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Register a new userThe two electron molecular bond revisited: from Bohr orbits to two-center orbitals
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In this review we first discuss extension of Bohrs 1913 molecular model and show that it corresponds to the large-D limit of a dimensional scaling (D-scaling) analysis, as developed by Herschbach and coworkers. In a separate but synergetic approach to the two-electron problem, we summarize recent advances in constructing analytical models for describing the two-electron bond. The emphasis here is not maximally attainable numerical accuracy, but beyond textbook accuracy as informed by physical insights. We demonstrate how the interplay of the cusp condition, the asymptotic condition, the electron-correlation, configuration interaction, and the exact one electron two-center orbitals, can produce energy results approaching chemical accuracy. Reviews of more traditional calculational approaches, such as Hartree-Fock, are also given. The inclusion of electron correlation via Hylleraas type functions is well known to be important, but difficult to implement for more than two electrons. The use of the D-scaled Bohr model offers the tantalizing possibility of obtaining electron correlation energy in a non-traditional way.
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The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can be useful in the study of different quantum mechanical problems in both the theory and practice of calculations dealing with atoms, molecules, nuclei and solids when the integer and noninteger n complex and real atomic orbitals basis sets are emploed. This work presented the development of our previous paper (I.I. Guseinov, Phys. Rev. A, 32 (1985) 1864).
We report an implementation of a program for visualizing complex-valued molecular orbitals. The orbital phase information is encoded on each of the vertices of triangle meshes using the standard color wheel. Using this program, we visualized the molecular orbitals for systems with spin-orbit couplings, external magnetic fields, and complex absorbing potentials. Our work has not only created visually attractive pictures, but also clearly demonstrated that the phases of the complex-valued molecular orbitals carry rich chemical and physical information of the system, which has often been unnoticed or overlooked.
The problem of thermal ignition in a homogeneous gas is revisited from a molecular dynamics perspective. A two-dimensional model is adopted, which assumes reactive disks of type A and B in a fixed area that react to form type C products if an activation threshold for impact is surpassed. Such a reaction liberates kinetic energy to the product particles, representative of the heat release. The results for the ignition delay are compared with those obtained from the continuum description assuming local thermodynamic equilibrium, in order to assess the role played by molecular fluctuations. Results show two regimes of non-equilibrium ignition whereby ignition occurs at different times as compared to that from the continuum description. The first regime is at low activation energies, where the ignition time is found to be higher than that expected from theory for all values of heat release, in agreement with predictions from Prigogine and Xhrouet who attribute this departure to non-equilibrium effects. Results suggest the ignition is spatially homogeneous in this regime. The second regime occurs at high activation energies and sufficiently large heat release values. In this regime, ignition times are found to be dependent on domain size, with larger domains yielding shorter ignition delays than expected. Results for larger systems agree with the expectations by Prigogine and Mahieu, who predict a non-equilibrium reaction rate larger than expected for a homogeneous system in equilibrium. Results yield a large variance for ignition times under these conditions, suggesting a departure from homogeneous combustion. The results obtained are in qualitative agreement with experimental observations of auto-ignition at relatively low temperatures, where hot-spot ignition and associated ignition delays lower than predicted are generally observed.
Halogen bonding has emerged as an important noncovalent interaction in a myriad of applications, including drug design, supramolecular assembly, and catalysis. Current understanding of the halogen bond is informed by electronic structure calculations on isolated molecules and/or crystal structures that are not readily transferable to liquids and disordered phases. To address this issue, we present a first-principles simulation-based approach for quantifying halogen bonds in molecular systems rooted in an understanding of nuclei-nuclei and electron-nuclei spatial correlations. We then demonstrate how this approach can be used to quantify the structure and dynamics of halogen bonds in condensed phases, using solid and liquid molecular chlorine as prototypical examples with high concentrations of halogen bonds. We close with a discussion of how the knowledge generated by our first-principles approach may inform the development of classical empirical models, with a consistent representation of halogen bonding.
We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant non-dynamical correlations are correctly reproduced once an appropriate number $n$ of molecular orbitals is considered. The value of $n$ is determined by requiring that, in the atomization limit, the atoms are described by Hartree-Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be2, B2, C2, N2, O2, and F2) and heteronuclear (LiF, and CN) dimers for which strong non-dynamical correlations and/or weak van der Waals interactions are present.
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