The virial theorem for the polarizable continuum model

Cammi, Roberto

doi:10.1063/1.4866174

Cited by 8 publications

(8 citation statements)

References 40 publications

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“…The derivatives of the electronic energy G er for the calculation of pressure p in eq are evaluated by an analytical theory which has been recently developed for XP-PCM by two of the present authors and Bo Chen (see eq 8 in the Supporting Information (SI)). This analytical theory exploits a specific extension of the Hellmann–Feynman theorem , to the electronic energy G er …”

Section: Methodsmentioning

confidence: 99%

“…This analytical theory exploits a specific extension of the Hellmann− Feynman theorem 56,57 to the electronic energy G er . 58 To gauge the volume of the cavity, its radius R C is expressed as the van der Waals (vdW) radius of the atom times a variable scaling factor f, i.e., R C = R vdW f. An upper value f 0 , R C 0 = R vdW f 0 , is set in correspondence to near standard condition of pressure (p < 1 GPa). To model compression and compare different atoms with each other in a meaningful way, we have used a consistent set of vdW radii 10 available for elements 1−96.…”

Section: ̂= ̂+ ̂+ ̂(1)mentioning

confidence: 99%

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Squeezing All Elements in the Periodic Table: Electron Configuration and Electronegativity of the Atoms under Compression

et al. 2019

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We present a quantum mechanical model capable of describing isotropic compression of single atoms in a non-reactive neon-like environment. Studies of 93 atoms predict drastic changes to ground-state electronic configurations and electronegativity in the pressure range of 0–300 GPa. This extension of atomic reference data assists in the working of chemical intuition at extreme pressure and can act as a guide to both experiments and computational efforts. For example, we can speculate on the existence of pressure-induced polarity (red-ox) inversions in various alloys. Our study confirms that the filling of energy levels in compressed atoms more closely follows the hydrogenic aufbau principle, where the ordering is determined by the principal quantum number. In contrast, the Madelung energy ordering rule is not predictive for atoms under compression. Magnetism may increase or decrease with pressure, depending on which atom is considered. However, Hund’s rule is never violated for single atoms in the considered pressure range. Important (and understandable) electron shifts, s→p, s→d, s→f, and d→f are essential chemical and physical consequences of compression. Among the specific intriguing changes predicted are an increase in the range between the most and least electronegative elements with compression; a rearrangement of electronegativities of the alkali metals with pressure, with Na becoming the most electropositive s1 element (while Li becomes a p group element and K and heavier become transition metals); phase transitions in Ca, Sr, and Ba correlating well with s→d transitions; spin-reduction in all d-block atoms for which the valence d-shell occupation is d n (4 ≤ n ≤ 8); d→f transitions in Ce, Dy, and Cm causing Ce to become the most electropositive element of the f-block; f→d transitions in Ho, Dy, and Tb and a s→f transition in Pu. At high pressure Sc and Ti become the most electropositive elements, while Ne, He, and F remain the most electronegative ones.

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Section: Methodsmentioning

confidence: 99%

Section: ̂= ̂+ ̂+ ̂(1)mentioning

confidence: 99%

Squeezing All Elements in the Periodic Table: Electron Configuration and Electronegativity of the Atoms under Compression

et al. 2019

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“…This derivative of the electronic energy G er can be evaluated by applying an extension of the Hellmann–Feynman theorem to the XP‐PCM model . According to this extension the derivative of the electronic energy G er with respect to the cavity scaling factor f is given by:

((), \frac{\partial G_{italicer}}{\partial f}) = < normalΨ ∣ \frac{\partial {\overset{false^}{V}}_{r}}{\partial f} ∣ normalΨ >,

where

\frac{\partial {\overset{false^}{V}}_{r}}{\partial f}

is the partial derivative of the Pauli repulsion operator

{\overset{false^}{V}}_{r}

of eq.…”

Section: Analytical Theory Of the Pressurementioning

confidence: 99%

Analytical calculation of pressure for confined atomic and molecular systems using the eXtreme‐Pressure Polarizable Continuum Model

2018

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We show that the pressure acting on atoms and molecular systems within the compression cavity of the eXtreme-Pressure Polarizable Continuum method can be expressed in terms of the electron density of the systems and of the Paulirepulsion confining potential. The analytical expression holds for spherical cavities as well as for cavities constructed from van der Waals spheres of the constituting atoms of the molecular systems.

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“…Assuming a variational electronic structure method (e.g., Hartree-Fock, DFT, etc.) and exploiting a generalized Hellmann-Feynman theorem, 14,21 the first derivative of the electronic energy G er can be written as 4…”

Section: The First Derivative ∂G Er =∂Fmentioning

confidence: 99%

“…According to Equation ( 18), ρ f is required for the analytical calculation of the second derivative ∂ 2 G er =∂ 2 f. ρ f has been evaluated according to the uncoupled first-order perturbation theory of Equation (19)(20)(21)(22).…”

Section: The First and Second Derivatives Of The Electronic Energy An...mentioning

confidence: 99%

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

Cammi

Chen

2022

J Comput Chem

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We present the analytical theory for the second derivative of the electronic energy with respect to the scaling factor of the compression cavity within the eXtreme pressure polarizable continuum model (XP‐PCM) for the study of compressed atomic and molecular systems. The theory has been exploited to study compression response functions describing how the atomic/molecular properties are effected by an external pressure. The response functions considered include the atomic compressibility and the pressure coefficients of the ionization energy (IE) and electron affinity (EA). The theory has been validated by numerical application to compressed neon, argon, and krypton atoms.

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The virial theorem for the polarizable continuum model

Cited by 8 publications

References 40 publications

Squeezing All Elements in the Periodic Table: Electron Configuration and Electronegativity of the Atoms under Compression

Squeezing All Elements in the Periodic Table: Electron Configuration and Electronegativity of the Atoms under Compression

Analytical calculation of pressure for confined atomic and molecular systems using the eXtreme‐Pressure Polarizable Continuum Model

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

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