Open-shell State Research Articles

Electronic spin transitions in finite-size graphene

Density Functional Theory study on graphene ribbons with various shapes and sizes shows that as ribbon increases in length and width, its orbital energy gap decreases and prefers a higher spin state. Such a transition occurs when the energy gap between the highest doubly occupied and the lowest unoccupied molecular orbitals of the ground state is about 1.13eV. Our results suggest that high-spin states are stable, and graphene ribbons have ferromagnetic properties. The results are consistent with recent observations where bulk graphene possesses both ferromagnetic and antiferromagnetic properties as in phase-separated systems. The open-shell singlet state was suggested previously for the antiferromagnetic property of graphene ribbons.

Communication: Spin-orbit splittings in degenerate open-shell states via Mukherjee's multireference coupled-cluster theory: A measure for the coupling contribution

We propose a generally applicable scheme for the computation of spin-orbit (SO) splittings in degenerate open-shell systems using multireference coupled-cluster (MRCC) theory. As a specific method, Mukherjee's version of MRCC (Mk-MRCC) in conjunction with an effective mean-field SO operator is adapted for this purpose. An expression for the SO splittings is derived and implemented using Mk-MRCC analytic derivative techniques. The computed SO splittings are found to be in satisfactory agreement with experimental data. Due to the symmetry properties of the SO operator, SO splittings can be considered a quality measure for the coupling between reference determinants in Jeziorski-Monkhorst based MRCC methods. We thus provide numerical insights into the coupling problem of Mk-MRCC theory.

Multi-Zinc-Expanded Oligoacenes: An Intriguing Class of Well-Defined Open-Shell Singlet Diradicals

Two classes of multi-Zn-expanded oligoacenes from benzene to pentacene are computationally designed through introducing a Zn array into acene rings in two ways: acene-chain axial versus single-ring quasi-transversal direction. Combined density functional theory, CASSCF, and CCSD calculations predict that all these multi-Zn-expanded oligoacenes have the open-shell singlet diradical ground states, in contrast with the common fact that their parent oligoacenes are closed-shell systems or may have a triplet ground state and only acenes larger than octacene have open-shell singlet diradical ground states. These results offer the first theoretical prediction that the multi-Zn introduction into the acene ring(s), forming the Zn-expanded oligoacenes, can lead them to diradical structures. The diradical character of the ground states of these molecules arises from the Zn-participation-induced disjoint nature of the nonbonding molecular orbitals that are singly occupied in the diradicals. This work provides a strategy to design perfect and stable singlet diradicals from oligoacenes or their derivatives.

Squaraine Dyes as Efficient Coupling Bridges between Triarylamine Redox Centres

Various indolenine squarylium dyes with additional electron-donating amine redox centres have been synthesised and their redox chemistry has been studied. A combination of cyclic voltammetry, spectro-electrochemistry and DFT calculations has been used to characterise the electronic structure of the mono-, di- and, in one case, trications. All monocations still retain the cyanine-like, delocalised character due to the relatively low redox potential of the squaraine bridge and are therefore compounds of Robin-Day class III. Thus we extended previous studies on organic mixed-valence systems by using the indolenine squaraine moiety as very electron-rich bridge between two electron-donating amine redox centres to provoke a strong coupling between the additional redox centres. We synthesised TA3, which has an N-N distance of 26 bonds between the triarylamine redox centres and is to our knowledge the longest bis(triarylamine) radical cation that is completely delocalised. We furthermore show that altering the symmetry of a squaraine dye by substitution of a squaric ring oxygen atom by a dicyanomethylene group has a direct impact on the optical properties of the monocations. In case of the dications, it turned out that the energetically most stable state of dianisylamine-substituted squaraines is an anti-ferromagnetically coupled open-shell singlet state.

Spectroscopy and Fragmentation of Undercoordinated Bromoiridates

We report gas-phase electronic photodissociation spectra of the undercoordinated bromoiridate complexes IrBr(4)(-) and IrBr(5)(-) at photon energies from 1 to 5.6 eV. Both ions have open-shell ground states with low-symmetry structures. The fragmentation is characterized by thresholds for the loss of one Br atom for IrBr(4)(-) and one or two Br atoms for IrBr(5)(-). The experimental spectra consist of ligand-to-metal charge transfer transitions and reveal a large density of electronic states that can be recovered by time-dependent density functional theory.

The Frontiers of Quinoidal Stability in Long Oligothiophenes: Raman Spectra of Dicationic Polaron Pairs

The transformation of bipolarons into polaron pairs in long oligothiophene dications has been reported by Raman spectroscopy. These polaron-pair dicationic species possess singlet open-shell biradicaloid ground electronic states. The formation of biradical polaron pairs marks the end of the quinoidal stability promoted by the intrinsic proaromatic character. The quinoidal stability in TCNQ oligothiophenes in comparison with dicationic oligothiophenes has been addressed.

Ditantalum Dinitrogen Complex: Reaction of H2 Molecule with “End-on-Bridged” [TaIV]2(μ-η1:η1-N2) and Bis(μ-nitrido) [TaV]2(μ-N)2 Complexes

To elucidate (i) the physicochemical properties of the {(η(5)-C(5)Me(5))[Ta(IV)](i-Pr)C(Me)N(i-Pr)}(2)(μ-η(1):η(1)-N(2)), I, [Ta(IV)](2)(μ-η(1):η(1)-N(2)), and {(η(5)-C(5)Me(5))[Ta(V)](i-Pr)C(Me)N(i-Pr)}(2)(μ-N)(2), II, [Ta(V)](2)(μ-N)(2), complexes; (ii) the mechanism of the I → II isomerization; and (iii) the reaction mechanism of these complexes with an H(2) molecule, we launched density functional (B3LYP) studies of model systems 1, 2, and 3 where the C(5)Me(5) and (i-Pr)C(Me)N(i-Pr) ligands of I (or II) were replaced by C(5)H(5) and HC(NCH(3))(2), respectively. These calculations show that the lower-lying electronic states of 1, [Ta(IV)](2)(μ-η(1):η(1)-N(2)), are nearly degenerate open-shell singlet and triplet states with two unpaired electrons located on the Ta centers. This finding is in reasonable agreement with experiments [J. Am Chem. Soc. 2007, 129, 9284-9285] showing easy accessibility of paramagnetic and diamagnetic states of I. The ground electronic state of the bis(μ-nitrido) complex 2, [Ta(V)](2)(μ-N)(2), is a closed-shell singlet state in agreement with the experimentally reported diamagnetic feature of II. The 1-to-2 rearrangement is a multistep and highly exothermic process. It occurs with a maximum of 28.7 kcal/mol free energy barrier required for the (μ-η(1):η(1)-N(2)) → (μ-η(2):η(2)-N(2)) transformation step. Reaction of 1 with H(2) leading to the 1,4-addition product 3 proceeds with a maximum of 24.2 kcal/mol free energy barrier associated by the (μ-η(1):η(1)-N(2)) → (μ-η(2):η(1)-N(2)) isomerization step. The overall reaction 1 + H(2) → 3 is exothermic by 20.0 kcal/mol. Thus, the addition of H(2) to 1 is kinetically and thermodynamically feasible and proceeds via the rate-determining (μ-η(1):η(1)-N(2)) → (μ-η(2):η(1)-N(2)) isomerization step. The bis(μ-nitrido) complex 2, [Ta(V)](2)(μ-N)(2), does not react with H(2) because of the large energy barrier (49.5 kcal/mol) and high endothermicity of the reaction. This conclusion is also in excellent agreement with the experimental observation [J. Am Chem. Soc. 2007, 129, 9284-9285].

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

We study the electronic structure of a spherical jellium in the presence of a central Gaussian impurity. We test how well the resulting inhomogeneity effects beyond spherical jellium are reproduced by several approximations of density functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals, namely local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA and orbital-dependent hybrid functionals are compared against our quantum Monte Carlo (QMC) benchmarks. We identify several distinct transitions in the ground state of the system as the electronic occupation changes between delocalized and localized states. We examine the parameter space of realistic densities ($1 \le r_s\le 5$) and moderate depths of the Gaussian impurity ($Z<7$). The selected 18 electron system (with closed-shell ground state) presents $1d \to 2s$ transitions while the 30 electron system (with open-shell ground state) exhibits $1f \to 2p$ transitions. For the former system, the accuracy for the transitions is clearly improving with increasing sophistication of functionals with meta-GGA and hybrid functionals having only small deviations from QMC. However, for the latter system, we find much larger differences for the underlying transitions between our pool of DFT functionals and QMC. We attribute this failure to treatment of the exact exchange within these functionals. Additionally, we amplify the inhomogeneity effects by creating the system with spherical shell which leads to even larger errors in DFT approximations.

Mechanisms of the Thermal Cyclotrimerizations of Fluoro- and Chloroacetylenes: Density Functional Theory Investigation and Intermediate Trapping Experiments

Theoretical studies of the mechanisms of the thermal cyclotrimerization of fluoro- and chloroacetylenes, which were reported by Viehe and Ballester, respectively, were conducted with the aid of density functional theory calculations of the (U)B3LYP functional, indicating that the thermal cyclotrimerizations of fluoro- and chloroacetylenes involve tandem processes of regioselectively stepwise [2+2] and stepwise [4+2] cycloadditions. These tandem processes generate 1,2,6-trihalo-Dewar benzenes and 1,2,4-trihalo-Dewar benzenes, which then isomerize to the corresponding benzenes when heated. The rate-determining step of the cyclotrimerizations of haloacetylenes is the dimerization step involving open-shell singlet diradical transition states and intermediates. The substituent effects in the thermal cyclotrimerization of haloacetylenes have been rationalized using frontier molecular orbital theory. The higher reactivity of fluoroacetylenes compared to that of chloroacetylenes is due to the fact that fluoroacetylenes have lower singlet-triplet gaps than chloroacetylenes and more easily undergo dimerization and cyclotrimerization. In this report, additional experiments were performed to verify the theoretical prediction about the cyclotrimerization of chloroacetylene and to trap the proposed 1,4-dichlorocyclobutadiene intermediate. Experiments revealed that the thermal reaction of phenylchloroacetylene at 110 °C gave 1,2,3-triphenyltrichlorobenzene and 1,2,4-triphenyltrichlorobenzene together with a tetramer, cis-1,2,5,6-tetrachloro-3,4,7,8-tetraphenyltricyclo[4.2.0.0(2,5)]octa-3,7-diene. The proposed 1,4-diphenyldichlorocyclobutadiene intermediate in the thermal cyclotrimerization of phenylchloroacetylene was successfully trapped using dienophiles of maleic anhydride and dimethyl acetylenedicarboxylate.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

The solution of the time-dependent Schrödinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.

Phenyloxenium Ions: More Like Phenylnitrenium Ions than Isoelectronic Phenylnitrenes?

The geometries and energies of the electronic states of phenyloxenium ion 1 (Ph-O(+)) were computed at the multireference CASPT2/pVTZ level of theory. Despite being isoelectronic to phenylnitrene 4, the phenyloxenium ion 1 has remarkably different energetic orderings of its electronic states. The closed-shell singlet configuration ((1)A(1)) is the ground state of the phenyloxenium ion 1, with a computed adiabatic energy gap of 22.1 kcal/mol to the lowest-energy triplet state ((3)A(2)). Open-shell singlet configurations ((1)A(2), (1)B(1), (1)B(2), 2(1)A(1)) are significantly higher in energy (>30 kcal/mol) than the closed-shell singlet configuration. These values suggest a revision to the current assignments of the ultraviolet photoelectron spectroscopy bands for the phenoxy radical to generate the phenyloxenium ion 1. For para-substituted phenyloxenium ions, the adiabatic singlet-triplet energy gap (ΔE(ST)) is found to have a positive linear free energy relationship with the Hammett-like σ(+)(R)/σ(+) substituent parameters; for meta substituents, the relationship is nonlinear and negatively correlated. CASPT2 analyses of the excited states of p-aminophenyloxenium ion 5 and p-cyanophenyloxenium ion 10 indicate that the relative orderings of the electronic states remain largely unperturbed for these para substitutions. In contrast, meta-donor-substituted phenyloxenium ions have low-energy open-shell states (open-shell singlet, triplet) due to stabilization of a π,π* diradical state by the donor substituent. However, all of the other phenyloxenium ions and larger aryloxenium ions (naphthyl, anthryl) included in this study have closed-shell singlet ground states. Consequently, ground-state reactions of phenyloxenium ions are anticipated to be more closely related to closed-shell singlet arylnitrenium ions (Ar-NH(+)) than their isoelectronic arylnitrene (Ar-N) counterparts.

The unique bonding characteristics of beryllium and the Group IIA metals

Having closed valence sub-shells, the alkaline earth atoms participate in covalent bonding via orbital hybridization and exchange interactions, with additional contributions from dispersion interactions. Starting from a closed ns2 configuration imparts different characteristics to the chemistry of this group, as compared to metals that have open-shell atomic ground states. Theoretical studies of the bonding of the Group IIA metals have been pursued for many years, and they are known to be challenging for ab initio electronic structure methods. The bonding motifs have been examined, and the differences between beryllium and the remainder of the group explored. Experimental studies that probe the bonding, particularly for beryllium, have lagged behind the theoretical work. In the present Letter we describe our recent spectroscopic and theoretical investigations of simple beryllium compounds, and discuss these results in terms of their relationship to the properties of the heavier Group IIA elements.

The electronic structure of p-xylylene and its reactivity with vinyl molecules

The electronic states of p-xylylene molecule were described at the multi-configurational CASSCF/MRMP2 level of theory. The closed-shell singlet state representing the quinoidal p-xylylene molecule was predicted to be the ground electronic state whereas the triplet (benzoidal) and the singlet open-shell states were found to be much higher in energy (by 159 and 423 kJ/mol, respectively, as found at the CASSCF(8,8)/6-31+G(d) level). The reactions of p-xylylene with variously substituted vinyl molecules (i.e., CH 2 CH 2, CH 2 CHCl, CH 2 CHCN, CH 2 CHNO 2, CH 2 CHCF 3, CH 2 CHC 6H 5, CH 2 CHCOOC 6F 5, and CH 2 C(CN) 2) were investigated with the DFT (using the B3LYP and MPW1 K functionals) and MP2 methods using the 6-31++G(d,p) basis set and the activation barriers in the 33–113 kJ/mol range were predicted. Since some of the activation barriers found are smaller than the energy required to initialize the parylene polymerization (63 kJ/mol) the reactions of the p-xylylene with vinyl molecules is postulated to be competitive with the polymerization process.

On the superconductor mechanism of [bis(ethylenedithio)tetraselenafuvalene] 2GaCl 4

The superconductivity of [BETS] 2GaCl 4, where BETS is bis(ethylenedithio)tetraselenafulvalene, is discussed in terms of electronic structure properties. The critical temperature, T c , for the organic superconductor is suggested to be determined by the energy splitting between two electronic states with different spatial extent of the orbitals at the Fermi level. The energetically lowest superconducting state has localized orbitals confined in the BETS moieties, whereas the conventionally conducting state has delocalized orbitals along the [BETS] 2GaCl 4 chains. The calculations suggest that the open-shell singlet state of [BETS] 2GaCl 4 pairs is the prerequisite of accepting the superconducting Cooper pairs.

Electrochemical and Photochemical Cyclization and Cycloreversion of Diarylethenes and Diarylethene-Capped Sexithiophene Wires

A combined theoretical and experimental study was performed on diarylethenes and diarylethene-capped sexithiophenes aiming at an improved understanding of the electrochemical and photochemical ring-opening and ring-closing mechanisms. Theoretical calculations, based on DFT and TDDFT, suggested that the spatial distribution and the occupancy of the frontier orbitals determine and control the diarylethenes' ring-opening and ring-closing upon photoirradiation and electrochemical oxidation. Optimized geometries, potential energy surfaces, and activation energies between the open-ring and closed-ring forms were calculated for diarylethenes in the neutral ground state, excited states, and mono- and dicationic states. Analysis of the frontier orbitals was employed to understand the cyclization and cycloreversion of diarylethenes and to predict and explain the switching properties of diarylethene-capped sexithiophene molecular wires. The TDDFT data were verified with experimentally measured UV/vis spectra. The DFT calculations estimated open-shell ground states of diarylethene-capped sexithiophene dications, which were verified with EPR spectroscopy, and the broadening of the peaks in the EPR spectra were explained with the calculated singlet-triplet splitting. The good agreement of experiment and theory allows for the understanding of switching behavior of diarylethenes in solutions, in metal break junctions, in monolayers on metal surfaces, and as a part of complex organic molecular wires.

Intermediate-Valence Tautomerism in Decamethylytterbocene Complexes of Methyl-Substituted Bipyridines

Multiconfigurational, intermediate valent ground states are established in several methyl-substituted bipyridine complexes of bis(pentamethylcyclopentadienyl)ytterbium, Cp2*Yb (Me(x)-bipy). In contrast to Cp2*Yb(bipy) and other substituted-bipy complexes, the nature of both the ground state and the first excited state are altered by changing the position of the methyl or dimethyl substitutions on the bipyridine rings. In particular, certain substitutions result in multiconfigurational, intermediate valent open-shell singlet states in both the ground state and the first excited state. These conclusions are reached after consideration of single-crystal X-ray diffraction (XRD), the temperature dependence of X-ray absorption near-edge structure (XANES), extended X-ray absorption fine-structure (EXAFS), and magnetic susceptibility data, and are supported by CASSCF-MP2 calculations. These results place the various Cp2*Yb(bipy) complexes in a new tautomeric class, that is, intermediate-valence tautomers.

Preparation and Characterization of (CNSSS)2(A)2(A = AsF6−, SbF6−, Sb2F11−) Containing the O2-like 5,5′-Bis(1,2,3,4-trithiazolium) Dication: The Second Example of a Simple Nonsterically Hindered Main-Group Diradical That Retains Its Paramagnetism in the Solid State

The reaction of NC-CN with a 1:1 mixture of S(4)(MF(6))(2) and S(8)(MF(6))(2) (M = As, Sb) (stoichiometrically equivalent to four "S(3)MF(6)" units) results in the quantitative formation of S(3)NCCNS(3)(MF(6))(2) [7(MF(6))(2)], which is the thermodynamic sink in this reaction. The Sb(2)F(11)(-) salt 7(Sb(2)F(11))(2) is prepared by the addition of an excess of SbF(5) to 7(AsF(6))(2). Crystal structure determinations for all three salts show that 7(2+) can be viewed as two R-CNS(3)(+) radical cations joined together by a C-C single bond. The two rings are coplanar and in a trans orientation due to electrostatic N(delta-)...S(delta+) interactions. The classically bonded alternative (quinoidal structure), in which the octet rule is obeyed, is not observed and is much higher in energy based on calculated estimates and a simple comparison of pi bond energies. Calculated molecular orbitals (MOs) support this, showing that the MO corresponding to the quinoidal structure lies higher in energy than the nearly degenerate singly occupied MOs of 7(2+). The vibrational spectra of 7(2+) in all salts were assigned based on a normal-coordinate analysis and theoretical vibrational frequencies calculated at the PBE0/6-31G* level. In the solid state, 7(2+) is a planar disjoint diradical with essentially degenerate open-shell singlet and triplet states. The disjoint nature of the diradical cation 7(2+) is established by magnetic susceptibility studies of the Sb(2)F(11)(-) salt doped in an isomorphous diamagnetic host material (CNSNS)(2)(Sb(2)F(11))(2) [10(Sb(2)F(11))(2)]. Intramolecular spin coupling is extremely weak corresponding to a singlet-triplet gap (DeltaE(ST) = 2J) of <+/-2 cm(-1). CASPT2[12,12]/6-311G* calculations support a triplet ground state with a small singlet-triplet gap. The single-crystal electron paramagnetic resonance (EPR) of 7(Sb(2)F(11))(2) doped in 10(Sb(2)F(11))(2) is in agreement with the triplet state arising from the weak coupling between the unpaired electrons residing in p(pi) orbitals in each of the rings. Variable-temperature susceptibility data for bulk samples of 7(A)(2) (A = SbF(6)(-), AsF(6)(-), Sb(2)F(11)(-)) are analyzed by employing both 1D chain and 2D sheet magnetic models. These studies reveal significant intermolecular exchange approximating that of a 1D chain for the SbF(6)(-) salt with |J| = 32 cm(-1). The exchange coupling is on the same order of magnitude as that for the AsF(6)(-) salt, although in this case it is likely that there are complex exchange pathways where no particular one is dominant. Intermolecular exchange in the Sb(2)F(11)(-) salt is an order of magnitude weaker. In solution, the EPR spectrum of 7(2+) shows a broad triplet resonance as well as a sharp resonance that is tentatively attributed to a rotomer of the 7(2+)/anion pair, which is likely the origin of the green species given on dissolution of the red 7(2+) salts in SO(2)/AsF(3)/MF(5). We account for the many similarities between O(2) and 7(2+), which are the only simple nonsterically hindered nonmetal diradicals to retain their paramagnetism in the solid state. 7(2+) is also the first isolable, essentially sulfur-based diradical as evidenced by calculated spin densities.

2-Pyridylnitrene and 3-Pyridazylcarbene and Their Relationship via Ring-Expansion, Ring-Opening, Ring-Contraction, and Fragmentation

Photolysis of triazolo[1,5-b]pyridazine 8 isolated in Ar matrix generates diazomethylpyridazines 9Z and 9E and diazopentenynes 11Z and 11E as detected by IR spectroscopy. ESR spectroscopy detected the 3-pydidazylcarbene 10 as well as pent-2-en-3-yn-1-ylidene 12 formed by loss of one and two molecules of N(2), respectively. Further photolysis caused rearrangement of the carbenes to 1,2-pentadien-4-yne 13 and 3-ethynylcyclopropene 14. Flash vacuum thermolysis (FVT) of 8 at 400-500 degrees C with Ar matrix isolation of the products yielded 13, 14, and 1,4-pentadiyne 15. At higher temperatures, glutacononitriles 27Z and 27E were formed as well together with minor amounts of 2- and 3-cyanopyrroles 28 and 29. Tetrazolo[1,5-a]pyridine/2-azidopyridine 22T/22A yields 2-pyridylnitrene 19 as well as the novel open-chain cyanodienylnitrene 23 and the ring-expanded 1,3-diazacyclohepta-1,2,4,6-tetraene 21 on short wavelength photolysis. Nitrenes 19 and 23 were detected by ESR spectroscopy, and cumulene 21 by IR and UV spectroscopy. FVT of 22T/22A also affords 2-pyridylnitrene 19 and diazacycloheptatetraene 21, as well as glutacononitriles 27Z,E and 2- and 3-cyanopyrroles 28 and 29. Photolysis of 21 above 300 nm yields the novel spiroazirene 25, identified by its matrix IR spectrum. The reaction pathways connecting the four carbenes (10Z,E and 12Z,E) and three nitrenes (19, 23EZ, and 23ZZ) in their open-shell singlet and triplet states are elucidated with the aid of theoretical calculations at DFT, CASSCF, and CASPT2 levels. Three possible mechanisms of ring-contraction in arylnitrenes are identified: (i) via ring-opening to dienylnitrenes, (ii) concerted ring-contraction, and (iii) via spiroazirenes 25, whereby (i) is the energetically most favorable.

Onset of diradical character in small nanosized graphene patches

A family of small graphene patches, i.e., rectangular polyaromatic hydrocarbons (PAHs), that have both zigzag and armchair edges is investigated to establish their ground state electronic structure. Broken symmetry density functional theory (DFT) and plane wave DFT were used to characterize the onset of diradical character via relative energies of open-shell and closed-shell singlet states. The perfect pairing (PP) active space approximation of coupled cluster theory was used to characterize diradical character on the basis of promotion of electrons from occupied to unoccupied molecular orbitals. The role of zigzag and armchair edges in the formation of open-shell singlet states is elucidated. In particular, it is found that elongation of the zigzag edge results in an increase of diradical character whereas elongation of the arm chair edge leads to a decrease of diradical character. Analysis of orbitals from PP calculations suggests that diradical states are formally Mobius aromatic multiconfigurational systems.

The subtleties of explicitly correlated Z-averaged perturbation theory: Choosing an R12 method for high-spin open-shell molecules

Explicitly correlated MP2-R12 and coupled cluster R12 methods have proven to be effective in achieving the basis set limit of correlated wave function methods. However, correlated methods for high-spin open-shell states are typically based on semicanonical orbitals, leading to an unrestricted formalism, which for double excitations requires three independent sets of amplitudes. In contrast, Z-averaged perturbation theory redefines the Hamiltonian with a symmetric exchange operator, thereby allowing a spin-restricted formulation with equivalent alpha and beta subspaces. In the current work, we present a preliminary study of explicitly correlated ZAPT for second-order perturbation theory. The superior basis set convergence of R12 methods is demonstrated for a set of atomization energies, showing the R12 results to be competitive with common basis set extrapolation techniques, albeit at a fraction of the cost. Given the efficiency gains associated with the symmetric exchange operator, we suggest ZAPT as a candidate for reducing the cost of current open-shell MP2-R12 and CCSD(T)-R12 computations.