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Register a new userReal-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems
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Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrodinger equation for low-dimensionality systems.
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Calculations of the hyperpolarizability are typically much more difficult to converge with basis set size than the linear polarizability. In order to understand these convergence issues and hence obtain accurate ab initio values, we compare calculations of the static hyperpolarizability of the gas-phase chloroform molecule (CHCl_3) using three different kinds of basis sets: Gaussian-type orbitals, numerical basis sets, and real-space grids. Although all of these methods can yield similar results, surprisingly large, diffuse basis sets are needed to achieve convergence to comparable values. These results are interpreted in terms of local polarizability and hyperpolarizability densities. We find that the hyperpolarizability is very sensitive to the molecular structure, and we also assess the significance of vibrational contributions and frequency dispersion.
Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our newcomputational toolbo x which implements the quantum chemical density matrix renormalization group in a second-generation algorithm. We present an overview of the different components of this toolbox.
In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals, and we discuss the main families of approximations for the exchange-correlation energy: semilocal approximations, single-determinant hybrid approximations, multideterminant hybrid approximations, dispersion-corrected approximations, as well as orbital-dependent exchange-correlation density functionals. The chapter aims at providing both a consistent birds-eye view of the field and a detailed description of some of the most used approximations. It is intended to be readable by chemists/physicists and applied mathematicians.
We present an open-source software for the simulation of observables in nuclear magnetic/quadrupole resonance experiments (NMR/NQR) on solid-state samples, developed to assist experimental research in the design of new strategies for the investigation of quantum materials inspired by the early NMR/NQR quantum computation protocols. % The software is based on a quantum mechanical description of nuclear spin dynamics in NMR/NQR experiments and has been widely tested on both theoretical and experimental available results. Moreover, the structure of the software allows an easy generalization of basic experiments to more sophisticated ones, as it includes all the libraries required for the numerical simulation of generic spin systems. In order to make the program easily accessible to a large user base, we developed a user-friendly graphical interface and fully-detailed documentation. Lastly, we portray several examples of the execution of the code that demonstrate the potential of NMR/NQR for the scopes of quantum control and quantum information processing.
We present SPARC: Simulation Package for Ab-initio Real-space Calculations. SPARC can perform Kohn-Sham density functional theory calculations for isolated systems such as molecules as well as extended systems such as crystals and surfaces, in both static and dynamic settings. It is straightforward to install/use and highly competitive with state-of-the-art planewave codes, demonstrating comparable performance on a small number of processors and increasing advantages as the number of processors grows. Notably, SPARC brings solution times down to a few seconds for systems with $mathcal{O}(100-500)$ atoms on large-scale parallel computers, outperforming planewave counterparts by an order of magnitude and more.
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