The second derivative of the electronic energy with respect to the compression scaling factor in the XP-PCM model: Theory and applications to compression response functions of atoms

Bond Lengths and Dipole Moments of Diatomic Molecules under Isotropic Pressure with the XP-PCM and GOSTSHYP Models

While high-pressure chemistry has a well-established history, methods to simulate pressure at the single-molecule level have been somewhat lacking. The current work aims at comparing two static models (XP-PCM and GOSTSHYP) to apply isotropic pressure to single molecules, focusing on the equilibrium bond length and electric dipole moment of diatomic molecules. Numerical challenges arising in the potential energy surface using the XP-PCM method were examined, and a pragmatic approach was followed to mitigate these. The definition of the cavity was scrutinized, and two approaches to retrieve the isotropic character that could potentially be lost when using the standard methodology were suggested. Subsequently, equilibrium bond lengths under pressure were evaluated, showing reasonable agreement between GOSTSHYP and XP-PCM, but some discrepancies persist. A Taylor series analysis introduced elsewhere was then applied to rationalize the observed trends in terms of the bond surface. Finally, the dipole moment was shown to be highly sensitive to the cavity definition, and qualitative agreement necessitates the use of our adapted procedure.

Studying and exploring potential energy surfaces of compressed molecules: a fresh theory from the eXtreme Pressure Polarizable Continuum Model

We present a new theory for studying and exploring the potential energy surface of compressed molecular systems as described within the XP-PCM framework. The effective potential energy surface is defined by the sum of the electronic energy of the compressed system and the pressure-volume work that is necessary in order to create the compression cavity at the given condition of pressure. We show that the resulting total energy Gt is related to the electronic energy by a Legendre transform, in which the pressure and volume of the compression cavity are the conjugate variables. We present an analytical expression for the evaluation of the gradient of the total energy ∇Gt to be used for the geometry optimization of equilibrium geometries and transition states of compressed molecular systems. We also show that, as a result of the Legendre transform property, the potential energy surface can be studied explicitly as function of the pressure, leading to an explicit connection with the well-known Hammond postulate. As a proof of concept, we present the application of the theory to studying and determining of the optimized geometry of compressed methane and the transition state of electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.