New tools for the systematic analysis and visualization of electronic excitations. I. Formalism

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2)

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

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.

Excitons in poly(para phenylene vinylene): a quantum-chemical perspective based on high-level ab initio calculations

Exciton analyses of high-level quantum-chemical computations for poly(paraphenylene vinylene) reveal the nature of the excitonic bands in PPV oligomers.

Connectivity matters – ultrafast isomerization dynamics of bisazobenzene photoswitches

We have investigated the ultrafast dynamics of o-, m- and p-bisazobenzenes, which represent elementary building blocks for photoswitchable multiazobenzene nanostructures.

X-Ray absorption spectra of microsolvated metal cations

Core excited states of microsolvated ions undergo substantial delocalisation whose degree strongly depends on the ion's charge.

Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconfigurational Ehrenfest approach

Photoinduced dynamics of electronic and vibrational unidirectional energy transfer between meta-linked building blocks in a phenylene ethynylene dendrimer is simulated using a multiconfigurational Ehrenfest in time-dependent diabatic basis (MCE-TDDB) method.

Graphyne and graphdiyne: theoretical insight into ground and excited state properties

The ground and excited state properties of the two carbon allotropes, graphyne (C₆₆H₁₈) (gr1) and graphdiyne (C₉₀H₁₈) (gr2), in the form of nanoflakes were studied with the help of density functional theory (DFT) and time dependent density functional theory (TDDFT).

Excited state analysis of absorption processes in metal decorated graphene nanoribbons

Transition density matrix (TDM) based excited state analysis presented for single metal atom doped graphene C₂₉H₁₄-X. Natural transition orbitals (NTOs) and e–h correlation plots of Ti-doped graphene are shown below.

Ultrafast structural flattening motion in photoinduced excited state dynamics of a bis(diimine) copper(i) complex

The intriguing ultrafast photoinduced structural change dynamics of a prototypical Cu(i) complex, namely, [Cu(dmp)₂]⁺ (dmp = 2,9-dimethyl-1,10-phenanthroline), is investigated based on the theoretical analysis of static and dynamical calculations at the all-atomic level.

Transition matrices and orbitals from reduced density matrix theory

In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.

Statistical analysis of electronic excitation processes: Spatial location, compactness, charge transfer, and electron-hole correlation

We report the development of a set of excited-state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual hole and electron densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge-resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge-resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited-state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core-excited states, and the possibility of using this information for an automatic characterization of state characters is discussed.

New tools for the systematic analysis and visualization of electronic excitations. II. Applications

The excited states of a diverse set of molecules are examined using a collection of newly implemented analysis methods. These examples expose the particular power of three of these tools: (i) natural difference orbitals (the eigenvectors of the difference density matrix) for the description of orbital relaxation effects, (ii) analysis of the one-electron transition density matrix in terms of an electron-hole picture to identify charge resonance and excitonic correlation effects, and (iii) state-averaged natural transition orbitals for a compact simultaneous representation of several states. Furthermore, the utility of a wide array of additional analysis methods is highlighted. Five molecules with diverse excited state characteristics are chosen for these tasks: pyridine as a prototypical small heteroaromatic molecule, a model system of six neon atoms to study charge resonance effects, hexatriene in its neutral and radical cation forms to exemplify the cases of double excitations and spin-polarization, respectively, and a model iridium complex as a representative metal organic compound. Using these examples a number of phenomena, which are at first sight unexpected, are highlighted and their physical significance is discussed. Moreover, the generality of the conclusions of this paper is verified by a comparison of single- and multireference ab initio methods.

Influence of base stacking geometry on the nature of excited states in G-quadruplexes: a time-dependent DFT study

G-quadruplexes are four-stranded structures of nucleic acids that are formed from the association of guanine nucleobases into cyclical arrangements known as tetrads. G-quadruplexes are involved in a host of biological processes and are of interest in nanomaterial applications. However, not much is known about their electronic properties. In this paper, we analyze electronic excited states of G-quadruplexes using a combination of time-dependent DFT calculations and molecular dynamics simulations. We systematically consider experimentally observed arrangements of stacked guanine tetrads. The effects of structural features on exciton delocalization and photoinduced charge separation are explored using a quantitative analysis of the transition electron density. It is shown that collective coherent excitations shared between two guanine nucleobases dominate in the absorption spectrum of stacked G-tetrads. These excitations may also include a significant contribution of charge transfer states. Large variation in exciton localization is also observed between different structures with a general propensity toward localization between two bases. We reveal large differences in how charge separation occurs within different nucleobase arrangements, with some geometries favoring separation within a single tetrad and others favoring separation between tetrads. We also investigate the effects of the coordinating K(+) ion located in the central cavity of G-quadruplexes on the relative excited state properties of such systems. Our results demonstrate how the nature of excited states in G-quadruplexes depends on the nucleobase stacking geometry resulting from the mutual arrangement of guanine tetrads.

Identifying and tracing potential energy surfaces of electronic excitations with specific character via their transition origins: application to oxirane

We show that the transition origins of electronic excitations identified by quantified natural transition orbital (QNTO) analysis can be employed to connect potential energy surfaces (PESs) according to their character across a wide range of molecular geometries.

Introducing asymmetry in tetradentate azadipyrromethene chromophores: a systematic study of the impact on electronic and photophysical properties

As analogues of the porphyrinoid and dipyrromethene families of dye, azadipyrromethene (ADPM) derivatives exhibit exciting photophysical properties.