Electronic Structure Calculations for Solids and Molecules

Abstract

Electronic structure problems are studied in condensed matter physics and theoretical chemistry to provide important insights into the properties of matter. This 2006 graduate textbook describes the main theoretical approaches and computational techniques, from the simplest approximations to the most sophisticated methods. It starts with a detailed description of the various theoretical approaches to calculating the electronic structure of solids and molecules, including density-functional theory and chemical methods based on Hartree-Fock theory. The basic approximations are thoroughly discussed, and an in-depth overview of recent advances and alternative approaches in DFT is given. The second part discusses the different practical methods used to solve the electronic structure problem computationally, for both DFT and Hartree-Fock approaches. Adopting a unique and open approach, this textbook is aimed at graduate students in physics and chemistry, and is intended to improve communication between these communities. It also serves as a reference for researchers entering the field.

Monitoring a simple hydrolysis process in an organic solid by observing methyl group rotation

“…Also, for this calculation, the ring atoms in all other molecules in the clusters for 1 and the five C atoms on the backbone for clusters of 2 were frozen at their X-ray determined positions in the crystal while all the other atoms in these molecules were allowed to relax. The basis set superposition error [5] was not corrected in the clusters since previous studies have shown that the basis set superposition error has little impact on the rotational barriers [2] while the computational cost is significant. All the calculations in the clusters were performed at the B3LYP/6-31G(d) level with the Grimme's D3BJ empirical correction for the London dispersion [19,20].…”

“…We have also performed solid state 1 H spin-lattice relaxation [1], field emission scanning electron microscopy [3], differential scanning calorimetry [4], electronic structure calculations [5], and single crystal X-ray diffraction [6] in pure samples of 1 and 2 as reference points in order to help interpret the solid state 1 H spin-lattice relaxation measurements in the mixtures. By comparing the solid state 1 H spin-lattice relaxation results and the field emission scanning electron microscopy images in the pure samples, we find support for a model that relates one of the fitted solid state 1 H spin-lattice relaxation parameters to a distribution of NMR activation energies for methyl group rotation [7].…”

A quantum-mechanics molecular-mechanics scheme for extended systems

“…In this line, Golze and co-workers elaborated a method for the treatment of metallic interfaces, where the interactions between the quantum-mechanical adsorbate and the classical substrate are handled at the molecular mechanics level [20]. To the best of our knowledge only Yarne et al [6] developed a hybrid QM-MM methodology imposing PBC to the whole system in a pseudopotentials planewaves (PPW) code [25]. In this case electrons were confined to a smaller unit cell inside the supercell needed to describe the whole system, and periodicity was limited to 1 or 2-D [6].…”

Ab-<i>initio</i> studies of adsorbate-surface interactions

“…In the literature such decoupling is termed as thhe Born-Oppenheimer or adiabatic approximation. [51][52][53] The Eq. (2.2) is the Hamiltonian of N interacting nonrelativistic electrons, which is frequently termed as the electronic hamiltonian.…”

“…In this chapter we will review some of the fundamental aspects of DFT, as described by Hohenberg Working independently, both Thomas (1927) and Fermi (1928) proposed writing the energy of a many body system in terms of electronic density, ρ( r). 52 Figure 3 perspective when we move from the many body electronic wave function ψ( r 1 , . .…”