Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes.

We develop a quartic-scaling implementation of coupled-cluster singles and doubles (CCSD) based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced (RR) coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Furthermore, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.

PySpawn: Software for Nonadiabatic Quantum Molecular Dynamics.

The ab initio multiple spawning (AIMS) method enables nonadiabatic quantum molecular dynamics simulations in an arbitrary number of dimensions, with potential energy surfaces provided by electronic structure calculations performed on-the-fly. However, the intricacy of the AIMS algorithm complicates software development, deployment on modern shared computer resources, and postsimulation data analysis. PySpawn is a nonadiabatic molecular dynamics software package that addresses these issues. The program is designed to be easily interfaced with electronic structure software, and an interface to the TeraChem software package is described here. PySpawn introduces a task-based reorganization of the AIMS algorithm, allowing fine-grained restart capability and setting the stage for efficient parallelization in a future release. PySpawn includes a user-friendly and interactive Python analysis module that will enable novice users to painlessly adopt AIMS. As a demonstration of PySpawn's simulation capability and analysis module, we report complete active space self-consistent field-based AIMS simulations of the 1,2-dithienyl-1,2-dicyanoethene molecule, a promising molecular photoswitch.

Performance of Coupled-Cluster Singles and Doubles on Modern Stream Processing Architectures.

We develop a new implementation of coupled-cluster singles and doubles (CCSD) optimized for the most recent graphical processing unit (GPU) hardware. We find that a single node with 8 NVIDIA V100 GPUs is capable of performing CCSD computations on roughly 100 atoms and 1300 basis functions in less than 1 day. Comparisons against massively parallel implementations of CCSD suggest that more than 64 CPU-based nodes (each with 16 cores) are required to match this performance.

TeraChem: Accelerating electronic structure and ab initio molecular dynamics with graphical processing units.

Developed over the past decade, TeraChem is an electronic structure and ab initio molecular dynamics software package designed from the ground up to leverage graphics processing units (GPUs) to perform large-scale ground and excited state quantum chemistry calculations in the gas and the condensed phase. TeraChem's speed stems from the reformulation of conventional electronic structure theories in terms of a set of individually optimized high-performance electronic structure operations (e.g., Coulomb and exchange matrix builds, one- and two-particle density matrix builds) and rank-reduction techniques (e.g., tensor hypercontraction). Recent efforts have encapsulated these core operations and provided language-agnostic interfaces. This greatly increases the accessibility and flexibility of TeraChem as a platform to develop new electronic structure methods on GPUs and provides clear optimization targets for emerging parallel computing architectures.

Fast transformations between configuration state function and Slater determinant bases for direct configuration interaction.

A hybrid configuration state function (CSF) and Slater determinant (SD) basis full configuration interaction (CI) program was developed to simultaneously take advantage of fast SD basis algorithms for σ = Hc formation and the smaller CI vector length and more robust convergence offered by a CSF basis. Graphical processing unit acceleration of the direct CSF-SD and SD-CSF basis transformation algorithms ensures that the combined transformation time per iteration relative to σ formation is small (∼15%). In addition to the obvious benefits of reducing the memory footprint of the CI vector, additional computational savings are demonstrated that rely directly on the size of the CI basis, in one particular case reducing the CI time-to-solution of a HF-CAS-(16,16)-CI/6-31G calculation of ethylene from 1954.79 s to 956 s by using a CSF basis, a 2.0× speedup.

Efficient Treatment of Large Active Spaces through Multi-GPU Parallel Implementation of Direct Configuration Interaction.

We have extended our graphical processing unit (GPU)-accelerated direct configuration interaction program to multiple devices, reducing iteration times for configuration spaces of 165 million determinants to only 3 s using NVIDIA P100 GPUs. Similar improvements in the one- and two-particle reduced density matrix formation allow for fast analytical energy gradients and electronic properties. Our parallel algorithm enables the calculation of arbitrarily large configuration spaces (limited only by available system memory), with iteration times of 13 min for an active space of 18 electrons in 18 orbitals (2.4 billion determinants) using six consumer grade NVIDIA 1080Ti GPUs. These advances enable routine molecular dynamics simulations, geometry optimizations, and absorption spectrum calculations for molecules with large configuration spaces, a task that has heretofore required massive computational effort. In this work, we demonstrate the utility of our program by generating the absorption spectrum for diphenyl acetylene at the floating occupation molecular orbital complete active space configuration interaction level of theory. Several active spaces were investigated to assess the dependence of spectral features on orbital space dimension.

Electronic and Structural Comparisons between Iron(II/III) and Ruthenium(II/III) Imide Analogs.

To examine structural and electronic differences between iron and ruthenium imido complexes, a series of compounds was prepared with different phosphine basal sets. The starting material for the ruthenium complexes was Ru(NAr/Ar*)(PMe3)3 (Ru1/Ru1*), where Ar = 2,6-(iPr)2C6H3 and Ar* = 2,4,6-(iPr)3C6H2, which were prepared from cis-RuCl2(PMe3)4 and 2 equiv of LiNHAr/Ar*. The starting materials for the iron complexes were the analogous Fe(NAr/Ar*)(PMe3)3 species (Fe1/Fe1*), which were not isolated but could be generated in situ from FeCl2, PMe3, and LiNHAr/Ar*. With both iron and ruthenium, the PMe3 starting materials underwent phosphine replacement with chelating ligands to give new group 8 imido complexes in the +2 oxidation state. Addition of 1,2-bis(diphenylphosphino)ethane (dppe) to M1/M1* gave Ru(NAr/Ar*)(PMe3)(dppe) and Fe(NAr/Ar*)(PMe3)(dppe). Addition of 1,2-bis(dimethylphosphino)ethane (dmpe) provided Ru(NAr/Ar*)(dmpe)2. A triphos ligand, {P(Me)2CH2}3SitBu (tP3), was also examined. Addition of tP3 to Fe1 provided Fe(NAr)(tP3) (Fe4), but a similar reaction with Ru1 only gave intractable materials. Oxidation of Fe4 with AgSbF6 gave {Fe(NAr)(tP3)}+SbF6- (Fe4a). Oxidation of Ru2 with AgSbF6 gave the unstable cation {Ru(NAr)(PMe3)(dppe)}+, which dimerized in the presence of acetonitrile via C-C bond formation at the aryl group C4 positions, affording {Ru(NAr)(PMe3)(NCMe)(dppe)}2+. This suggested that there was substantial radical character in the imide π system on oxidation and that an aromatic group substituted at the 4-position might provide greater stability. The cations {Fe(NAr*)(PMe3)(dppe)}+ (Fe2a*), {Ru(NAr*)(PMe3)(dppe)}+ (Ru2a*), and Fe4a were examined by EPR spectroscopy, which suggested differences in electronic structure depending on the metal and ligand set. CASPT2 calculations on model systems for Ru2a* and Fe2a* suggested that the large differences in electronic structure are related to the energy gap between the π-antibonding HOMO and the π-bonding HOMO-1. Both the geometry of the phosphines, which is slightly different between the iron and ruthenium analogs, and the metal center seem to contribute to this energetic difference.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials.

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.

Simulating Electron Dynamics of Complex Molecules with Time-Dependent Complete Active Space Configuration Interaction.

Time-dependent electronic structure methods are growing in popularity as tools for modeling ultrafast and/or nonlinear processes, for computing spectra, and as the electronic structure component of mean-field molecular dynamics simulations. Time-dependent configuration interaction (TD-CI) offers several advantages over the widely used real-time time-dependent density functional theory: namely, that it correctly models Rabi oscillations; it offers a spin-pure description of open-shell systems; and a hierarchy of TD-CI methods can be defined that systematically approach the exact solution of the time-dependent Schrodinger equation (TDSE). In this work, we present a novel TD-CI approach that extends TD-CI to large complete active-space configuration expansions. Such extension is enabled by use of a direct configuration interaction approach that eliminates the need to explicitly build, store, or diagonalize the Hamiltonian matrix. Graphics processing unit (GPU) acceleration enables fast solution of the TDSE even for large active spaces-up to 12 electrons in 12 orbitals (853776 determinants) in this work. A symplectic split operator propagator yields long-time norm conservation. We demonstrate the applicability of our approach by computing the response of a large molecule with a strongly correlated ground state, decacene (C42H24), to various pulses (δ-function, transform limited, chirped). Our simulations predict that chirped pulses can be used to induce dipole-forbidden transitions. Simulations of decacene using the 6-31G(d) basis set and a 12 electrons/12 orbitals active space took 20.1 h to propagate for 100 fs with a 1 attosecond time step on a single NVIDIA K40 GPU. Convergence with respect to time step is found to depend on the property being computed and the chosen active space.

Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction.

We present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix-vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 1016 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2-5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.

Dynamics of recombination via conical intersection in a semiconductor nanocrystal.

Conical intersections are well known to introduce nonradiative decay pathways in molecules, but have only recently been implicated in nonradiative recombination processes in materials. Here we apply excited state ab initio molecular dynamics simulations based on a multireference description of the electronic structure to defective silicon nanocrystals up to 1.7 nm in diameter to search for accessible nonradiative recombination pathways. Dangling bond defects are found to induce conical intersections between the ground and first excited electronic states of five systems of various sizes. These defect-induced conical intersections are accessible at energies that are in the visible range (2.4-2.7 eV) and very weakly dependent on particle size. The dynamic simulations suggest that these intersections are accessed 40-60 fs after creation of a defect-localized excitation. This ultrafast recombination is attributed to the fact that Jahn-Teller distortion on the first excited state drives the defect directly towards a conical intersection with the ground electronic state.

Complete active space configuration interaction from state-averaged configuration interaction singles natural orbitals: Analytic first derivatives and derivative coupling vectors.

A new complete active space configuration interaction (CASCI) method was recently introduced that uses state-averaged natural orbitals from the configuration interaction singles method (configuration interaction singles natural orbital CASCI, CISNO-CASCI). This method has been shown to perform as well or better than state-averaged complete active space self-consistent field for a variety of systems. However, further development and testing of this method have been limited by the lack of available analytic first derivatives of the CISNO-CASCI energy as well as the derivative coupling between electronic states. In the present work, we present a Lagrangian-based formulation of these derivatives as well as a highly efficient implementation of the resulting equations accelerated with graphical processing units. We demonstrate that the CISNO-CASCI method is practical for dynamical simulations of photochemical processes in molecular systems containing hundreds of atoms.

Robust and Efficient Spin Purification for Determinantal Configuration Interaction.

The limited precision of floating point arithmetic can lead to the qualitative and even catastrophic failure of quantum chemical algorithms, especially when high accuracy solutions are sought. For example, numerical errors accumulated while solving for determinantal configuration interaction wave functions via Davidson diagonalization may lead to spin contamination in the trial subspace. This spin contamination may cause the procedure to converge to roots with undesired ⟨S2⟩, wasting computer time in the best case and leading to incorrect conclusions in the worst. In hopes of finding a suitable remedy, we investigate five purification schemes for ensuring that the eigenvectors have the desired ⟨S2⟩. These schemes are based on projection, penalty, and iterative approaches. All of these schemes rely on a direct, graphics processing unit-accelerated algorithm for calculating the S2c matrix-vector product. We assess the computational cost and convergence behavior of these methods by application to several benchmark systems and find that the first-order spin penalty method is the optimal choice, though first-order and Löwdin projection approaches also provide fast convergence to the desired spin state. Finally, to demonstrate the utility of these approaches, we computed the lowest several excited states of an open-shell silver cluster (Ag19) using the state-averaged complete active space self-consistent field method, where spin purification was required to ensure spin stability of the CI vector coefficients. Several low-lying states with significant multiply excited character are predicted, suggesting the value of a multireference approach for modeling plasmonic nanomaterials.

Understanding Nonradiative Recombination through Defect-Induced Conical Intersections.

Defects are known to introduce pathways for the nonradiative recombination of electronic excitations in semiconductors, but implicating a specific defect as a nonradiative center remains challenging for both experiment and theory. In this Perspective, we present recent progress toward this goal involving the identification and characterization of defect-induced conical intersections (DICIs), points of degeneracy between the ground and first excited electronic states of semiconductor materials that arise from the deformation of specific defects. Analysis of DICIs does not require the assumption of weak correlation between the electron and hole nor of stationary nuclei. It is demonstrated that in some cases an energetically accessible DICI is present even when no midgap state is predicted by single-particle theories (e.g., density functional theory). We review recent theoretical and computational developments that enable the location of DICIs in semiconductor nanomaterials and present insights into the photoluminescence of silicon nanocrystals gleaned from DICIs.

Mechanisms and time-resolved dynamics for trihydrogen cation (H3+) formation from organic molecules in strong laser fields.

Strong-field laser-matter interactions often lead to exotic chemical reactions. Trihydrogen cation formation from organic molecules is one such case that requires multiple bonds to break and form. We present evidence for the existence of two different reaction pathways for H3+ formation from organic molecules irradiated by a strong-field laser. Assignment of the two pathways was accomplished through analysis of femtosecond time-resolved strong-field ionization and photoion-photoion coincidence measurements carried out on methanol isotopomers, ethylene glycol, and acetone. Ab initio molecular dynamics simulations suggest the formation occurs via two steps: the initial formation of a neutral hydrogen molecule, followed by the abstraction of a proton from the remaining CHOH2+ fragment by the roaming H2 molecule. This reaction has similarities to the H2 + H2+ mechanism leading to formation of H3+ in the universe. These exotic chemical reaction mechanisms, involving roaming H2 molecules, are found to occur in the ~100 fs timescale. Roaming molecule reactions may help to explain unlikely chemical processes, involving dissociation and formation of multiple chemical bonds, occurring under strong laser fields.

A direct-compatible formulation of the coupled perturbed complete active space self-consistent field equations on graphical processing units.

We recently developed an algorithm to compute response properties for the state-averaged complete active space self-consistent field method (SA-CASSCF) that capitalized on sparsity in the atomic orbital basis. Our original algorithm was limited to treating small to moderate sized active spaces, but the recent development of graphical processing unit (GPU) based direct-configuration interaction algorithms provides an opportunity to extend this to large active spaces. We present here a direct-compatible version of the coupled perturbed equations, enabling us to compute response properties for systems treated with arbitrary active spaces (subject to available memory and computation time). This work demonstrates that the computationally demanding portions of the SA-CASSCF method can be formulated in terms of seven fundamental operations, including Coulomb and exchange matrix builds and their derivatives, as well as, generalized one- and two-particle density matrix and σ vector constructions. As in our previous work, this algorithm exhibits low computational scaling and is accelerated by the use of GPUs, making possible optimizations and nonadiabatic dynamics on systems with O(1000) basis functions and O(100) atoms, respectively.

Nanoscale multireference quantum chemistry: full configuration interaction on graphical processing units.

Methods based on a full configuration interaction (FCI) expansion in an active space of orbitals are widely used for modeling chemical phenomena such as bond breaking, multiply excited states, and conical intersections in small-to-medium-sized molecules, but these phenomena occur in systems of all sizes. To scale such calculations up to the nanoscale, we have developed an implementation of FCI in which electron repulsion integral transformation and several of the more expensive steps in σ vector formation are performed on graphical processing unit (GPU) hardware. When applied to a 1.7 × 1.4 × 1.4 nm silicon nanoparticle (Si72H64) described with the polarized, all-electron 6-31G** basis set, our implementation can solve for the ground state of the 16-active-electron/16-active-orbital CASCI Hamiltonian (more than 100,000,000 configurations) in 39 min on a single NVidia K40 GPU.

Defect-Induced Conical Intersections Promote Nonradiative Recombination.

We apply multireference electronic structure calculations to demonstrate the presence of conical intersections between the ground and the first excited electronic states of three silicon nanocrystals containing defects characteristic of the oxidized silicon surface. These intersections are accessible upon excitation at visible wavelengths and are predicted to facilitate nonradiative recombination with a rate that increases with decreasing particle size. This work illustrates a new framework for identifying defects responsible for nonradiative recombination.