Activation volume and quantum tunneling in the hydrogen transfer reaction between methyl radical and methane: A first computational study.

We present a theory of the effect of quantum tunneling on the basic parameter that characterizes the effect of pressure on the rate constant of chemical reactions in a dense phase, the activation volume. This theory results in combining, on the one hand, the extreme pressure polarizable continuum model, a quantum chemical method to describe the effect of pressure on the reaction energy profile in a dense medium, and, on the other hand, the semiclassical version of the transition state theory, which includes the effect of quantum tunneling through a transmission coefficient. The theory has been applied to the study of the activation volume of the model reaction of hydrogen transfer between methyl radical and methane, including the primary isotope substitution of hydrogen with deuterium (H/D). The analysis of the numerical results offers, for the first time, a clear insight into the effect of quantum tunneling on the activation volume for this hydrogen transfer reaction: this effect results from the different influences that pressure has on the competing thermal and tunneling reaction mechanisms. Furthermore, the computed kinetic isotope effect (H/D) on the activation volume for this model hydrogen transfer correlates well with the experimental data for more complex hydrogen transfer reactions.

Inverse design of molecule-metal nanoparticle systems interacting with light for desired photophysical properties.

Molecules close to a metal nanoparticle (NP) have significantly different photophysical properties from those of the isolated one. In order to harness the potential of the molecule-NP system, appropriate design guidelines are required. Here, we propose an inverse design method of the optimal molecule-NP systems and incident electric field for desired photophysical properties. It is based on a gradient-based optimization search within the time-dependent quantum chemical description for the molecule and the continuum model for the metal NP. We designed the optimal molecule, relative molecule-NP spatial conformation, and incident electric field of a molecule-NP system to maximize the population transfer to the target electronic state of the molecule. The design results were presented and discussed. The present method is promising as the basis for designing molecule-NP systems and incident fields and accelerates discoveries of efficient molecular plasmonics systems.

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 extreme pressure polarizable continuum model framework. The effective potential energy surface is defined as 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 a 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 the optimized geometry of compressed methane and the transition states of the electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.

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.

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.

High-Pressure Reaction Profiles and Activation Volumes of 1,3-Cyclohexadiene Dimerizations Computed by the Extreme Pressure-Polarizable Continuum Model (XP-PCM).

Quantum chemical calculations are reported for the thermal dimerizations of 1,3-cyclohexadiene at 1 atm and high pressures up to the GPa range. Computed activation enthalpies of plausible dimerization pathways at 1 atm agree well with the experiment activation energies and the values from previous calculations. High-pressure reaction profiles, computed by the recently developed extreme pressure-polarizable continuum model (XP-PCM), show that the reduction of reaction barrier is more profound in concerted reactions than in stepwise reactions, which is rationalized on the basis of the volume profiles of different mechanisms. A clear shift of the transition state towards the reactant under pressure is revealed for the [6+4]-ene reaction by the calculations. The computed activation volumes by XP-PCM agree excellently with the experimental values, confirming the existence of competing mechanisms in the thermal dimerization of 1,3-cyclohexadiene.

Toward an Understanding of the Pressure Effect on the Intramolecular Vibrational Frequencies of Sulfur Hexafluoride.

The structural and vibrational properties of the molecular units of sulfur hexafluoride crystal as a function of pressure have been studied by the Extreme Pressure Polarizable Continuum Model (XP-PCM) method. Within the XP-PCM model, single molecule calculations allow a consistent interpretation of the experimental measurements when considering the effect of pressure on both the molecular structure and the vibrational normal modes. This peculiar aspect of XP-PCM provides a detailed description of the electronic origin of normal modes variations with pressure, via the curvature of the potential energy surface and via the anharmonicity of the normal modes. When applied to the vibrational properties of the sulfur hexafluoride crystal, the XP-PCM method reveals a hitherto unknown interpretation of the effects of the pressure on the vibrational normal modes of the molecular units of this crystal.

Relating atomic energy, radius and electronegativity through compression.

Trends in atomic properties are well-established tools for guiding the analysis and discovery of materials. Here, we show how compression can reveal a long sought-after connection between two central chemical concepts - van-der-Waals (vdW) radii and electronegativity - and how these relate to the driving forces behind chemical and physical transformations.

Non-Bonded Radii of the Atoms Under Compression.

We present quantum mechanical estimates for non-bonded, van der Waals-like, radii of 93 atoms in a pressure range from 0 to 300 gigapascal. Trends in radii are largely maintained under pressure, but atoms also change place in their relative size ordering. Multiple isobaric contractions of radii are predicted and are explained by pressure-induced changes to the electronic ground state configurations of the atoms. The presented radii are predictive of drastically different chemistry under high pressure and permit an extension of chemical thinking to different thermodynamic regimes. For example, they can aid in assignment of bonded and non-bonded contacts, for distinguishing molecular entities, and for estimating available space inside compressed materials. All data has been made available in an interactive web application.

High-Pressure-Promoted and Facially Selective Diels-Alder Reactions of Enzymatically Derived cis-1,2-Dihydrocatechols and Their Acetonide Derivatives: Enantiodivergent Routes to Homochiral and Polyfunctionalized Bicyclo[2.2.2]octenes.

cis-1,2-Dihydrocatechols 5 (X = Me and Cl), which are available in the homochiral form through the whole-cell biotransformation of toluene and chlorobenzene, respectively, undergo Diels-Alder cycloaddition reactions with a range of electron-deficient dienophiles at 19 kbar (1.9 GPa). The favored products of such reactions are adducts of the general form 7 and that arise through the operation of a contrasteric or syn-addition pathway. In contrast, the acetonide derivatives of metabolites 5 undergo anti-selective addition reactions under the same conditions and so producing adducts of the general form 11. Bicyclo[2.2.2]octenes 7 and 11, which embody carbocyclic frameworks of opposite enantiomeric form, are useful scaffolds for chemical synthesis. Computational studies reveal that syn-adduct formation is kinetically and normally thermodynamically favored over anti-adduct formation when the free diols 5 are involved, but the reverse is so when the corresponding acetonides participate as the 4π-addend. Furthermore, the reactions become more exothermic as pressure increases while, concurrently, the activation barrier diminishes and at 6 GPa (60 kbar) almost vanishes.

Varying Electronic Configurations in Compressed Atoms: From the Role of the Spatial Extension of Atomic Orbitals to the Change of Electronic Configuration as an Isobaric Transformation.

A quantum chemical model for the study of the electronic structure of compressed atoms lends itself to a perturbation-theoretic analysis. It is shown, both analytically and numerically, that the increase of the electronic energy with increasing compression depends on the electronic configuration, as a result of the variable spatial extent of the atomic orbitals involved. The different destabilization of the electronic states may lead to an isobaric change of the ground-state electronic configuration, and the same first-order model paves the way to a simple thermodynamical interpretation of this process.

An open quantum system theory for polarizable continuum models.

The problem of a solute described by Quantum Chemistry within a solvent represented as a polarizable continuum model (PCM) is here reformulated in terms of the open quantum systems (OQS) theory. Using its stochastic Schrödinger equation formulation, we are able to provide a more comprehensive picture of the electronic energies and the coupling between solute and solvent electronic dynamics. In particular, the OQS-PCM proves to be a unifying theoretical framework naturally including polarization and dispersion interactions, the effect of solvent fluctuations, and the non-Markovian solvent response. As such, the OQS-PCM describes the interplay between the solute and the solvent typical electronic dynamical times and yields both the standard PCM and the so-called Born-Oppenheimer solvation regime, where the solvent electronic response is considered faster than any electronic dynamics taking place in the solute. In analyzing the OQS-PCM, we obtained an expression for the solute-solvent dispersion (van der Waals) interactions, which is very transparent in terms of a physical interpretation based on fluctuations and response functions. Finally, we present various numerical tests that support the theoretical findings.

Quantum optimal control theory for solvated systems.

In this work, we generalize the quantum optimal control theory (QOCT) of molecules subject to ultrashort laser pulses to the case of solvated systems, explicitly including the solvent dielectric properties in the system's quantum Hamiltonian. A reliable description of the solvent polarization is accounted for within the polarizable continuum model (PCM). The electron dynamics for the molecules in solution is coupled with the dynamics of the surrounding polarizable environment, which affects the features of the optimized laser pulse. To illustrate such effects, numerical applications of the developed method to the study of optimal population of selected excited states of two molecular solvated systems are presented and discussed.

The Role of Computational Chemistry in the Experimental Determination of the Dipole Moment of Molecules in Solution.

The methods for the experimental determination of electric dipole moment of molecules in solution from measurements of dielectric permittivity and refractive index are traditionally based on the classical Onsager model. In this model the molecular solute is approximated as a simple polarizable point dipole inside a spherical or ellipsoidal cavity of a dielectric medium representing the solvent. However, the inadequacies of the model resulting from the assumption of a simple shape of the cavity, for the evaluation of the cavity field effect, and from the uncertainty of the polarizability of the molecular solute influences the results and hampers the comparison with the electric dipole moments computed from quantum chemical solvation models. In this article we propose a new method for the experimental determination of the electric dipole moment in solution in which information from the Polarizable Continuum Model calculations are used in place of the Onsager model. The new method overcomes the limitations of this latter model regarding both the cavity field effect and the polarizability of the molecular solutes, and thus allows a coherent comparison between experimental and computed dipole moments of solvated molecules. © 2019 Wiley Periodicals, Inc.

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

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.

Linear chains of hydrogen molecules under pressure: An extreme-pressure continuum model study.

New analytical gradients of the electronic energy of a confined molecular system within the extreme-pressure continuum model are presented and applied to the study of the equilibrium geometries of linear chains of hydrogen molecules nH2 under pressures. The decrease in inter- and intramolecular H-H distances with the increase in the pressure has been studied up to 80 GPa. We have also shown that the compression of the bond-lengths can be interpreted in terms of the effect of the confining potential of the electron density of the molecular systems.

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

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 Pauli-repulsion 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. © 2018 Wiley Periodicals, Inc.

Insights on the Realgar Crystal Under Pressure from XP-PCM and Periodic Model Calculations.

The spectroscopic properties of As4S4 with pressure have been computed by the quantum mechanical XP-PCM method and by density functional theory periodic calculations. The comparison has allowed the interpretation of the available experimental data. By comparison of the two methods and with experiments, we show that the XP-PCM method is able to reproduce the same behavior of the periodic calculations with much lower computational cost allowing to be adopted as a first choice computational tool for a qualitative interpretation of molecular crystals properties under pressure.

The Effect of Pressure on Organic Reactions in Fluids-a New Theoretical Perspective.

This Review brings a new perspective to the study of chemical reactions in compressed fluid media. We begin by reviewing the substantial insight gained from more than 50 years of experimental studies on organic reactions in solution under pressure. These led to a proper estimation of the critical roles of volume of activation (Δ≠ V) and reaction volume (ΔV) in understanding pressure effect on rates and equilibria of organic reactions. A recently developed computational method, the XP-PCM (extreme pressure polarizable continuum model) method, capable of carrying out quantum mechanical calculations of reaction pathways of molecules under pressure, is introduced. A case study of the Diels-Alder cycloaddition of cyclopentadiene with ethylene serves, in pedagogical detail, to describe the methodology. We then apply the XP-PCM method to a selection of other pericyclic reactions, including the parent Diels-Alder cycloaddition of butadiene with ethylene, electrocyclic ring-opening of cyclobutene, electrocyclic ring-closing of Z-hexatriene, the [1,5]-H shift in Z-pentadiene, and the Cope rearrangement. These serve as examples of some of the most common combinations of Δ≠ V and ΔV. Interesting phenomena such as a shift in a transition state along a reaction coordinate, a switch of rate-determining step, and the possible turning of a transition state into a stable minimum are revealed by the calculations. A reaction volume profile, the change in the volume of the reacting molecules as the reaction proceeds, emerges as being useful.

Diels-Alder Cycloaddition of Cyclopentadiene and C60 at the Extreme High Pressure.

High-pressure Diels-Alder cycloaddition reaction of fullerenes is an important synthetic method for the thermally stable cycloadducts. The effects of high pressure on the potential energy surfaces of Diels-Alder cycloaddition of cyclopentadiene and C60 were studied with a recently developed approach, the polarizable continuum model for extreme pressure (XP-PCM). It is revealed that the high pressure reduces the activation energies and increases reaction energies drastically, making the DA reaction more favorable. The pressure effects on the reaction energetics can be divided into the cavitation and electronic contributions. For the activation energy, the cavitation contribution is significant in comparison with the electronic contribution. To assist future experiments, the activation volume and reaction volume were computed on the basis of the relationship between activation energy or reaction energy with the pressure as a consequence of the fitting linear correlation between activation energy or reaction energy with the pressure.