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Density Functional Theory (DFT): Periodic Advancement and New Challenges
Published in Tanmoy Chakraborty, Lalita Ledwani, Research Methodology in Chemical Sciences, 2017
Despite the rapid advancement in theoretical chemistry, to build proper functional remains a very challenging task to date. In principle, a well behaved and standard functional should work for the whole of chemistry, solid-state physics, and biology in different situations and diverse conditions. But in general applications, there are many disappointments in the real-time solutions. These are not breakdowns of the theory itself, but rather are shortcomings of the currently used approximation techniques available for the exchange-correlation functionals. This inherent limitation is clearly observed in case of the two simplest chemical systems (molecules), namely, stretched H2? and stretched H2. Even for these simple systems, the existing functionals are pushed to its limit. The fascinating aspect of DFT, namely, its simplicity will be in trouble if the computations with the proposed functionals become as complicated as full configuration interaction. The simplest functional, the LDA, has its limitation in many areas of chemistry. Although LDA gives good geometries, it massively overbinds molecules. The first step enabling chemists to use DFT satisfactorily is the inclusion of the first derivative of density in the form of the GGA. The next major outbreak came in the early 1990s with the inclusion of a fraction of HF exact exchange in the functional, as described by Becke. This work exhibits the fundamental basis for the development of B3LYP,16,18 and it is the most widely used of all the contemporary functionals. The concept of hybrid functional (B3LYP) shows promising potential to extend the application of DFT to a wide range of systems along with impressive performance. Development of new functionals that improved upon B3LYP will provide a significant contribution in the progress of DFT-based computation.
Solvent Extraction through the Lens of Advanced Modeling and Simulation
Published in Bruce A. Moyer, Ion Exchange and Solvent Extraction: Volume 23, 2019
Aurora E. Clark, Michael J. Servis, Zhu Liu, Ernesto Martinez-Baez, Jing Su, Enrique R. Batista, Ping Yang, Andrew Wildman, Torin Stetina, Xiaosong Li, Ken Newcomb, Edward J. Maginn, Jochen Autschbach, David A. Dixon
The type of complexes that are relevant in transition metal (TM), lanthanide (Ln), and actinide (An) separations may have open-shell metal centers, namely unpaired electrons that are formally localized at one or several metal centers. The electronic structure may, in this case, require two or more electron configurations, for even a qualitatively correct description. This is referred to as a multi-configuration (MC) or multi-reference case (not to be confused with multiple resonance structures), or static correlation as opposed to the dynamic correlation, which describes the explicit avoidance of two electrons in the wave function. The approximate correlation functionals in DFT and low-order truncated CC WFT, for instance, are good at describing the dynamic correlation of single-configuration systems, but they can have severe difficulties with MC cases. The full CC (or full configuration interaction, CI) wave function treats both static and dynamic correlation, but in practice, as usual, a compromise must be made. For an MC system, the first priority is to get its description qualitatively correct, that is, to treat the static correlation. Among the more frequently applied methods for MC systems is complete active space26 (CAS) WFT and its variants. In a CAS calculation, an active space of orbitals and electrons, comprising the open shells and often additional orbitals, is selected, and a full CI calculation in this active space is performed, usually with simultaneous orbital optimization. Factorial scaling with the active space size severely limits these calculations, but in recent years CAS variants based on electronic states from density-matrix renormalization group (DMRG) calculations with polynomial scaling are showing much promise for large MC problems.27–29 CAS-type calculations can be performed with relativistic spinors,30 also with DMRG,31 but often only SR effects are treated variationally while the SO interaction is introduced via a CI-like state interaction.32,33The dynamic correlation in CAS-type calculations is usually treated approximately by perturbation theory (PT).34,35 There is also truncated multi-reference configuration interaction (MR-CI),36 which remains in use in particular for calculations of electronic spectra and to introduce dynamic correlation in a MC ground state. Promising singlet-paired CC methods37,38 and multi-configuration pair-density-functional methods39 have also been developed in recent years that may allow routine calculations of MC systems with the inclusion of dynamic correlation, and progress in MC–CC theory40 has been reported.
Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes
Published in Molecular Physics, 2018
Susi Lehtola, John Parkhill, Martin Head-Gordon
Systems with strong correlation, in which many electronic configurations contribute significantly to the wave function, are important in many areas of chemistry such as catalysis. Unfortunately, their accurate yet efficient modelling is still an unsolved question in theoretical chemistry. The exact wave function for any system is available in theory by diagonalising the molecular Hamiltonian in the basis of electron configurations, yielding the full configuration interaction (FCI) approach. But, FCI exhibits exponential scaling that limits its use to tiny systems [1–6].