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Theoretical Studies of Rydberg Atoms, Interaction with Ground-state Atoms and Interference in External Fields

November 29, 2019.

 

 

       The figure above shows the latest version of Siam Quantum [1]  program that users from around the world can freely download. The program clearly demonstrates the academic capabilities of Thai scientists in terms of software and theoretical developments. Siam Quantum is the only quantum chemistry program that is available in Southeast Asia.

 

       The goal of our research is to study the properties of atoms in the excited state, specifically called Rydberg state. In this state, electrons possess high level of energy, so they can be farther away from their nucleus. Hence, the effects of nucleus on these electrons is diminished. The electrons then become more sensitive to external forces such as gravitational field or electric field. So, in this particular state, they can be used to detect the fields that surrounding them with much higher sensitivity.

 

       However, instead of focusing on just the goal and use the previously existing programs and theory to study the Rydberg state, we decided to take the long journey: developing our own known-how from the ground-up: theoretically, within the framework of the density functional theory, and computationally by developing our own software package. It may be slow at first, but in the long run, we believe this route will strengthen the theoretical and academic development in the field of quantum chemistry in Thailand and in the South East Asia region.

 

2017 - We developed and exchange functional for density functional theory [2]. According to the data, it was one of the most accurate exchange functional to date.

 

2018 - The functional was included in the LibXC [3], a comprehensive exchange-correlation library used by many quantum software around the world.

 

2018 - Its accuracy was confirmed by an independent study [4]. The formula was formally called Chachiyo generalized gradient exchange functional or Chachiyo exchange.

 

2018 - The functional was discussed in length in a Ph.D. thesis from Delaware [5]. For example,

 

“The functional simplicity and accuracy are astounding; in fact, it probably represents the first-of-a-kind, fully non-empirical expression.”

 

2018 - We developed a correlation functional [6]. According to the presented data, it was also one of the most accurate functional to date; despite its unique simplicity.

 

2019 - The correlation functional was included to the LibXC and the presented data was confirmed to 6 decimal places by a LibXC developer [7].

 

2019 - The manuscript on the correlation functional has gone through a peer-review process and is currently under “Minor-Revision” status.

 

2019 - Both the Chachiyo exchange and Chachiyo correlation was implemented in the Siam Quantum program.

 

 

       Possibly, the most astounding achievement from our research is shown in the figure above. It is usually believed that the accuracy of an exchange-correlation functional depends on which “rung” it is. The most primitive rung is the LDA or Local Density Approximation where the functional depends only on the electron density at a point. The next “rung” is called GGA: generalized gradient approximation which incorporates the gradient of density into the calculation. The Chachiyo exchange and correlation belong to this type of DFT functional.

 

       Higher rungs mean higher complexity such as hybrid or meta-GGA and the conventional thinking is that higher rungs bring better accuracy. Nonetheless, the figure above tells an opposite story. For this very limited test, the GGA outperforms all other functionals in other rungs. More data is needed before jumping into any conclusion, but the preliminary data is very promising and may change the way we think about the rungs and ladders of the DFT functionals.

 

References

 

[1] Siam Quantum: a compact open-source quantum simulation software for molecules. https://sites.google.com/site/siamquantum

[2] Chachiyo, Teepanis, and Hathaithip Chachiyo. "Simple and accurate exchange energy for density functional theory." arXiv preprint arXiv:1706.01343 (2017).

[3] Marques, Miguel A. L., Micael J. T. Oliveira, and Tobias Burnus. “Libxc: A library of exchange and correlation functionals for density functional theory.” Computer Physics Communications 183.10 (2012): 2272-2281.

 [4] Lehtola, Susi. “Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient.” Journal of Chemical Theory and Computation 15.3 (2019): 1593-1604.

[5] Alexander V. Mironenko, “Untangling complexities of selective carbon-oxygen bond activation using multiscale modeling and quantum theory”. 2018. University of Delaware, Thesis.

[6] Chachiyo, Teepanis and Hathaithip Chachiyo. “Understanding electron correlation energy through density functional theory.” arXiv preprint arXiv:1811.00712 (2018).

[7] See discussion of the LibXC team https://gitlab.com/libxc/libxc/merge_requests/235

[8] D. P. O’Neill, P. M. W. Gill, “Benchmark correlation energies for small molecules,” Mol. Phys. 103 (2005) 763–766. doi:10.1080/00268970512331339323.

 

Reported by

 

Dr. Teepanis Chachiyo* and Dr. Hathaithip Chachiyo+

* Dept. of Physics, Fac. of Science, Naresuan University, Phitsanulok-65000, Thailand

E-mail: teepanisc@nu.ac.th

+ E-mail: hathaithip.chachiyo@gmail.com