Electronic Spectra from TDDFT and Machine Learning in Chemical Space

Due to its favorable computational efficiency time-dependent (TD) density functional theory (DFT) enables the prediction of electronic spectra in a high-throughput manner across chemical space. Its predictions, however, can be quite inaccurate. We resolve this issue with machine learning models trained on deviations of reference second-order approximate coupled-cluster singles and doubles (CC2) spectra from TDDFT counterparts, or even from DFT gap. We applied this approach to low-lying singlet-singlet vertical electronic spectra of over 20 thousand synthetically feasible small organic molecules with up to eight CONF atoms. The prediction errors decay monotonously as a function of training set size. For a training set of 10 thousand molecules, CC2 excitation energies can be reproduced to within $\pm$0.1 eV for the remaining molecules. Analysis of our spectral database via chromophore counting suggests that even higher accuracies can be achieved. Based on the evidence collected, we discuss open challenges associated with data-driven modeling of high-lying spectra, and transition intensities

Ab initio simulation of the ultrafast circular dichroism spectrum of provitamin D ring-opening

We present a method to simulate ultrafast pump-probe time-resolved circular dichroism (TRCD) spectra based on time-dependent density functional theory trajectory surface hopping. The method is applied to simulate the TRCD spectrum along the photoinduced ring-opening of provitamin D. Simulations reveal that the initial decay of the signal is due to excited state relaxation, forming the rotationally flexible previtamin D. We further show that oscillations in the experimental TRCD spectrum arise from isomerizations between previtamin D rotamers with different chirality, which are associated with the helical conformation of the triene unit. We give a detailed description of the formation dynamics of different rotamers, playing a key role in the natural regulation vitamin D photosynthesis. Going beyond the sole extraction of decay rates, simulations greatly increase the amount of information that can be retrieved from ultrafast TRCD, making it a sensitive tool to unravel details in the sub-picosecond dynamics of photoinduced chirality changes

Development of a non-adiabatic ab initio molecular dynamics method and its application to photodynamical processes

Photoprocesses are ubiquitous in nature, science, and engineering. The understanding as well as the optimization of photochemical and photophysical properties of molecular systems requires computational tools that are able to describe the dynamical evolution of the system in electronically excited states. Ab Initio Molecular Dynamics (AIMD) based on Density Functional Theory (DFT) has become an established tool for elucidating mechanisms of chemical reactions that occur in the electronic ground state. However, to describe photoprocesses by AIMD, an underlying electronic-structure method that is able to treat excited states is necessary. This complicates the description of these processes because in the past this implied the use of computationally expensive wavefunction-based methods, which in addition are not straightforward to use. Time-Dependent Density Functional Theory (TDDFT) provides an in principle exact description of electronically excited states, although in practice, approximations have to be introduced. Compared to wavefunction-based methods, TDDFT is computationally less demanding and is relatively straightforward and easy to use. Recently, TDDFT nuclear gradients have become available and allow to carry out AIMD in excited states. In this thesis a TDDFT-based AIMD method that is able to account for non-adiabatic effects is developed and implemented. The non-adiabatic couplings are computed by means of a Kohn-Sham orbital based reconstruction of the many-electron wavefunction for ground and excited states. The non-adiabatic scheme is based on the fewest switches trajectory surface hopping (SH) method introduced by Tully. The method is applied to describe decay processes, such as fragmentation or isomerization, that occur upon photoexcitation of the molecules protonated formaldimine and oxirane. In the case of protonated formaldimine, the results of the TDDFT-SH method are in good agreement with SH simulations based on the state-averaged complete active space (SA-CASSCF) method, both with respect to the observed reaction mechanisms and the excited state life times. In the case of oxirane, the TDDFT-SH simulations confirm the main experimental results and provide an additional refinement of the postulated reaction mechanism. The accuracy of TDDFT is investigated with respect to different issues that are especially important for the proper description of photoprocesses. These aspects include the accuracy of non-adiabatic coupling (NAC) vectors, the description of S1-S0 conical intersections, and the description of locally excited states in systems where charge transfer (CT) states are present, that are affected by the well-known CT failure of TDDFT. Concerning the NAC vectors, a qualitative agreement with SA-CASSCF is found, although magnitudes are underestimated by TDDFT/PBE. Regarding the description of conical intersections to the ground state, we find as expected that TDDFT in the adiabatic approximation (ALDA) is not able to predict an intersection that is strictly conical. However, we find that TDDFT is able to approximate a conical intersection that has a similar shape as the one predicted by SA-CASSCF. For an electron donor-bridge-acceptor molecule it is shown that the CT failure of TDDFT can also considerably affect properties of non-CT states. The use of TDDFT using conventional exchange-correlation functionals is thus not recommended for the description of such systems. Using the second-order approximate coupled cluster (CC2) method in conjunction with a high quality basis set, an accurate and balanced description of both locally excited and CT states can be made. The use of CC2 with large basis sets for AIMD simulations is however still computationally unaffordable for larger systems. TDDFT is still in its infancy and several attempts to cure some of its defiencies have already been made. These attempts mainly concern improvements of the approximations of the exchange-correlation functionals and associated TDDFT kernels. The TDDFT-SH method that has been developed in this thesis can in principle be applied in combination with any approximation for the exchange correlation functional, provided that nuclear gradients for this approximation are available and the computational cost remains acceptable. In this way, the method developed here is able to directly profit from the ongoing improvements in the active research field of exchange-correlation functionals and kernels

Assessment of self-healing capabilities, a route towards standardization, International Conference on Self-Healing Materials

In the last decade, an increasing attention has been given to the development of repairing capabilities in materials, with an emphasis in specific strategies that can promote self-healing, with or without external triggers. Self-healing has opened several new possibilities, especially in applications where long-term reliability is demanded and either maintenance or replace of these materials is difficult to perform. Depending on the material class, different approaches in order to achieve self-healing, can be adopted. This led to distinct evaluation methods of the self-healing efficiency, depending on the material and its final use. One of the new challenges in self-repairing materials lays in the establishment of a common testing procedure for different materials classes, such as ceramics, concrete, polymers and composites. Normalized procedures can conduct to a standardization of the healing evaluation, which will set a common ground towards a better understanding of the concept and its quantification. The assessment of self-healing capabilities is one of the major goals in the SHeMat project. SHeMat is a Training Network for Self-Healing Materials funded within the scope of the Seventh Framework Programme by the European Commission's Marie Curie programme. The focus of this work will be the development of a standard procedure and its applicability to the specific materials developed within the project. The comparative analysis of the results will act as a support to establish a common base for the definition of self-healing as a quantifiable characteristic. This discussion covers the work that has been conducted so far in the SHeMat project and possible future directions

Molecular Dynamics Simulation of Apolipoprotein E3 Lipid Nanodiscs

Nanodiscs are binary discoidal complexes of a phospholipid bilayer circumscribed by belt-like helical scaffold proteins. Using coarse-grained and all-atom molecular dynamics simulations, we explore the stability, size, and structure of nanodiscs formed between the N-terminal domain of apolipoprotein E3 (apoE3-NT) and variable number of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) molecules. We study both parallel and antiparallel double-belt configurations, consisting of four proteins per nanodisc. Our simulations predict nanodiscs containing between 240 and 420 DMPC molecules to be stable. The antiparallel configurations exhibit an average of 1.6 times more amino acid interactions between protein chains and 2 times more ionic contacts, compared to the parallel configuration. With one exception, DMPC order parameters are consistently larger in the antiparallel configuration than in the parallel one. In most cases, the root mean square deviation of the positions of the protein backbone atoms is smaller in the antiparallel configuration. We further report nanodisc size, thickness, radius of gyration, and solvent accessible surface area. Combining all investigated parameters, we hypothesize the antiparallel protein configuration leading to more stable and more rigid nanodiscs than the parallel one

Calculation of vibrationally resolved absorption spectra of acenes and pyrene

The absorption spectra of naphthalene, anthracene, pentacene and pyrene in the ultraviolet-visible (UV-Vis) range have been simulated by using an efficient real-time generating function method that combines calculated adiabatic electronic excitation energies with vibrational energies of the excited states. The vertical electronic excitation energies have been calculated at the density functional theory level using the PBE0 functional and at the second-order approximate coupled-cluster level (CC2). The absorption spectra have been calculated at the PBE0 level for the studied molecules and at the CC2 level for naphthalene. The transition probabilities between vibrationally resolved states were calculated by using the real-time generating function method employing the full Duschinsky formalism. The absorption spectrum for naphthalene calculated at the PBE0 and CC2 levels agrees well with the experimental one after the simulated spectra have been blue-shifted by 0.48 eV and 0.12 eV at the PBE0 and CC2 level, respectively. The absorption spectra for anthracene, pentacene and pyrene simulated at the PBE0 level agree well with the experimental ones when they are shifted by 0.49 eV, 0.57 eV and 0.46 eV, respectively. The strongest transitions of the main vibrational bands have been assigned.Peer reviewe

Autoionizing Resonances in Time-Dependent Density Functional Theory

Autoionizing resonances that arise from the interaction of a bound single-excitation with the continuum can be accurately captured with the presently used approximations in time-dependent density functional theory (TDDFT), but those arising from a bound double excitation cannot. In the former case, we explain how an adiabatic kernel, which has no frequency-dependence, can yet generate the strongly frequency-dependent resonant structures in the interacting response function, not present in the Kohn-Sham response function. In the case of the bound double-excitation, we explain that a strongly frequency-dependent kernel is needed, and derive one for the vicinity of a resonance of the latter type, as an {\it a posteriori} correction to the usual adiabatic approximations in TDDFT. Our approximation becomes exact for an isolated resonance in the limit of weak interaction, where one discrete state interacts with one continuum. We derive a "Fano TDDFT kernel" that reproduces the Fano lineshape within the TDDFT formalism, and also a dressed kernel, that operates on top of an adiabatic approximation. We illustrate our results on a simple model system.Comment: 10 pages, appeared in Special Issue in TDDFT in PCCP (2009