Isotopic Effects on Covalent Bond Confined in a Penetrable Sphere

Abstract

A model of confinement of the covalent bond by a finite potential beyond the Born-Oppenheimer approximation is presented. A two-electron molecule is located at the center of a penetrable spherical cavity. The Schrödinger equation has been solved by using the diffusion Monte Carlo method. Total energies, internuclear distances, and vibrational frequencies of the confined molecular system have been obtained. Even for confining potentials of a few electronvolts, a noticeable increase in the bond energy and the nuclear vibrational frequency is observed, and the internuclear distance is lowered. The gap between the zero point energy of different molecular isotopes increases with confinement. The confinement of the electron pair might play a role in chemical reactivity, providing an alternative explanation for the tunnel effect, when large values of primary kinetic isotopic effect are observed. The Swain-Schaad relation is still verified when confinement changes the zero point energy. A semiquantitative illustration is proposed using the data relative to an hydrogen transfer involving a C-H cleavage catalyzed by the bovine serum amine oxidase. Changes on the confining conditions, corresponding to a confinement/deconfinement process, result in a significant decrease in the activation energy of the chemical transformation. It is proposed that confinement/deconfinement of the electron-pair bonding by external electrostatic forces inside the active pocket of an enzyme could be one of the basic mechanisms of the enzyme catalysis.

Benchmark values of Shannon entropy for spherically confined hydrogen atom

“…The confined hydrogen atom within an impenetrable sphere, that is, hard wall, has long time been of special interest in modeling the high pressure environment in the interiors of planets and interpreting the astrophysical phenomena . Great interests of confined systems in either soft or hard wall with different boundary conditions have also been found in semiconductor quantum dots, chemical reactions in extreme conditions, and many other physical and chemical systems . During past years, considerable numbers of powerful methods were developed to study the confined atomic systems and abundant physical quantities have been investigated extensively, such as the energy spectrum, oscillator strength and life time, static polarizability and hyperpolarizability, laser induced excitation and harmonic generation, effective quantum pressure due to finite volume, electronic quantum entanglement, and the current interest classical information entropy …”

Electron Density Analysis for the H2+ System Confined by Hard Walls: The Chemical Bond Under Extreme Conditions

“…Some people argue that this potential is realistic and its results can be compared with experimental data. In fact, to the best of our knowledge only four molecules, H + 2 , [21][22][23][24][25] HeH ++ , [21] H 2 , [26][27][28][29] and LiH [30] have been studied when they are submitted to spatial restrictions and all of them deal with one or two electrons (See a recent review by Ley-Koo [31] ). [16] Besides, this model has been useful to test exchange-correlation functionals designed within the Kohn-Sham density functional theory.…”

“…The main reason for scarce reports on molecular systems confined by penetrable or impenetrable walls is well understood; there are no codes to deal with these restrictions. In fact, to the best of our knowledge only four molecules, H + 2 , [21][22][23][24][25] HeH ++ , [21] H 2 , [26][27][28][29] and LiH [30] have been studied when they are submitted to spatial restrictions and all of them deal with one or two electrons (See a recent review by Ley-Koo [31] ). In these reports, the aim has been the behavior of the total energy as a function of the confinement and the analysis of the wave-function or the electron density has not been carried out, which is disappointing since the study of some related phenomena such as chemical bonding under extreme conditions is fascinating for several scientific fields.…”

Ionization probability of the hydrogen atom suddenly released from confinement

“…A spherical hard wall with the atom in the center has been widely employed to analyze the changes in the electronic structure of the system . Finite size potentials have also been considered to study confinement by surfaces that can be penetrated by the electron charge . The impenetrable spherical cavity model has shown to be a good starting point for reproducing the effects of pressure on atoms, which has proved useful for studying different confined quantum systems see for example, Ref.…”