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3 pages, 199 KiB

Open AccessEditorial

Dedication: Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of His 80th Birthday

by Peter Blaha and Henry Chermette

Computation 2022, 10(5), 78; https://doi.org/10.3390/computation10050078 - 23 May 2022

Viewed by 1836

Abstract

Karlheinz Schwarz was born in January 1941 in Vienna (Austria), and he married Christine Schwarz in 1969 [...] Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

Research

Jump to: Editorial

13 pages, 938 KiB

Open AccessArticle

Regression Machine Learning Models Used to Predict DFT-Computed NMR Parameters of Zeolites

by Robin Gaumard, Dominik Dragún, Jesús N. Pedroza-Montero, Bruno Alonso, Hazar Guesmi, Irina Malkin Ondík and Tzonka Mineva

Computation 2022, 10(5), 74; https://doi.org/10.3390/computation10050074 - 13 May 2022

Cited by 10 | Viewed by 3728

Abstract

Machine learning approaches can drastically decrease the computational time for the predictions of spectroscopic properties in materials, while preserving the quality of the computational approaches. We studied the performance of kernel-ridge regression (KRR) and gradient boosting regressor (GBR) models trained on the isotropic [...] Read more.

Machine learning approaches can drastically decrease the computational time for the predictions of spectroscopic properties in materials, while preserving the quality of the computational approaches. We studied the performance of kernel-ridge regression (KRR) and gradient boosting regressor (GBR) models trained on the isotropic shielding values, computed with density-functional theory (DFT), in a series of different known zeolites containing out-of-frame metal cations or fluorine anion and organic structure-directing cations. The smooth overlap of atomic position descriptors were computed from the DFT-optimised Cartesian coordinates of each atoms in the zeolite crystal cells. The use of these descriptors as inputs in both machine learning regression methods led to the prediction of the DFT isotropic shielding values with mean errors within 0.6 ppm. The results showed that the GBR model scales better than the KRR model. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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12 pages, 4549 KiB

Open AccessArticle

Influence of the Chemical Pressure on the Magnetic Properties of the Mixed Anion Cuprates Cu₂OX₂ (X = Cl, Br, I)

by William Lafargue-Dit-Hauret and Xavier Rocquefelte

Computation 2022, 10(5), 73; https://doi.org/10.3390/computation10050073 - 12 May 2022

Cited by 2 | Viewed by 2815

Abstract

In this study, we theoretically investigate the structural, electronic and magnetic properties of the Cu₂OX₂ (X = Cl, Br, I) compounds. Previous studies reported potential spin-driven ferroelectricity in Cu₂OCl₂, originating from a non-collinear magnetic phase existing [...] Read more.

In this study, we theoretically investigate the structural, electronic and magnetic properties of the Cu₂OX₂ (X = Cl, Br, I) compounds. Previous studies reported potential spin-driven ferroelectricity in Cu₂OCl₂, originating from a non-collinear magnetic phase existing below

T_{N}

∼70 K. However, the nature of this low-temperature magnetic phase is still under debate. Here, we focus on the calculation of J exchange couplings and enhance knowledge in the field by (i) characterizing the low-temperature magnetic order for Cu₂OCl₂ and (ii) evaluating the impact of the chemical pressure on the magnetic interactions, which leads us to consider the two new phases Cu₂OBr₂ and Cu₂OI₂. Our ab initio simulations notably demonstrate the coexistence of strong antiferromagnetic and ferromagnetic interactions, leading to spin frustration. The

T_{N}

Néel temperatures were estimated on the basis of a quasi-1D AFM model using the

ab initio

J couplings. It nicely reproduces the

T_{N}

value for Cu₂OCl₂ and allows us to predict an increase of

T_{N}

under chemical pressure, with

T_{N}

= 120 K for the dynamically stable phase Cu₂OBr₂. This investigation suggests that chemical pressure is an effective key factor to open the door of room-temperature multiferroicity. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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11 pages, 3695 KiB

Open AccessArticle

LFDFT—A Practical Tool for Coordination Chemistry

by Harry Ramanantoanina

Computation 2022, 10(5), 70; https://doi.org/10.3390/computation10050070 - 2 May 2022

Cited by 4 | Viewed by 3165

Abstract

The electronic structure of coordination compounds with lanthanide ions is studied by means of density functional theory (DFT) calculations. This work deals with the electronic structure and properties of open-shell systems based on the calculation of multiplet structure and ligand-field interaction, within the [...] Read more.

The electronic structure of coordination compounds with lanthanide ions is studied by means of density functional theory (DFT) calculations. This work deals with the electronic structure and properties of open-shell systems based on the calculation of multiplet structure and ligand-field interaction, within the framework of the Ligand–Field Density-Functional Theory (LFDFT) method. Using effective Hamiltonian in conjunction with the DFT, we are able to reasonably calculate the low-lying excited states of the molecular [Eu(NO

_{3}

)

_{3}

(phenanthroline)

_{2}

] complex, subjected to the Eu

^{3 +}

configuration 4f

^{6}

. The results are compared with available experimental data, revealing relative uncertainties of less than 5% for many energy levels. We also demonstrate the ability of the LFDFT method to simulate absorption spectrum, considering cerocene as an example. Ce M

_{4, 5}

X-ray absorption spectra are simulated for the complexes [Ce(

η^{8} -

C

_{8}

H

_{8}

)

_{2}

] and [Ce(

η^{8} -

C

_{8}

H

_{8}

)

_{2}

][Li(tetrahydrofurane)

_{4}

], which are approximated by the Ce oxidation states

4 +

and

3 +

, respectively. The results showed a very good agreement with the experimental data for the Ce

^{3 +}

compound, unlike for the Ce

^{4 +}

one, where charge transfer electronic structure is still missing in the theoretical model. Therefore this presentation reports the benefits of having a theoretical method that is primarily dedicated to coordination chemistry, but it also outlines limitations and places the ongoing developmental efforts in the broader context of treating complex molecular systems. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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13 pages, 359 KiB

Open AccessArticle

Generation of Basis Sets for Accurate Molecular Calculations: Application to Helium Atom and Dimer

by Ignacio Ema, Guillermo Ramírez, Rafael López and José Manuel García de la Vega

Computation 2022, 10(5), 65; https://doi.org/10.3390/computation10050065 - 20 Apr 2022

Cited by 4 | Viewed by 2769

Abstract

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment [...] Read more.

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respect. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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23 pages, 1389 KiB

Open AccessArticle

Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals

by Sajanthan Sekaran, Matthieu Saubanère and Emmanuel Fromager

Computation 2022, 10(3), 45; https://doi.org/10.3390/computation10030045 - 18 Mar 2022

Cited by 7 | Viewed by 2730

Abstract

Quantum embedding is a divide and conquer strategy that aims at solving the electronic Schrödinger equation of sizeable molecules or extended systems. We establish in the present work a clearer and in-principle-exact connection between density matrix embedding theory (DMET) and density-functional theory (DFT) [...] Read more.

Quantum embedding is a divide and conquer strategy that aims at solving the electronic Schrödinger equation of sizeable molecules or extended systems. We establish in the present work a clearer and in-principle-exact connection between density matrix embedding theory (DMET) and density-functional theory (DFT) within the simple but nontrivial one-dimensional Hubbard model. For that purpose, we use our recent reformulation of single-impurity DMET as a Householder transformed density-matrix functional embedding theory (Ht-DMFET). On the basis of well-identified density-functional approximations, a self-consistent local potential functional embedding theory (LPFET) is formulated and implemented. Combining both LPFET and DMET numerical results with our formally exact density-functional embedding theory reveals that a single statically embedded impurity can in principle describe the density-driven Mott–Hubbard transition, provided that a complementary density-functional correlation potential (which is neglected in both DMET and LPFET) exhibits a derivative discontinuity (DD) at half filling. The extension of LPFET to multiple impurities (which would enable to circumvent the modeling of DDs) and its generalization to quantum chemical Hamiltonians are left for future work. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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18 pages, 953 KiB

Open AccessArticle

Performance Enhancement of APW+lo Calculations by Simplest Separation of Concerns

by Long Zhang, Anton Kozhevnikov, Thomas Schulthess, Hai-Ping Cheng and Samuel B. Trickey

Computation 2022, 10(3), 43; https://doi.org/10.3390/computation10030043 - 16 Mar 2022

Cited by 8 | Viewed by 2805

Abstract

Full-potential linearized augmented plane wave (LAPW) and APW plus local orbital (APW+

l o

) codes differ widely in both their user interfaces and in capabilities for calculations and analysis beyond their common central task of all-electron solution of the Kohn–Sham equations. However, [...] Read more.

Full-potential linearized augmented plane wave (LAPW) and APW plus local orbital (APW+

l o

) codes differ widely in both their user interfaces and in capabilities for calculations and analysis beyond their common central task of all-electron solution of the Kohn–Sham equations. However, that common central task opens a possible route to performance enhancement, namely to offload the basic LAPW/APW+

l o

algorithms to a library optimized purely for that purpose. To explore that opportunity, we have interfaced the Exciting-Plus (“EP”) LAPW/APW+

l o

DFT code with the highly optimized SIRIUS multi-functional DFT package. This simplest realization of the separation of concerns approach yields substantial performance over the base EP code via additional task parallelism without significant change in the EP source code or user interface. We provide benchmarks of the interfaced code against the original EP using small bulk systems, and demonstrate performance on a spin-crossover molecule and magnetic molecule that are of size and complexity at the margins of the capability of the EP code itself. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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15 pages, 1895 KiB

Open AccessArticle

Periodic DFTB for Supported Clusters: Implementation and Application on Benzene Dimers Deposited on Graphene

by Mathias Rapacioli and Nathalie Tarrat

Computation 2022, 10(3), 39; https://doi.org/10.3390/computation10030039 - 14 Mar 2022

Cited by 7 | Viewed by 3013

Abstract

The interest for properties of clusters deposited on surfaces has grown in recent years. In this framework, the Density Functional based Tight Binding (DFTB) method appears as a promising tool due to its ability to treat extended systems at the quantum level with [...] Read more.

The interest for properties of clusters deposited on surfaces has grown in recent years. In this framework, the Density Functional based Tight Binding (DFTB) method appears as a promising tool due to its ability to treat extended systems at the quantum level with a low computational cost. We report the implementation of periodic boundary conditions for DFTB within the deMonNano code with k-points formalism and corrections for intermolecular interactions. The quality of DFTB results is evaluated by comparison with dispersion-corrected DFT calculations. Optimized lattice properties for a graphene sheet and graphite bulk are in agreement with reference data. The deposition of both benzene monomer and dimers on graphene are investigated and the observed trends are similar at the DFT and DFTB levels. Moreover, interaction energies are of similar orders of magnitude for these two levels of calculation. This study has evidenced the high stability of a structure made of two benzene molecules deposited close to each other on the graphene sheet. This work demonstrates the ability of the new implementation to investigate surface-deposited molecular clusters properties. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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21 pages, 4859 KiB

Open AccessArticle

Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives

by Eduardo Fabiano, Fulvio Sarcinella, Lucian A. Constantin and Fabio Della Sala

Computation 2022, 10(2), 30; https://doi.org/10.3390/computation10020030 - 15 Feb 2022

Cited by 9 | Viewed by 3047

Abstract

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations [...] Read more.

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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16 pages, 519 KiB

Open AccessArticle

Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO

by Manuel Richter, Seo-Jin Kim, Klaus Koepernik, Helge Rosner and Arnulf Möbius

Computation 2022, 10(2), 28; https://doi.org/10.3390/computation10020028 - 11 Feb 2022

Cited by 5 | Viewed by 4237

Abstract

Electronic structure calculations in the framework of density functional theory are based on complex numerical codes which are used in a multitude of applications. Frequently, existing experimental information is used as a gauge for the reliability of such codes. However, their results depend [...] Read more.

Electronic structure calculations in the framework of density functional theory are based on complex numerical codes which are used in a multitude of applications. Frequently, existing experimental information is used as a gauge for the reliability of such codes. However, their results depend both on the chosen exchange-correlation energy functional and on the specific numerical implementation of the Kohn-Sham equations. The only way to disentangle these two items is a direct comparison of two or more electronic structure codes. Here, we address the achievable numerical accuracy and numerical precision in the total energy computation of the two all-electron density-functional codes Wien2k and FPLO. Both codes are based on almost independent numerical implementations and largely differ in the representation of the Bloch wave function. Thus, it is a highly encouraging result that the total energy data obtained with both codes agree within less than

10^{- 6}

. We here relate the term numerical accuracy to the value of the total energy E, while the term numerical precision is related to the numerical noise of E as observed in total energy derivatives. We find that Wien2k achieves a slightly higher accuracy than FPLO at the price of a larger numerical effort. Further, we demonstrate that the FPLO code shows somewhat higher precision, i.e., less numerical noise in E than Wien2k, which is useful for the evaluation of physical properties based on derivatives of E. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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14 pages, 2026 KiB

Open AccessArticle

Should We Gain Confidence from the Similarity of Results between Methods?

by Pascal Pernot and Andreas Savin

Computation 2022, 10(2), 27; https://doi.org/10.3390/computation10020027 - 11 Feb 2022

Cited by 2 | Viewed by 2233

Abstract

Confirming the result of a calculation by a calculation with a different method is often seen as a validity check. However, when the methods considered are all subject to the same (systematic) errors, this practice fails. Using a statistical approach, we define measures [...] Read more.

Confirming the result of a calculation by a calculation with a different method is often seen as a validity check. However, when the methods considered are all subject to the same (systematic) errors, this practice fails. Using a statistical approach, we define measures for reliability and similarity, and we explore the extent to which the similarity of results can help improve our judgment of the validity of data. This method is illustrated on synthetic data and applied to two benchmark datasets extracted from the literature: band gaps of solids estimated by various density functional approximations, and effective atomization energies estimated by ab initio and machine-learning methods. Depending on the levels of bias and correlation of the datasets, we found that similarity may provide a null-to-marginal improvement in reliability and was mostly effective in eliminating large errors. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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10 pages, 2054 KiB

Open AccessArticle

Length-Gauge Optical Matrix Elements in WIEN2k

by Oleg Rubel and Peter Blaha

Computation 2022, 10(2), 22; https://doi.org/10.3390/computation10020022 - 26 Jan 2022

Cited by 2 | Viewed by 3156

Abstract

Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with [...] Read more.

Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with the position operator, the momentum matrix elements do not fully capture the oscillator strength, while the length-gauge velocity matrix elements do. So far, length-gauge velocity matrix elements were not accessible in the all-electron full-potential WIEN2k package. We demonstrate the feasibility of computing length-gauge matrix elements in WIEN2k for a hybrid exchange-correlation functional based on a finite difference approach. To illustrate the implementation we determined matrix elements for optical transitions between the conduction and valence bands in GaAs, GaN, (CH

_{3}

NH

_{3}

)PbI

_{3}

and a monolayer MoS

_{2}

. The non-locality of the Hartree–Fock exact exchange potential leads to a strong enhancement of the oscillator strength as noticed recently in calculations employing pseudopotentials (Laurien and Rubel: arXiv:2111.14772 (2021)). We obtained an analytical expression for the enhancement factor for the difference in eigenvalues not captured by the kinetic energy. It is expected that these results can also be extended to other non-local potentials, e.g., a many-body

G W

approximation. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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9 pages, 2216 KiB

Open AccessArticle

Hexatetra-Carbon: A Novel Two-Dimensional Semiconductor Allotrope of Carbon

by Mosayeb Naseri, Jaafar Jalilian, Dennis R. Salahub, Maicon Pierre Lourenço and Ghasem Rezaei

Computation 2022, 10(2), 19; https://doi.org/10.3390/computation10020019 - 25 Jan 2022

Cited by 11 | Viewed by 4029

Abstract

Employing first-principles calculations based on density functional theory (DFT), we designed a novel two-dimensional (2D) elemental monolayer allotrope of carbon called hexatetra-carbon. In the hexatetra-carbon structure, each carbon atom bonds with its four neighboring atoms in a 2D double layer crystal structure, which [...] Read more.

Employing first-principles calculations based on density functional theory (DFT), we designed a novel two-dimensional (2D) elemental monolayer allotrope of carbon called hexatetra-carbon. In the hexatetra-carbon structure, each carbon atom bonds with its four neighboring atoms in a 2D double layer crystal structure, which is formed by a network of carbon hexagonal prisms. Based on our calculations, it is found that hexatetra-carbon exhibits a good structural stability as confirmed by its rather high calculated cohesive energy −6.86 eV/atom, and the absence of imaginary phonon modes in its phonon dispersion spectra. Moreover, compared with its hexagonal counterpart, i.e., graphene, which is a gapless material, our designed hexatetra-carbon is a semiconductor with an indirect band gap of 2.20 eV. Furthermore, with a deeper look at the hexatetra-carbon, one finds that this novel monolayer may be obtained from bilayer graphene under external mechanical strain conditions. As a semiconductor with a moderate band gap in the visible light range, once synthesized, hexatetra-carbon would show promising applications in new opto-electronics technologies. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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13 pages, 15027 KiB

Open AccessArticle

Impact of Charge-Resonance Excitations on CT-Mediated J-Type Aggregation in Singlet and Triplet Exciton States of Perylene Di-Imide Aggregates: A TDDFT Investigation

by Yasi Dai, Maria Zubiria-Ulacia, David Casanova and Fabrizia Negri

Computation 2022, 10(2), 18; https://doi.org/10.3390/computation10020018 - 25 Jan 2022

Cited by 5 | Viewed by 3628

Abstract

The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the [...] Read more.

The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the exciton states of molecular aggregates, and it has been shown to provide reliable results when coupled with the appropriate choice of the functional. Here we apply a general procedure to analyze the aggregates’ exciton states derived from TDDFT calculations in terms of diabatic states chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space. We apply the approach to study energy profiles, interstate couplings, and the charge-transfer character of singlet and triplet exciton states of perylene di-imide aggregates (PDI). We focus on the intermolecular displacement along the longitudinal translation coordinate, which mimics different amounts of slip-stacking observed in PDI crystals. The analysis, in terms of symmetry-adapted Frenkel excitations (FE) and charge-resonance (CR) states and their interactions, discloses how the interchange of the H/J character for small longitudinal shifts, previously reported for singlet exciton states, also occurs for triplet excitons. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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11 pages, 2961 KiB

Open AccessArticle

A Theoretical Survey of the UV–Visible Spectra of Axially and Peripherally Substituted Boron Subphthalocyanines

by Al Mokhtar Lamsabhi, M. Merced Montero-Campillo, Otilia Mó and Manuel Yáñez

Computation 2022, 10(2), 14; https://doi.org/10.3390/computation10020014 - 18 Jan 2022

Cited by 5 | Viewed by 2707

Abstract

The UV–visible spectra of a series of subphthalocyanines (SubPcs) characterized by three different axial substituents (A_n) in combination with H, F, NO₂, SO₂H and SO₂CH₃ peripheral substituents (R_i) were predicted and analyzed [...] Read more.

The UV–visible spectra of a series of subphthalocyanines (SubPcs) characterized by three different axial substituents (A_n) in combination with H, F, NO₂, SO₂H and SO₂CH₃ peripheral substituents (R_i) were predicted and analyzed by means of time-dependent DFT calculations, including chloroform as a solvent. In this analysis, we paid particular attention to the Q band, which remained almost unchanged regardless of the nature of the axial substituent. For the same axial substituent, changes in the Q band were also rather small when hydrogens at the periphery were replaced by R₁ = SO₂H and R₁ = R₂ = SO₂H. However, the shifting of the Q band was almost 10 times larger when R₁ = NO₂ and R₁ = R₂ = NO₂ due to the participation of this substituent in the π SubPc cloud. In most cases, the characteristics of the spectra can be explained considering only the transitions involving the HOMO-1, HOMO, LUMO and LUMO + 1 orbitals, where the Q band can be decomposed into two main contributions, leading to charge separation. Only for SubPc(A₃,F,F,H) would one of the two contributions from the deepest orbital involved not lead to charge transfer. For this latter case, the HOMO-2 orbital must also be taken into account. In summary, the results obtained with the analysis of the MO indicate that the studied SubPcs are appropriate for photochemical devices. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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12 pages, 2249 KiB

Open AccessArticle

Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT

by Juan-Carlos Sancho-García and Emilio San-Fabián

Computation 2022, 10(2), 13; https://doi.org/10.3390/computation10020013 - 18 Jan 2022

Cited by 6 | Viewed by 3020

Abstract

The lowest-energy singlet (

S_{1}

) and triplet (

T_{1}

) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying [...] Read more.

The lowest-energy singlet (

S_{1}

) and triplet (

T_{1}

) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying on the exchange-correlation functional employed. However, there are challenging cases for which this cannot be the case, due to the fact that those excited states are not exclusively formed by single excitations and/or are affected by marked correlation effects, and thus TD-DFT might fall short. We will tackle here a set of molecules belonging to the azaphenalene family, for which research recently documented an inversion of the relative energy of

S_{1}

and

T_{1}

excited states giving rise to a negative energy difference (

Δ E_{S T}

) between them and, thereby, contrary to most of the systems thus far treated by TD-DFT. Since methods going beyond standard TD-DFT are not extensively applied to excited-state calculations and considering how challenging this case is for the molecules investigated, we will prospectively employ here a set of non-standard methods (Multi-Configurational Pair Density Functional Theory or MC-PDFT) and correlation functionals (i.e., Lie–Clementi and Colle–Salvetti) relying not only on the electronic density but also on some modifications considering the intricate electronic structure of these systems. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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11 pages, 630 KiB

Open AccessArticle

Plasma Confined Ground and Excited State Helium Atom: A Comparison Theorem Study Using Variational Monte Carlo and Lagrange Mesh Method

by Salah B. Doma, Mahmoud A. Salem and Kalidas D. Sen

Computation 2021, 9(12), 138; https://doi.org/10.3390/computation9120138 - 10 Dec 2021

Cited by 12 | Viewed by 2671

Abstract

The energy eigenvalues of the ground state helium atom and lowest two excited states corresponding to the configurations 1s2s embedded in the plasma environment using Hulthén, Debye–Hückel and exponential cosine screened Coulomb model potentials are investigated within the variational Monte Carlo method, starting [...] Read more.

The energy eigenvalues of the ground state helium atom and lowest two excited states corresponding to the configurations 1s2s embedded in the plasma environment using Hulthén, Debye–Hückel and exponential cosine screened Coulomb model potentials are investigated within the variational Monte Carlo method, starting with the ultracompact trial wave functions in the form of generalized Hylleraas–Kinoshita functions and Guevara–Harris–Turbiner functions. The Lagrange mesh method calculations of energy are reported for the He atom in the ground and excited ¹S and ³S states, which are in excellent agreement with the variational Monte Carlo results. Interesting relative ordering of eigenvalues are reported corresponding to the different screened Coulomb potentials in the He ground and excited electronic states, which are rationalized in terms of the comparison theorem of quantum mechanics. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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13 pages, 7597 KiB

Open AccessArticle

Density Functional Theory Study of Metal and Metal-Oxide Nucleation and Growth on the Anatase TiO₂(101) Surface

by Leila Kalantari, Fabien Tran and Peter Blaha

Computation 2021, 9(11), 125; https://doi.org/10.3390/computation9110125 - 19 Nov 2021

Cited by 5 | Viewed by 3175

Abstract

Experimental studies have shown the possible production of hydrogen through photocatalytic water splitting using metal oxide (MO

_{y}

) nanoparticles attached to an anatase TiO

_{2}

surface. In this work, we performed density functional theory (DFT) calculations to provide a detailed description of [...] Read more.

Experimental studies have shown the possible production of hydrogen through photocatalytic water splitting using metal oxide (MO

_{y}

) nanoparticles attached to an anatase TiO

_{2}

surface. In this work, we performed density functional theory (DFT) calculations to provide a detailed description of the stability and geometry of M

_{x}

O

_{y}

clusters M = Cu, Ni, Co, Fe and Mn, x = 1–5, and y = 0–5 on the anatase TiO

_{2}

(101) surface. It is found that unsaturated 2-fold-coordinated O-sites may serve as nucleation centers for the growth of metal clusters. The formation energy of Ni-containing clusters on the anatase surface is larger than for other M clusters. In addition, the Ni

_{n}

adsorption energy increases with cluster size n, which makes the formation of bigger Ni clusters plausible as confirmed by transition electron microscopy images. Another particularity for Ni-containing clusters is that the adsorption energy per atom gets larger when the O-content is reduced, while for other M atoms it remains almost constant or, as for Mn, even decreases. This trend is in line with experimental results. Also provided is a discussion of the oxidation states of M

_{5}

O

_{y}

clusters based on their magnetic moments and Bader charges and their possible reduction with oxygen depletion. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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6 pages, 235 KiB

Open AccessArticle

Density Functional Theory of Coulombic Excited States Based on Nodal Variational Principle

by Ágnes Nagy

Computation 2021, 9(8), 93; https://doi.org/10.3390/computation9080093 - 23 Aug 2021

Cited by 3 | Viewed by 2132

Abstract

The density functional theory developed earlier for Coulombic excited states is reconsidered using the nodal variational principle. It is much easier to solve the Kohn–Sham equations, because only the correct number of nodes of the orbitals should be insured instead of the orthogonality. [...] Read more.

The density functional theory developed earlier for Coulombic excited states is reconsidered using the nodal variational principle. It is much easier to solve the Kohn–Sham equations, because only the correct number of nodes of the orbitals should be insured instead of the orthogonality. Full article

(This article belongs to the Special Issue Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of his 80th Birthday)

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