Electronic structure of rhombus-shaped nanographenes: system size evolution from closed- to open-shell ground states.

We theoretically study and characterize a set of rhombus-shaped nanographenes of increasing size, or n-rhombenes, where n = 2-6, displaying zigzag edges leading to an enhancement of the (poly)radicaloid nature and the appearance of intrinsic magnetism as a function of n. Due to that system-dependent radicaloid nature, we employ spin-flip methods able to capture the challenging physics of the problem, thus providing accurate energy differences between high- and low-spin solutions. The theoretical predictions agree with the experimentally available magnetic exchange coupling for the recently synthesized 5-rhombene, as well as with the size at which the transition from a closed-shell to an open-shell ground-state solution occurs. We also investigate if standard DFT methods are able to reproduce the trend disclosed by spin-flip methods and if the results are highly dependent on the functional choice and/or the intrinsic spin contamination.

peri-Acenoacene molecules: tuning of the singlet and triplet excitation energies by modifying their radical character.

The energy difference between singlet and triplet excitons, or ΔEST, is a key parameter for novel light-emission mechanisms (i.e., TADF or thermally activated delayed fluorescence) or other photoactivated processes. We have studied a set of conjugated molecules (peri-acenoacenes and their heteroatom-doped analogues) to observe the evolution of their excited-state properties upon increasing the system size with and without substitution with a pair of N atoms. Since these molecules exhibit a (ground-state) diradicaloid character, together with marked correlation effects influencing the excited-states formed, we have applied a variety of theoretical methods (FT-DFT, TD-DFT, SF-TD-DFT, CIS, CIS(D), SCS-CC2, SA-CASSCF, and SC-NEVPT2) to bracket the accuracy of the results while concomitantly providing insights into electronic structure. The results show how this chemical strategy (N-doping) largely modifies not only the excited-state energies but also the oscillator strengths and the ΔEST values, constituting versatile platforms for fine-tuned photophysical applications.

Singlet-Triplet Excited-State Inversion in Heptazine and Related Molecules: Assessment of TD-DFT and ab initio Methods.

We have investigated the origin of the S1 -T1 energy levels inversion for heptazine, and other N-doped π-conjugated hydrocarbons, leading thus to an unusually negative singlet-triplet energy gap ( ΔEST<0 ). Since this inversion might rely on substantial doubly-excited configurations to the S1 and/or T1 wavefunctions, we have systematically applied multi-configurational SA-CASSCF and SC-NEVPT2 methods, SCS-corrected CC2 and ADC(2) approaches, and linear-response TD-DFT, to analyze if the latter method could also face this challenging issue. We have also extended the study to B-doped π-conjugated systems, to see the effect of chemical composition on the results. For all the systems studied, an intricate interplay between the singlet-triplet exchange interaction, the influence of doubly-excited configurations, and the impact of dynamic correlation effects, serves to explain the ΔEST<0 values found for most of the compounds, which is not predicted by TD-DFT.

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 using an analysis tool known as fractional occupation number weighted electron density (ρFOD) and the RAS-SF method, revealing for the first time significant differences in static correlation effects depending on how the rings (i.e. chemical units) are fused and/or connected until closing the loop. We choose to study in detail linear and cyclic oligoacene molecules of increasing size, and relate the emerging differences with the difficulties for the synthesis of the latter due to their radicaloid character. We finally explore how minor structural modifications of the cyclic forms can alter these results, showing the potential use of these systems as molecular templates for the growth of well-shaped carbon nanotubes as well as the usefulness of theoretical tools for molecular design.

Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems? PAH and graphene.

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an 'effective' Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

Improvements in DFT Calculations of Spin-Spin Coupling Constants.

Different types of spin-spin coupling constants (SSCCs) for several representative small molecules are evaluated and analyzed using a combination of 10 exchange functionals with 12 correlation functionals. For comparison, calculations performed using MCSCF, SOPPA, other common DFT methods, and also experimental data are considered. A detailed study of the percentage of Hartree-Fock exchange energy in SSCCs and in its four contributions is carried out. From the above analysis, a combined functional formed with local Slater (34%), Hartree-Fock exchange (66%), and P86 correlation functional (S66P86) is proposed in this paper. The accuracy of the values obtained with this hybrid functional (mean absolute deviation of 4.5 Hz) is similar to that of the SOPPA method (mean absolute deviation of 4.6 Hz).

Prediction of the secondary structure and functional sites of major histocompatibility complex molecules.

A method for the theoretical prediction of the antigenic determinants and the antigen-interactive receptor sites of immunological proteins from their primary structure would constitute a useful tool for their study. Such a method developed in this laboratory uses hydrophilicity, accessibility, flexibility, and recognition profiles, together with the predicted secondary structure (alpha-helices, beta-sheets, and turns). The secondary structure is determined by a modification of the method of Lim (1974), as described below. A study of human and mouse class I and class II major histocompatibility complex (MHC) antigens, central to the regulation of immune responses and to the phenomenon of graft rejection, was carried out using the above method. Comparison of the predictions with some of the available experimental and theoretical information supports the validity and usefulness of the approach.