A comparison of singlet and triplet states for one- and two-dimensional graphene nanoribbons using multireference theory

Five-Membered Rings Create Off-Zero Modes in Nanographene

The low-energy electronic structure of nanographenes can be tuned through zero-energy π-electron states, typically referred to as zero-modes. Customizable electronic and magnetic structures have been engineered by coupling zero-modes through exchange and hybridization interactions. Manipulation of the energy of such states, however, has not yet received significant attention. We find that attaching a five-membered ring to a zigzag edge hosting a zero-mode perturbs the energy of that mode and turns it into an off-zero mode: a localized state with a distinctive electron-accepting character. Whereas the end states of typical 7-atom-wide armchair graphene nanoribbons (7-AGNRs) lose their electrons when physisorbed on Au(111) (due to its high work function), converting them into off-zero modes by introducing cyclopentadienyl five-membered rings allows them to retain their single-electron occupation. This approach enables the magnetic properties of 7-AGNR end states to be explored using scanning tunneling microscopy (STM) on a gold substrate. We find a gradual decrease of the magnetic coupling between off-zero mode end states as a function of GNR length, and evolution from a more closed-shell to a more open-shell ground state.

Polyradical character assessment using multireference calculations and comparison with density-functional derived fractional occupation number weighted density analysis

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties. In this work, the unpaired electron densities and numbers of unpaired electrons (NU values) calculated at the high-level multireference averaged quadratic coupled-cluster (MR-AQCC) method are used to develop a test set to assess the capabilities of different biradical descriptors based on density functional theory. A benchmark collection of 29 different compounds has been selected. The DFT descriptors contain primarily the fractional occupation number weighted electron density (FOD) based on simplified thermally-assisted-occupation density functional theory (TAO-DFT) calculations, but the singlet-triplet energy difference and other descriptors denoted as y0 and nLUNO have been considered as well. After adjustment of the literature-recommended finite temperatures, a very good, detailed agreement between unpaired density and FOD analysis is observed which is also manifested in excellent statistical correlations. The other two descriptors also show good correlations even though the absolute scaling is not satisfactory. A new linear fit of FOD data to the MR-AQCC reference values leads to an improved regression relation for determining the recommended finite temperature value in dependence of the Hartree-Fock exchange. This provides the basis for fast and reliable assessment of the biradical character of many classes of PAHs without the need for performing computationally extended MR calculations.

Visualisation of Chemical Shielding Tensors (VIST) to Elucidate Aromaticity and Antiaromaticity

Aromaticity is a central concept in chemistry, pervading areas from biochemistry to materials science. Recently, chemists also started to exploit intricate phenomena such as the interplay of local and global (anti)aromaticity or aromaticity in non-planar systems and three dimensions. These phenomena pose new challenges in terms of our fundamental understanding and the practical visualisation of aromaticity. To overcome these challenges, a method for the visualisation of chemical shielding tensors (VIST) is developed here that allows for a 3D visualisation with quantitative information about the local variations and anisotropy of the chemical shielding. After exemplifying the method in different planar hydrocarbons, we study two non-planar macrocycles to show the unique benefits of the VIST method for molecules with competing π-conjugated systems and conclude with a norcorrole dimer showing clear evidence of through-space aromaticity. We believe that the VIST method will be a highly valuable addition to the computational toolbox.

Spin-Flip Pair-Density Functional Theory: A Practical Approach To Treat Static and Dynamical Correlations in Large Molecules

We present a practical approach to treat static and dynamical correlation accurately in large multiconfigurational systems. The static correlation is taken into account by using the spin-flip approach, which is well-known for capturing static correlation accurately at low-computational expense. Unlike previous approaches to add dynamical correlation to spin-flip models which use perturbation theory or coupled-cluster theory, we explore the ability to use the on-top pair-density functional theory approaches recently developed by Gagliardi and co-workers (J. Comput. Theor. Chem., 2014, 10, 3669). External relaxations are performed in the spin-flip calculations through a restricted active space framework for which a truncation scheme for the orbitals used in the external excitation is presented. The performance of the approach is demonstrated by computing energy gaps between ground and excited states for diradicals, triradicals, and linear polyacene chains ranging from naphthalene to dodecacene. Accurate results are obtained using the new approach for these challenging open-shell molecular systems.

Unravelling the Open-Shell Character of Peripentacene on Au(111)

Polycyclic aromatic hydrocarbons (PAHs) are a family of organic compounds comprising two or more fused aromatic rings which feature manifold applications in modern technology. Among these species, those presenting an open-shell magnetic ground state are of particular interest for organic electronic, spintronic, and non-linear optics and energy storage devices. Within PAHs, special attention has been devoted in recent years to the synthesis and study of the acene and fused acene (periacene) families, steered by their decreasing HOMO-LUMO gap with length and predicted open-shell character above some size. However, an experimental fingerprint of such magnetic ground state has remained elusive. Here, we report on the in-depth electronic characterization of isolated peripentacene molecules on a Au(111) surface. Scanning tunnelling spectroscopy, complemented by computational investigations, reveals an antiferromagnetic singlet ground state, characterized by singlet-triplet inelastic excitations with an experimental effective exchange coupling (J_eff) of 40.5 meV. Our results deepen the fundamental understanding of organic compounds with magnetic ground states, featuring perspectives in carbon-based spintronic devices.

Diradical Organic One-Dimensional Polymers Synthesized on a Metallic Surface

We report on the synthesis and characterization of atomically precise one-dimensional diradical peripentacene polymers on a Au(111) surface. By means of high-resolution scanning probe microscopy complemented by theoretical simulations, we provide evidence of their magnetic properties, which arise from the presence of two unpaired spins at their termini. Additionally, we probe a transition of their magnetic properties related to the length of the polymer. Peripentacene dimers exhibit an antiferromagnetic (S=0) singlet ground state. They are characterized by singlet-triplet spin-flip inelastic excitations with an effective exchange coupling (Jeff ) of 2.5 meV, whereas trimers and longer peripentacene polymers reveal a paramagnetic nature and feature Kondo fingerprints at each terminus due to the unpaired spin. Our work provides access to the precise fabrication of polymers featuring diradical character which are potentially useful in carbon-based optoelectronics and spintronics.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

Toward an understanding of electronic excitation energies beyond the molecular orbital picture

Can we gain an intuitive understanding of excitation energies beyond the molecular picture?

From cyclic nanorings to single-walled carbon nanotubes: disclosing the evolution of their electronic structure with the help of theoretical methods

We systematically investigate the relationships between structural and electronic effects of finite size zigzag or armchair carbon nanotubes of various diameters and lengths, starting from a molecular template of varying shape and diameter, i.e. cyclic oligoacene or oligophenacene molecules, and disclosing how adding layers and/or end-caps (i.e. hemifullerenes) can modify their (poly)radicaloid nature. We mostly used tight-binding and finite-temperature density-based methods, the former providing a simple but intuitive picture about their electronic structure, and the latter dealing effectively with strong correlation effects by relying on a fractional occupation number weighted electron density (ρFOD), with additional RAS-SF calculations backing up the latter results. We also explore how minor structural modifications of nanotube end-caps might influence the results, showing that topology, together with the chemical nature of the systems, is pivotal for the understanding of the electronic properties of these and other related systems.

A Practical General Method for the Preparation of Long Acenes

The field of long acenes, the narrowest of the zig-zag graphene nanoribbons, has been an area of significant interest in the past decade because of its potential applications in organic electronics, spintronics and plasmonics. However the low solubility and high reactivity of these compounds has so far hindered their preparation on large scales. We report here a concise strategy for the synthesis of higher acenes through Diels-Alder condensation of arynes with a protected tetraene ketone. After deprotection by cleavage of the ketal, the obtained monoketone precursors cleanly yield the corresponding acenes through quantitative cheletropic thermal decarbonylation in the solid state, at moderate temperatures of 155 to 205 °C. This approach allows the preparation of heptacene, benzo[a]hexacene, cis- and trans-dibenzopentacene and offers a valuable new method for the synthesis of even larger acenes.

Automatic Construction of the Initial Orbitals for Efficient Generalized Valence Bond Calculations of Large Systems

We propose an efficient general strategy for generating initial orbitals for generalized valence bond (GVB) calculations which makes routine black-box GVB calculations on large systems feasible. Two schemes are proposed, depending on whether the restricted Hartree-Fock (RHF) wave function is stable (scheme I) or not (scheme II). In both schemes, the first step is the construction of active occupied orbitals and active virtual orbitals. In scheme I, active occupied orbitals are composed of the valence orbitals (the inner core orbitals are excluded), and the active virtual orbitals are obtained from the original virtual space by requiring its maximum overlap with the virtual orbital space of the same system at a minimal basis set. In scheme II, active occupied orbitals and active virtual orbitals are obtained from the set of unrestricted natural orbitals (UNOs), which are transformed from two sets of unrestricted HF spatial orbitals. In the next step, the active occupied orbitals and active virtual ones are separately transformed to localized orbitals. Localized occupied and virtual orbital pairs are formed using the Kuhn-Munkres (KM) algorithm and are used as the initial guess for the GVB orbitals. The optimized GVB wave function is obtained using the second-order self-consistent-field algorithm in the GAMESS program. With this procedure, GVB energies have been obtained for the lowest singlet and triplet states of polyacenes (up to decacene with 96 pairs) and the singlet ground state of two di-copper-oxygen-ammonia complexes. We have also calculated the singlet-triplet gaps for some polyacenes and the relative energy between two di-copper-oxygen-ammonia complexes with the block-correlated second-order perturbation theory based on the GVB reference.

The stability limits of highly active nitrogen doped carbon ORR nano-catalysts: a mechanistic study of degradation reactions

A new approach in electrode catalysis bearing immense potential for electrochemical technologies is the prospect of carbon-based electrodes. Pristine carbon nanostructures are relatively inert and modifications like nitrogen doping are known for their beneficial effects on the electrochemical activity of carbon nanomaterials in both alkaline and acidic media. However, the long-term stability of these materials, especially in an acidic environment, is rarely mentioned. Here, we evaluate the stability and long-term degradation of nitrogen doped graphene flakes as an oxygen reduction electrocatalyst with theoretical and experimental techniques. We assume that nitrogen dopants in the graphene sheet interact with e- and H+ at the electrode-electrolyte interface, leading to NH3 scission and continuous catalyst deactivation. With Density Functional Theory calculations, NH3 scission pathways of pyridinic, graphitic and pyrrolic nitrogen species were analyzed and compared under different operating conditions which are relevant for low and intermediate temperature fuel cells. The computational results are correlated with electrochemical measurements in solid acid fuel cells in a humidified oxygen environment at 240 °C.

The role of topology in organic molecules: origin and comparison of the radical character in linear and cyclic oligoacenes and related oligomers

We discuss the nature of electron-correlation effects in carbon nanorings and nanobelts by a combined approach based on FT-DFT and RAS-SF methods.

Singlet La and Lb Bands for N-Acenes (N = 2-7): A CASSCF/CASPT2 Study

In this work CASPT2 calculations of polyacenes (from naphthalene to heptacene) were performed to find a methodology suitable for calculations of the absorption spectra, in particular of the L_a (B_2u state) and L_b (B_3u state) bands, of more extended systems. The effect of the extension of the active space and of freezing σ orbitals was investigated. The MCSCF excitation energy of the B_2u state is not sensitive to the size of the active space used. However, the CASPT2 results depend strongly on the amount of σ orbitals frozen reflecting the ionic character of the B_2u state. On the other hand, the excitation energies of the B_3u state are much more sensitive to the size of the active space used in the calculations reflecting its multiconfigurational character. We found a good agreement with experimental data for both bands by including 14 electrons in 14 π orbitals in the active space followed by the CASPT2(14,14) perturbation scheme in which both σ and π orbitals are included.

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. We recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functional theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet-triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet-triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.

How to efficiently tune the biradicaloid nature of acenes by chemical doping with boron and nitrogen

Strong modulation of the biradical character of acenes with dopant positions is demonstrated by tracking the unpaired electron densities.

Fast Degradation for High Activity: Oxygen- and Nitrogen-Functionalised Carbon Nanotubes in Solid-Acid Fuel-Cell Electrodes

Similar to polymer electrolyte membrane fuel cells, the widespread application of solid acid fuel cells (SAFCs) has been hindered partly by the necessity of the use of the precious-metal catalyst Pt in the electrodes. Here we investigate multi-walled carbon nanotubes (MWCNTs) for their potential catalytic activity by using symmetric cell measurements of solid-acid-based electrochemical cells in a cathodic environment. For all measurements, the carbon nanotubes were Pt free and subject to either nitrogen or oxygen plasma treatment. AC impedance spectroscopy of the electrochemical cells, with and without a DC bias, was performed and showed significantly lower initial impedances for oxygen-plasma-treated MWCNTs compared to those treated with a nitrogen plasma. In symmetric cell measurements with a DC bias, the current declines quickly for oxygen-plasma-treated MWCNTs and more slowly, over 12 days, for nitrogen-plasma-treated MWCNTs. To elucidate the degradation mechanisms of the oxygen-plasma-treated MWCNTs under SAFC operating conditions, theoretical calculations were performed using DFT. The results indicate that several degradation mechanisms are likely to occur in parallel through the reduction of the surface oxygen groups that were introduced by the plasma treatment. This finally leads to an inert MWCNT surface and a very low electrode performance. Nitrogen-plasma-treated MWCNTs appear to have a higher stability and may be worthwhile for future investigations.

Role of Kekulé and Non-Kekulé Structures in the Radical Character of Alternant Polycyclic Aromatic Hydrocarbons: A TAO-DFT Study

We investigate the role of Kekulé and non-Kekulé structures in the radical character of alternant polycyclic aromatic hydrocarbons (PAHs) using thermally-assisted-occupation density functional theory (TAO-DFT), an efficient electronic structure method for the study of large ground-state systems with strong static correlation effects. Our results reveal that the studies of Kekulé and non-Kekulé structures qualitatively describe the radical character of alternant PAHs, which could be useful when electronic structure calculations are infeasible due to the expensive computational cost. In addition, our results support previous findings on the increase in radical character with increasing system size. For alternant PAHs with the same number of aromatic rings, the geometrical arrangements of aromatic rings are responsible for their radical character.

The Antiferromagnetic Spin Coupling in Non-Kekulé Acenes-Impressive Polyradical Character Revealed by High-Level Multireference Methods

Complete active space (CASSCF) and multireference (MR-CISD(Q) and MR-AQCC) calculations were performed for non-Kekulé analogues of acenes, dimethylenepolycyclobutadienes, with lengths of up to eight cyclobutadiene (CBD) units. Multireference calculations predict that the most stable energy state of the system is either triplet (if there is an odd number of CBD units) or singlet (if there is an even number of CBD units) due to antiferromagnetic spin coupling, which thus violates Hund's rule in larger molecules. We also show an impressive polyradical character in the system that increases with the size of the molecule, as witnessed by more than eleven unpaired electrons in the singlet state of the molecule with eight CBD units. Together with the small energy gap between singlet and higher multiplicity energy states even above the triplet state, this demonstrates the exceptional polyradical properties of these π-conjugated oligomeric chains.

Polyradical Character of Triangular Non-Kekulé Structures, Zethrenes, p-Quinodimethane-Linked Bisphenalenyl, and the Clar Goblet in Comparison: An Extended Multireference Study

In this work, two different classes of polyaromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekulé triangular structures phenalenyl, triangulene and a π-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet containing varying polyradical character in their singlet ground state. The first class of structures already have open-shell character because of their high-spin ground state, which follows from the bonding pattern, whereas for the second class the open-shell character is generated either because of the competition between the closed-shell quinoid Kekulé and the open-shell singlet biradical resonance structures or the topology of the π-electron arrangement of the non-Kekulé form. High-level ab initio calculations based on multireference theory have been carried out to compute singlet–triplet splitting for the above-listed compounds and to provide insight into their chemical reactivity based on the polyradical character by means of unpaired densities. Unrestricted density functional theory and Hartree–Fock calculations have been performed for comparison also in order to obtain better insight into their applicability to these types of complicated radical systems.

Electronic Properties of Zigzag Graphene Nanoribbons Studied by TAO-DFT

Accurate prediction of the electronic properties of zigzag graphene nanoribbons (ZGNRs) has been very challenging for conventional electronic structure methods due to the presence of strong static correlation effects. To meet the challenge, we study the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy (i.e., a measure of polyradical character) of hydrogen-terminated ZGNRs with different widths and lengths using our recently developed thermally-assistedoccupation density functional theory (TAO-DFT) [Chai, J.-D. J. Chem. Phys. 2012, 136, 154104], a very efficient method for the study of large strongly correlated systems. Our results are in good agreement with the available experimental and high-accuracy ab initio data. The ground states of ZGNRs are shown to be singlets for all the widths and lengths investigated. With the increase of ribbon length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy increase monotonically. On the basis of the calculated orbitals and their occupation numbers, the longer ZGNRs are shown to possess increasing polyradical character in their ground states, where the active orbitals are mainly localized at the zigzag edges.

Electronic and Optical Properties of the Narrowest Armchair Graphene Nanoribbons Studied by Density Functional Methods

In the present study, a series of planar poly(p-phenylene) (PPP) oligomers with n phenyl rings (n = 1–20), designated as n-PP, are taken as finite-size models of the narrowest armchair graphene nanoribbons with hydrogen passivation. The singlet-triplet energy gap, vertical ionization potential, vertical electron affinity, fundamental gap, optical gap, and exciton binding energy of n-PP are calculated using Kohn-Sham density functional theory and time-dependent density functional theory with various exchange-correlation density functionals. The ground state of n-PP is shown to be singlet for all the chain lengths studied. In contrast to the lowest singlet state (i.e., the ground state) of n-PP, the lowest triplet state of n-PP and the ground states of the cation and anion of n-PP are found to exhibit some multi-reference character. Overall, the electronic and optical properties of n-PP obtained from the ωB97 and ωB97X functionals are in excellent agreement with the available experimental data.

Shedding light on the soft and efficient free radical induced reduction of graphene oxide: hidden mechanisms and energetics

Reduction of graphene oxide in aqueous dispersions by strongly reducing free radicals has been found to be a very powerful approach – functional groups are removed softly but efficiently, and non-volatile impurities as well as defects are avoided.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.