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Simulation of Crystalline Nanoporous Materials and the Computation of Adsorption/Diffusion Properties
Published in T. Grant Glover, Bin Mu, Gas Adsorption in Metal-Organic Frameworks, 2018
Atoms are made up of protons (positively charged), neutrons (neutral), and electrons (negatively charged). The first (dominating) force inside an atom is the nuclear force that interacts between neutron–neutron, neutron–proton, and proton–proton. Surrounding the nucleus are electrons that move around the nucleus. The second interaction is an electromagnetic interaction between electron–electron, electron–proton, and proton–proton. As two atoms approach one another, the protons of one atom attract the electrons of the other atom. When the electron–proton interaction overcomes the repulsive electron–electron interaction, bond-formation can occur and molecules are formed. Interaction between charged particles is governed by Coulomb's law: F ∝ q1q2/r2, where F is the electrical force acting between two electrical charges q1 and q2, and r is the distance between the two charges. The computation of the time-averaged interactions of electron clouds surrounding atoms is very involved and to make computations tractable, many approximations must be made. Hartree–Fock methods optimize the molecular orbitals by evaluating the energy of an electron in each molecular orbital moving in the mean field of all other electrons [35]. To account for electron correlation is an active research field and include methods like Configurational Interaction (CI), Møller–Plesset perturbation theory (MP2, MP3, MP4, etc.), and multiconfigurational self-consistent field (MCSCF) [35–39].
Density Functional Theory (DFT): Periodic Advancement and New Challenges
Published in Tanmoy Chakraborty, Lalita Ledwani, Research Methodology in Chemical Sciences, 2017
This particular study concentrates on the significant contributions of DFT toward chemical science and the probable modifications, adding extra dimension to the accuracy of the formalism that makes it more compact. DFT is the computationally cost-effective solution for higher level computation on relatively large systems. Applications of DFT associated with approximate functionals significantly improve the performance of theoretical computation over a wide realm of chemical science. Currently, DFT becomes the subject of intense interest throughout the globe. The scope of theoretical manipulation for a wide range of properties from energetics and geometries of molecules to reaction barriers and van der Waals interactions is possible with the development of highly advanced theoretical techniques. However, we have also emphasized on some important shortcomings in terms of the contributory effects to get reasonable accuracy in the computations. The mutual interactions of the electrons, that is, electron correlation effect, complicate its theoretical description and manipulation enormously. Time-dependent DFT provides a sophisticated tool to investigate these dynamic properties in atoms, molecules, and clusters. Although some fundamental problems remain and computational techniques still require further upgradation, DFT presents promising growth with impressive outcome throughout the last two decades.
Basics of Nanothin Film Magnetism
Published in Evgeny Y. Tsymbal, Žutić Igor, Spintronics Handbook: Spin Transport and Magnetism, Second Edition, 2019
Bretislav Heinrich, Pavlo Omelchenko, Erol Girt
where S is the area of the film. Calculations of energy differences are simplified by using the force theorem. The main problem is how to treat electron correlations self-consistently. The force theorem says that the energy difference between the two configurations is well accounted for by taking the difference in single particle energies. It is adequate to take an approximate spin-dependent potential and to calculate the single particle energies in the P and AP configurations. This difference in energy is very close to that obtained from self-consistent calculations, see the further discussion in Ref. [32]. In fact, this section closely follows Stiles’s Section 4.3 in [32]. This procedure based on the force theorem significantly simplifies the calculation of exchange coupling and interface magnetic anisotropies. In calculations of the interlayer exchange coupling energies, one does not create a large error by neglecting spin-orbit interactions, while in calculations of the interface anisotropies spin-orbit coupling is the crucial ingredient. Single particle energy calculations require one to evaluate the electron energy for four QWS, see Figure 2.6. For thick F layers, one finds large energy contributions. However, these large contributions cancel out in the difference Equati on 2.41. In order to avoid mistakes in this procedure, it is better to calculate the cohesive energy of the QWS by subtracting the bulk contributions, ΔEQWS=Etot−EFVF−ENMVNM,
A perturbative approach to multireference equation-of-motion coupled cluster
Published in Molecular Physics, 2021
Marvin H. Lechner, Róbert Izsák, Marcel Nooijen, Frank Neese
Electron correlation effects play a vital role in calculating molecular properties and taking them into account accurately is often inevitable even to obtain a merely qualitative description of a system. Apart from dynamical correlation effects that arise from the inadequate treatment of short-range electron repulsion at the single-reference (SR) level, static correlation effects must also be considered in many important chemical systems. Examples include long-range dissociation problems and situations with near electronic degeneracy. The standard treatment in these cases accounts for the static effects by a relatively small multiconfigurational expansion which also serves as a starting point for quantitatively accurate multireference (MR) methods [1] that may rely on perturbation (PT), configuration interaction (CI) or coupled-cluster (CC) theory. In contrast to current density functional theory (DFT) approaches, such treatment can be systematically improved upon, possibly until the point of reaching chemical accuracy [2].
Equation-of-motion coupled-cluster method for ionised states with spin-orbit coupling using open-shell reference wavefunction
Published in Molecular Physics, 2018
Relativistic effects [1–4] can be divided into scalar relativistic (SR) effects and spin-orbit coupling (SOC). SOC is important for systems containing heavy elements, particularly heavy p-block elements. In fact, SOC is already imperative for light-element systems in calculating properties such as fine structure splitting of degenerate states. On the other hand, electron correlation is usually critical to achieve reliable theoretical estimates in electronic structure calculations. Coupled-cluster (CC) method [5] is one of the most popular approaches in calculating dynamical correlation with high accuracy. CC methods based on four-component and two-component all-electron relativistic Hamiltonians [6–10] as well as those based on relativistic effective core potentials (RECPs) [11] with SOC [12–16] have been developed, where SOC is included in self-consistent field (SCF) calculations in determining molecular spinors. Those CC approaches can achieve accurate results for heavy and superheavy element atoms or molecules with a dominant single reference character. However, such calculations are usually rather expensive and can be applied mainly to quite small systems due to the use of the complex two-component or four-component molecular spinors.
Photosensitivity, substituent and solvent-induced shifts in UV-visible absorption bands of naphthyl-ester liquid crystals: a comparative theoretical approach
Published in Liquid Crystals, 2014
P. Lakshmi Praveen, Durga P. Ojha
The first method is based on DFT theory. An understanding of absorption behaviour requires the knowledge of molecular orbital’s properties, spectral shifts and appropriate excited states. Moreover, their photophysics and chemistry represent a challenge in understanding of the excited states dynamics. The main difficulties against reliable theoretical approaches are concerned with the size of systems and the presence of strong electron correlation effects. Both properties are difficult to treat in the framework of the quantum mechanical methods rooted in the Hartree–Fock (HF) theory. The DFT is successful to evaluate a variety of ground-state properties with accuracy close to that of the post-HF methods.[11]