Response of Periodic Systems to External Electric and Magnetic Fields
Final Report Abstract
The project is devoted to the development of theoretical methods with which the responses of macroscopic systems to electromagnetic fields can be calculated. The systems of our interest are those that at best can be classified as being infinite and periodic, i.e., crystalline materials. The presence of even static (i.e., not time-dependent), homogenous (i.e., not position-dependent) electromagnetic fields destroy the translational symmetry when treated as usually is done in the molecular case. However, by comparing with the molecular case it has become possible to derive a theory that preserves the translational symmetry and gives the same responses per repeated cell as is found in the molecular case for sufficiently large, finite systems. This theory for the electrostatic field had been presented before the beginning of the present project, although even this could not be considered completely mature. Thus, during the present project we have worked in different directions in order to extend the above-mentioned theory. At first, we extended it to the case of static magnetic fields. Thereby, it turned out that hermicity becomes an important issue. Thus, even for the electrostatic field, hermicity could be a problem that, however, happens to be solved by the fact that the single-particle orbitals are orthonormal. A similar property does not exist automatically for the operator for the magnetic field and, therefore, the Hamilton operator for this has to be made hermitian. Having done so, we could prove that then also the single-particle, Fock or Kohn-Sham operator becomes hermitian in the set of its eigenfunctions even if these are approximated through, for instance, an LCAO approach. For the electrostatic field we could prove that changing the phase factors of the single-particle orbitals will change the energy due to the electrostatic field. Moreover, a similar change occurs when the shape and/or surface charges of a large, finite sample are changed, thereby providing an interpretation of the phase factors of the single-particle orbitals: they describe the shapes and surfaces of the large, finite sample that is being modelled. Unfortunately, we have not yet been able to establish the complete relation between the two. On the other hand, we have demonstrated that, as a result, the converse piezoelectric effect contains a contribution from the surfaces and/or shapes even in the thermodynamic limit. For the static magnetic field a similar effect does not exist. Instead, in this case changing the phase factors of the single-particle orbitals for the infinite, periodic system is equivalent to changing the origin of the gauge that is used in describing the magnetic vector potential. This gauge origin is unphysical and should therefore not affect the results of a calculation. As a side-product we have also studied the so-called density-functional-theory catastrophe, i.e., the fact that the responses of large systems to electric fields as calculated with currently used approximate functionals are much too large. Through a carefully constructed model system we could identify the source for this failure as being related to long-range exchange interactions that then at best are treated through so-called range-separated functionals. In the future we are planning to implement our theory in the CRYSTAL computer program package, developed in Torino, in a collaboration with the authors of those programs. Moreover, further fundamental issues shall be addressed, i.e., the precise role of shape on the piezoelectric responses of large, finite systems, as well as an automatic determination of structure for the infinite, periodic system exposed to a static electromagnetic field.
Publications
- (2017) Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case. The Journal of chemical physics 147 (10) 104101
Springborg, Michael; Molayem, Mohammad; Kirtman, Bernard
(See online at https://doi.org/10.1063/1.5001261) - (2017) Surface effects on converse piezoelectricity of crystals. Physical chemistry chemical physics : PCCP 19 (36) 24724–24734
Molayem, Mohammad; Springborg, Michael; Kirtman, Bernard
(See online at https://doi.org/10.1039/C7CP03161K) - Response properties of periodic materials subjected to external electric and magnetic fields. (2018). In: Marek J. Wójcik, Hiroshi Nakatsuji, Bernard Kirtman und Yukihiro Ozaki (Hg.): Frontiers of Quantum Chemistry. Singapore: Springer Singapore, S. 87–115
B. Kirtman, L. Maschio, M. Rérat, and M. Springborg
(See online at https://doi.org/10.1007/978-981-10-5651-2_5) - The response of extended systems to electrostatic fields, in Handbook of Computational Chemistry. Ed. J. Leszcynski, Springer Verlag (2017) 1415–1458
M. Springborg, B. Kirtman, and M. Molayem
