scholarly journals Localized inverse factorization

2020 ◽  
Author(s):  
Emanuel H Rubensson ◽  
Anton G Artemov ◽  
Anastasia Kruchinina ◽  
Elias Rudberg
Keyword(s):  
Electronic Structure ◽  
Density Functional ◽  
Nearest Neighbor ◽  
Programming Model ◽  
Iterative Refinement ◽  
Divide And Conquer ◽  
Basis Set ◽  
Approximate Factorization ◽  
Matrix Formulation ◽  
Index Set

Abstract We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the index set of $S$. The algorithm is a reformulation of recursive inverse factorization (Rubensson et al. (2008) Recursive inverse factorization. J. Chem. Phys., 128, 104105) but makes use of localized operations only. At each level of the recursion, the problem is cut into two subproblems and their solutions are combined using iterative refinement (Niklasson (2004) Iterative refinement method for the approximate factorization of a matrix inverse. Phys. Rev. B, 70, 193102) to give a solution to the original problem. The two subproblems can be solved in parallel without any communication and, using the localized formulation, the cost of combining their results is negligible compared to the overall cost for sufficiently large systems and appropriate partitions of the problem. We also present an alternative derivation of iterative refinement based on a sign matrix formulation, analyze the stability and propose a parameterless stopping criterion. We present bounds for the initial factorization error and the number of iterations in terms of the condition number of $S$ when the starting guess is given by the solution of the two subproblems in the binary recursion. These bounds are used in theoretical results for the decay properties of the involved matrices. We demonstrate the localization properties of our algorithm for matrices corresponding to nearest neighbor overlap on one-, two- and three-dimensional lattices, as well as basis set overlap matrices generated using the Hartree–Fock and Kohn–Sham density functional theory electronic structure program Ergo (Rudberg et al. (2018) Ergo: an open-source program for linear-scaling electronic structure. SoftwareX, 7, 107). We evaluate the parallel performance of our implementation based on the chunks and tasks programming model, showing that the proposed localization of the algorithm results in a dramatic reduction of communication costs.

scholarly journals r2SCAN-3c: An Efficient “Swiss Army Knife” Composite Electronic-Structure Method

2020 ◽  
Author(s):  
Stefan Grimme ◽  
Andreas Hansen ◽  
Sebastian Ehlert ◽  
Jan-Michael Mewes
Keyword(s):  
Electronic Structure ◽  
Density Functional ◽  
Chemical Space ◽  
Noncovalent Interactions ◽  
New Method ◽  
Basis Set ◽  
Basis Set Superposition Error ◽  
Benchmark Database ◽  
The Cost ◽  
Conformational Energies

The recently proposed second revision of the SCAN meta-GGA density-functional approximation (DFA) {Furness et al., J. Phys. Chem. Lett. 2020, 11, 8208-8215, termed r<sup>2</sup>SCAN} is used to construct an efficient composite electronic-structure method termed r<sup>2</sup>SCAN-3c, expanding the "3c'' series (hybrid: HSE/PBEh-3c, GGA: B97-3c, HF: HF-3c) to themGGA level. To this end, the unaltered r<sup>2</sup>SCAN functional is combined with a tailor-made <br>triple-zeta Gaussian AO-basis as well as with refitted D4 and gCP corrections for London-dispersion and basis-set superposition error. The performance of the new method is evaluated for the GMTKN55 thermochemical database covering large parts of chemical space with about 1500 <br>data points, as well as additional benchmarks for noncovalent interactions, organometallic reactions, lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r<sup>2</sup>SCAN-3c for reaction energies and noncovalent interactions in molecular and periodic systems, as well as outstanding conformational energies, and consistent structures. At just one tenth of the cost, r<sup>2</sup>SCAN-3c provides one of the best results of all semi-local DFT/QZ methods ever tested for the GMTKN55 benchmark database. Specifically for reaction and conformational energies as well as for noncovalent interactions, the new method outperforms hybrid-DFT/QZ approaches, compared to which the computational savings are even larger (factor 100-1000).<br>In relation to other "3c'' methods, r<sup>2</sup>SCAN-3c by far surpasses the accuracy of its predecessor B97-3c at only about twice the cost. The perhaps most relevant remaining systematic deviation of r<sup>2</sup>SCAN-3c is due to self-interaction-error, owing to its mGGA nature. However, SIE is notably reduced compared to other (m)GGAs, as is demonstrated for several examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous low-level DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.<br><br>

scholarly journals r2SCAN-3c: An Efficient “Swiss Army Knife” Composite Electronic-Structure Method

2020 ◽  
Author(s):  
Stefan Grimme ◽  
Andreas Hansen ◽  
Sebastian Ehlert ◽  
Jan-Michael Mewes
Keyword(s):  
Electronic Structure ◽  
Density Functional ◽  
Chemical Space ◽  
Noncovalent Interactions ◽  
New Method ◽  
Basis Set ◽  
Basis Set Superposition Error ◽  
Benchmark Database ◽  
The Cost ◽  
Conformational Energies

The recently proposed second revision of the SCAN meta-GGA density-functional approximation (DFA) {Furness et al., J. Phys. Chem. Lett. 2020, 11, 8208-8215, termed r<sup>2</sup>SCAN} is used to construct an efficient composite electronic-structure method termed r<sup>2</sup>SCAN-3c, expanding the "3c'' series (hybrid: HSE/PBEh-3c, GGA: B97-3c, HF: HF-3c) to themGGA level. To this end, the unaltered r<sup>2</sup>SCAN functional is combined with a tailor-made <br>triple-zeta Gaussian AO-basis as well as with refitted D4 and gCP corrections for London-dispersion and basis-set superposition error. The performance of the new method is evaluated for the GMTKN55 thermochemical database covering large parts of chemical space with about 1500 <br>data points, as well as additional benchmarks for noncovalent interactions, organometallic reactions, lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r<sup>2</sup>SCAN-3c for reaction energies and noncovalent interactions in molecular and periodic systems, as well as outstanding conformational energies, and consistent structures. At just one tenth of the cost, r<sup>2</sup>SCAN-3c provides one of the best results of all semi-local DFT/QZ methods ever tested for the GMTKN55 benchmark database. Specifically for reaction and conformational energies as well as for noncovalent interactions, the new method outperforms hybrid-DFT/QZ approaches, compared to which the computational savings are even larger (factor 100-1000).<br>In relation to other "3c'' methods, r<sup>2</sup>SCAN-3c by far surpasses the accuracy of its predecessor B97-3c at only about twice the cost. The perhaps most relevant remaining systematic deviation of r<sup>2</sup>SCAN-3c is due to self-interaction-error, owing to its mGGA nature. However, SIE is notably reduced compared to other (m)GGAs, as is demonstrated for several examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous low-level DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.<br><br>

scholarly journals Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

2021 ◽  
Vol 8 ◽  
Author(s):  
Qin Yang ◽  
Marco Mendolicchio ◽  
Vincenzo Barone ◽  
Julien Bloino
Keyword(s):  
Perturbation Theory ◽  
Electronic Structure ◽  
Density Functional ◽  
Computational Cost ◽  
Theoretical Data ◽  
Infrared Region ◽  
Second Order ◽  
Basis Set ◽  
Molecular Systems ◽  
The Impact

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the interstellar medium or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or “black-box” protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given. The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns.

Renormalization from Density Functional Theory to Strong Coupling Models for the Electronic Structure of La2CuO4

1989 ◽  
Vol 169 ◽  
Author(s):  
Mark S. Hybertsen ◽  
Michael Schluter ◽  
E.B. Stechel ◽  
D.R. Jennison
Keyword(s):  
Electronic Structure ◽  
Hubbard Model ◽  
Strong Coupling ◽  
Density Functional ◽  
Nearest Neighbor ◽  
Quantitative Agreement ◽  
Energy Scale ◽  
Low Energy ◽  
Energy Spectra ◽  
Functional Theory

AbstractStrong coupling models for the electronic structure of La2CuO4 are derived in two successive stages of renormalization. First, a three-band Hubbard model is derived using a constrained density functional approach. Second, exact diagonalization studies of finite clusters within the three band Hubbard model are used to select and map the low energy spectra onto effective one-band Hamiltonians. At each stage, some observables are calculated and found to be in quantitative agreement with experiment. The final results suggest the following models to be adequate descriptions of the low energy scale dynamics: (1) a spin 1/2 Heisenberg model for the insulating case with nearest neighbor J≈130 meV; (2) a "t–t'–J" model with nearly identical parameters for the electron and hole doped cases.

scholarly journals r2SCAN-3c: An Efficient “Swiss Army Knife” Composite Electronic-Structure Method

2020 ◽  
Author(s):  
Stefan Grimme ◽  
Andreas Hansen ◽  
Sebastian Ehlert ◽  
Jan-Michael Mewes
Keyword(s):  
Electronic Structure ◽  
Density Functional ◽  
Chemical Space ◽  
Noncovalent Interactions ◽  
New Method ◽  
Basis Set ◽  
Basis Set Superposition Error ◽  
Benchmark Database ◽  
The Cost ◽  
Conformational Energies

The recently proposed second revision of the SCAN meta-GGA density-functional approximation (DFA) {Furness et al., J. Phys. Chem. Lett. 2020, 11, 8208-8215, termed r<sup>2</sup>SCAN} is used to construct an efficient composite electronic-structure method termed r<sup>2</sup>SCAN-3c, expanding the "3c'' series (hybrid: HSE/PBEh-3c, GGA: B97-3c, HF: HF-3c) to themGGA level. To this end, the unaltered r<sup>2</sup>SCAN functional is combined with a tailor-made <br>triple-zeta Gaussian AO-basis as well as with refitted D4 and gCP corrections for London-dispersion and basis-set superposition error. The performance of the new method is evaluated for the GMTKN55 thermochemical database covering large parts of chemical space with about 1500 <br>data points, as well as additional benchmarks for noncovalent interactions, organometallic reactions, lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r<sup>2</sup>SCAN-3c for reaction energies and noncovalent interactions in molecular and periodic systems, as well as outstanding conformational energies, and consistent structures. At just one tenth of the cost, r<sup>2</sup>SCAN-3c provides one of the best results of all semi-local DFT/QZ methods ever tested for the GMTKN55 benchmark database. Specifically for reaction and conformational energies as well as for noncovalent interactions, the new method outperforms hybrid-DFT/QZ approaches, compared to which the computational savings are even larger (factor 100-1000).<br>In relation to other "3c'' methods, r<sup>2</sup>SCAN-3c by far surpasses the accuracy of its predecessor B97-3c at only about twice the cost. The perhaps most relevant remaining systematic deviation of r<sup>2</sup>SCAN-3c is due to self-interaction-error, owing to its mGGA nature. However, SIE is notably reduced compared to other (m)GGAs, as is demonstrated for several examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous low-level DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.<br><br>

scholarly journals How Many Electrons Holds a Molecular Electride?

2021 ◽  
Author(s):  
Sebastian Sitkiewicz ◽  
Eloy Ramos-Cordoba ◽  
Josep M. Luis ◽  
Eduard Matito
Keyword(s):  
Electronic Structure ◽  
Crystal Lattice ◽  
Electron Density ◽  
Density Functional ◽  
Salient Feature ◽  
Basis Set ◽  
Correct Description ◽  
Functional Approximation ◽  
Ionic Compounds

<div> <div> <div> <p>Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often group forming channels or surfaces, furnishing electrides with a plethora of traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides with the goal of determining the number of isolated electrons that are held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in the design of new electrides.</p> </div> </div> </div>

scholarly journals How Many Electrons Holds a Molecular Electride?

2021 ◽  
Author(s):  
Sebastian Sitkiewicz ◽  
Eloy Ramos-Cordoba ◽  
Josep M. Luis ◽  
Eduard Matito
Keyword(s):  
Electronic Structure ◽  
Crystal Lattice ◽  
Electron Density ◽  
Density Functional ◽  
Salient Feature ◽  
Basis Set ◽  
Correct Description ◽  
Functional Approximation ◽  
Ionic Compounds

<div> <div> <div> <p>Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often group forming channels or surfaces, furnishing electrides with a plethora of traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides with the goal of determining the number of isolated electrons that are held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in the design of new electrides.</p> </div> </div> </div>

scholarly journals Theoretical B3LYP Study on Electronic Structure of Contrast Agent Iopamidol

2021 ◽  
Vol 68 (2) ◽  
pp. 320-331
Author(s):  
Fatma Genç ◽  
Sedat Giray Kandemirli ◽  
Fatma Kandemirli
Keyword(s):  
Electronic Structure ◽  
Dipole Moment ◽  
Contrast Agent ◽  
Contrast Agents ◽  
Density Functional ◽  
Natural Bond Orbital ◽  
Solvent Polarity ◽  
Natural Bond Orbital Analysis ◽  
Basis Set ◽  
Orbital Analysis

Nonionic low-osmolar contrast agents are thought about safe for intravenous or intra-arterial administration. Iopamidol is one of the contrast agents used for diagnostic clinical computed tomography (CT) protocols last four decades years. The molecular structure of Iopamidol was calculated by the B3LYP density functional model with the LANL2DZ basis set by the Gaussian program. The natural bond orbital analysis in terms of the hybridization of atoms and the electronic structure of the title molecule have been analyzed by using the data obtained from the quantum chemical results. First-order hyperpolarizability (βtot), the dipole moment (μ) and polarizability (α) and anisotropic polarizability (Δα) of the molecule have been reported. HOMO and LUMO energies and parameters related to energies, and dipole moment, polarizability and hyperpolarizability show minor dependences on the solvent polarity. The hardness of Iopamidol decreases with increasing solvent polarity. The stability of the Iopamidol contrast agent with the hyper conjugative interactions, charge delocalization has been analyzed using natural bond orbital analysis. In addition, thermodynamic properties were obtained in the range of 200–1000 K.

Investigated electronic structure and magnetic ordering of rare earth impurities (Eu, Gd) in ZnO

2016 ◽  
Vol 30 (31) ◽  
pp. 1650225 ◽  
Author(s):  
F. Benosman ◽  
Z. Dridi ◽  
Y. Al-Douri ◽  
B. Bouhafs
Keyword(s):  
Electronic Structure ◽  
Rare Earth ◽  
Density Functional ◽  
Nearest Neighbor ◽  
Magnetic Coupling ◽  
Magnetic Ordering ◽  
Hole Doping ◽  
High Electron ◽  
Functional Theory ◽  
Good Agreement

First-principles calculations of the electronic structure of substitutional rare earth (RE) impurity (Eu and Gd) in wurtzite ZnO have been performed using density functional theory within a Hubbard potential correction to the RE 4f states. For Eu-doped ZnO, the magnetic coupling between Eu ions in the nearest neighbor sites is ferromagnetic (FM). The room temperature (RT) ferromagnetism (FM) can be enhanced by an appropriate hole doping into the sample. The ZnO:Gd is found to favor the antiferromagnetic (AFM) phase. The FM can be achieved by high electron doping. The native defects effect (V[Formula: see text], V[Formula: see text]) on the FM is also studied. The oxygen vacancies seem to play an important role in the generation of the FM in both ZnO:Eu and ZnO:Gd, which is in good agreement with recent experimental results.

Reaction mechanism and kinetics of the atmospheric oxidation of 1,4-thioxane by NO3 — A theoretical study

2012 ◽  
Vol 90 (4) ◽  
pp. 384-394 ◽  
Author(s):  
L. Sandhiya ◽  
P. Kolandaivel ◽  
K. Senthilkumar
Keyword(s):  
Electronic Structure ◽  
Hydrogen Atom ◽  
Density Functional ◽  
Electronic Structure Calculations ◽  
State Theory ◽  
Hydrogen Atom Transfer ◽  
Basis Set ◽  
Radical Intermediate ◽  
Atmospheric Species ◽  
Structure Calculations

Volatile organic compounds (VOCs) are emitted as pollutants into the atmosphere from many natural and artificial sources. The oxidation of VOCs by atmospheric species plays a key role in the degradation of VOCs. In the present investigation, the atmospheric degradation of a cyclic organosulfur compound, 1,4-thioxane, by an NO3• radical is studied. Pathways for the reaction of 1,4-thioxane with the NO3• radical were modeled through electronic structure calculations using density functional theory methods B3LYP, M06-2X, and MP2 with the 6–31G(d,p) basis set. The NO3•-initiated reaction of 1,4-thioxane was found to proceed in three ways: by single-hydrogen atom abstraction, by direct transfer of the O atom of NO3• to the S atom moiety of 1,4-thioxane, or by two-hydrogen atom transfer reactions leading to the formation of a peroxy radical intermediate, which further undergoes secondary reactions with other atmospheric species. Structures, energies, and vibrational frequencies obtained from M06-2X/6–31G(d,p) electronic structure calculations were subsequently used to perform canonical variational transition-state theory calculations to determine the rate constants over the temperature range of 278–350 K and to study the lifetime of 1,4-thioxane in the atmosphere. The rate constant calculated for the reaction of 1,4-thioxane with the NO3• radical is in good agreement with the available experimental data.

Sign in / Sign up

Export Citation Format

Share Document