Meta-control of social learning strategies.

Social learning, copying other's behavior without actual experience, offers a cost-effective means of knowledge acquisition. However, it raises the fundamental question of which individuals have reliable information: successful individuals versus the majority. The former and the latter are known respectively as success-based and conformist social learning strategies. We show here that while the success-based strategy fully exploits the benign environment of low uncertainly, it fails in uncertain environments. On the other hand, the conformist strategy can effectively mitigate this adverse effect. Based on these findings, we hypothesized that meta-control of individual and social learning strategies provides effective and sample-efficient learning in volatile and uncertain environments. Simulations on a set of environments with various levels of volatility and uncertainty confirmed our hypothesis. The results imply that meta-control of social learning affords agents the leverage to resolve environmental uncertainty with minimal exploration cost, by exploiting others' learning as an external knowledge base.

Machine Learning of Quasiparticle Energies in Molecules and Clusters.

We present a Δ-machine learning approach for the prediction of GW quasiparticle energies (ΔMLQP) and photoelectron spectra of molecules and clusters, using orbital-sensitive representations (OSRs) based on molecular Cartesian coordinates in kernel ridge regression-based supervised learning. Coulomb matrix, bag-of-bond, and bond-angle-torsion representations are made orbital-sensitive by augmenting them with atom-centered orbital charges and Kohn-Sham orbital energies, both of which are readily available from baseline calculations at the level of density functional theory (DFT). We first illustrate the effects of different constructions of the OSRs on the prediction of frontier orbital energies of 22k molecules of the QM8 data set and show that it is possible to predict the full photoelectron spectrum of molecules within the data set using a single model with a mean absolute error below 0.1 eV. We further demonstrate that the OSR-based ΔMLQP captures the effects of intra- and intermolecular conformations in application to water monomers and dimers. Finally, we show that the approach can be embedded in multiscale simulation workflows, by studying the solvatochromic shifts of quasiparticle and electron-hole excitation energies of solvated acetone in a setup combining molecular dynamics, DFT, the GW approximation, and the Bethe-Salpeter equation. Our findings suggest that the ΔMLQP model allows us to predict quasiparticle energies and photoelectron spectra of molecules and clusters with GW accuracy at DFT cost.

Excited-State Geometry Optimization of Small Molecules with Many-Body Green's Functions Theory.

We present a benchmark study of gas phase geometry optimizations in the excited states of carbon monoxide, acetone, acrolein, and methylenecyclopropene using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation (BSE) employing numerical gradients. We scrutinize the influence of several typical approximations in the GW-BSE framework; we used one-shot G0W0 or eigenvalue self-consistent evGW, employing a fully analytic approach or plasmon-pole model for the frequency dependence of the electron self-energy, or performing the BSE step within the Tamm-Dancoff approximation. The obtained geometries are compared to reference results from multireference perturbation theory (CASPT2), variational Monte Carlo (VMC) method, second-order approximate coupled cluster (CC2) method, and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the GW-BSE calculations with CASPT2, with an average relative error of around 1% for the G0W0 and 1.5% for the evGW variants based on a PBE0 ground state, respectively, while the other approximations have negligible influence. The relative errors are also smaller than those for CC2 and TDDFT with different functionals and only larger than VMC, indicating that the GW-BSE method does not only yield excitation energies but also geometries in good agreement with established higher-order wave function methods.

Evolutionary Approach to Constructing a Deep Feedforward Neural Network for Prediction of Electronic Coupling Elements in Molecular Materials.

We present a general framework for the construction of a deep feedforward neural network (FFNN) to predict distance and orientation dependent electronic coupling elements in disordered molecular materials. An evolutionary algorithm automatizes the selection of an optimal architecture of the artificial neural network within a predefined search space. Systematic guidance, beyond minimizing the model error with stochastic gradient descent based backpropagation, is provided by simultaneous maximization of a model fitness that takes into account additional physical properties, such as the field-dependent carrier mobility. As a prototypical system, we consider hole transport in amorphous tris(8-hydroxyquinolinato)aluminum. Reference data for training and validation is obtained from multiscale ab initio simulations, in which coupling elements are evaluated using density-functional theory, for a system containing 4096 molecules. The Coulomb matrix representation is chosen to encode the explicit molecular pair coordinates into a rotation and translation invariant feature set for the FFNN. The final optimized deep feedforward neural network is tested for transport models without and with energetic disorder. It predicts electronic coupling elements and mobilities in excellent agreement with the reference data. Such a FFNN is readily applicable to much larger systems at negligible computational cost, providing a powerful surrogate model to overcome the size limitations of the ab initio approach.

Electronic Excitations in Complex Molecular Environments: Many-Body Green's Functions Theory in VOTCA-XTP.

Many-body Green's functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE) is implemented in the open-source VOTCA-XTP software, aiming at the calculation of electronically excited states in complex molecular environments. Based on Gaussian-type atomic orbitals and making use of resolution of identity techniques, the code is designed specifically for nonperiodic systems. Application to a small molecule reference set successfully validates the methodology and its implementation for a variety of excitation types covering an energy range from 2 to 8 eV in single molecules. Further, embedding each GW-BSE calculation into an atomistically resolved surrounding, typically obtained from Molecular Dynamics, accounts for effects originating from local fields and polarization. Using aqueous DNA as a prototypical system, different levels of electrostatic coupling between the regions in this GW-BSE/MM setup are demonstrated. Particular attention is paid to charge-transfer (CT) excitations in adenine base pairs. It is found that their energy is extremely sensitive to the specific environment and to polarization effects. The calculated redshift of the CT excitation energy compared to a nucelobase dimer treated in vacuum is of the order of 1 eV, which matches expectations from experimental data. Predicted lowest CT energies are below that of a single nucleobase excitation, indicating the possibility of an initial (fast) decay of such an UV excited state into a binucleobase CT exciton. The results show that VOTCA-XTP's GW-BSE/MM is a powerful tool to study a wide range of types of electronic excitations in complex molecular environments.