Unrestricted Density Functional Theory Research Articles

On Entangled Singlet Pure Diradicals.

This work addresses a class of conjugated hydrocarbons that are expected to be singlet diradicals according to the topological Hückel Hamiltonian while possibly satisfying full on-bond electron pairing. These systems possess two degenerate singly occupied molecular orbitals (SOMOs), but aromaticity brought by properly positioned six-membered rings does prevent Jahn-Teller distortions. Density functional theory (DFT) calculations performed on two emblematic examples confirm the strong bond-length alternation in the closed-shell solutions and the clear spatial symmetry in the open-shell spin-unrestricted determinants, the latter solution always being found to have significantly lower energy. Since the SOMOs are here of different symmetry, the wave function is free from ionic valence-bond component, and spin decontamination of the unrestricted DFT solutions and wave function calculations at the CASSCF-plus-second-order-perturbation level confirm the expected pure diradical character of such molecules. In contrast to disjoint diradicals, the SOMOs of present systems have large amplitudes on neighbor atoms, and we propose to name them entangled pure diradicals, further providing some prescription rules for their design. Additional calculations point out the qualitative contrast between these molecules and the related diradicaloids.

Mechanistic Insights into the N-Hydroxylations Catalyzed by the Binuclear Iron Domain of SznF Enzyme: Key Piece in the Synthesis of Streptozotocin.

SznF, a member of the emerging family of heme-oxygenase-like (HO-like) di-iron oxidases and oxygenases, employs two distinct domains to catalyze the conversion of Nω-methyl-L-arginine (L-NMA) into N-nitroso-containing product, which can subsequently be transformed into streptozotocin. Using unrestricted density functional theory (UDFT) with the hybrid functional B3LYP, we have mechanistically investigated the two sequential hydroxylations of L-NMA catalyzed by SznF's binuclear iron central domain. Mechanism B primarily involves the O-O bond dissociation, forming Fe(IV)=O, induced by the H+/e- introduction to the FeA side of μ-1,2-peroxo-Fe2(III/III), the substrate hydrogen abstraction by Fe(IV)=O, and the hydroxyl rebound to the substrate N radical. The stochastic addition of H+/e- to the FeB side (mechanism C) can transition to mechanism B, thereby preventing enzyme deactivation. Two other competing mechanisms, involving the direct O-O bond dissociation (mechanism A) and the addition of H2O as a co-substrate (mechanism D), have been ruled out.

Ferrocene-Bearing Homoleptic and Heteroleptic Paddlewheel-Type Dirhodium Complexes

Two ferrocenecarboxylate (fca)-bridged dirhodium (Rh2) complexes, [Rh2(fca)4] (1) and [Rh2(fca)(piv)3] (2; piv = pivalate), were prepared through the carboxylate-exchange reactions of [Rh2(O2CCH3)4(H2O)2] and [Rh2(piv)4], respectively, with fcaH and characterized by 1H NMR, ESI-TOF-MS, and elemental analyses. Single-crystal X-ray diffraction analyses of [Rh2(fca)4(MeOH)2] (1(MeOH)2) and [Rh2(fca)(piv)3(MeOH)2] (2(MeOH)2), which are recrystallized from MeOH-containing solutions of 1 and 2, revealed that (1) 1(MeOH)2and 2(MeOH)2possess homoleptic and heteroleptic paddlewheel-type dinuclear structures, respectively; (2) both complexes have a single Rh–Rh bond (2.3771(3) Å for 1(MeOH)2, 2.3712(3) Å for 2(MeOH)2); and (3) the cyclopentadienyl rings of the fca ligands in 1(MeOH)2 adopt an eclipsed conformation, whereas those in 2(MeOH)2 are approximately 12–14° rotated from the staggered conformation. Density functional theory (DFT) calculations revealed that (1) the electronic configurations of the Rh2 core in 1(MeOH)2 and 2(MeOH)2are π4σ2δ2π*2δ*2π*2 and π4σ2δ2δ*2π*4, respectively; and (2) the occupied molecular orbitals (MOs) localized on the fca ligands are energetically degenerate and relatively more unstable than those on the Rh2 cores. Absorption features and electrochemical properties of 1 and 2 were investigated in a 9:1 CHCl3-MeOH solution and compared with those of fcaH and [Rh2(piv)4]. Through examining the obtained results in detail using time-dependent DFT (TDDFT) and unrestricted DFT, we found that 1 and 2 exhibit charge transfer excitations between the fca ligands and Rh2 cores, and 1 shows electronic interactions between ferrocene units through the Rh2 core in the electrochemical oxidation process.

Electronic and Magnetic Properties of FeCl3 Intercalated Bilayer Graphene

Graphene has gained significant attention since its discovery in 2004, and the modification of few-layer graphene provides a platform to tailor its physical and electronic properties. In this study, we employed unrestricted density functional theory (DFT) with the PBE+U functional to investigate the electronic and magnetic properties of FeCl3-intercalated bilayer graphene (BLG). Both in BLG and stage-2 intercalated graphite, a distinct localization of electrons on a specific Fe atom is evident, gaining approximately 0.245 electrons evaluated with Bader analysis, while the holes are delocalized within the graphene layers. This results in p-doped graphene, characterized by a shift of the Dirac cone by 0.74 eV for BLG and 0.70 eV for stage-2 intercalated graphite. Ferromagnetic ordering is observed within the plane of FeCl3-intercalated BLG, whereas the FeCl3 layers exhibit antiferromagnetic coupling in stage-2 intercalated graphite. The ferromagnetic nature and electronic structure of the FeCl3-intercalated BLG is retained under pressure.

On the aromaticity and stability of benzynes in the ground and lowest-lying triplet excited states.

In this work, we have revisited the aromaticity of benzyne isomers at the unrestricted density functional theory level (UDFT) using the energetic, magnetic, and delocalization criteria. In addition, this last criterion has also been analyzed employing complete active space (CASSCF) calculations. The results show conservation of aromaticity in these monocycles. Additionally it is observed that this trend is maintained in polycyclic aromatic hydrocarbon derivatives such as biradical didehydrophenanthrenes. Do these results imply a violation of Baird's rule? The answer is No, because this conservation in aromaticity is due to the loss of hydrogen atoms affects only the electronic σ skeleton and exerts a minor influence on the π cloud. Additionally, we have analyzed the relative stability of benzyne isomers and their relationship with experimental ΔES-T values. According to the literature, the stability of the benzynes in the singlet state is due to an effective interaction between the electrons of the biradical centers; however, this effect is completely reversed in the triplet state, which explains why the para isomer has the lowest ΔES-T gap.

Structure of Copper(II) N-Methylbenzoylhydroxamate in the Crystalline State and in Solution

The geometrical structure of CuL2 (I), where L = R1N(O)–(O)CR2, R1 = Me, R2 = Ph, was studied by X-ray diffraction in the crystalline state and by stationary ESR spectroscopy in solution. In the crystalline state, I is a chain polynuclear complex. According to ESR data, in frozen solutions, complex I exists as three species, two being mononuclear and one being binuclear. The magnetic resonance parameters and concentrations of the species in frozen solutions were determined. The electronic structure of the complex with full geometry optimization of all systems was calculated in terms of the unrestricted density functional theory (DFT) method.

Extremely Long C-C Bonds Predicted beyond 2.0 Å.

A number of conjugated molecules are designed with extremely long single C-C bonds beyond 2.0 Å. Some of the investigated molecules are based on analogues to the recently discovered molecule by Kubo et al. These bonds are analyzed by a variety of indices in addition to their equilibrium bond length including the Wiberg bond index, bond dissociation energy (BDE), and measures of diradicaloid character. All unrestricted DFT calculations indicate no diradical character supported by high-level multireference calculations. Finally, NFOD was computed through fractional orbital density (FOD) calculations and used to compare relative differences of diradicaloid character across twisted molecules without central C-C bonding and those with extremely elongated C-C bonds using a comparison with the C-C bond breaking in ethane. No example of direct C-C bonds beyond 2.4 Å are seen in the computational modeling; however, extremely stretched C-C bonds in the vicinity of 2.2 Å are predicted to be achievable with a BDE of 15-25 kcal mol-1.

Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law.

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH3 radical and the superoctazethrene molecule are also illustrated.

Low-rank approximations for accelerating plane-wave hybrid functional calculations in unrestricted and noncollinear spin density functional theory.

The adaptively compressed exchange (ACE) operator combined with interpolative separable density fitting (ISDF) decomposition has been utilized to accelerate plane-wave hybrid functional calculations for restricted Kohn-Sham density functional theory (DFT), but the neglect of spin degree of freedom has limited its application in the exploration of systems where the spin property of the electron is critical. Herein, we derive the ACE-ISDF formulation for hybrid functional calculations in both unrestricted and noncollinear spin DFT with plane waves and periodic boundary conditions. We proposed an improved ISDF algorithm for the sum of Kohn-Sham orbital pairs to further reduce the computational cost for the spin-noncollinear case. Numerical results demonstrate that these improved ACE-ISDF low-rank approximations can not only significantly reduce the computational time by two orders of magnitude compared with conventional plane-wave hybrid functional calculations but also lead to a good convergence behavior when a moderate rank parameter is set, even for complex periodic magnetic systems. By using these ACE-ISDF approximations, we investigate the electronic and magnetic properties of two-dimensional periodic ferromagnetic semiconductors consisting of triangular zigzag graphene quantum dots and transition metal atoms. Our computational results showcase that hybrid functional calculations in spin DFT can provide not only accurate electronic structures but also accurate magnetic order temperature of ferromagnetic semiconductors compared to local or semilocal functional calculations.

Benchmark Study on Phosphorescence Energies of Anthraquinone Compounds: Comparison between TDDFT and UDFT

Phosphorescent material is widely used in light-emitting devices and in the monitoring of cell phenomena. Anthraquinone compounds (AQs), as important phosphorescent materials, have potential applications as emitters for highly efficient organic light-emitting diodes (OLEDs). Therefore, the accurate calculation of the phosphorescence energy of anthraquinone compounds is particularly important. This study mainly analyzes the phosphorescence energy calculation method of anthraquinone compounds. The time-dependent density functional theory (TDDFT) and the unrestricted density functional theory (UDFT) with seven functionals are selected to calculate the phosphorescence of AQs, taking the high-precision coupled-cluster singles and doubles (CC2) method as a reference. The results showed that the mean unsigned error (MUE) of UDFT was 0.14 eV, which was much smaller than that of TDDFT at 0.29 eV. Therefore, UDFT was more suitable for calculating the phosphorescence energy of AQs. The results obtained by different functionals indicate that the minimum MUE obtained by M06-2X was 0.14 eV. More importantly, the diffuse function in the basis set played an important role in calculating the phosphorescence energy in the M06-HF functional. In the BDBT, FBDBT, and BrBDBT, when M06-HF selected the basis set containing a diffuse function, the differences with CC2 was 0.02 eV, which is much smaller than the one obtained without a diffuse function at 0.80 eV. These findings might be of great significance for the future study of the phosphorescence energy of organic molecules.

Influence of Number of Ligands and Point Group on the Electronic Structure of Co2+ Aqua-Complexes

The nucleation process of zeolitic imidazolate frameworks (ZIFs) is, to date, not yet completely understood, making the search for tailored materials very difficult. Recently, it has been shown that, during the formation process, the symmetry of the precursors is reduced by ligand elimination and substitution reactions. The octahedral precursors with simple ligands, such as water, methanol, and/or NO3-, are transformed to five- and finally four-coordinated complexes with imidazole ligands. This reduction of symmetry, caused both by the changing coordination environment and distortions from the perfect symmetry leading to another point group, will have a large influence on the electronic structure and more specifically on the d-orbital splitting. This, in turn, will affect the d-d electronic excitations, which can be followed using UV-vis spectroscopy and which can help to unravel the formation process. In this work, we systematically investigate how the lowering of the number of ligands affects the symmetry and thus the geometry and electronic structure of Co2+ complexes with six, five, and four aqua ligands. Therefore, we first resort to qualitative techniques, such as crystal field theory (CFT) and ligand field theory (LFT), which reveal that the orbital splitting is characteristic for the number of ligands. However, as these techniques are not capable of providing quantitative results without the use of experimental data as input, we perform various computational calculations. Both average of configuration (AOC) and unrestricted density functional theory (UDFT) are thoroughly investigated, and we will determine which technique is the best suited to properly describe the ground state of these systems. To investigate the dependency on the d-orbital occupation, we also investigated V2+, Mn2+, and Ni2+ hexa-aqua-complexes and compared them to the Co systems.

A Comparative Density Functional Theory Study of Hydrogen Storage in Cellulose and Chitosan Functionalized by Transition Metals (Ti, Mg, and Nb).

The focus of this work is hydrogen storage in pristine cellulose, chitosan, and cellulose. Chitosan doped with magnesium, titanium, and niobium is analyzed using spin unrestricted plane-wave density functional theory implemented in the Dmol3 module. The results of this study demonstrate that hydrogen interaction with pure cellulose and chitosan occurred in the gas phase, with an adsorption energy of Eb = 0.095 eV and 0.090 eV for cellulose and chitosan, respectively. Additionally, their chemical stability was determined as Eb= 4.63 eV and Eb = 4.720 eV for pure cellulose and chitosan, respectively, by evaluating their band gap. Furthermore, the presence of magnesium, titanium, and niobium on cellulose and chitosan implied the transfer of an electron from metal to cellulose and chitosan. Moreover, our calculations predict that cellulose doped with niobium is the most favorable medium where 6H2 molecules are stored compared with molecules stored in niobium-doped chitosan with Tmax = 818 K to release all H2 molecules. Furthermore, our findings showed that titanium-doped cellulose has a storage capacity of five H2 molecules, compared to a storage capacity of four H2 molecules in titanium-doped chitosan. However, magnesium-doped cellulose and chitosan have insufficient hydrogen storage capacity, with only two H2 molecules physisorbed in the gas phase. These results suggest that niobium-doped cellulose and chitosan may play a crucial role in the search for efficient and inexpensive hydrogen storage media.

Exchange Spin Coupling in Optically Excited States.

In optically excited states in molecules and materials, coupling between local electron spins plays an important role for their photoemission properties and is interesting for potential applications in quantum information processing. Recently, it was experimentally demonstrated that the photogenerated local spins in donor-acceptor metal complexes can interact with the spin of an attached radical, resulting in a spin-coupling-dependent mixing of excited doublet states, which controls the local spin density distributions on donor, acceptor, and radical subunits in optically excited states. In this work, we propose an energy-difference scheme to evaluate spin coupling in optically excited states, using unrestricted and spin-flip simplified time-dependent density functional theory. We apply it to three platinum complexes which have been studied experimentally to validate our methodology. We find that all computed coupling constants are in excellent agreement with the experimental data. In addition, we show that the spin coupling between donor and acceptor in the optically excited state can be fine-tuned by replacing platinum with palladium and zinc in the structure. Besides the two previously discussed excited doublet states (one bright and one dark), our calculations reveal a third, bright excited doublet state which was not considered previously. This third state possesses the inverse spin polarization on donor and acceptor with respect to the previously studied bright doublet state and is by an order of magnitude brighter, which might be interesting for optically controlling local spin polarizations with potential applications in spin-only information transfer and manipulation of connected qubits.

Dipolar and Contact Paramagnetic NMR Chemical Shifts in AnIV Complexes with Dipicolinic Acid Derivatives.

Actinide +IV complexes (AnIV = ThIV, UIV, NpIV, and PuIV) with two dipicolinic acid derivatives (DPA and Et-DPA) have been studied by 1H and 13C NMR spectroscopies and first-principles calculations. The Fermi contact and dipolar contributions to the actinide-induced shifts (AIS) are evaluated from a temperature dependence analysis, combined with ab initio results. It allows an experimental estimation of the axial anisotropy of the magnetic susceptibility Δχax and of the hyperfine coupling constants of the NMR-active nuclei. Due to the compactness of the coordination sphere, the magnetic anisotropy of the paramagnetic center is small, and this makes the contact contribution to be the dominant one, even on the remote atoms. The sign of the hyperfine coupling constants and related spin densities is alternating on the nuclei of the ligand cycle, denoting a preponderant spin polarization mechanism. This is well reproduced by unrestricted density functional theory (DFT) calculations. Those values are furthermore slightly decreasing in the actinide series, which indicates a small decrease of the covalency from UIV to PuIV.

Tuning the Diradical Character of Indolocarbazoles: Impact of Structural Isomerism and Substitution Position.

In this study, a set of 10 positional indolocarbazole (ICz) isomers substituted with dicyanomethylene groups connected via para or meta positions are computationally investigated with the aim of exploring the efficiency of structural isomerism and substitution position in controlling their optical and electronic properties. Unrestricted density functional theory (DFT), a spin-flip time-dependent DFT approach, and the multireference CASSCF/NEVPT2 method have been applied to correlate the diradical character with the energetic trends (i.e., singlet–triplet energy gaps). In addition, the nucleus-independent chemical shift together with ACID plots and Raman intensity calculations were used to strengthen the relationship between the diradical character and (anti)aromaticity. Our study reveals that the substitution pattern and structural isomerism represent a very effective way to tune the diradical properties in ICz-based systems with meta-substituted systems with a V-shaped structure displaying the largest diradical character. Thus, this work contributes to the elucidation of the challenging chemical reactivity and physical properties of diradicaloid systems, guiding experimental chemists to produce new molecules with desirable properties.

Spin Alternation Rule in USCF for Through-Bond Magnetic Coupling─A New Look: Why and When Does It Arise and How To See It.

This work takes a new look at the spin alternation rule in unrestricted self-consistent-field (USCF) calculations in terms of structural characteristics such as periodicity, impurity location, and Coulomb exchange. For clarity, the systems considered are biradicals produced from linear conjugated hydrocarbons. Both site-parametrized Hamiltonian models for theoretical analysis and spin unrestricted density functional theory (DFT) calculations are used. Theoretical analysis leads to the following conclusions: (1) The diradical state is an excited state of a linear chain of N conjugated carbon atoms (when N is about ≤ 10). Spin alternation is a consequence of the (truncated) periodic symmetry combined with filling each closed-shell pi orbital with two electrons and each singly occupied molecular orbital (SOMO) with one electron. Spin polarization is evident in triplet (T) and broken symmetry (BS) solutions for an odd N and only in the T solution for an even N. Spin alternation is visible in the BS for an odd N and always remains muted in the calculated T. (2) For a doped chain with two radical centers, spin alternation is generally visible in the BS for an odd N. The sign of spin population on the radical centers in the BS indicates the stable spin. For radical centers separated by an odd (even) number of pz electrons, spin alternation favors T (S) state with FM (AFM) interaction. Spin oscillation remains less transparent for an even N without exchange. (3) In an unrestricted treatment with exchange, spin alternation becomes observable. Without SCF iterations, the more stable state can be identified from a clear spin oscillation in the BS. An irregular oscillation indicates a possible singlet ground state. These observations are supported by density functional calculations using the B3LYP functional and the 6-311+g(d,p) basis set on linear decapentaene diradicals with nitronyl nitroxide moieties substituted on two sets of conjugated atoms, (3,9) and (3,10). Because of the SCF procedure, one finds spin alternation in the T (BS) solution and erratic oscillation in the BS (T) solution of the 3,9 (3,10) diradical in respective equilibrium geometries. The ground state is T (S). DFT adiabatic coupling constants, SOMO energies, spin population plots, and SOMO lobe diagrams compare well with molecular electronic characteristics from theoretical analysis using Hamiltonian parameters.

Electrochromism of Nanographenes in the Near-Infrared Region.

Nanographene (NG) is a potential candidate for organic EC materials because of its large π-conjugated system, chemical stability, absorption band covering the visible region, and tunable optical properties by postsynthetic modification. We show that NGs carrying redox-active triphenylamine (TPA) units covalently linked to the NG edge function as EC materials in the NIR region. The hybrid materials can be obtained by the installation of TPA units onto the NG edge and display changes in the absorption spectrum in the NIR region extending to a wavelength of over 2000 nm upon one-electron oxidation and reduction at low potentials (<1.1 V). Time-dependent unrestricted density functional theory calculation of a model NG at the UB3LYP/6-31G(d,p) level of theory suggests that a narrow energy gap between the basal plane and the oxidized TPA unit is responsible for the observed EC function in the NIR region.

Electrochromism of Nanographenes in the Near‐Infrared Region

AbstractNanographene (NG) is a potential candidate for organic EC materials because of its large π‐conjugated system, chemical stability, absorption band covering the visible region, and tunable optical properties by postsynthetic modification. We show that NGs carrying redox‐active triphenylamine (TPA) units covalently linked to the NG edge function as EC materials in the NIR region. The hybrid materials can be obtained by the installation of TPA units onto the NG edge and display changes in the absorption spectrum in the NIR region extending to a wavelength of over 2000 nm upon one‐electron oxidation and reduction at low potentials (&lt;1.1 V). Time‐dependent unrestricted density functional theory calculation of a model NG at the UB3LYP/6‐31G(d,p) level of theory suggests that a narrow energy gap between the basal plane and the oxidized TPA unit is responsible for the observed EC function in the NIR region.

Theoretical Investigation on Electron Transport Capabilities of Helically Twisted Molecules Based on Decay Constants of Exchange Interaction

Abstract The electron transport capabilities of helically twisted molecules were theoretically evaluated based on the decay constant of the exchange interaction (βJ) between terminal nitronyl nitroxide radicals using broken-symmetry unrestricted density functional theory (UDFT) calculations. A small βJ value (βJ = 0.16 Å−1) was estimated for a homogeneously π-extended helicene consisting of a helically fused oligo-phenanthrenes, which is less than half that of the original carbohelicene (βJ = 0.39 Å−1) and comparable to that of rylene (βJ = 0.13 Å−1). The excellent electron transport capability suggested by the small βJ of the π-extended helicene can be attributed to the olefinic electronic nature found inside the helical framework.

Computational Study of Electronic Properties in Oligoacenes

Calculations were performed for closed shell singlet states, open shell singlet states and open-shell triplet states using DFT and B3LYP functional in oligoacenes. 6-31+G(d,p) basis set was used to calculate energies for polyacenes in Hartrees at various levels of spin-state configuration. For systems beyond pentacene, open shell sing let state is more stablilized for hexacene, heptacene, octacene and nonacene and singlet triplet gap decreases as size of polyacene increases. This work is used to describe unrestricted DFT calculations, spin contamination and quantum mechanical applications..