Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Double-buffered, heterogeneous CPU + GPU integral digestion algorithm for single-excitation calculations involving a large number of excited states.

The most widely used quantum-chemical models for excited states are single-excitation theories, a category that includes configuration interaction with single substitutions, time-dependent density functional theory, and also a recently developed ab initio exciton model. When a large number of excited states are desired, these calculations incur a significant bottleneck in the "digestion" step in which two-electron integrals are contracted with density or density-like matrices. We present an implementation that moves this step onto graphical processing units (GPUs), and introduce a double-buffer scheme that minimizes latency by computing integrals on the central processing units (CPUs) concurrently with their digestion on the GPUs. An automatic code generation scheme simplifies the implementation of high-performance GPU kernels. For the exciton model, which requires separate excited-state calculations on each electronically coupled chromophore, the heterogeneous implementation described here results in speedups of 2-6× versus a CPU-only implementation. For traditional time-dependent density functional theory calculations, we obtain speedups of up to 5× when a large number of excited states is computed. © 2018 Wiley Periodicals, Inc.

Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene.

Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

Evidence for Singlet Fission Driven by Vibronic Coherence in Crystalline Tetracene.

Singlet fission proceeds rapidly and with high quantum efficiency in both crystalline tetracene and pentacene, which poses a conundrum given that the process in tetracene is disfavored by the electronic energetics. Here, we use an ab initio exciton model to compute nonadiabatic couplings in the unit cell of tetracene in order to identify the modes that promote this process. Four intramolecular modes in the range of 1400-1600 cm-1, which are nearly resonant with the single-exciton/multiexciton energy gap, appear to play a key role. Ab initio calculations of the electron/phonon coupling constants for these modes reveal that they are almost entirely of "Holstein" type, modulating the site energies rather than the intersite couplings. The constants are used to parametrize a vibronic Hamiltonian, simulations with which suggest a vibronically coherent singlet fission mechanism that proceeds spontaneously despite unfavorable electronic energetics. In the absence of vibronic coupling, there is no significant fission according to our model.

Beyond Time-Dependent Density Functional Theory Using Only Single Excitations: Methods for Computational Studies of Excited States in Complex Systems.

Single-excitation methods, namely, configuration interaction singles and time-dependent density functional theory (TDDFT), along with semiempirical versions thereof, represent the most computationally affordable electronic structure methods for describing electronically excited states, scaling as [Formula: see text] absent further approximations. This relatively low cost, combined with a treatment of electron correlation, has made TDDFT the most widely used excited-state quantum chemistry method over the past 20+ years. Nevertheless, certain inherent problems (beyond just the accuracy of this or that exchange-correlation functional) limit the utility of traditional TDDFT. For one, it affords potential energy surfaces whose topology is incorrect in the vicinity of any conical intersection (CI) that involves the ground state. Since CIs are the conduits for transitions between electronic states, the TDDFT description of photochemistry (internal conversion and intersystem crossing) is therefore suspect. Second, the [Formula: see text] cost can become prohibitive in large systems, especially those that involve multiple electronically coupled chromophores, for example, the antennae structures of light-harvesting complexes or the conjugated polymers used in organic photovoltaics. In such cases, the smallest realistic mimics might already be quite large from the standpoint of ab initio quantum chemistry. This Account describes several new computational methods that address these problems. Topology around a CI can be rigorously corrected using a "spin-flip" version of TDDFT, which involves an α → ß spin-flipping transition in addition to occupied → virtual excitation of one electron. Within this formalism, singlet states are generated via excitation from a high-spin triplet reference state, doublets from a quartet, etc. This provides a more balanced treatment of electron correlation between ground and excited states. Spin contamination is problematic away from the Franck-Condon region, but we describe a "spin-complete" version of the theory in which proper spin eigenstates are obtained by construction. For systems of coupled chromophores, we have developed an ab initio version of the Frenkel-Davydov exciton model in which collective excitations of the system are expanded in a basis of excited states computed for individual chromophores. The monomer calculations are trivially parallelizable, as is computation of the coupling matrix elements needed to construct the exciton Hamiltonian, and systems containing hundreds of chromophores can be tackled on commodity hardware. This enables calculations on organic semiconductors, where even small model systems exhibit a semicontinuum of excited states that renders traditional TDDFT computationally challenging. Despite including only single excitations on each monomer, the exciton model can describe entangled spins on two or more monomers, an effect that is responsible for excitation energy transfer between chromophores, for example, in singlet fission. Excitonic approximations can also be applied to the TDDFT equations themselves, and a particularly promising application is to describe the effects of environment on an excitation that is localized on a single chromophore. This "local excitation approximation" to TDDFT allows an essentially arbitrary number of solvent molecules to be included in the calculation in a highly parallelizable way such that the time-to-solution increases only very slowly as additional solvent molecules are added. It is therefore possible to converge the calculation with respect to describing an ever-larger portion of the environment at a quantum-mechanical level.

Low-Scaling Quantum Chemistry Approach to Excited-State Properties via an ab Initio Exciton Model: Application to Excitation Energy Transfer in a Self-Assembled Nanotube.

We introduce a charge-embedding scheme for an excited-state quantum chemistry method aimed at weakly interacting molecular aggregates. The Hamiltonian matrix for the aggregate is constructed in a basis of direct products of configuration-state functions for the monomers, and diagonalization of this matrix affords excitation energies within ∼0.2 eV of the corresponding supersystem calculation. Both the basis states and the coupling matrix elements can be computed in a distributed way, resulting in an algorithm whose time-to-solution is independent of the number of chromophores, and we report calculations on systems with almost 55 000 basis functions using fewer than 450 processors. In a semiconducting organic nanotube, we find evidence of ultrafast, coherent dynamics followed by energy localization driven by static disorder. Truncation of the model system has a qualitative effect on the energy-transfer dynamics, demonstrating the importance of simulating an extended portion of the nanotube, which is not feasible using traditional quantum chemistry.

Ab Initio Implementation of the Frenkel-Davydov Exciton Model: A Naturally Parallelizable Approach to Computing Collective Excitations in Crystals and Aggregates.

A fragment-based method for computing vertical excitation energies of molecular clusters is introduced based on an ab initio implementation of a Frenkel-Davydov exciton model consisting of singly excited monomer basis states. Our strategy is to construct and diagonalize the exact Hartree-Fock Hamiltonian in such a basis. Matrix elements between nonorthogonal determinants are computed via the corresponding orbital transformation and the resulting generalized eigenvalue problem is solved to determine collective excitation energies and wave functions. The basis may be expanded to include higher-lying fragment excited states in order to account for interfragment polarization effects. Absolute errors of ≲0.1 eV (relative to supersystem methods) are achievable for systems such as water clusters and crystalline arrays of organic chromophores such as pentacene and napthalenediimide. Preliminary tests for a nine-chromophore subunit of an organic nanotube suggest that it is possible to target the optically bright state, even when it is a high-lying excitation, by using carefully selected basis states. The highly parallel nature of this method provides a foundation for further developments to treat collective excitations in large molecular assemblies.