. NMR Solvent Shifts of Adenine in Aqueous Solution from Hybrid QM/MM Molecular Dynamics Simulations. J Phys Chem B 2007; 111:5225-32. [PMID: 17458990 DOI: 10.1021/jp067263l] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present first principles calculations of the NMR solvent shift of adenine in aqueous solution. The calculations are based on snapshots sampled from a molecular dynamics simulation, which were obtained via a hybrid quantum-mechanical/mechanical modeling approach, using an all-atom force field (TIP3P). We find that the solvation via the strongly fluctuating hydrogen bond network of water leads to nontrivial changes in the NMR spectra of the solutes regarding the ordering of the resonance lines. Although there are still sizable deviations from experiment, the overall agreement is satisfactory for the 1H and 15N NMR shifts. Our work is another step toward a realistic first-principles prediction of NMR chemical shifts in complex chemical environments.
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Affiliation(s)
- Sittipong Komin
- Max-Planck-Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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Sebastiani D. Current Densities and Nucleus-Independent Chemical Shift Maps from Reciprocal-Space Density Functional Perturbation Theory Calculations. Chemphyschem 2006; 7:164-75. [PMID: 16331722 DOI: 10.1002/cphc.200500438] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
A method to calculate condensed-matter nucleus independent chemical shift maps (NICS maps) from first principles in the framework of density functional theory is presented. I use a pseudopotential plane-wave approach in which the electronic current density and the NICS map are obtained from an inverse Fourier transformation of the induced magnetic field represented in reciprocal space (G space). Due to its intrinsically periodic description, the method is suitable for isolated molecules (by using a supercell technique) and for condensed-phase systems like solids. The periodic NICS method was applied to hydrogen-bonded calixhydroquinone nanotubes, crystalline graphite, and two carbon nanotube systems.
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Affiliation(s)
- Daniel Sebastiani
- Max-Planck-Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
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18
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Thonhauser T, Ceresoli D, Vanderbilt D, Resta R. Orbital magnetization in periodic insulators. PHYSICAL REVIEW LETTERS 2005; 95:137205. [PMID: 16197172 DOI: 10.1103/physrevlett.95.137205] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2005] [Indexed: 05/04/2023]
Abstract
Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulklike Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.
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Affiliation(s)
- T Thonhauser
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
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Resta R, Ceresoli D, Thonhauser T, Vanderbilt D. Orbital Magnetization in Extended Systems. Chemphyschem 2005; 6:1815-9. [PMID: 16086345 DOI: 10.1002/cphc.200400641] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
While the orbital magnetic dipole moment of any finite sample is well-defined, it becomes ill-defined in the thermodynamic limit as a result of the unboundedness of the position operator. Effects due to surface currents and to bulk magnetization are not easily disentangled. The corresponding electrical problem, where surface charges and bulk polarization appear as entangled, was solved about a decade ago by the modern theory of polarization, based on a Berry phase. We follow a similar path here, making progress toward a bulk expression for the orbital magnetization in an insulator represented by a lattice-periodic Hamiltonian with broken time-reversal symmetry. We therefore limit ourselves to the case where the macroscopic (i.e. cell-averaged) magnetic field vanishes. We derive an expression for the contribution to the magnetization arising from the circulating currents internal to the bulk Wannier functions, and then transform to obtain a Brillouin zone integral involving the occupied Bloch orbitals. A version suitable for practical implementation in discretized reciprocal space is also derived, and the gauge invariance of both versions is explicitly shown. However, tests on a tight-binding model indicate the presence of additional edge currents, and it remains to be determined whether these can be related to the bulk band structure.
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Affiliation(s)
- R Resta
- INFM Democritos National Simulation Center and Dipartimento di Fisica Teorica, Università di Trieste, Strada Costiera 11, 34014 Trieste, Italy
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20
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Rossano S, Mauri F, Pickard CJ, Farnan I. First-Principles Calculation of 17O and 25Mg NMR Shieldings in MgO at Finite Temperature: Rovibrational Effect in Solids. J Phys Chem B 2005; 109:7245-50. [PMID: 16851828 DOI: 10.1021/jp044251w] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The temperature dependence of (17)O and (25)Mg NMR chemical shifts in solid MgO have been calculated using a first-principles approach. Density functional theory, pseudopotentials, a plane-wave basis set, and periodic boundary conditions were used both to describe the motion of the nuclei and to compute the NMR chemical shifts. The chemical shifts were obtained using the gauge-including projector augmented wave method. In a crystalline solid, the temperature dependence is due to both (i) the variation of the averaged equilibrium structure and (ii) the fluctuation of the atoms around this structure. In MgO, the equilibrium structure at each temperature is uniquely defined by the cubic lattice parameters, which we take from experiment. We evaluate the effect of the fluctuations within a quasiharmonic approximation. In particular, the dynamical matrix, defining the harmonic Hamiltonian, has been computed for each equilibrium volume. This harmonic Hamiltonian was used to generate nuclear configurations that obey quantum statistical mechanics. The chemical shifts were averaged over these nuclear configurations. The results reproduce the previously published experimental NMR data measured on MgO between room temperature and 1000 degrees C. It is shown that the chemical shift behavior with temperature cannot be explained by thermal expansion alone. Vibrational corrections due to the fluctuations of atoms around their equilibrium position are crucial to reproduce the experimental results.
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Affiliation(s)
- Stéphanie Rossano
- Laboratoire des Géomatériaux, Université de Marne la Vallée, CNRS FRE2455, 5 Bd Descartes, Champs/Marne, 77454 Noisy-Champs Cedex 2, France.
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Cai W, Galli G. Ab initio calculations in a uniform magnetic field using periodic supercells. PHYSICAL REVIEW LETTERS 2004; 92:186402. [PMID: 15169514 DOI: 10.1103/physrevlett.92.186402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2003] [Indexed: 05/24/2023]
Abstract
We present a formulation of ab initio electronic structure calculations in a finite magnetic field, which retains the simplicity and efficiency of techniques widely used in first principles molecular dynamics simulations, based on plane-wave basis sets and Fourier transforms. In addition we discuss results obtained with this method for the energy spectrum of interacting electrons in quantum wells, and for the electronic properties of dense fluid deuterium in a uniform magnetic field.
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Affiliation(s)
- Wei Cai
- Lawrence Livermore National Laboratory, University of California, Livermore, CA 94550, USA
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22
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Pickard CJ, Mauri F. Nonlocal pseudopotentials and magnetic fields. PHYSICAL REVIEW LETTERS 2003; 91:196401. [PMID: 14611593 DOI: 10.1103/physrevlett.91.196401] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2003] [Indexed: 05/24/2023]
Abstract
We show how to describe the coupling of electrons to nonuniform magnetic fields in the framework of the widely used norm-conserving pseudopotential approximation for electronic structure calculations. Our derivation applies to magnetic fields that are smooth on the scale of the core region. The method is validated by application to the calculation of the magnetic susceptibility of molecules within density functional theory (DFT) in the local density approximation. Our results are compared with high-quality all-electron DFT results obtained using Gaussian basis sets and another recently proposed pseudopotential formalism.
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Affiliation(s)
- Chris J Pickard
- TCM Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
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Ismail-Beigi S, Chang EK, Louie SG. Coupling of nonlocal potentials to electromagnetic fields. PHYSICAL REVIEW LETTERS 2001; 87:087402. [PMID: 11497982 DOI: 10.1103/physrevlett.87.087402] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2001] [Indexed: 05/23/2023]
Abstract
Nonlocal Hamiltonians are used widely in first-principles quantum calculations; the nonlocality stems from eliminating undesired degrees of freedom, e.g., core electrons. To date, attempts to couple nonlocal systems to external electromagnetic (EM) fields have been heuristic or limited to weak or long wavelength fields. Using Feynman path integrals, we derive an exact, closed-form coupling of arbitrary EM fields to nonlocal systems. Our results justify and clarify the couplings used to date and are essential for systematic computation of linear and especially nonlinear responses.
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Affiliation(s)
- S Ismail-Beigi
- Department of Physics, University of California, Berkeley, 94720, USA
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Mauri F, Vast N, Pickard CJ. Atomic structure of icosahedral B4C boron carbide from a first principles analysis of NMR spectra. PHYSICAL REVIEW LETTERS 2001; 87:085506. [PMID: 11497959 DOI: 10.1103/physrevlett.87.085506] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2001] [Indexed: 05/23/2023]
Abstract
Density functional theory is demonstrated to reproduce the 13C and 11B NMR chemical shifts of icosahedral boron carbides with sufficient accuracy to extract previously unresolved structural information from experimental NMR spectra. B4C can be viewed as an arrangement of 3-atom linear chains and 12-atom icosahedra. According to our results, all the chains have a CBC structure. Most of the icosahedra have a B11C structure with the C atom placed in a polar site, and a few percent have a B (12) structure or a B10C2 structure with the two C atoms placed in two antipodal polar sites.
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Affiliation(s)
- F Mauri
- Laboratoire de Minéralogie-Cristallographie, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris, France
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Sebastiani D, Parrinello M. A New ab-Initio Approach for NMR Chemical Shifts in Periodic Systems. J Phys Chem A 2001. [DOI: 10.1021/jp002807j] [Citation(s) in RCA: 190] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel Sebastiani
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Michele Parrinello
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
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Buda F, Giannozzi P, Mauri F. Density Functional Theory Study of the Structure and 13C Chemical Shifts of Retinylidene Iminium Salts. J Phys Chem B 2000. [DOI: 10.1021/jp001739y] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- F. Buda
- Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands, Scuola Normale Superiore and INFM, Piazza dei Cavalieri 7, I-56126 Pisa, Italy, and Laboratoire de Minéralogie-Cristallographie de Paris Université Pierre et Marie Curie, tour 16, case 115 4 Place Jussieu, F-75252 Paris Cedex 05 France
| | - P. Giannozzi
- Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands, Scuola Normale Superiore and INFM, Piazza dei Cavalieri 7, I-56126 Pisa, Italy, and Laboratoire de Minéralogie-Cristallographie de Paris Université Pierre et Marie Curie, tour 16, case 115 4 Place Jussieu, F-75252 Paris Cedex 05 France
| | - F. Mauri
- Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands, Scuola Normale Superiore and INFM, Piazza dei Cavalieri 7, I-56126 Pisa, Italy, and Laboratoire de Minéralogie-Cristallographie de Paris Université Pierre et Marie Curie, tour 16, case 115 4 Place Jussieu, F-75252 Paris Cedex 05 France
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Gregor T, Mauri F, Car R. A comparison of methods for the calculation of NMR chemical shifts. J Chem Phys 1999. [DOI: 10.1063/1.479451] [Citation(s) in RCA: 120] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mauri F, Pfrommer BG, Louie SG. Ab Initio Theory of NMR Chemical Shifts in Solids and Liquids. PHYSICAL REVIEW LETTERS 1996; 77:5300-5303. [PMID: 10062766 DOI: 10.1103/physrevlett.77.5300] [Citation(s) in RCA: 89] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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