In the course of working with DFT-based software packages, we were forced to circumvent numerous problems arising from the nature of the spatial-wave mismatch with real physical models. For this reason, it is interesting for us to approach the study of the structural features of materials in a new way, as well as the defects that arise in them as a result of different types of interventions. The study of matter by means of annihilation spectroscopy is a relatively well-modeled process, but the exact comparison with the experiment determines a significant deviation from the current models we use. For this reason, we would like to try to model correlation effects of positron-electron wave functions including long-range correlations by using a quantum Monte Carlo approach.
Tasks
As mentioned above, the task of accurately determining the positron lifetime in a perfect lattice was performed by colleagues K. A. Simula et al., which opens up an opportunity for us to test our capabilities and continue work towards determining the momentum density by the Monte Carlo method. Thus, we formulate the main task of this project: "Theoretical justification of the electron momentum density by calculating positron annihilation by the Monte Carlo method".
Preliminary schedule by topics/tasks
1 To understand and prepare a brief review of the Two-Component DFT.
2 To review the work of K. A. Simula et al. and try to establish contact with their working group in order to understand what steps they have taken.
3 To attempt to add additional code to the current version of the program - an upgrade.
Required skills
Fortran programming, Basic concepts of what TCDFT is, Knowledge of Monte Carlo modeling.
Acquired skills and experience
Acquisition of skills for working with algorithms serving modeling of positron annihilation in condensed matter.
Recommended literature
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[2] B. Barbiellini and J. Kuriplach, Proposed parameter-free model for interpreting the measured positron annihila tion spectra of materials using a generalized gradient ap proximation, Phys. Rev. Lett. 114, 147401 (2015),
[3] K. A. Simula, J. E. Muff, I. Makkonen, and N. D. Drummond, Quantum Monte Carlo study of positron lifetimes in solids, Phys Rev Lett. 2022 Oct 14;129(16):166403,
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[15] I. Makkonen, M. Hakala, and M. J. Puska, Modeling the momentum distributions of annihilating electron positron pairs in solids, Phys. Rev. B 73, 035103 (2006),
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[17] E. Boroński and R. M. Nieminen, Electron-positron density-functional theory, Phys. Rev. B 34, 3820 (1986),
[18] D. Alf`e and M. J. Gillan, Efficient localized basis set for quantum Monte Carlo calculations on condensed matter, Phys. Rev. B 70, 161101(R) (2004),
[19] N. D. Drummond, M. D. Towler, and R. J. Needs, Jas trow correlation factor for atoms, molecules, and solids, Phys. Rev. B 70, 235119 (2004),
[20] N. D. Drummond and R. J. Needs, Variance minimization scheme for optimizing Jastrow factors, Phys. Rev. B 72, 085124 (2005),
[21] C.J. Umrigar, J. Toulouse, C. Filippi, S. Sorella, and R. G. Hennig, Alleviation of the fermion-sign problem by optimization of many-body wave functions, Phys. Rev. Lett. 98, 110201 (2007).
