Unveiling the Multielectron Acceptor Properties of π-Expanded Pyracylene: Reversible Boat to Chair Conversion

In this work, the chemical reduction of a hybrid pyracylene-hexa-peri-hexabenzocoronene (HPH) nanographene was investigated with different alkali metals (Na, K, Rb) to reveal its remarkable multielectron acceptor abilities. The UV-vis and 1H NMR spectroscopy monitoring of the stepwise reduction reactions supports the existence of all intermediate reduction states up to the hexaanion for HPH. Tuning the experimental conditions enabled the synthesis of the HPH anions with gradually increasing reduction states (up to -5) isolated with different alkali metal ions as crystalline materials. The single-crystal X-ray diffraction structure analysis demonstrates that the highly negatively charged HPH anions (-4 and -5) exhibit a drastic geometry change from boat-shaped (observed in the neutral parent, mono- and dianions) to a chair conformation, which was proved to be fully reversible by NMR spectroscopy. DFT calculations show that this geometry change is induced by an enhanced interaction between the coordinated metal ions and negatively charged HPH core in the chair conformation.

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals

σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.

Atomic diffusion in liquid gallium and gallium-nickel alloys probed by quasielastic neutron scattering and molecular dynamic simulations

The atomic mobility in liquid pure gallium and a gallium-nickel alloy with 2 at% of nickel is studied experimentally by incoherent quasielastic neutron scattering. The integral diffusion coefficients for all-atom diffusion are derived from the experimental data at different temperatures. DFT-basedab-initiomolecular dynamics (MD) is used to find numerically the diffusion coefficient of liquid gallium at different temperatures, and numerical theory results well agree with the experimental findings at temperatures below 500 K. Machine learning force fields derived fromab-initiomolecular dynamics (AIMD) overestimate within a small 6% error the diffusion coefficient of pure gallium within the genuine AIMD. However, they better agree with experiment for pure gallium and enable the numerical finding of the diffusion coefficient of nickel in the considered melted alloy along with the diffusion coefficient of gallium and integral diffusion coefficient, that agrees with the corresponding experimental values within the error bars. The temperature dependence of the gallium diffusion coefficientDGa(T)follows the Arrhenius law experimentally for all studied temperatures and below 500 K also in the numerical simulations. However,DGa(T)can be well described alternatively by an Einstein-Stokes dependence with the metallic liquid viscosity following the Arrhenius law, especially for the MD simulation results at all studied temperatures. Moreover, a novel variant of the excess entropy scaling theory rationalized our findings for gallium diffusion. Obtained values of the Arrhenius activation energies are profoundly different in the competing theoretical descriptions, which is explained by different temperature-dependent prefactors in the corresponding theories. The diffusion coefficient of gallium is significantly reduced (at the same temperature) in a melted alloy with natural nickel, even at a tiny 2 at% concentration of nickel, as compared with its pure gallium value. This highly surprising behavior contradicts the existing excess entropy scaling theories and opens a venue for further research.

Geometries and vibrational frequencies with Kohn-Sham methods using σ-functionals for the correlation energy

Recently, Kohn-Sham (KS) methods with new correlation functionals, called σ-functionals, have been introduced. Technically, σ-functionals are closely related to the well-known random phase approximation (RPA); formally, σ-functionals are rooted in perturbation theory along the adiabatic connection. If employed in a post-self-consistent field manner in a Gaussian basis set framework, then, σ-functional methods are computationally very efficient. Moreover, for main group chemistry, σ-functionals are highly accurate and can compete with high-level wave-function methods. For reaction and transition state energies, e.g., chemical accuracy of 1 kcal/mol is reached. Here, we show how to calculate first derivatives of the total energy with respect to nuclear coordinates for methods using σ-functionals and then carry out geometry optimizations for test sets of main group molecules, transition metal compounds, and non-covalently bonded systems. For main group molecules, we additionally calculate vibrational frequencies. σ-Functional methods are found to yield very accurate geometries and vibrational frequencies for main group molecules superior not only to those from conventional KS methods but also to those from RPA methods. For geometries of transition metal compounds, not surprisingly, best geometries are found for RPA methods, while σ-functional methods yield somewhat less good results. This is attributed to the fact that in the optimization of σ-functionals, transition metal compounds could not be represented well due to the lack of reliable reference data. For non-covalently bonded systems, σ-functionals yield geometries of the same quality as the RPA or as conventional KS schemes combined with dispersion corrections.

Chemical accuracy with σ-functionals for the Kohn-Sham correlation energy optimized for different input orbitals and eigenvalues

Recently, a new type of orbital-dependent functional for the Kohn-Sham (KS) correlation energy, σ-functionals, was introduced. Technically, σ-functionals are closely related to the well-known direct random phase approximation (dRPA). Within the dRPA, a function of the eigenvalues σ of the frequency-dependent KS response function is integrated over purely imaginary frequencies. In σ-functionals, this function is replaced by one that is optimized with respect to reference sets of atomization, reaction, transition state, and non-covalent interaction energies. The previously introduced σ-functional uses input orbitals and eigenvalues from KS calculations with the generalized gradient approximation (GGA) exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE). Here, σ-functionals using input orbitals and eigenvalues from the meta-GGA TPSS and the hybrid-functionals PBE0 and B3LYP are presented and tested. The number of reference sets taken into account in the optimization of the σ-functionals is larger than in the first PBE based σ-functional and includes sets with 3d-transition metal compounds. Therefore, also a reparameterized PBE based σ-functional is introduced. The σ-functionals based on PBE0 and B3LYP orbitals and eigenvalues reach chemical accuracy for main group chemistry. For the 10 966 reactions from the highly accurate W4-11RE reference set, the B3LYP based σ-functional exhibits a mean average deviation of 1.03 kcal/mol compared to 1.08 kcal/mol for the coupled cluster singles doubles perturbative triples method if the same valence quadruple zeta basis set is used. For 3d-transition metal chemistry, accuracies of about 2 kcal/mol are reached. The computational effort for the post-self-consistent evaluation of the σ-functional is lower than that of a preceding PBE0 or B3LYP calculation for typical systems.

Lattice Opening upon Bulk Reductive Covalent Functionalization of Black Phosphorus

The chemical bulk reductive covalent functionalization of thin-layer black phosphorus (BP) using BP intercalation compounds has been developed. Through effective reductive activation, covalent functionalization of the charged BP by reaction with organic alkyl halides is achieved. Functionalization was extensively demonstrated by means of several spectroscopic techniques and DFT calculations; the products showed higher functionalization degrees than those obtained by neutral routes.

Noncovalent Functionalization and Charge Transfer in Antimonene

Antimonene, a novel group 15 two-dimensional material, is functionalized with a tailormade perylene bisimide through strong van der Waals interactions. The functionalization process leads to a significant quenching of the perylene fluorescence, and surpasses that observed for either graphene or black phosphorus, thus allowing straightforward characterization of the flakes by scanning Raman microscopy. Furthermore, scanning photoelectron microscopy studies and theoretical calculations reveal a remarkable charge-transfer behavior, being twice that of black phosphorus. Moreover, the excellent stability under environmental conditions of pristine antimonene has been tackled, thus pointing towards the spontaneous formation of a sub-nanometric oxide passivation layer. DFT calculations revealed that the noncovalent functionalization of antimonene results in a charge-transfer band gap of 1.1 eV.

Exploring the Formation of Black Phosphorus Intercalation Compounds with Alkali Metals

Black phosphorus intercalation compounds (BPICs) with alkali metals (namely: K and Na) have been synthesized in bulk by solid‐state as well as vapor‐phase reactions. By means of a combination of in situ X‐ray diffraction, Raman spectroscopy, and DFT calculations the structural behavior of the BPICs at different intercalation stages has been demonstrated for the first time. Our results provide a glimpse into the very first steps of a new family of intercalation compounds, with a distinct behavior as compared to its graphite analogues (GICs), showing a remarkable structural complexity and a dynamic behavior.

The Dalton quantum chemistry program system

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Competition for graphene: graphynes with direction-dependent Dirac cones

The existence of Dirac cones in the band structure of two-dimensional materials accompanied by unprecedented electronic properties is considered to be a unique feature of graphene related to its hexagonal symmetry. Here, we present other two-dimensional carbon materials, graphynes, that also possess Dirac cones according to first-principles electronic structure calculations. One of these materials, 6,6,12-graphyne, does not have hexagonal symmetry and features two self-doped nonequivalent distorted Dirac cones suggesting electronic properties even more amazing than that of graphene.

Frequency-dependent nonlinear optical properties with explicitly correlated coupled-cluster response theory using the CCSD(R12) model

Response theory up to infinite order is combined with the explicitly correlated coupled-cluster singles and doubles model including linear-r(12) corrections, CCSD(R12). The additional terms introduced by the linear-r(12) contributions, not present in the conventional CCSD calculation, are derived and discussed with respect to the extra costs required for their evaluation. An implementation is presented up to the cubic response function for one-electron perturbations, i.e., up to frequency-dependent second hyperpolarizabilities. As first applications the authors computed the electronic polarizabilities and second hyperpolarizabilities of BH, N(2), and formaldehyde and show that the improvement in the one-electron basis set convergence known from the R12 method for ground state energies is retained for higher-order optical properties. Frequency-dependent results are presented for the second hyperpolarizability of N(2).

Quintuple-ζ quality coupled-cluster correlation energies with triple-ζ basis sets

The explicitly-correlated coupled-cluster method CCSD(T)(R12) is extended to include F12 geminal basis functions that decay exponentially with the interelectronic distance and reproduce the form of the average Coulomb hole more accurately than linear-r(12). Equations derived using the Ansatz 2 strong orthogonality projector are presented. The convergence of the correlation energy with orbital basis set for the new CCSD(T)(F12) method is studied and found to be rapid, 98% of the basis set limit correlation energy is typically recovered using triple-zeta orbital basis sets. The performance for reaction enthalpies is assessed via a test set of 15 reactions involving 23 molecules. The title statement is found to hold equally true for total and relative correlation energies.

Extensions of r12 corrections to CC2-R12 for excited states

As known since about two decades, R12 methods, which include terms linear in the interelectronic distance r(12) in the wave function, improve substantially the basis set convergence of the ground state correlation energy. In a previous study, however, it was found that the same approach does not give a similar systematic improvement if applied to excited states in the framework of coupled cluster response theory. In the present work, we examine the reason for this behavior and show that the inclusion of additional orbitals in the construction of the r(12) pair functions leads to an enhanced basis set convergence (and thus a balanced description) also for the excited states.

Molecular Dynamics Simulation of the LOV2 Domain from Adiantum capillus-veneris

The mechanism for signal transduction from the LOV-domains toward the kinase region of phototropin is still not well understood. We have performed molecular dynamics (MD) simulations and CONCOORD calculations on the LOV2 domain of Adiantum capillus-veneris, with the goal to detect possible differences between the two forms of the LOV domain which may not show up in the static crystal structures. Since no such clear differences are found in the MD simulations also, we suggest that the real, biologically active conformation of the LOV domain within the whole phototropin is different from the crystal structure of the isolated LOV domains. The MD simulations do offer, however, insight into details of the dynamics of the dark and illuminated LOV domains, which are discussed in the light of recent experiments.

Ab initio quantum chemical investigation of the first steps of the photocycle of phototropin: a model study

Phototropin is a blue light-activated photoreceptor that plays a dominant role in the phototropism of plants. The protein contains two subunits that bind flavin mononucleotide (FMN), which are responsible for the initial steps of the light-induced reaction. It has been proposed that the photoexcited flavin molecule adds a cysteine residue of the protein backbone, thus activating autophosphorylation of the enzyme. In this study, the electronic properties of several FMN-related compounds in different charge and spin states are characterized by means of ab initio quantum mechanical calculations. The model compounds serve as idealized model chromophores for phototropism. Reaction energies are estimated for simple model reactions, roughly representing the addition of a cysteine residue to the flavin molecule. Excitation energies were calculated with the help of time-dependent density functional theory. On the basis of these calculations we propose the following mechanism for the addition reaction: (1) after photoexcitation of FMN out of the singlet ground state S0, excited singlet state(s) are populated; these relax to the lowest excited singlet state S1, and subsequently by intersystem crossing FMN in the lowest triplet state, T1 is formed; (2) the triplet easily removes the neutral hydrogen atom from the H-S group of the cysteine residue; and (3) the resulting thio radical is added.