Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients

Łazarski, Roman; Burow, Asbjoern Manfred; Grajciar, Lukáš; Sierka, Marek

doi:10.1002/jcc.24477

Cited by 36 publications

(44 citation statements)

References 87 publications

(163 reference statements)

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“…For complicated aggregate structures, evolutionary algorithms and, possibly, neural networks might be applied for further refining the aggregate candidate set. Periodic boundary conditions might be used at any growth step to check whether experimental properties of extended supramolecular systems are sufficiently well reproduced at that growth step . In this work, we demonstrate the basic working principle on the prototypal tasks of finding diverse sets of dimers of urea, porphin (see Fig.…”

Section: Introductionmentioning

confidence: 84%

A program for automatically predicting supramolecular aggregates and its application to urea and porphin

et al. 2018

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Not only the molecular structure but also the presence or absence of aggregates determines many properties of organic materials. Theoretical investigation of such aggregates requires the prediction of a suitable set of diverse structures. Here, we present the open-source program EnergyScan for the unbiased prediction of geometrically diverse sets of small aggregates. Its bottom-up approach is complementary to existing ones by performing a detailed scan of an aggregate's potential energy surface, from which diverse local energy minima are selected. We crossvalidate this approach by predicting both literature-known and heretofore unreported geometries of the urea dimer. We also predict a diverse set of dimers of the less intensely studied case of porphin, which we investigate further using quantum chemistry. For several dimers, we find strong deviations from a reference absorption spectrum, which we explain using computed transition densities. This proof of principle clearly shows that EnergyScan successfully predicts aggregates exhibiting large structural and spectral diversity. © 2018 Wiley Periodicals, Inc.

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Section: Introductionmentioning

confidence: 84%

A program for automatically predicting supramolecular aggregates and its application to urea and porphin

et al. 2018

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“…Details of the calculation of

D_{μν}^{{boldL}^{'}}

and

W_{μν}^{{boldL}^{'}}

are given in Refs. and . Next sections describe details of our stress tensor implementation for XC and Coulomb terms, following the derivation of first energy derivatives with respect to nuclear displacements (nuclear gradients) by Lazarski et al…”

Section: Methodsmentioning

confidence: 99%

“…Instead, the integral is evaluated numerically using a finite set of grid points { r m } with associated weights { w m }, so that

E_{XC} = \sum_{m} w_{m} f ((),,, ρ_{normalc}^{m}, γ^{m}, τ^{m}),

where

ρ_{c}^{m}

, γ m , and τ m denote the values of ρ c , γ , and τ on a grid point r m . Our implementation uses the scheme of Stratmann et al for calculation of { w m }. The XC contribution to stress tensor can formally be written as

σ_{ab}^{XC} = \frac{1}{V} \frac{\partial E_{XC}}{\partial ε_{ab}} = \frac{1}{V} \sum_{L} \sum_{I} \frac{\partial E_{XC}}{\partial r_{I boldL}^{a}} r_{I boldL}^{b}

= \frac{1}{V} \sum_{L} \sum_{I} \sum_{m} ([], \frac{\partial w_{m}}{\partial r_{I boldL}^{a}} f ((),,, ρ_{normalc}^{m}, γ^{m}, τ^{m}) + w_{m} \frac{\partial f ((),,, ρ_{normalc}^{m}, γ^{m}, τ^{m})}{\partial r_{I boldL}^{a}}) r_{I boldL}^{b}

= {σ_{italicab}^{XC}}^{(w_{m})} + {σ_{italicab}^{XC}}^{(f)} .

…”

Section: Methodsmentioning

confidence: 99%

“…We employ the standard notation for Coulomb integrals where subscripts L and L ′ on the right‐hand side of Coulomb integrals denote lattice summation . We define ρ as the electron density in the central reference UC, which is identical to ρ L = 0 in eq.…”

Section: Methodsmentioning

confidence: 99%

“…Here, we present a full implementation of the analytical stress tensor and energy first derivatives with respect to lattice vectors within the Kohn–Sham (KS) DFT formalism employing GTO basis functions. It is an extension of the analytical energy gradient implementation by Lazarski et al that allows for calculation of the Coulomb contribution with an asymptotic O ( N ) scaling employing DF–CFMM. In addition, the hierarchical numerical integration scheme for the exchange‐correlation (XC) term is extended to weight derivatives and stress tensor calculations.…”

Section: Introductionmentioning

confidence: 99%

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Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

Becker

Sierka

2019

J Comput Chem

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A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn–Sham density functional theory using Gaussian‐type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518–2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange‐correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097–3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn–Sham matrix formation. © 2019 Wiley Periodicals, Inc.

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Interfacial Engineering for Improved Photocatalysis in a Charge Storing 2D Carbon Nitride: Melamine Functionalized Poly(heptazine imide)

Kröger

Jiménez‐Solano

Savaşçı

et al. 2020

Advanced Energy Materials

107

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Carbon nitrides constitute a class of earth‐abundant polymeric semiconductors, which have high potential for tunability on a molecular level, despite their high chemical and thermal inertness. Here the first postsynthetic modification of the 2D carbon nitride poly(heptazine imide) (PHI) is reported, which is decorated with terminal melamine (Mel) moieties by a functional group interconversion. The covalent attachment of this group is verified based with a suite of spectroscopic and microscopic techniques supported by quantum–chemical calculations. Using triethanolamine as a sacrificial electron donor, Mel‐PHI outperforms most other carbon nitrides in terms of hydrogen evolution rate (5570 µmol h−1 g−1), while maintaining the intrinsic light storing properties of PHI. The origin of the observed superior photocatalytic performance is traced back to a modified surface electronic structure and enhanced interfacial interactions with the amphiphile triethanolamine, which imparts improved colloidal stability to the catalyst particles especially in contrast to methanol used as donor. However, this high activity can be limited by oxidation products of donor reversibly building up at the surface, thus blocking active centers. The findings lay out the importance of surface functionalization to engineer the catalyst–solution interface, an underappreciated tuning parameter in photocatalytic reaction design.

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Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients

Cited by 36 publications

References 87 publications

A program for automatically predicting supramolecular aggregates and its application to urea and porphin

A program for automatically predicting supramolecular aggregates and its application to urea and porphin

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

Interfacial Engineering for Improved Photocatalysis in a Charge Storing 2D Carbon Nitride: Melamine Functionalized Poly(heptazine imide)

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