Quantum pressure focusing in solids: a reconstruction from experimental electron density

Abstract

Here an approach is presented for reconstructing the distribution of electronic internal quantum pressure in the electronic continuum of solids from the experimental electron density. Using the formalism of the density functional theory, the spatial inner-crystal map of the quantum pressure is obtained. The results are visualized via the indicator of quantum pressure focusing (IQPF) which reveals the regions where the pressure is concentrated or depleted due to quantum effects. IQPF contains all quantum electron-shell structure-forming contributions resulting from kinetic, exchange and correlation effects, and presents a clear picture of the chemical bond features in crystals with different type of bonding mechanisms.

WinXPRO, 3DPlot and TrajPlot computer software: new options for orbital-free quantum crystallography studies

“…Local loss of spatial structuring of the electron density The Wigner-Parr bonding entropy density (Tsirelson & Nagy, 2009) s WP b ðrÞ ¼ sðgÞ þ sðÞ þ sðÞ § § Carries information about the redistribution of both the electron density and the kinetic energy of electrons during the formation of a crystal from atoms Inner-crystal quantum pressure in electron continuum (Tsirelson et al, 2016) pðrÞ ¼ ð2=3ÞgðrÞ À ð1=4Þr 2 ðrÞ Àð1=4Þð3=Þ 1=3 4=3 ðrÞ Self-organization of the quantum part of electronic energy density in the position space Indicator of inner-crystal quantum pressure focusing (Tsirelson et al, 2019) The TrajPlot program portrays the 2D gradient fields of scalar functions, while the 3DPlot program produces 3D images of scalar functions as computed by WinXPRO. 3DPlot also has the ability to calculate both ascending and descending gradients of these functions using nodes of the current grid file.…”

Negative Linear Compressibility of Formate Crystals from the Viewpoint of Quantum Electronic Pressure

“…That is why, in the present paper, we aim to establish what the reference to the level of quantum chemical characteristics and electronic properties of crystals can yield for studying the nature of NLC. To carry this out, we have analyzed the features of changes in the electron density under increasing compression and the inner-crystal quantum electronic pressure p(r) [32,33] that depends on it. This function describes the change in the average internal energy of the electron continuum unit volume under local deformation, which changes this volume but not its shape [32].…”

“…The quantum terms, such as the kinetic and exchange-correlation contributions to stress tensor, are expressed in terms of the DFT functionals [34]. The influence of instantaneous electron correlation is much weaker than the exchange contribution [33]; therefore, it is considered negligible.…”

Variations of quantum electronic pressure under the external compression in crystals with halogen bonds assembled in Cl3-, Br3-, I3-synthons

“…While the classical electrostatic potential illustrates the predisposition of a halogenated molecule to the halogen bond formation, by virtue of including an exchange contribution, the potential acting on an electron in a molecule (PAEM) (Yang & Davidson, 1997;Zhao & Yang, 2014) can be successfully applied for more detailed characterization of noncovalent bonds . Tao et al (2008) and Tsirelson et al (2019) have indicated that the quantum internal pressure of inhomogeneous electron continuum in the nuclei field reflects the space electron concentrations and depletions in molecules and crystals. Internal pressure describes the variations in the average internal energy of a unit volume of the electron continuum under the local deformation that changes the volume without changing its shape (Tsirelson et al, 2016).…”

“…The kinetic contribution to the quantum electronic pressure, QEP(r), can be expressed via the electron continuum stress tensor (Bader, 1990); the exchange-correlation contribution can be expressed via DFT functionals (Becke, 1988). The effect of electron correlation is significantly weaker than exchange contribution (Tsirelson et al, 2019), and it may be neglected in the first approximation. As a result, the function QEP(r) is defined in a simple form:…”