Double-Hybrid DFT Functionals for the Condensed Phase: Gaussian and Plane Waves Implementation and Evaluation

In this work, the interaction of C 20 with N 2 X 2 ( X = H , F , Cl , Br , Me ) molecules has been explored using the B3LYP, M062x methods and 6-311G(d,p) and 6-311+G(d,p) basis sets. The interaction energies (IEs) obtained with standard method were corrected by basis set superposition error (BSSE) during the geometry optimization for all molecules at the same levels of theory. It was found C 20… N 2 H 2 interaction is stronger than the interaction of other N 2 X 2 ( X = F , Cl , Br , Me ) with C 20. Highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO, respectively) levels are illustrated by density of states spectra (DOS). The nucleus-independent chemical shifts (NICSs) confirm that C 20… N 2 X 2 molecules exhibit aromatic characteristics. Geometries obtained from DFT calculations were used to perform NBO analysis. Also, 14 N NQR parameters of the C 20… N 2 X 2 molecules are predicted.

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On the Use of DFT+U to Describe the Electronic Structure of TiO2 Nanoparticles: (TiO2)35 as a Case Study

10.26434/chemrxiv.12213536.v1 ◽

2020 ◽

Author(s):

Angel Morales ◽

Stephen Rhatigan ◽

Michael Nolan ◽

Frances Illas

Keyword(s):

Density Functional ◽

Energy Gap ◽

Plane Waves ◽

Basis Set ◽

Basis Sets ◽

Functional Theory ◽

The Density Functional Theory ◽

Structural And Electronic Properties ◽

Rotationally Invariant

One of the main drawbacks in the density functional theory (DFT) formalism is the underestimation of the energy gaps in semiconducting materials. The combination of DFT with an explicit treatment of electronic correlation with a Hubbard-like model, known as DFT+U method, has been extensively applied to open up the energy gap in materials. Here, we introduce a systematic study where the selection of U parameter is analyzed considering two different basis sets: plane-waves (PWs) and numerical atomic orbitals (NAOs), together with different implementations for including U, to investigate the structural and electronic properties of a well-defined bipyramidal (TiO2)35 nanoparticle (NP). This study reveals, as expected, that a certain U value can reproduce the experimental value for the energy gap. However, there is a high dependence on the choice of basis set and, and on the +U parameter employed. The present study shows that the linear combination of the NAO basis functions, as implemented in FHI-aims, requires a lower U value than the simplified rotationally invariant approaches as implemented in VASP. Therefore, the transferability of U values between codes is unfeasible and not recommended, demanding initial benchmark studies for the property of interest as a reference to determine the appropriate value of U.

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Formulation and Implementation of Density Functional Embedding Theory using Products of Basis Functions

10.26434/chemrxiv.13498704 ◽

2020 ◽

Author(s):

Vladimir Rybkin

Keyword(s):

Condensed Phase ◽

Density Functional ◽

Large Scale ◽

Plane Waves ◽

Basis Functions ◽

Basis Set ◽

Transfer Reactions ◽

Molecular Systems ◽

Embedding Theory ◽

Proton Transfer Reactions

The representation of embedding potential in using products of AO basis functions has been developed in the context of density functional embedding theory (DFET). The formalism allows to treat pseudopotential and all-electron calculations on the same footing and enables simple transfer of the embedding potential in the compact matrix form. In addition, a simple cost-reduction procedure for basis set and potential reduction has been proposed. The theory has been implemented for the condensed-phase and molecular systems using Gaussian and Plane Waves (GPW) and Gaussian and Augmented Plane Waves (GAPW) formalisms and tested for proton transfer reactions in the cluster and the condensed phase. The computational scaling of the embedding potential optimization is similar to this of hybrid DFT with a significantly reduced prefactor and allows for large-scale applications.<div> </div>

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Formulation and Implementation of Density Functional Embedding Theory using Products of Basis Functions

10.26434/chemrxiv.13498704.v1 ◽

2020 ◽

Author(s):

Vladimir Rybkin

Keyword(s):

Condensed Phase ◽

Density Functional ◽

Large Scale ◽

Plane Waves ◽

Basis Functions ◽

Basis Set ◽

Transfer Reactions ◽

Molecular Systems ◽

Embedding Theory ◽

Proton Transfer Reactions

The representation of embedding potential in using products of AO basis functions has been developed in the context of density functional embedding theory (DFET). The formalism allows to treat pseudopotential and all-electron calculations on the same footing and enables simple transfer of the embedding potential in the compact matrix form. In addition, a simple cost-reduction procedure for basis set and potential reduction has been proposed. The theory has been implemented for the condensed-phase and molecular systems using Gaussian and Plane Waves (GPW) and Gaussian and Augmented Plane Waves (GAPW) formalisms and tested for proton transfer reactions in the cluster and the condensed phase. The computational scaling of the embedding potential optimization is similar to this of hybrid DFT with a significantly reduced prefactor and allows for large-scale applications.<div> </div>

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Basis Set Extrapolations for Density Functional Theory

10.26434/chemrxiv.12552998.v1 ◽

2020 ◽

Author(s):

Peter Kraus

Keyword(s):

Density Functional Theory ◽

Density Functional ◽

Computational Cost ◽

Basis Set ◽

Basis Sets ◽

Density Functionals ◽

Functional Theory ◽

Common Basis ◽

Basis Set Extrapolation

Improving results of correlated wavefunction theory calculations by extrapolating from successive basis sets is nowadays a common practice. However, such approaches are uncommon in density functional theory, especially due its faster convergence towards the basis set limit. In this work I present approaches for basis set extrapolation in density functional theory that enable users to obtain results of 4-zeta quality from 3- and 2-zeta calculations, i.e. at a fraction of the computational cost. The extrapolation techniques work well with modern density functionals and common basis sets.

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Benchmarking Density Functionals, Basis Sets, and Solvent Models in Predicting Thermodynamic Hydricities of Organic Hydrides

10.26434/chemrxiv-2021-ssfpt ◽

2021 ◽

Author(s):

Christina Yeo ◽

Minh Nguyen ◽

Lee-Ping Wang

Keyword(s):

Density Functional ◽

Mean Squared Error ◽

Theoretical Calculations ◽

Computational Cost ◽

Hydrogen Gas ◽

Basis Set ◽

Basis Sets ◽

Density Functionals ◽

Solvent Models ◽

Solvent Model

Many renewable energy technologies, such as hydrogen gas synthesis and carbon dioxide reduction, rely on chemical reactions involving hydride anions. When selecting molecules to be used in such applications, an important quantity to consider is the thermodynamic hydricity, which is the free energy required for a species to donate a hydride anion. Theoretical calculations of thermodynamic hydricity depend on several parameters, mainly the density functional, basis set, and solvent model. In order to assess the effects of the above three parameters, we carry out hydricity calculations for a set of molecules with known experimental hydricity values, generate linear �fits, and compare the R-squared, root-mean-squared error, and Akaike Information Criterion across different combinations of density functionals, basis sets, and solvent models. Based on these results we are able to quantify the accuracy of theoretical predictions of hydricity and recommend the parameters with the best compromise between accuracy and computational cost.

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Ab initio MO Optimizations of Osmiumtetracarbonyldihydride and Metallacyclophanes with two Osmium Atoms and their Molecular Complexes with Different Guests

Zeitschrift für Naturforschung B ◽

10.1515/znb-1998-1020 ◽

1998 ◽

Vol 53 (10) ◽

pp. 1223-1235

Author(s):

Inge Warttmann ◽

Günter Häfelinger

Keyword(s):

Ab Initio ◽

Density Functional ◽

Cyano Group ◽

Single Point ◽

Molecular Complexes ◽

Basis Set ◽

Basis Sets ◽

Basis Set Superposition Error ◽

Hartree Fock ◽

Surprising Effect

AbstractAb initio Hartree-Fock (HF) and density functional (DFT) optimizations on the test m olecule osmiumtetracarbonyldihydride (13) with various basis sets show that the lanl2mb pseudopotential basis set for osmium leads in the HF approximation to more reliable molecular geometries than the DFT calculations. This HF procedure was used for the optimizations of molecular geometries of three isomeric 4,4,4,4,17,17,17,17-octacarbonyl-4,17-diosma[7.7]ortho-, meta- and paracyclophanes 1 to 3, of which 3 was found to be predestined for formation of various host-guest complexes with possible guests benzene (4), fluorobenzene (5), 1,3,5- trifluorobenzene (6), 1,2,4,5-tetrafluorobenzene (7), hexafluorobenzene (8), fluoroanil (9), tetrafluoroethene (10), tetracyanoethene (11) and aniline (12). Results of optimized hostguest geometries are presented graphically for inclusions and associations of guest 4 to 12 with 3. Calculated lanl2mb interaction energies, after correction for basis set superposition error (BSSE), remain favourable only for inclusion of 5 and associations of 5, 10, 11 and 12. Additionally lanl2dz single point calculations for inclusion, which may not need BSSE correction because of the improved basis set, are favourable for 6 and 12. According to lanl2mb HOMO and LUMO energies, 3 may as well easily donate or accept electrons. This may be an interpretation to the surprising effect, that Mulliken total charges are positive on the electron accepting guest molecules 4 to 11. There are geometrical peculiarities in the optimized host-guest complexes for inclusion and association. Fluorine atoms of 5 to 10 and nitrogen atoms of a cyano group of 11 and the amino group of 12 like to come close to one or two carbonyl groups. Similar distances of 2.70 Å to 3.57 Å between the O atom of the carbonyl group and the F atom or N atom appear in all optimizations of inclusion and association of 5 to 12 except in the case of association of tetrafluoroethene (10).

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On the Use of DFT+U to Describe the Electronic Structure of TiO2 Nanoparticles: (TiO2)35 as a Case Study

10.26434/chemrxiv.12213536 ◽

2020 ◽

Author(s):

Angel Morales ◽

Stephen Rhatigan ◽

Michael Nolan ◽

Frances Illas

Keyword(s):

Density Functional ◽

Energy Gap ◽

Plane Waves ◽

Basis Set ◽

Basis Sets ◽

Functional Theory ◽

The Density Functional Theory ◽

Structural And Electronic Properties ◽

Rotationally Invariant

One of the main drawbacks in the density functional theory (DFT) formalism is the underestimation of the energy gaps in semiconducting materials. The combination of DFT with an explicit treatment of electronic correlation with a Hubbard-like model, known as DFT+U method, has been extensively applied to open up the energy gap in materials. Here, we introduce a systematic study where the selection of U parameter is analyzed considering two different basis sets: plane-waves (PWs) and numerical atomic orbitals (NAOs), together with different implementations for including U, to investigate the structural and electronic properties of a well-defined bipyramidal (TiO2)35 nanoparticle (NP). This study reveals, as expected, that a certain U value can reproduce the experimental value for the energy gap. However, there is a high dependence on the choice of basis set and, and on the +U parameter employed. The present study shows that the linear combination of the NAO basis functions, as implemented in FHI-aims, requires a lower U value than the simplified rotationally invariant approaches as implemented in VASP. Therefore, the transferability of U values between codes is unfeasible and not recommended, demanding initial benchmark studies for the property of interest as a reference to determine the appropriate value of U.

Download Full-text

Basis Set Extrapolations for Density Functional Theory

10.26434/chemrxiv.12552998 ◽

2020 ◽

Author(s):

Peter Kraus

Keyword(s):

Density Functional Theory ◽

Density Functional ◽

Computational Cost ◽

Basis Set ◽

Basis Sets ◽

Density Functionals ◽

Functional Theory ◽

Common Basis ◽

Basis Set Extrapolation

Improving results of correlated wavefunction theory calculations by extrapolating from successive basis sets is nowadays a common practice. However, such approaches are uncommon in density functional theory, especially due its faster convergence towards the basis set limit. In this work I present approaches for basis set extrapolation in density functional theory that enable users to obtain results of 4-zeta quality from 3- and 2-zeta calculations, i.e. at a fraction of the computational cost. The extrapolation techniques work well with modern density functionals and common basis sets.

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Oxane dendrimers of tetravalent elements as models for their dioxide polymorphs

Surface ◽

10.15407/surface.2021.13.003 ◽

2021 ◽

Vol 13(28) ◽

pp. 3-14

Author(s):

A.G. Grebenyuk ◽

Keyword(s):

Quantum Chemical ◽

Density Functional ◽

Tin Dioxide ◽

Basis Set ◽

Basis Sets ◽

Hydroxyl Groups ◽

High Symmetry ◽

Molecular Models ◽

Basis Set Superposition Error ◽

Theoretical Approaches

Oxides of tetravalent elements are well known to have a lot of crystalline modifications. For example, most of silica polymorphs are characterized by tetrahedral coordination environment of silicon atoms. On the contrary, crystals of stishovite and of some silicate minerals have their silicon atoms in octahedral coordination spheres. It has been found experimentally that the phase transitions between silica polymorphs accompanied by a rearrangement of silica-oxygen tetrahedrons into octahedra require an energy income (preference energy) of 54 kJ/mol. When increasing the atomic mass of the oxide forming element, the former decreases extremely and for tin dioxide is equal to -59 kJ/mol. These values can be reproduced in a theoretical way, within the frameworks of modern quantum chemical methods and periodic models. High disperse silica nanoparticles (as well as those for other oxides) have only the nearest order of atomic stationing, so that theoretical approaches developed for crystals cannot be applied to small particles. These particles can be transformed into stishovite form under hydrothermal conditions. Such a process can be simulated within cluster approximation by use of molecular models. This work is devoted to quantum chemical simulation of formation of the fragments with hexa-coordinated atoms of silicon and of its analogs in the structure of oxane dendrimers. A row of high symmetry models was examined containing two, three, five, and seventeen atoms of silicon and of germanium, titanium and tin, terminated with hydroxyl groups. These structures can be rearranged into another ones including oxide forming atoms with elevated (equal to 5 or 6) coordination number, so mimicking the rutile-like structure. Such models let it possible to fulfill the procedure of transformation without rupturing siloxane bonds, so remaining within a deformation approach. Another advantage is the exclusion of the basis set superposition error due to use of molecular models of the same total formula for all the coordination states. All calculations were carried out by Hartree-Fock and density functional theory methods with the all-electron (3-21G*) and valent (SBKJC) basis sets by means of the GAMESS program. Models of various size have been examined, in particular, disiloxane (HO)3Si-O-Si(OH)3 witch can be transformed into a self-coordinated form where one of silicon atoms becomes a five-coordinated; trisiloxane (HO)3Si-O-Si(OH)2-O-Si(OH)3 can be rearranged into symmetric isomer with one hexa-coordinated silicon atom. Pentasiloxane with neo-structure of [(HO)3Si-O]4Si forms three coordination structures, the most stable of them mimicking the stishovite crystal; it contains one 6-coordinated and two 5-coordinated silicon atoms. Siloxane containing 17 silicon atoms has a super-neo-structure of {[(HO)3Si-O]3Si-O}4Si; it includes seven six-coordinated and four five-coordinated silicon atoms. Relative models for silicon analogs have been also examined. When analyzing a dependence of the energy differences between open and coordinated oxane structures on the number of atoms of the oxide forming element in the cluster, one can jump to the conclusion that the specific value of this characteristic monotonously decreases with the increase in the number of atoms of the molecular model, so becoming close to the experimental data.

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