Modified participation ratio approach: application to edge-localized states in carbon nanoclusters

For nanoclusters and solids, the localization analysis of one-electron states, or MOs (molecular orbitals), is frequently provided by using the so-called participation ratio (PR) index. To this conventional PR approach, we add for each MO the new index σIPR which we define as an average fluctuation of the inverse PR (IPR) value. Typically, the σIPR index displays a significant sensitivity to any spatial irregularity in the MO distribution over molecule. We apply the thus extended PR analysis to the graphene nanoflakes of different types, and small nanodiamond structures including NV color centers as well. The proposed scheme has the virtue of being quite simple, and in case of huge clusters it allows one to rapidly detect orbitals with unusual non-uniform distribution. In particular, the localization of edge states in graphene molecules is examined in this way

Single-molecule electronic materials. Conductance of π-conjugated oligomers within quasi-correlated tight-binding model

For computing electric conductance through organic nanowire of conjugated type we make use of the recently proposed quasi-correlated tight-binding (QCTB) method. The appropriate Green's function (GF) matrices are constructed, and simple numerical algorithms are given for them. Moreover, the GF analytical solutions are obtained for finite-sized polyene chains and other systems. A special attention is paid to conjugated oligomers with various strength of electron correlation. In particular, we find that in polyquinoids the conventional Huckel and restricted Hartree-Fock methods lead, in contrast to QCTB, to a nonphysical increase of GF matrix elements for far separate contacts

Kirchhoff and electron curvature indexes for SiC nanoclusters

To characterize carborundum nanoclusters (nano-SiC) we employ the topological Kirchhoff index and average energy of molecular graphs. Additionally, electron-kinematic indexes which reflect an average curvature of electron paths in molecule, are invoked. The main polytypes, namely, 3C-SiC and 2pH-SiC, p = 1÷4, are investigated. It is established that the topological indexes make only a slight distinction between nano-SiC of the different polytypes. Quite the opposite, the electron curvature indexes provide a clear discrimination of the polytypes. In particular, the curvature indexes are ordered just in the same manner as the hexagonality measure known for such polytypes. For the electron curvatures, an effective algorithm is elaborated, allowing us to analyze nano-SiC with 10⁴ and more atoms even by using laptops

Simplified computations of spin excitations in high-spin carbon nanoclusters and related systems

Spin excitation spectra for possible molecule-based magnetic structures are evaluated semiempirically. A simplest spin-flip model with singly-excited configurations (SF-CIS) is used. While only a small amount of electron correlation is captured by the SF-CIS scheme, it turns out to be practically useful tool for computing quasi-magnon spectra in large polyradicals. We study examples of three different structural types (graphene nanoribbon with methylene edges, triangulene and Mataga-type model organic ferromagnet). We demonstrate that these systems show different behavior of the spin excitation spectra and different spin heat capacity temperature dependences. It is also shown that the same SF-CIS technique can be useful for describing high-spin states in nanodiamonds with defects

Effectively unpaired electrons in bipartite lattices within the generalized tight-binding approximation: application to graphene nanoflakes

A semiempirical technique is proposed for bipartite structures (lattice-like systems with two interpenetrating sublattices). For such systems, the corresponding one-electron tight-binding model can be easily modified to include electron correlation effects, although in a rough manner. It allows one to describe the so-called effectively unpaired electrons (EUE) in giant many-electron systems by using even uncomplicated hardware. The average EUE occupancy is interpreted as a counterpart of the order parameter reflecting a hidden antiferromagnetic structure of the strongly correlated system. We illustrate the developed method by analyzing EUE for several model problems (nanoflakes and nanoribbons) mimicking the graphene-based materials

Excited state structural analysis for correlated many-electron systems

The excited states structural analysis (ESSA) which was previously developed by the author and coll. (1980, 2010) is extended to a typical equation-of-motion approach within the coupled cluster theory. The extended ESSA allows one to interpret highly correlated excited states, particularly those which occur in molecular singlet fission processes and related optoelectronic devices

About theoretical peculiarities of lowest excitations in modified nanodiamond color centers

The moderate-size carbon nanoclusters with paramagnetic color centers are studied by using a rather good-working simplified scheme of CNDOL type. Various electronic structure aspects of the clusters are studied. These are the localization of molecular orbitas, the electronic excitation localization and charge-transfer structure of the lowest triplet-triplet transitions, spin density distributions and spin correlations in the ground and excited states. The comparison is made between the respective characteristics of the diamondoid with nitrogen-vacancy (NV⁻) and oxygen-vacancy color centers. It is shown that in the asymmetrical NV⁻ center, significant variations of excitation localization and charge/spin transfer take place whereas the energetic properties vary slightly

Positive chirality measures from chiroptical pseudoscalars: applications to carbon-containing molecular systems

A new chirality quantification scheme is proposed based on a special procedure transforming molecular pseudoscalar into positive index. The optical rotatory strengths (estimated semiempirically) are used for the corresponding characterization of chiral molecules. We show several specific examples of using the present method. The focus is made on dissymmetric π-conjugated systems constituting some special molecular materials (helicens etc.). A simplified technique of partitioning the chirality index into atomic contributions is reported. For most presented examples, the atomic distribution of chirality are found to be highly delocalized over the whole carbon backbone

Excited state structural analysis (ESSA) for correlated states of spin-flip type: application to electronic excitations in nanodiamonds with defects

The previously developed ESSA for configuration interaction singles (CIS) method is extended to a more rigorous many-body theory of excited states based on spin-flip (SF) transformations. The so-called SF-CIS (SF approach for CIS) is used, and the respective ESSA indices are constructed. These are atomic excitation indexes L*A, interatomic charge-transfer numbers lA - > B, and others. By using these quantities, low-lying excitations in the modelled nanodiamonds with color centers (first of all, nitrogen-vacancy (NV) centers) are investigated at a semiempirical level of the theory. It is shown that the lowest excitations are significantly localized in a vicinity of the vacancy. Furthermore, the same excitations are characterized by a high interatomic charge transfer. All these features are common to both types of the NV centers (neutral NV0 and negative NV-)