Diamagnetic susceptibility with path integral Monte Carlo method
Tolvanen, Alpi (2021)
2021
Teknis-luonnontieteellinen DI-ohjelma - Master's Programme in Science and Engineering
Tekniikan ja luonnontieteiden tiedekunta - Faculty of Engineering and Natural Sciences
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Hyväksymispäivämäärä
2021-05-27
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tuni-202105245376
https://urn.fi/URN:NBN:fi:tuni-202105245376
Tiivistelmä
The diamagnetic susceptibility is an essential magnetic property, as it describes magnetization response of material to an external magnetic field. However, accurate computational data is not available for systems at finite temperatures, because nuclear motion and finite temperature are not well-supported by common ab initio simulation methods.
We utilize path integral Monte Carlo method (PIMC), which combines non-relativistic quantum mechanics with statistical mechanics at finite temperatures. PIMC takes exact many-body effects into account, which brings precise simulation of electronic correlation and non-adiabatic nuclei. The accuracy of results is limited by statistical error, which can be controlled with the extent of computation.
In this work, we formulate path integrals and derive an estimator for diamagnetic susceptibility in the limit of zero magnetic field. The estimator is applied in PIMC simulations, and the diamagnetic susceptibility is calculated for He, H, H2, H2+, D2, HD, Ps and Ps2, where D is a deuterium and Ps is a positronium. The systems are simulated both with nonadiabatic nuclei and with fixed Born--Oppenheimer nuclei. Temperature is varied on range from 300 K to 3000 K.
The hydrogen atom and the hydrogen molecule express significant nonadiabatic effects in diamagnetic susceptibility, but the helium atom does not. The susceptibility of monatomic systems do not correlate with the temperature, which is expected. The susceptibility of diatomic molecules increases at higher temperatures, which can be explained by a nuclear separation caused by centrifugal forces. The susceptibility of positronium decreases at higher temperatures, which is unexpected.
Obtained PIMC results are compared to 0 K reference values, because there are nearly no published calculations available at finite temperatures. If the PIMC results are extrapolated at 0 K, they are fairly well in line with the reference values. Overall, PIMC appears to be a good method for calculating exact diamagnetic properties of small molecules.
We utilize path integral Monte Carlo method (PIMC), which combines non-relativistic quantum mechanics with statistical mechanics at finite temperatures. PIMC takes exact many-body effects into account, which brings precise simulation of electronic correlation and non-adiabatic nuclei. The accuracy of results is limited by statistical error, which can be controlled with the extent of computation.
In this work, we formulate path integrals and derive an estimator for diamagnetic susceptibility in the limit of zero magnetic field. The estimator is applied in PIMC simulations, and the diamagnetic susceptibility is calculated for He, H, H2, H2+, D2, HD, Ps and Ps2, where D is a deuterium and Ps is a positronium. The systems are simulated both with nonadiabatic nuclei and with fixed Born--Oppenheimer nuclei. Temperature is varied on range from 300 K to 3000 K.
The hydrogen atom and the hydrogen molecule express significant nonadiabatic effects in diamagnetic susceptibility, but the helium atom does not. The susceptibility of monatomic systems do not correlate with the temperature, which is expected. The susceptibility of diatomic molecules increases at higher temperatures, which can be explained by a nuclear separation caused by centrifugal forces. The susceptibility of positronium decreases at higher temperatures, which is unexpected.
Obtained PIMC results are compared to 0 K reference values, because there are nearly no published calculations available at finite temperatures. If the PIMC results are extrapolated at 0 K, they are fairly well in line with the reference values. Overall, PIMC appears to be a good method for calculating exact diamagnetic properties of small molecules.