Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

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Density‐functional thermochemistry. III. The role of exact exchange

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

Toward reliable density functional methods without adjustable parameters: The PBE0 model

First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.

https://iopscience.iop.org/article/10.1088/0953-8984/14/11/301/pdf

First-principles simulation: ideas, illustrations and the CASTEP code

We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation-strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001

Chemistry with ADF

Generalized gradient approximations (GGA's) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3--4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.

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Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation.

Erratum: Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation [Phys. Rev. B 46, 6671 (1992)]

We show that the computational complexity associated with the density-functional-based determination of infrared intensities and nonresonant Raman scattering activities is the same as that required for vibrational modes. Further, we use extremely large basis sets to determine the intrinsic accuracy for calculating such phenomena within the density-functional theory. We present benchmark calculations on ${\mathrm{CH}}_{4}$, ${\mathrm{H}}_{2}$O, ${\mathrm{C}}_{2}$${\mathrm{H}}_{2}$, ${\mathrm{C}}_{2}$${\mathrm{H}}_{4}$, and ${\mathrm{C}}_{2}$${\mathrm{H}}_{6}$ within both the local-density approximation (LDA) and the generalized gradient approximation (GGA). Tests of the reliability and numerical stability of the theoretical scheme are presented. We show that in order to obtain reliable results, appropriate polarization basis functions and well-converged wave functions are necessary. While most of the Raman spectra predicted by LDA agree very well with experimental data, some of the infrared intensities show substantial errors. The GGA functional overcomes most of these deficiencies, leading to an overall good agreement with experiment. \textcopyright{} 1996 The American Physical Society.

Infrared intensities and Raman-scattering activities within density-functional theory

Developpement d'un algorithme variationnel pour generer une maille d'integration a utiliser dans les calculs de structures electroniques. La methode inclut un nouvel algorithme pour integrer au-dela des regions interstitielles arbitraires, et une technique d'integration des spheres atomiques amelioree (les erreurs diminuant avec le nombre de points radiaux). Les points de la maille et les elements de volume sont optimises afin de s'assurer qu'un grand nombre d'integrales sont evaluees exactement. Explicitation des deux idees retenues pour optimiser la maille. On montre comment les algorithmes de force peuvent etre utilises pour affiner les mailles resultantes. La precision et l'efficacite de cette methode sont evaluees en presentant des integrations de densite de charge sur une variete de clusters isoles. Comparaison de cette methode aux algorithmes conventionnels a points speciaux. Exemple de l'etat fondamental tetraedrique du fragment cristallin C 5 H 12

Variational mesh for quantum-mechanical simulations.

Fullerene tubules are shown to be highly polarizable ``molecular straws'' capable of ingesting dipolar molecules Local-density-functional calculations on HF molecules within a finite-length tubule, of size 144 atoms, demonstrate this effect The energy of incarceration is several times the thermal ambient at room temperature These calculations, now feasible on desktop workstations, open the way to the study of nanoscale capillarity and to, perhaps, precise control over shielding of specific ``guest'' compounds from external electric and magnetic fields

Mark R. Pederson

Papers

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation.

Erratum: Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation [Phys. Rev. B 46, 6671 (1992)]

Infrared intensities and Raman-scattering activities within density-functional theory

Variational mesh for quantum-mechanical simulations.

Nanocapillarity in fullerene tubules.