Gunter Hermann

ORBKIT: A modular python toolbox for cross‐platform postprocessing of quantum chemical wavefunction data

ORBKIT is a toolbox for postprocessing electronic structure calculations based on a highly modular and portable Python architecture. The program allows computing a multitude of electronic properties of molecular systems on arbitrary spatial grids from the basis set representation of its electronic wavefunction, as well as several grid‐independent properties. The required data can be extracted directly from the standard output of a large number of quantum chemistry programs. ORBKIT can be used as a standalone program to determine standard quantities, for example, the electron density, molecular orbitals, and derivatives thereof. The cornerstone of ORBKIT is its modular structure. The existing basic functions can be arranged in an individual way and can be easily extended by user‐written modules to determine any other derived quantity. ORBKIT offers multiple output formats that can be processed by common visualization tools (VMD, Molden, etc.). Additionally, ORBKIT possesses routines to order molecular orbitals computed at different nuclear configurations according to their electronic character and to interpolate the wavefunction between these configurations. The program is open‐source under GNU‐LGPLv3 license and freely available at https://github.com/orbkit/orbkit/. This article provides an overview of ORBKIT with particular focus on its capabilities and applicability, and includes several example calculations.

Multidirectional Angular Electronic Flux during Adiabatic Attosecond Charge Migration in Excited Benzene

Recently, adiabatic attosecond charge migration (AACM) has been monitored and simulated for the first time, with application to the oriented iodoacetylene cation where AACM starts from the initial superposition of the ground state (φ0) and an electronic excited state (φ1). Here, we develop the theory for electronic fluxes during AACM in ring-shaped molecules, with application to oriented benzene prepared in the superposition of the ground and first excited singlet states. The initial state and its time evolution are analogous to coherent tunneling where φ0 and φ1 have different meanings; however, they denote the wave functions of the lowest tunneling doublet. This analogy suggests to transfer the theory of electronic fluxes during coherent tunneling to AACM, with suitable modifications which account for (i) the different time scales and (ii) the different electronic states, and which make use of (iii) the preparation of the initial state for AACM by a linearly polarized laser pulse. Application to benzene yields the multidirectional angular electronic flux with a pincer-motion type pattern during AACM: this unequivocal result confirms a previous working hypothesis. Moreover, the theory of AACM allows quantification of the electronic flux; that is, the maximum number of electrons (out of 42) which flow concertedly during AACM in benzene is 6 × 0.08 = 0.48.

Imaging the Ultrafast Photoelectron Transfer Process in Alizarin-TiO2

In this work, we adopt a quantum mechanical approach based on time-dependent density functional theory (TDDFT) to study the optical and electronic properties of alizarin supported on TiO2 nano-crystallites, as a prototypical dye-sensitized solar cell. To ensure proper alignment of the donor (alizarin) and acceptor (TiO2 nano-crystallite) levels, static optical excitation spectra are simulated using time-dependent density functional theory in response. The ultrafast photoelectron transfer from the dye to the cluster is simulated using an explicitly time-dependent, one-electron TDDFT ansatz. The model considers the δ-pulse excitation of a single active electron localized in the dye to the complete set of energetically accessible, delocalized molecular orbitals of the dye/nano-crystallite complex. A set of quantum mechanical tools derived from the transition electronic flux density is introduced to visualize and analyze the process in real time. The evolution of the created wave packet subject to absorbing boundary conditions at the borders of the cluster reveal that, while the electrons of the aromatic rings of alizarin are heavily involved in an ultrafast charge redistribution between the carbonyl groups of the dye molecule, they do not contribute positively to the electron injection and, overall, they delay the process.

An open-source framework for analyzing N-electron dynamics. I. Multideterminantal wave functions

The aim of the present contribution is to provide a framework for analyzing and visualizing the correlated many‐electron dynamics of molecular systems, where an explicitly time‐dependent electronic wave packet is represented as a linear combination of N‐electron wave functions. The central quantity of interest is the electronic flux density, which contains all information about the transient electronic density, the associated phase, and their temporal evolution. It is computed from the associated one‐electron operator by reducing the multideterminantal, many‐electron wave packet using the Slater‐Condon rules. Here, we introduce a general tool for post‐processing multideterminant configuration‐interaction wave functions obtained at various levels of theory. It is tailored to extract directly the data from the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions. The procedure is implemented in the open‐source Python program detCI@ORBKIT, which shares and builds on the modular design of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). The new procedure is applied to ultrafast charge migration processes in different molecular systems, demonstrating its broad applicability. Convergence of the N‐electron dynamics with respect to the electronic structure theory level and basis set size is investigated. This provides an assessment of the robustness of qualitative and quantitative statements that can be made concerning dynamical features observed in charge migration simulations.

Ultrafast photoelectron migration in dye-sensitized solar cells: Influence of the binding mode and many-body interactions

In the present contribution, the ultrafast photoinduced electron migration dynamics at the interface between an alizarin dye and an anatase TiO2 thin film is investigated from first principles. Comparison between a time-dependent many-electron configuration interaction ansatz and a single active electron approach sheds light on the importance of many-body effects, stemming from uniquely defined initial conditions prior to photoexcitation. Particular emphasis is put on understanding the influence of the binding mode on the migration process. The dynamics is analyzed on the basis of a recently introduced toolset in the form of electron yields, electronic fluxes, and flux densities, to reveal microscopic details of the electron migration mechanism. From the many-body perspective, insight into the nature of electron-electron and hole-hole interactions during the charge transfer process is obtained. The present results reveal that the single active electron approach yields quantitatively and phenomenologically similar results as the many-electron ansatz. Furthermore, the charge migration processes in the dye-TiO2 model clusters with different binding modes exhibit similar mechanistic pathways but on largely different time scales.

An open-source framework for analyzing N-electron dynamics. II. Hybrid density functional theory/configuration interaction methodology

In this contribution, we extend our framework for analyzing and visualizing correlated many‐electron dynamics to non‐variational, highly scalable electronic structure method. Specifically, an explicitly time‐dependent electronic wave packet is written as a linear combination of N‐electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time‐dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open‐source Python program detCI@ORBKIT, which extends the capabilities of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one‐electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser‐driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher‐level method provided a judicious choice of functional is made. Broadband excitation of a medium‐sized organic chromophore further demonstrates the scalability of the method. In addition, the time‐dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance.

Influence of Mesoionic Carbenes on Electro- and Photoactive Ru and Os Complexes: A Combined (Spectro-)Electrochemical, Photochemical, and Computational Study

In recent years, mesoionic carbenes (MICs) are finding increasing use as building blocks of electro- and photoactive metal complexes. We present here a series of RuII and OsII polypyridine complexes where one or two pyridyl moieties of the well-known tris(bipyridine) analogues are replaced by MICs. We probe the structural, electrochemical, UV-vis-NIR/electron paramagnetic resonance spectroelectrochemical, and photophysical properties of these complexes as a function of the number of MICs in them. Insights from theoretical studies are used to describe the electronic structures of the various redox states. Additionally, electron flux density calculations provide an idea of the flow of electron densities in the excited states of these molecules. This is the first time that such electron flux density calculations are used to probe the excited state properties of transition metal complexes. Our results conclusively prove that the incorporation of MICs into Ru/Os-polypyridyl complexes has a profound influence on the ground and the excited state redox potentials, the position of the emission bands, as well as on the lifetimes of the excited states. These observations might thus be useful for the generation of novel photocatalysts and photosensitizers for dye-sensitized-solar-cells based on MICs.

Charge Effects on the Efflorescence in Single Levitated Droplets

The influence of electrical excess charges on the crystallization from supersaturated aqueous sodium chloride solutions is reported. This is accomplished by efflorescence studies on single levitated microdroplets using optical and electrodynamic levitation. Specifically, a strong increase in efflorescence humidity is observed as a function of the droplets negative excess charge, ranging up to -2.1 pC, with a distinct threshold behavior, increasing the relative efflorescence humidity, at which spontaneous nucleation occurs, from 44% for the neutral microparticle to 60%. These findings are interpreted by using molecular dynamics simulations for determining plausible structural patterns located near the particle surface that could serve as suitable precursors for the formation of critical clusters overcoming the nucleation barrier. These results, facilitating heterogeneous nucleation in the case of negatively charged microparticles, are compared to recent work on charge-induced nucleation of neat supercooled water, where a distinctly different nucleation behavior as a function of droplet charge has been observed.

Charge Migration in Eyring, Walter and Kimball’s 1944 Model of the Electronically Excited Hydrogen-Molecule Ion

In an elementary variational treatment of the electronic structure of H2+, Eyring, Walter, and Kimball (EWK) serendipitously discovered charge migration (CM) in 1944. Using an analytic expression for the electronic probability density (EPD), they found that if the electron is initially localized on one of the protons (by taking the initial state to be a superposition of the ground and first excited electronic energy eigenstates), then it oscillates adiabatically between fixed protons with a period T inversely proportional to the energy gap between the eigenstates. At the equilibrium internuclear separation, T = 550.9 as. As shown here, the EWK model also yields an analytic formula for the electronic flux density (EFD). While the EPD indicates where the electron is at any instant, the EFD reveals the pathways the electron follows during its migration. Thus, the EFD complements the EPD, providing valuable new insight into the mechanism of CM. The formula for the EFD is a simple product of a time factor and a spatial factor. This factoring exposes a plethora of spatial-temporal symmetry relations which imply novel and surprising properties. An especially significant finding is that, in contrast to multielectron systems, where electron correlation may play a role in CM, in the EWK model of H2+, CM is due strictly to quantum interference between the ground and first excited electronic states.