## Relativity and Reduced Quantities

**Mauricio Rodríguez-Mayorga**

Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, The Netherlands

Lundi 5 Septembre 2022, 11H00

Bibiothèque du LCT, tour 12-13, 4^{ème} étage

ZOOM :

ID de réunion :

Code secret :

In quantum chemistry, relativistic effects cannot be neglected for stuying heavy elements and the compounds that contain them; therefore, reliable and **affordable** methods able to account for these effects (and for electronic correlation ones) need to be proposed. In this seminar, I will present the theoretical foundations of relativistic reduced density matrix functional theory[1], including the extension of the non-relativistic functional approximations to the relativistic domain.

Secondly, I will also discuss the effect of relativity on the probability density (PPD), which has remained unknown till now. In this study, we analyze the effect of relativity on the PPD using the radial Intracule (Extracule) Probability Density [*I*(*u*)] ([*E*(*U*)] [2-4]. Our numerical results indicate that the mean inter-electronic distance, i.e.

<*u*> = ∫ *duI*(*u*)*u*

is reduced (mostly) due to scalar-relativistic effects. As a consequence, an increase of the Coulombic electron-electron repulsion energy (*V*^{C}_{ee}[*I*(*u*)] = ∫ *du**I*(*u*)/*u*) is observed. Finally, preliminary results suggest that our observations are also valid when electron correlation effects are considered.

**Figure 1.** a) Change on the mean value of the rIPD (Δ<*u*>) due to relativistic effects. b) Change on the integrated Coulomb electron-electron repulsion energy Δ*V*^{C}_{ee} = *V*^{C,rel}_{ee} - *V*^{C,nonrel}_{ee} due to relativistic effects. Results obtained with Dyall-DZ basis.

_________________________________

References :

[1] M. Rodríguez-Mayorga, K. J. H. Giesbertz, and L. Visscher, *SciPost Chem.* **2022**, *1*, 004.

[2] P. Debye, *Ann. Physik* **1915**, *46*, 809.

[3] P. Debye, *Physik Z.* **1923**, *24*, 161.

[2] A. J. Thakkar, and N. J. Moore, *Int. J. Quant. Chem.* **1981**, *20*, 393.