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We explore transfer learning models from a pre-trained graph convolutional neural network representation of molecules, obtained from SchNet, to predict 13C-NMR, pKa, and log S solubility. SchNet learns a graph representation of a molecule by associating each atom with an "embedding vector" and interacts the atom-embeddings with each other by leveraging graph convolutional filters on their interatomic distances. We pre-trained SchNet on molecular energy and demonstrate that the pre-trained atomistic embeddings can then be used as a transferable representation for a wide array of properties. On the one hand, for atomic properties such as micro-pK1 and 13C-NMR, we investigate two models, one linear and one neural net, that input pre-trained atom-embeddings of a particular atom (e.g. carbon) and predict a local property (e.g., 13C-NMR). On the other hand, for molecular properties such as solubility, a size-extensive graph model is built using the embeddings of all atoms in the molecule as input. For all cases, qualitatively correct predictions are made with relatively little training data (<1000 training points), showcasing the ease with which pre-trained embeddings pick up on important chemical patterns. The proposed models successfully capture well-understood trends of pK1 and solubility. This study advances our understanding of current neural net graph representations and their capacity for transfer learning applications in chemistry. [ABSTRACT FROM AUTHOR]

The phase diagram for the configuration mixed Interacting Boson Model is investigated for the special case of U(5)-O(6) mixing using the methods provided by Catastrophe Theory. It will be shown that this phase diagram exhibits properties not present when only a single configuration is considered. [ABSTRACT FROM AUTHOR]

Very recently the atomic masses of neutron-rich Zr isotopes, from 96Zr to 104Zr, have been measured with high precision. Using a schematic Interacting Boson Model (IBM) Hamiltonian, the evolution from spherical to deformed shapes along the chain of Zr isotopes, describing at the same time the excitation energies as well as the two-neutron separation energies, can be rather well reproduced. The interplay between phase transitions and configuration mixing of intruder excitations in this mass region is succinctly addressed. [ABSTRACT FROM AUTHOR]

The variational quantum eigensolver algorithm recently became a popular method to compute the quantum chemical properties of molecules on noisy intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation from the NISQ device in the quantum circuit, it is important to keep the so-called quantum depth of the circuit at a minimum, defined as the minimum number of quantum gates that must be operated sequentially. In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit compared to previously proposed architectures without loss of chemical accuracy. Moreover, by virtue of the simplicity of the cluster circuit, it is possible to assign a valence bond chemical interpretation to the cluster circuit. The design was tested on the H 2 , (H 2 ) 2 , and LiH molecules, as well as the finite-size transverse-field Ising model, as the latter provides additional insights into the construction of the circuit in a resonating valence bond picture.

The failure of many approximate electronic structure methods can be traced to their erroneous description of fractional charge and spin redistributions in the asymptotic limit toward infinity, where violations of the flat-plane conditions lead to delocalization and static correlation errors. Although the energetic consequences of the flat-planes are known, the underlying quantum phase transitions that occur when (spin)charge is redistributed have not been characterized. In this study, we use open subsystems to redistribute (spin)charges in the tilted Hubbard model by imposing suitable Lagrange constraints on the Hamiltonian. We computationally recover the flat-plane conditions and quantify the underlying quantum phase transitions using quantum entanglement measures. The resulting entanglement patterns quantify the phase transition that gives rise to the flat-plane conditions and quantify the complexity required to accurately describe charge redistributions in strongly correlated systems. Our study indicates that entanglement patterns can uncover those phase transitions that have to be modeled accurately if the delocalization and static correlation errors of approximate methods are to be reduced.

Clar's aromatic π -sextet rule is a widely used qualitative method for assessing the electronic structure of polycyclic benzenoid hydrocarbons. Unfortunately, many of the quantum chemical concordances for this rule have a limited range of applicability. Here, we show that the fundamental probabilities associated with a distribution of electrons over domain partitions support Clar's rule in both mean-field and static correlation regimes. In particular, domain partitions that maximize those probabilities reflect the dominance of Clar structures in the electronic structure of these molecules. These findings suggest that extending methods that aim to maximize probabilities by deforming domain partitions could lead to novel quantum chemical underpinnings for many chemical concepts., (© 2022 Wiley Periodicals LLC.)

The failure of many density functional approximations can be traced to their behavior under fractional (spin)population redistributions in the asymptotic limit toward infinite bonding distances, which should obey the flat-plane conditions. However, such errors can only be characterized sufficiently in terms of those redistributions if exact energies are available for many possible (spin)population redistributions at different bonding distances. In this study, we propose to model such redistributions by imposing (spin)populations on atomic domains by constraining full configuration interaction wave functions. The resulting N-representable descriptions of small hydrogen chains at different bonding distances allow us to computationally illustrate the effects of the flat-plane conditions in the limit to infinite bond distances, leading to more chemical insight into those flat-plane conditions. As the proposed methodology is able to capture the effects of the flat plane conditions, it could be used to generate the reference data that is required to measure the extent to which approximate methods violate the requirements of the exact functional, leading to a quantification of the delocalization and static correlation error of such methods.

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction Ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltonians, and we present results for atoms and dissociation curves that are in agreement with doubly occupied configuration interaction data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly correlated electrons.

Adiabatically varying the driving frequency of a periodically driven many-body quantum system can induce controlled transitions between resonant eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic transitions in the Floquet spectrum and presenting a general tool in quantum many-body control. Using the central spin model as an application, we show how such controlled driving processes can lead to a polarization-based decoupling of the central spin from its decoherence-inducing environment at resonance. While it is generally impossible to obtain the exact Floquet Hamiltonian in driven interacting systems, we exploit the integrability of the central spin model to show how techniques from quantum quenches can be used to explicitly construct the Floquet Hamiltonian in a restricted many-body basis and model Floquet resonances.

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.