Machine Learning, Quantum Mechanics, and Chemical Compound Space

We review recent studies dealing with the generation of machine learning models of molecular and solid properties. The models are trained and validated using standard quantum chemistry results obtained for organic molecules and materials selected from chemical space at random

Machine Learning of Molecular Electronic Properties in Chemical Compound Space

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of \textit{ab initio} calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to \emph{ab initio} methods, \emph{i.e.} nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost

Frustration-induced exotic properties of magnetic molecules

Geometric frustration of interacting spin systems is the driving force of a variety of fascinating phenomena in low-dimensional magnetism. In this contribution I will review recent results on frustration-induced effects in magnetic molecules, i.e. zero-dimensional magnetic systems, as well as in a recently synthesized frustrated molecule-based spin tube, i.e. a one-dimensional spin system.Comment: 5 pages, 9 eps figures; proceedings of the symposium on "Spin- and charge-correlations in molecule-based materials", October 2005, Koenigstein (Taunus), German

Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited

The fluctuations exhibited by the cross-sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Gamma_corr of the cross-section correlation function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as function of the parameter under consideration. They, actually, stated that the product of the average number of maxima per unit energy range and Gamma_corr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances

Inverse Quantum Chemistry: Concepts and Strategies for Rational Compound Design

The rational design of molecules and materials is becoming more and more important. With the advent of powerful computer systems and sophisticated algorithms, quantum chemistry plays an important role in rational design. While traditional quantum chemical approaches predict the properties of a predefined molecular structure, the goal of inverse quantum chemistry is to find a structure featuring one or more desired properties. Herein, we review inverse quantum chemical approaches proposed so far and discuss their advantages as well as their weaknesses.Comment: 43 pages, 5 figure

Dirty-boson physics with magnetic insulators

We review recent theoretical and experimental efforts aimed at the investigation of the physics of interacting disordered bosons (so-called dirty bosons) in the context of quantum magnetism. The physics of dirty bosons is relevant to a wide variety of condensed matter systems, encompassing Helium in porous media, granular superconductors and ultracold atoms in disordered optical potentials, to cite a few. Nevertheless, the understanding of the transition from a localized, Bose-glass phase to an ordered, superfluid condensate phase still represents a fundamentally open problem. Still to be constructed is also a quantitative description of the highly inhomogeneous and strongly correlated phases connected by the transition. We discuss how disordered magnetic insulators in a strong magnetic field can provide a well controlled realization of the above transition. Combining numerical simulations with experiments on real materials can shed light on some fundamental properties of the critical behavior, such as the scaling of the critical temperature to condensation close to the quantum critical point

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

A well-defined notion of chemical compound space (CCS) is essential for gaining rigorous control of properties through variation of elemental composition and atomic configurations. Here, we review an atomistic first principles perspective on CCS. First, CCS is discussed in terms of variational nuclear charges in the context of conceptual density functional and molecular grand-canonical ensemble theory. Thereafter, we revisit the notion of compound pairs, related to each other via "alchemical" interpolations involving fractional nuclear chargens in the electronic Hamiltonian. We address Taylor expansions in CCS, property non-linearity, improved predictions using reference compound pairs, and the ounce-of-gold prize challenge to linearize CCS. Finally, we turn to machine learning of analytical structure property relationships in CCS. These relationships correspond to inferred, rather than derived through variational principle, solutions of the electronic Schr\"odinger equation