Stretched or noded orbital densities and self-interaction correction in density functional theory

Semilocal approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semilocal approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semilocal approximations satisfy, suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus, PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here, in particular, to the strongly constrained and appropriately normed (SCAN) meta-GGA, for which the correlation part is already self-interaction-free. This property makes SCAN a natural first candidate for a generalized SIC. Published under license by AIP Publishing.Peer reviewe

Emerging DFT Methods and Their Importance for Challenging Molecular Systems with Orbital Degeneracy

We briefly present some of the most modern and outstanding non-conventional density-functional theory (DFT) methods, which have largely broadened the field of applications with respect to more traditional calculations. The results of these ongoing efforts reveal that a DFT-inspired solution always exists even for pathological cases. Among the set of emerging methods, we specifically mention FT-DFT, OO-DFT, RSX-DFT, MC-PDFT, and FLOSIC-DFT, complementing the last generation of existing density functionals, such as local hybrid and double-hybrid expressions.This research was funded by “Generalitat Valenciana”, grant number AICO/2018/175, and by “Ministerio de Ciencia, Innovación y Universidades", project FIS2015-64222-C2-2-P

Improvements on non-equilibrium and transport Green function techniques: the next-generation transiesta

We present novel methods implemented within the non-equilibrium Green function code (NEGF) transiesta based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes ($N_e\ge1$) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour opti- mizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallellization. Additionally, a generic NEGF post-processing code (tbtrans/phtrans) for electron and phonon transport is presented with several novelties such as Hamiltonian interpolations, $N_e\ge1$ electrode capability, bond-currents, generalized interface for user-defined tight-binding transport, transmission projection using eigenstates of a projected Hamiltonian, and fast inversion algorithms for large-scale simulations easily exceeding $10^6$ atoms on workstation computers. The new features of both codes are demonstrated and bench-marked for relevant test systems.Comment: 24 pages, 19 figure

Basis set convergence and extrapolation of connected triple excitation contributions (T) in computational thermochemistry: the W4-17 benchmark with up to k functions

The total atomization energy of a molecule is the thermochemical cognate of the heat of formation in the gas phase, its most fundamental thermochemical property. We decompose it into different components and provide a survey of them. It emerges that the connected triple excitations contribution is the third most important one, about an order of magnitude less important than the "big two" contributions (mean-field Hartree-Fock and valence CCSD correlation), but 1-2 orders of magnitude more important than the remainder. For the 200 total atomization energies of small molecules in the W4-17 benchmark, we have investigated the basis set convergence of the connected triple excitations contribution (T). Achieving basis set convergence for the valence triple excitations energy is much easier than for the valence singles and doubles correlation energy. Using reference data obtained from spdfghi and spdfghik basis sets, we show that extrapolation from quintuple-zeta and sextuple-zeta yields values within about 0.004 kcal/mol RMS. Convergence to within about 0.01 kcal/mol is achievable with quadruple- and quintuple-zeta basis sets, and to within about 0.05 kcal/mol with triple- and quadruple-zeta basis sets. It appears that radial flexibility in the basis set is more important here than adding angular momenta L: apparently, replacing nZaPa basis sets with truncations of 7ZaPa at L=n gains about one angular momentum for small values of n. We end the article with a brief outlook for the future of accurate electronic structure calculations.Comment: chapter for upcoming Springer book "Quantum Science-Frontier of Chemistry and Physics", edited by Taku Onishi. Revised version with additional background sections requested by edito

Cellulose and cellobiose: adventures of a wandering organic chemist in theoretical chemistry

Single-point energies resulting from the rotations of free -OH groups in the central residue of a cellulose Iα fragment consisting of nine cellotriose chains were obtained using restricted Hartree-Fock (RHF) with the 6-31G(d,p) basis set, density functional theory with the B3LYP functional using the 6-31G(d,p), and the fragment molecular orbital (FMO) method at the FMO2 method with second order perturbation theory (MP2) and the 6-31G(d) basis set. Potential energy curves calculated using these three methods are in excellent agreement with each other for the dihedral angles corresponding to energy maxima and minima. The calculated relative energies using the DFT/B3LYP and FMO2/MP2 levels of theory differ from each other by an average of 0.5 kcal/mol, 0.5 kcal/mol, and 1.1 kcal/mol when each of the -OH groups attached to the C2, C3, and C6 atoms, respectively, were rotated. The use of the pair interaction energy decomposition analysis (PIEDA) with the pair interaction energies from the dimer part of the FMO2 calculations also allowed the identification of the glucose residues most significantly involved in contributing to the rotational energy barriers. Intrachain and interchain interactions (those occurring between residues found in the same cellulose sheet) were seen to be stronger than intersheet interactions (occurring between residues found in different cellulose sheets) in contributing to the relative energy changes due to the rotations of free -OH groups in cellulose. Restricted Hartree-Fock (RHF) and density functional theory (DFT) methods were used to determine the energies involved in the acid-catalyzed hydrolysis of cellobiose in the gas phase. A stepwise mechanism for the reaction was used to determine the different species involved. The initial step was protonation of a cellobiose molecule with a hydronium ion, which was followed by removal of a molecule of water to produce protonated cellobiose. Dissociation of the protonated cellobiose followed to produce a β-D-glucose molecule and a glucosyl cation. The cation in turn was hydrated to produce an α-D-glucose molecule. The energy change for the dissociation step was determined to be +36.8 kcal/mol using density functional theory with the B3LYP functional and 6-311+G(d,p) basis set. The calculated value is similar to those obtained from experimental data and from a recent solution phase Car-Parrinello molecular dynamics calculation

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

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). Quantum 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 inter-operable 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.Comment: 36 pages, 5 figures, resubmitted to J.Phys.: Condens. Matte

Recent Developments in the General Atomic and Molecular Electronic Structure System

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized