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Development and Implementation of Theoretical Methods for the Calculation of EPR Parameters in Periodic Simulations

Reinout Declerck UGent (2008)
abstract
For many years now, the determination and prediction of the properties of matter at the level of the nanoscale, based only on the fundamental laws of quantum physics (ab initio), has been a very active and valuable field of research. Density functional theory (DFT) is a particularly successful ab-initio technique, which was developed by Hohenberg and Kohn, and formulated into a useful algorithm by Kohn and Sham. Essentially, the theorem of Hohenberg-Kohn states that the electronic ground-state wave function of any molecular system is uniquely determined by the electronic ground-state density. The latter is a lot easier to handle than the many-body wave function, both conceptually and practically. Electron paramagnetic resonance (EPR), or electron-spin resonance (ESR), is one of the main spectroscopic techniques for the investigation of specimens featuring one or more unpaired electrons. The basic idea of EPR is analogous to the one of the well-known nuclear magnetic resonance (NMR) technique: in the former, the spin of the electrons is excited, whereas in the latter, the spin of the atomic nuclei is excited. The energy levels and intensities of the spin centra, which follow from an EPR experiment, can be reproduced by employing a so-called effective Hamiltonian (effective in the sense that it is a purely mathematical object, which does not follow from fundamental physical principles). Often, an effective Hamiltonian which includes only the lowest-order interaction terms is sufficient: i) the g tensor which describes the interaction of the net electron spin with an external magnetic field, ii) the A or hyperfine tensors which describe the interaction of the net electron spin with the spins of the atomic nuclei, and iii) in the case of a net electron spin higher than 1/2, the D- or zero-field splitting tensor resulting from magnetic-dipole interactions between multiple unpaired electrons. In recent years, interest in the ab-initio calculation of EPR parameters has grown steadily. Theoretical calculations represent a powerful tool for the experimentalist in the analysis of the spectra which can sometimes be very complex. Through comparison of the experimentally obtained EPR parameters with theoretically-determined values, it becomes possible to identify and analyze more thoroughly the molecular structure in the surroundings of the spin center. Until very recently, the calculation of EPR parameters was feasible only in gasphase simulations, in which the molecule under examination is surrounded by vacuum. However, many interesting applications which would potentially benefit from a theoretical EPR study are found in the solid phase, in which the spin centers are fully embedded in matter. A successful technique for the simulation of the solid phase imposes periodic boundary conditions (PBC) on a simulation cell. This is usually a correct approach, since the solid phase of many substances features a periodic structure. The adaptation to PBC simulations of the theoretical methods for calculating EPR parameters proves to be far from trivial, and only a limited number of attempts have been made so far. However, all of these implementations share a number of methodological and/or practical limitations, and for this reason, theoretical EPR parameters of solid-phase structures were still mainly calculated using cluster-in-vacuo models. In this technique, only a limited portion of the molecular environment is included, an approximation which in many cases leads to a noticeable loss of accuracy. This doctoral research focuses on the development, implementation, validation, and application of DFT methods for the fast and accurate calculation of the g and A tensors in PBC simulations. To this end, a number of newly-developed theoretical methods were implemented in CPMD (http://www.cpmd.org) and CP2K (http://cp2k.berlios.de, two popular program packages that adopt periodic boundary conditions. These theoretical methods were validated by comparing the EPR parameters of a wide range of atoms and small molecules in the gas phase with existing gas-phase methods (through special techniques, both CPMD and CP2K can also simulate the gas phase). Then, using these new methods, the EPR parameters of several periodic structures were calculated and thoroughly compared with available experimental data from literature and results obtained with, amongst others, cluster-invacuo models. Several ideas for the acceleration of the methods, such as for example the usage of a three-layered hybrid scheme combining an accurate allelectron treatment for the radical center and a relatively cheap pseudopotential approximation or classical molecular mechanics for the remainder of the simulation cell, have been carefully tested. Subsequently, a number of exciting applications have been carried out, such as for example the study of the molecular environment dependence of A tensors in a set of sugar crystal radicals, the calculation of the A tensors of the R2 center in b-D-fructose along a complete molecular dynamics trajectory at finite temperature, and the calculation of the g tensor for the E01 center in a-quartz using a 15551-atom simulation cell and the aforementioned threelayered hybrid scheme. It is likely that the CP2K methods will last longer than their CPMD counterparts, as they are the most generally applicable. Through the Gaussian and augmented-plane-wave (GAPW) representation and the aforementioned layered approach, the CP2K methods offer a very attractive accuracy/cost trade-off over the few competing methods applicable to PBC simulations. All source code has been included in the public distributions of the aforementioned program packages (available on the respective websites). Projects on the side - The acquired expertise in the simulation of solids on the DFT level was used in a collaboration with the Physico-Chemical Laboratory of Catholic University of Leuven. We have been working on a new semi-empirical energy model for the study of surface phenomenae in metallic alloys, fitted to calculations on the DFT level. The proposed model was used in the theoretical prediction of surface segregation in CuPt alloys. In addition, based on molecular-dynamics simulations and metadynamics in an explicit periodic solvent model, we unraveled the solvation and isomerisation characteristics of lithiated 3-chloro-1-azaallylic anions in a tetrahydrofuran solution. Our findings were independently confirmed by ROESYNMR experiments, conducted at the Department of Organic Chemistry of Ghent University. A detailed knowledge of the structure of these solvated anions leads to a better understanding of the chemical reactions (e.g. aldolor Mannich-type reactions) in which they play a key role. Just as this thesis was nearing completion, a further project on silica-template interactions during the initial stages of zeolite synthesis was finished. This project was carried out in conjunction with the Department of Chemical Engineering and Chemistry of Eindhoven University of Technology, the Department of Fuels Chemistry and Technology of Wroclaw University of Technology, and the Centre for Surface Chemistry and Catalysis of Catholic University of Leuven.
Please use this url to cite or link to this publication:
author
promoter
UGent
organization
alternative title
Ontwikkeling en implementatie van theoretische methodes voor de berekening van EPR-parameters in periodieke simulaties
year
type
dissertation (monograph)
subject
pages
310 pages
place of publication
Gent
defense location
Faculty of Engineering, J. Plateaustraat, Ghent University
defense date
2008-09-09 17:00
ISBN
978-90-8578-000-7
language
English
UGent publication?
yes
classification
D1
additional info
Dit onderzoekswerk werd uitgevoerd binnen het Centrum voor Moleculaire Modellering.
copyright statement
I have retained and own the full copyright for this publication
id
517341
handle
http://hdl.handle.net/1854/LU-517341
alternative location
http://lib.ugent.be/fulltxt/RUG01/001/286/138/RUG01-001286138_2010_0001_AC.pdf
date created
2009-03-12 09:11:11
date last changed
2009-04-03 09:11:48
@phdthesis{517341,
  abstract     = {For many years now, the determination and prediction of the properties of matter at the level of the nanoscale, based only on the fundamental laws of quantum physics (ab initio), has been a very active and valuable field of research. Density functional theory (DFT) is a particularly successful ab-initio technique, which was developed by Hohenberg and Kohn, and formulated into a useful algorithm by Kohn and Sham. Essentially, the theorem of Hohenberg-Kohn states that the electronic ground-state wave function of any molecular system is uniquely determined by the electronic ground-state density. The latter is a lot easier to handle than the many-body wave function, both conceptually and practically.

Electron paramagnetic resonance (EPR), or electron-spin resonance (ESR), is one of the main spectroscopic techniques for the investigation of specimens featuring one or more unpaired electrons. The basic idea of EPR is analogous to the one of the well-known nuclear magnetic resonance (NMR) technique: in the former, the spin of the electrons is excited, whereas in the latter, the spin of the atomic nuclei is excited. The energy levels and intensities of the spin centra, which follow from an EPR experiment, can be reproduced by employing a so-called effective Hamiltonian (effective in the sense that it is a purely mathematical object, which does not follow from fundamental physical principles). Often, an effective Hamiltonian which includes only the lowest-order interaction terms is sufficient: i) the g tensor which describes the interaction of the net electron spin with an external magnetic field, ii) the A or hyperfine tensors which describe the interaction of the net electron spin with the spins of the atomic nuclei, and iii) in the case of a net electron spin higher than 1/2, the D- or zero-field splitting tensor resulting from magnetic-dipole interactions between multiple unpaired electrons.

In recent years, interest in the ab-initio calculation of EPR parameters has grown steadily. Theoretical calculations represent a powerful tool for the experimentalist in the analysis of the spectra which can sometimes be very complex. Through comparison of the experimentally obtained EPR parameters with theoretically-determined values, it becomes possible to identify and analyze more thoroughly the molecular structure in the surroundings of the spin center.

Until very recently, the calculation of EPR parameters was feasible only in gasphase simulations, in which the molecule under examination is surrounded by vacuum. However, many interesting applications which would potentially benefit from a theoretical EPR study are found in the solid phase, in which the spin centers are fully embedded in matter. A successful technique for the simulation of the solid phase imposes periodic boundary conditions (PBC) on a simulation cell. This is usually a correct approach, since the solid phase of many substances features a periodic structure.

The adaptation to PBC simulations of the theoretical methods for calculating EPR parameters proves to be far from trivial, and only a limited number of attempts have been made so far. However, all of these implementations share a number of methodological and/or practical limitations, and for this reason, theoretical EPR parameters of solid-phase structures were still mainly calculated using cluster-in-vacuo models. In this technique, only a limited portion of the molecular environment is included, an approximation which in many cases leads to a noticeable loss of accuracy.

This doctoral research focuses on the development, implementation, validation, and application of DFT methods for the fast and accurate calculation of the g and A tensors in PBC simulations. To this end, a number of newly-developed theoretical methods were implemented in CPMD (http://www.cpmd.org) and CP2K (http://cp2k.berlios.de, two popular program packages that adopt periodic boundary conditions. These theoretical methods were validated by comparing the EPR parameters of a wide range of atoms and small molecules in the gas phase with existing gas-phase methods (through special techniques, both CPMD and CP2K can also simulate the gas phase). Then, using these new methods, the EPR parameters of several periodic structures were calculated and thoroughly compared with available experimental data from literature and results obtained with, amongst others, cluster-invacuo models. Several ideas for the acceleration of the methods, such as for example the usage of a three-layered hybrid scheme combining an accurate allelectron treatment for the radical center and a relatively cheap pseudopotential approximation or classical molecular mechanics for the remainder of the simulation cell, have been carefully tested. Subsequently, a number of exciting applications have been carried out, such as for example the study of the molecular environment dependence of A tensors in a set of sugar crystal radicals, the calculation of the A tensors of the R2 center in b-D-fructose along a complete molecular dynamics trajectory at finite temperature, and the calculation of the g tensor for the E01 center in a-quartz using a 15551-atom simulation cell and the aforementioned threelayered hybrid scheme.

It is likely that the CP2K methods will last longer than their CPMD counterparts, as they are the most generally applicable. Through the Gaussian and augmented-plane-wave (GAPW) representation and the aforementioned layered approach, the CP2K methods offer a very attractive accuracy/cost trade-off over the few competing methods applicable to PBC simulations.

All source code has been included in the public distributions of the aforementioned program packages (available on the respective websites).

Projects on the side - The acquired expertise in the simulation of solids on the DFT level was used in a collaboration with the Physico-Chemical Laboratory of Catholic University of Leuven. We have been working on a new semi-empirical energy model for the study of surface phenomenae in metallic alloys, fitted to calculations on the DFT level. The proposed model was used in the theoretical prediction of surface segregation in CuPt alloys.
In addition, based on molecular-dynamics simulations and metadynamics in an explicit periodic solvent model, we unraveled the solvation and isomerisation characteristics of lithiated 3-chloro-1-azaallylic anions in a tetrahydrofuran solution. Our findings were independently confirmed by ROESYNMR experiments, conducted at the Department of Organic Chemistry of Ghent University. A detailed knowledge of the structure of these solvated anions leads to a better understanding of the chemical reactions (e.g. aldolor Mannich-type reactions) in which they play a key role.
Just as this thesis was nearing completion, a further project on silica-template interactions during the initial stages of zeolite synthesis was finished. This project was carried out in conjunction with the Department of Chemical Engineering and Chemistry of Eindhoven University of Technology, the Department of Fuels Chemistry and Technology of Wroclaw University of Technology, and the Centre for Surface Chemistry and Catalysis of Catholic University of Leuven.},
  author       = {Declerck, Reinout},
  isbn         = {978-90-8578-000-7},
  language     = {eng},
  pages        = {310},
  school       = {Ghent University},
  title        = {Development and Implementation of Theoretical Methods for the Calculation of EPR Parameters in Periodic Simulations},
  url          = {http://lib.ugent.be/fulltxt/RUG01/001/286/138/RUG01-001286138\_2010\_0001\_AC.pdf},
  year         = {2008},
}

Chicago
Declerck, Reinout. 2008. “Development and Implementation of Theoretical Methods for the Calculation of EPR Parameters in Periodic Simulations”. Gent.
APA
Declerck, R. (2008). Development and Implementation of Theoretical Methods for the Calculation of EPR Parameters in Periodic Simulations. Gent.
Vancouver
1.
Declerck R. Development and Implementation of Theoretical Methods for the Calculation of EPR Parameters in Periodic Simulations. [Gent]; 2008.
MLA
Declerck, Reinout. “Development and Implementation of Theoretical Methods for the Calculation of EPR Parameters in Periodic Simulations.” 2008 : n. pag. Print.