Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. However, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We avoid cumbersome machine-generated code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.

Coupled-cluster methods provide highly accurate models of molecular structure through explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix–matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts to extend the Libtensor framework to work in the distributed memory environment in a scalable and energy-efficient manner. We achieve up to 240× speedup compared with the optimized shared memory implementation of Libtensor. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures (Cray XC30 and XC40, and IBM Blue Gene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance, tasking and bulk synchronous models. Nevertheless, we preserve a unified interface to both programming models to maintain the productivity of computational quantum chemists.

Libtensor is a framework designed to implement the tensor contractions arising form the coupled cluster and equations of motion computational quantum chemistry equations. It has been optimized for symmetry and sparsity to be memory efficient. This allows it to run efficiently on the ubiquitous and cost-effective SMP architectures. Unfortunately, movement of memory controllers on chip has endowed these SMP systems with strong NUMA properties. Moreover, the manycore trend in processor architecture demands that the implementation be extremely thread-scalable on node. To date, Libtensor has been generally agnostic of these effects. To that end, in this paper, we explore a number of optimization techniques including a thread-friendly and NUMA-aware memory allocator and garbage collector, tuning the tensor tiling factor, and tuning the scheduling quanta. In the end, our optimizations can improve the performance of contractions implemented in Libtensor by up to 2× on representative Ivy Bridge, Nehalem, and Opteron SMPs.

Ultrafast table-top X-ray spectroscopy at the carbon K-edge is used to measure the X-ray spectral features of benzene radical cations (Bz⁺). The ground state of the cation is prepared selectively by two-photon ionization of neutral benzene, and the X-ray spectra are probed at early times after the ionization by transient absorption using X-rays produced by high harmonic generation (HHG). Bz⁺ is well-known to undergo Jahn-Teller distortion, leading to a lower symmetry and splitting of the π orbitals. Comparison of the X-ray absorption spectra of the neutral and the cation reveals a splitting of the two degenerate π* orbitals as well as an appearance of a new peak due to excitation to the partially occupied π-subshell. The π* orbital splitting of the cation, elucidated on the basis of high-level calculations in a companion theoretical paper [Vidal et al. J. Phys. Chem. A. http://dx.doi.org/10.1021/acs.jpca.0c08732], is discovered to be due to both the symmetry distortion and even more dominant spin coupling of the unpaired electron in the partially vacant π orbital (from ionization) with the unpaired electrons resulting from the transition from the 1s_C core orbital to the fully vacant π* orbitals.

Application of photoionization mass spectroscopy, a technique capable of assessing protonation states in complex molecules in the gas phase, is challenging for arginine due to its fragility. We report photoionization efficiencies in the valence region of aqueous aerosol particles produced from arginine solutions under various pH and vaporization conditions. By using ab initio calculations, we investigate the stability of different conformers. Our results show that neutral arginine fragments upon ionization in the gas phase but solvation stabilizes the molecular ion, resulting in different photoionization dynamics. We also report the valence-band photoelectron spectra of the aerosol solutions obtained at different pH values.

We report a theoretical investigation and elucidation of the X-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization and the measurement of the carbon K-edge spectra of both species using a table-top high-harmonic generation source are described in the companion experimental paper [Epshtein, M.; et al. J. Phys. Chem. A http://dx.doi.org/10.1021/acs.jpca.0c08736]. We show that the 1s_C → π transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence of the unpaired (spectator) electron in the π-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1s_C → π* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation. The prominent split structure of the 1s_C → π* band of the cation is attributed to the interplay between the coupling of the core → π* excitation with the unpaired electron in the π-subshell and the Jahn-Teller distortion. The calculations attribute most of the splitting (∼1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and we estimate the additional splitting due to structural relaxation to be around ∼0.1-0.2 eV. These results suggest that X-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller effect in the benzene cation.

A production-level implementation of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) for electron attachment and excitation energies augmented by a complex absorbing potential (CAP) is presented. The new method enables the treatment of metastable states within the EOM-CC formalism in a similar manner as bound states. The numeric performance of the method and the sensitivity of resonance positions and lifetimes to the CAP parameters and the choice of one-electron basis set are investigated. A protocol for studying molecular shape resonances based on the use of standard basis sets and a universal criterion for choosing the CAP parameters are presented. Our results for a variety of π(*) shape resonances of small to medium-size molecules demonstrate that CAP-augmented EOM-CCSD is competitive relative to other theoretical approaches for the treatment of resonances and is often able to reproduce experimental results.

Tabletop X-ray spectroscopy measurements at the carbon K-edge complemented by ab initio calculations are used to investigate the influence of the bromine atom on the carbon core-valence transitions in the bromobenzene cation (BrBz⁺). The electronic ground state of the cation is prepared by resonance-enhanced two-photon ionization of neutral bromobenzene (BrBz) and probed by X-rays produced by high-harmonic generation (HHG). Replacing one of the hydrogen atoms in benzene with a bromine atom shifts the transition from the 1s_C* orbital of the carbon atom (C*) bonded to bromine by ∼1 eV to higher energy in the X-ray spectrum compared to the other carbon atoms (C). Moreover, in BrBz⁺, the X-ray spectrum is dominated by two relatively intense transitions, 1s_C→π* and 1s_C*→σ*(C*-Br), where the second transition is enhanced relative to the neutral BrBz. In addition, a doublet peak shape for these two transitions is observed in the experiment. The 1s_C→π* doublet peak shape arises due to the spin coupling of the unpaired electron in the partially vacant π orbital (from ionization) with the two other unpaired electrons resulting from the transition from the 1s_C core orbital to the fully vacant π* orbitals. The 1s_C*→σ* doublet peak shape results from several transitions involving σ* and vibrational C*-Br mode activations following the UV ionization, which demonstrates the impact of the C*-Br bond length on the core-valence transition as well as on the relaxation geometry of BrBz⁺.