Quantum confinement of the covalent bond beyond the Born-Oppenheimer approximation

Partial Separability of the Schrödinger Equation Combined with a Jastrow Factor

Describing the Coulomb interactions between electrons in atomic or molecular systems is an important step to help us obtain accurate results for the different observables in the system. One convenient approach is to separate the dynamic electronic correlation, i.e., Coulomb electron-electron repulsion, from the motion of the electrons in the nucleus electric field. The wave function is written as the product of two terms, one accounting for the electron-electron interactions, which is symmetric under identical particle exchange, and the other is antisymmetric and represents the dynamics and exchange of electrons within the nuclear electric field. In this work, we present a novel computational scheme based on this idea that leads to an expression of the energy as the sum of two terms. To illustrate the method, we look into few-body Coulombic systems, H2, H3+, and Li(1s2,2s), and discuss the possible extension to larger systems. A simple correlation factor, based on the Jastrow exponential term, is employed to represent the dynamics of the electron pairs, leading to simple analytical forms and accurate results. We also present and illustrate a different approach with the Li atom based on the partial separability applied to a portion of the atom.

DFT and spatial confinement: a benchmark study on the structural and electrical properties of hydrogen bonded complexes

An extended set of 37 exchange correlation functionals, representing different DFT approximations, has been evaluated on a difficult playground represented by the dipole moment (μ_z), polarizability (α_zz), first hyperpolarizability (β_zzz), and the corresponding interaction-induced electrical properties (Δμ_z, Δα_zz, Δβ_zzz) of spatially confined hydrogen bonded (HB) dimers. A two-dimensional harmonic oscillator potential was used to exert the effect of spatial restriction. The performance of DFT methods in predicting hydrogen bond lengths in the studied molecular complexes upon confinement has also been examined. The data determined using a high-level CCSD(T) method serve as a reference. The conducted analyses allow us to conclude that methods rooted in DFT constitute a precise tool for the calculation of μ_z and α_zz as well as Δμ_z and Δα_zz, as most of the tested functionals provide results affected by rather small relative errors. On the other hand, an accurate description of the nonlinear optical response of the studied HB systems remains a great challenge for most of the analyzed DFT functionals, both in vacuum and in the presence of an analytical confining potential. Some of the tested DFT methods are found to be prone to catastrophic failure in the prediction of β_zzz as well as Δβ_zzz. The obtained results indicate that there is no great chasm in performance between functionals belonging to different DFT approximations or functionals including different amount of Hartree-Fock exchange when the values of dipole moment and first hyperpolarizability as well as the corresponding interaction-induced electrical properties are considered. However, a higher fraction of Hartree-Fock exchange improves the quality of predictions of α_zz and Δα_zz. Additionally, it has been shown that only three functionals from the examined set, namely B2PLYP, B3LYP and ωB97X-D, provide highly accurate structural parameters for the investigated systems. Of significant importance is the conclusion that the ωB97X-D functional, representing a modern and highly parametrized range-separated hybrid, demonstrates the most coherent behavior, showing rather small deviations from the reference data in the case of μ_z, α_zz, Δμ_z and Δα_zz as well as the structural parameters of the studied HB dimers. Moreover, our results indicate that the presence of spatial confinement has a rather small effect on the performance of DFT methods.

Exclusion principle repulsion effects on the covalent bond beyond the Born-Oppenheimer approximation

The changes in the covalent bond of the hydrogen molecule limited in space by a spherical hard boundary are studied. The sphere is moved along an axis parallel or orthogonal to the molecular axis. The diffusion Monte Carlo approach is used to solve the Schrödinger equation with the relevant boundary conditions and to evaluate the changes in the bond energy versus the location of the sphere. The vertical and lateral quantum forces exerted on the sphere are evaluated by calculating the energy derivative versus the distances to the sphere. The results show that the quantum forces present an important dependence on the distance and vanish rapidly as the separation between the sphere and the molecule increases. In the limiting case the molecular bond breaks due to the electronic depletion induced in the covalent bond. An application of this study is the modelisation of the forces exerted on the passivated cantilever of an atomic force microscope probing the electron cloud in the contact mode in the Pauli exclusion regime.

Isotopic Effects on Covalent Bond Confined in a Penetrable Sphere

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.

On the particular importance of vibrational contributions to the static electrical properties of model linear molecules under spatial confinement

The influence of the spatial confinement on the electronic and vibrational contributions to longitudinal electric-dipole properties of model linear molecules including HCN, HCCH and CO₂ is analyzed.