The self‐consistent charge density functional tight‐binding theory study of carbon adatoms using tuned Hubbard U parameters

The self‐consistent charge density functional tight‐binding (DFTB) theory is a useful tool for realizing the electronic structures of large molecular complex systems. In this study, the electronic structure of C₆₁ formed by fullerene C₆₀ with a carbon adatom is analyzed, using the fully localized limit and pseudo self‐interaction correction methods of DFTB to adjust the Hubbard U parameter (DFTB + U). The results show that both the methods used to adjust U can significantly reduce the molecular orbital energy of occupied states localized on the defect carbon atom and improve the gap between highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) of C₆₁. This work will provide a methodological reference point for future DFTB calculations of the electronic structures of carbon materials.     

Studies on structure and conformational stability of free canonical 2′‐deoxyribonucleosides: Approximate SCC‐DFTB and LMP2 methods

The molecular structure of free canonical 2′‐deoxyribonucleosides have been studied by applying the electron‐correlated local second‐order Møller–Plesset perturbation theory (LMP2) and self‐consistent‐charge density‐functional tight‐binding (SCC‐DFTB) methods. The variation of structural parameters for C2, C3 endo and exo conformations, and anti, syn orientation of the base unit with furanose ring have been discussed. The relative energies have been calculated for the anti and syn conformations of dT, dC, dG, and dA. Conformational analysis has been performed using the results of the LMP2 and SCC‐DFTB methods. Chemical hardness and chemical potential have been used to study the conformational stability of the conformers. The maximum hardness principle is obeyed for the furanose ring conformations and not for the nucleosides. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Performance of density‐functional tight‐binding models in describing hydrogen‐bonded anionic‐water clusters

Density‐functional tight‐binding (DFTB) models are computationally efficient approximations to density‐functional theory that have been shown to predict reliable structural and energetic properties for various systems. In this work, the reliability and accuracy of the self‐consistent‐charge DFTB model and its recent extension(s) in predicting the structures, binding energies, charge distributions, and vibrational frequencies of small water clusters containing polyatomic anions of the Hofmeister series (carbonate, sulfate, hydrogen phosphate, acetate, nitrate, perchlorate, and thiocyanate) have been carefully and systematically evaluated on the basis of high‐level ab initio quantum‐chemistry [MP2/aug‐cc‐pVTZ and CCSD(T)/aug‐cc‐pVQZ] reference data. Comparison with available experimental data has also been made for further validation. The self‐consistent‐charge DFTB model, and even more so its recent extensions, are shown to properly account for the structural properties, energetics, intermolecular polarization, and spectral signature of hydrogen‐bonding in anionic water clusters at a fraction of the computational cost of ab initio quantum‐chemistry methods. This makes DFTB models candidates of choice for investigating much larger systems such as seeded water droplets, their structural properties, formation thermodynamics, and infrared spectra. © 2014 Wiley Periodicals, Inc.     

Quantifying the effects of the self-interaction error in DFT: when do the delocalized states appear?

The self-interaction error in density-functional theory leads to artificial stabilization of delocalized states, most evident in systems with an odd number of electrons. Clear examples are dissociations of carbocation radicals that often give delocalized states at long distances and large errors in computed binding energies. On the other hand, many mixed-valence transition-metal dimers known to exhibit valence trapping are correctly predicted to be localized. To understand the effects of the self-interaction error on these different systems, energy differences between delocalized and localized states are calculated with B3LYP. In the dissociation of radicals into symmetric fragments at infinite distance, this energy difference equals the error of the density-functional treatment. The energy difference decreases with increasing size of the system, from 55 kcal/mol in H2(+) to 15 kcal/mol for C12H26(+). Solvent corrections stabilize the localized state and result in smaller errors. Most reactions are asymmetric and this decreases the effect of the self-interaction error. In many systems, delocalization will not occur if the cost to move the electron from one fragment to the other is 70-80 kcal/mol (3.0-3.5 eV). This estimate refers to a situation where the distance between the fragments is infinite. The limit decreases with decreasing fragment distance. B3LYP calculations on the ferromagnetic state of a Mn(III,IV) dimer predict that the correct localized state is 22 kcal/mol more stable than the incorrect delocalized state. At short metal-metal distances the effect of the self-interaction error is predicted to be small. However, as the distance between the two manganese centers is increased to 7 A, the dimer starts to delocalize and the energy artificially decreases. In the dissociation limit, the error is 10 kcal/mol. This is interpreted as an artifact originating from the self-interaction error. Delocalization is not encountered in many systems due to relatively short metal-metal distances and asymmetric ligand environments. However, some charge-transfer complexes cannot be properly calculated and delocalized states may become a problem in large models of enzyme systems with multiple transition-metal complexes.     

Three‐body expansion of the fragment molecular orbital method combined with density‐functional tight‐binding

The three‐body fragment molecular orbital (FMO3) method is formulated for density‐functional tight‐binding (DFTB). The energy, analytic gradient, and Hessian are derived in the gas phase, and the energy and analytic gradient are also derived for polarizable continuum model. The accuracy of FMO3‐DFTB is evaluated for five proteins, sodium cation in explicit solvent, and three isomers of polyalanine. It is shown that FMO3‐DFTB is considerably more accurate than FMO2‐DFTB. Molecular dynamics simulations for sodium cation in water are performed for 100 ps, yielding radial distribution functions and coordination numbers. © 2017 Wiley Periodicals, Inc.     

Exploring the applicability of density functional tight binding to transition metal ions. Parameterization for nickel with the spin-polarized DFTB3 model

In this work, we explore the applicability and limitations of the current third order density functional tight binding (DFTB3) formalism for treating transition metal ions using nickel as an example. To be consistent with recent parameterization of DFTB3 for copper, the parametrization for nickel is conducted in a spin-polarized formulation and with orbital-resolved Hubbard parameters and their charge derivatives. The performance of the current parameter set is evaluated based on structural and energetic properties of a set of nickel-containing compounds that involve biologically relevant ligands. Qualitatively similar to findings in previous studies of copper complexes, the DFTB3 results are more reliable for nickel complexes with neutral ligands than for charged ligands; nevertheless, encouraging agreement is noted in comparison to the reference method, B3LYP/aug-cc-pVTZ, especially for structural properties, including cases that exhibit Jahn–Teller distortions; the structures also compare favorably to available X-ray data in the Cambridge Crystallographic Database for a number of nickel-containing compounds. As to limitations, we find it is necessary to use different d shell Hubbard charge derivatives for Ni(I) and Ni(II), due to the distinct electronic configurations for the nickel ion in the respective complexes, and substantial errors are observed for ligand binding energies, especially for charged ligands, d orbital splitting energies and splitting between singlet and triplet spin states for Ni(II) compounds. These observations highlight that future improvement in intra-d correlation and ligand polarization is required to enable the application of the DFTB3 model to complex transition metal ions. © 2018 Wiley Periodicals, Inc.     

A new nonempirical tuning scheme with single self‐consistent field calculation: Comparison with global and IP‐tuned range‐separated functional

System‐dependent nonempirical tuning of range‐separated functional provides a way to minimize the delocalization error of the system. However, existing nonempirical tuning method requires the computation of several ΔSCF calculations to determine the optimal μ value. In this article, we have defined a scheme to evaluate the optimal μ value with single self‐consistent field calculation. Our method is based on the evaluation of the spherically symmetric average Electron localization function (ELF) region. According to this scheme, the radius of the spherically symmetric average ELF region gives is a measure of the distance at which the long‐range part of the range‐separated functional becomes dominant. Numerical results indicate that our method improves the reproduction of HOMO energies and HOMO‐LUMO gap in comparison to global and IP‐tuned range‐separated functional. Moreover, in case of HOMO energies, maximum error of the ELF‐tuned functional is considerably smaller than the global and IP‐tuned functional. Furthermore, our method gives considerably smaller deviation of HOMO energies from ΔSCF IP than global range‐separated functional. © 2017 Wiley Periodicals, Inc.     

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Intramolecular Charge Transfer of Carotene‐porphyrin‐fullerene Triad: Sequential or Superexchange Cechanism

As an excellent artificial photosynthetic reaction center, the carotene (C)‐porphyrin (P)‐fullerene (F) triad was extensively investigated experimentally. To reveal the mechanism of the intramolecular charge transfer (ICT) on the mimic of photosynthetic solar energy conversion (such as singlet energy transfer between pigments, and photoinduced electron transfer from excited singlet states to give long‐lived charge‐separated states), the ICT mechanisms of C‐P‐F triad on the exciton were theoretically studied with quantum chemical methods as well as the 2D and 3D real space analysis approaches. The results of quantum chemical methods reveal that the excited states are the ICT states, since the densities of HOMO are localized in the carotene or porphyrin unit, and the densities of LUMO are localized in the fullerene unit. Furthermore, the excited states should be the intramolecular superexchange charge transfer (ISCT) states for the orbital transition from the HOMO whose densities are localized in the carotene to the LUMO whose densities are localized in the fullerene unit. The 3D charge difference densities can clearly show that some excited states are ISCT excited states, since the electron and hole are resident in the fullerene and carotene units, respectively. From the results of the electron‐hole coherence of the 2D transition density matrix, not only 3D results are supported, but also the delocalization size on the exciton can be observed. These phenomena were further interpreted with non‐linear optical effect. The large changes of the linear and non‐linear polarizabilities on the exciton result in the charge separate states, and if their changes are large enough, the ICT mechanism can become the ISCT on the exciton.     

Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide‐and‐conquer,density‐functional tight‐binding,and massively parallel computation

The linear‐scaling divide‐and‐conquer (DC) quantum chemical methodology is applied to the density‐functional tight‐binding (DFTB) theory to develop a massively parallel program that achieves on‐the‐fly molecular reaction dynamics simulations of huge systems from scratch. The functions to perform large scale geometry optimization and molecular dynamics with DC‐DFTB potential energy surface are implemented to the program called DC‐DFTB‐K. A novel interpolation‐based algorithm is developed for parallelizing the determination of the Fermi level in the DC method. The performance of the DC‐DFTB‐K program is assessed using a laboratory computer and the K computer. Numerical tests show the high efficiency of the DC‐DFTB‐K program, a single‐point energy gradient calculation of a one‐million‐atom system is completed within 60 s using 7290 nodes of the K computer. © 2016 Wiley Periodicals, Inc.     

Density functional theory study of a molecular allosteric switch for 2,2′‐bipyridyl‐3,3′‐15‐crown‐5

A classical model of “molecular machine,” which acts as an ON–OFF switch for 2,2′‐bipyridyl‐3,3′‐15‐crown‐5 ( L ), has been theoretically studied. It is highly important to understand the mechanism of this switch. The alkali‐metal cations (Na⁺ and K⁺) and W(CO)₄ fragment are introduced to coordinate with the different active sites of L , respectively. The density functional theory (DFT) method is used for understanding the stereochemical structural natures and thermodynamic properties of all the target molecules at B3LYP/6‐31G(d) and SDD (Stuttgart–Dresden) level, together with the corresponding effective core potential (ECP) for tungsten (W). The fully optimized geometries have been performed with real frequencies, which indicate the minima states. The nucleophilicity of L has been investigated by the Fukui functions. The natural bond orbital analysis is used to study the intermolecular charge‐transfer interactions and explore the origin of the internal forces of the molecular switch. In addition, the binding energies, enthalpies, Gibbs free energies, and the cation exchange energies have been studied for L , W(CO)₄ L , and their corresponding complexes. The properties of the complexes displayed by in presence or absence of the W(CO)₄ fragment are also analyzed. The calculated results of allosterism displayed by L are in a good agreement with the experimental results. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Noninnocence of the ligand atoms in iron‐porphine: Chemical consequences of the delocalized electron spin

It is well recognized that the electronic spin density in transition metal complexes in high‐spin states, tends to delocalize from the metal ion itself to the donor atoms of the ligand. In square planar iron‐porphine [PFe]⁺ the delocalization occurs even further and spin corresponding to roughly one electron is delocalized over a large part of the ligand. In this article, density functional theory is applied to explore the chemical consequences of the delocalized spin in four‐coordinate iron‐porphine. It is shown that the porphine ligand has a moderate affinity for radicals, and that covalent bonds can form through spin‐pairing of the unpaired delocalized electron on the porphine ligand and the unpaired electron of another radical species. The hydrogen atom is used as a probe to evaluate the radical affinity of the different nitrogen and carbon atoms that constitute the porphine ligand. It is computationally predicted that the porphine ligand of four‐coordinate iron‐porphine is kinetically capable of activating weak C? H bonds of, for example, unsaturated organic compounds. Hydrogen atom transfer becomes spontaneous via subsequent homo‐coupling of the organic radical created. Whether or not the radical affinity of the porphine ligand has any mechanistic implications for heme‐containing enzymes is left as an open question.     

Automated error control in divide‐and‐conquer self‐consistent field calculations

In linear‐scaling divide‐and‐conquer (DC) electronic structure calculations, a buffer region is used to control the error introduced by the DC approximation. In this study, an energy‐based error estimation scheme is proposed for the DC self‐consistent field method with a two‐layer buffer region scheme. Based on this scheme, a procedure to automatically determine the appropriate buffer region in the DC method is proposed. It was confirmed that the present method works satisfactorily in calculations of water clusters and proteins, although its performance was insufficient for the calculation of a delocalized graphene system. © 2018 Wiley Periodicals, Inc.     

Density‐functional theory study of the interaction mechanism and optical properties of flavonols on the boron nitride nanotubes

The flavonols are natural pigments with multiple colors. They are found ubiquitously in plants and are relevant to flower colors and the UV protection in plants. Their antioxidant, anticancer, and anti‐allergic features attract researchers much attention to explore their potential applications in biological and nanomedical areas. In this study, the interaction mechanism and optical properties of four representative flavonols, on both the surface and confined in the single‐walled boron nitride nanotubes (BNNTs), have been explored comparatively by self‐consistent density‐functional based tight‐binding method (SCC‐DFTB) and density‐functional theory (DFT). The results indicate a stronger binding when flavonols are confined inside the BNNTs. The influence of mutual interaction between flavonols and BNNTs on the excited properties and UV/vis feature of the complex structure was studied by time‐dependent DFT. Due to the interaction of flavonols with BNNTs and the weakness of the intramolecular hydrogen bond, our results indicate a red‐shift of the flavonol spectra when they are outside or inside the tube. The study concludes that the properties of flavonols can be fine‐tuned by the interaction with BNNTs.     

The Role of Torsional Dynamics on Hole and Exciton Stabilization in π‐Stacked Assemblies: Design of Rigid Torsionomers of a Cofacial Bifluorene

Exciton and charge delocalization across π‐stacked assemblies is of importance in biological systems and functional polymeric materials. To examine the requirements for exciton and hole stabilization, cofacial bifluorene ( F 2) torsionomers were designed, synthesized, and characterized: unhindered (model) ^Me F 2, sterically hindered ^tBu F 2, and cyclophane‐like ^C F 2, where fluorenes are locked in a perfect sandwich orientation via two methylene linkers. This set of bichromophores with varied torsional rigidity and orbital overlap shows that exciton stabilization requires a perfect sandwich‐like arrangement, as seen by strong excimeric‐like emission only in ^C F 2 and ^Me F 2. In contrast, hole delocalization is less geometrically restrictive and occurs even in sterically hindered ^tBu F 2, as judged by 160 mV hole stabilization and a near‐IR band in the spectrum of its cation radical. These findings underscore the diverse requirements for charge and energy delocalization across π‐stacked assemblies.     

Superconducting first‐order pairing: Finite‐temperature simulations

A recently developed first‐order mechanism for superconducting pairing has been extended from T = 0 K to finite temperatures. On the basis of quantum statistical considerations, we have suggested a direct pairing interaction that does not necessarily involve second‐order elements, such as the electron–phonon coupling or specific magnetic interactions submitted by spin fluctuations. The driving force for the (energy‐driven) first‐order pairing is an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). Only the moves of unpaired fermions are controlled by the PAP, while the moves of superconducting Cooper pairs are not. The quantum statistics of Cooper pairs is of a mixed type, as it combines fermionic on‐site and bosonic intersite properties. The strong correlation between the strength of PAP constraints and system topology in combination with the electron number has been discussed for some larger clusters. Detailed finite‐temperature simulations on first‐order pairing have been performed for four‐center–four‐electron clusters with different topologies. A canonical ensemble statistics has been employed to derive the electronic energy, the electronic configuration entropy, and the free energy of paired and unpaired states in thermal equilibrium. The simulations show that pairing can be caused by either the electronic energy or the electronic configuration entropy. The coexistence of two different sets of quantum particles in paired states (i.e., the Cooper pairs and the unpaired electrons) can lead to an enhanced configuration entropy. In this context, we discuss the possibility of an entropy‐driven high‐temperature superconductor emerging from a low‐temperature unpaired state. The charge and spin degrees of freedom of the four‐center–four‐electron systems have been studied with the help of the charge and spin fluctuations. The spin fluctuations are helpful in judging the validity of pairing theories based on magnetic interactions. The charge fluctuations are a measure for the carrier delocalization in unpaired and paired states. The well‐known proximity between Jahn–Teller activity and superconductivity is analyzed in the zero‐temperature limit. It is demonstrated that both processes compete in their ability to reduce PAP constraints. All theoretical results have been derived within the framework of the simple Hubbard Hamiltonian. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Nanoparticle‐Mediated Intervalence Charge Transfer: Core‐Size Effects

Two types of platinum nanoparticles (NPs) functionalized with ethynylferrocene were prepared. The subnanometer‐sized NPs (Pt₁₀eFc) showed semiconductor‐like characteristics with a bandgap of about 1.0 eV, and the other was metal‐like with a core size of about 2 nm (Pt₃₁₄eFc) and no significant bandgap. IR spectroscopic measurements showed a clear red‐shift of the C≡C and ferrocenyl ring =C?H vibrational energies with increasing particle core size owing to enhanced intraparticle charge delocalization between the particle‐bound ferrocenyl moieties. Electrochemical measurements showed two pairs of voltammetric peaks owing to intervalence charge transfer between the ferrocenyl groups on the nanoparticle surface, which was apparently weaker with Pt₁₀eFc than with Pt₃₁₄eFc. Significantly, the former might be markedly enhanced with UV photoirradiation owing to enhanced nanoparticle electronic conductivity, whereas no apparent effects were observed with the latter.