Reduced-Scaling Approach for Configuration Interaction Singles and Time-Dependent Density Functional Theory Calculations Using Hybrid Functionals

Overview of Developments in the MRCC Program System

mrcc is a versatile suite of quantum chemistry programs designed for accurate ab initio and density functional theory (DFT) calculations. This contribution outlines the general features and recent developments of the package. The most popular features include the open-ended coupled-cluster (CC) code, state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)], second-order algebraic-diagrammatic construction, and combined wave function theory-DFT approaches. Cost-reduction techniques are implemented, such as natural orbital (NO), local NO (LNO), and natural auxiliary function approximations, which significantly decrease the computational demands of these methods. This paper also details the method developments made over the past five years, including efficient schemes to approach the complete basis set limit for CCSD(T) and the extension of our LNO-CCSD(T) method to open-shell systems. Additionally, we discuss the new approximations introduced to accelerate the self-consistent field procedure and the cost-reduction techniques elaborated for analytic gradient calculations at various levels. Furthermore, embedding techniques and novel range-separated double-hybrid functionals are presented for excited-state calculations, while the extension of the theories established to describe core excitations and ionized states is also discussed. For academic purposes, the program and its source code are available free of charge, and its commercial use is also facilitated.

Theoretical investigation of distal charge separation in a perylenediimide trimer

An exciton-phonon (ex-ph) model based on our recently developed block interaction product basis framework is introduced to simulate the distal charge separation (CS) process in aggregated perylenediimide (PDI) trimer incorporating the quantum dynamic method, i.e., the time-dependent density matrix renormalization group. The electronic Hamiltonian in the ex-ph model is represented by nine constructed diabatic states, which include three local excited (LE) states and six charge transfer (CT) states from both the neighboring and distal chromophores. These diabatic states are automatically generated from the direct products of the leading localized neutral or ionic states of each chromophore's reduced density matrix, which are obtained from ab initio quantum chemical calculation of the subsystem consisting of the targeted chromophore and its nearest neighbors, thus considering the interaction of the adjacent environment. In order to quantum-dynamically simulate the distal CS process with massive coupled vibrational modes in molecular aggregates, we used our recently proposed hierarchical mapping approach to renormalize these modes and truncate those vibrational modes that are not effectively coupled with electronic states accordingly. The simulation result demonstrates that the formation of the distal CS process undergoes an intermediate state of adjacent CT, i.e., starts from the LE states, passes through an adjacent CT state to generate the intermediates (∼200 fs), and then formalizes the targeted distal CS via further charge transference (∼1 ps). This finding agrees well with the results observed in the experiment, indicating that our scheme is capable of quantitatively investigating the CS process in a realistic aggregated PDI trimer and can also be potentially applied to exploring CS and other photoinduced processes in larger systems.

Artificial design of organic emitters via a genetic algorithm enhanced by a deep neural network

The design of molecules requires multi-objective optimizations in high-dimensional chemical space with often conflicting target properties. To navigate this space, classical workflows rely on the domain knowledge and creativity of human experts, which can be the bottleneck in high-throughput approaches. Herein, we present an artificial molecular design workflow relying on a genetic algorithm and a deep neural network to find a new family of organic emitters with inverted singlet-triplet gaps and appreciable fluorescence rates. We combine high-throughput virtual screening and inverse design infused with domain knowledge and artificial intelligence to accelerate molecular generation significantly. This enabled us to explore more than 800 000 potential emitter molecules and find more than 10 000 candidates estimated to have inverted singlet-triplet gaps (INVEST) and appreciable fluorescence rates, many of which likely emit blue light. This class of molecules has the potential to realize a new generation of organic light-emitting diodes.

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules

We report a minimal auxiliary basis model for time-dependent density functional theory (TDDFT) with hybrid density functionals that can accurately reproduce excitation energies and absorption spectra from TDDFT while reducing cost by about 2 orders of magnitude. Our method, dubbed TDDFT-ris, employs the resolution-of-the-identity technique with just one s-type auxiliary basis function per atom for the linear response operator, where the Gaussian exponents are parametrized across the periodic table using tabulated atomic radii with a single global scaling factor. By tuning on a small test set, we determine a single functional-independent scale factor that balances errors in excitation energies and absorption spectra. Benchmarked on organic molecules and compared to standard TDDFT, TDDFT-ris has an average energy error of only 0.06 eV and yields absorption spectra in close agreement with TDDFT. Thus, TDDFT-ris enables simulation of realistic absorption spectra in large molecules that would be inaccessible from standard TDDFT.

Automated Generation of Optimized Auxiliary Basis Sets for Long-Range-Corrected TDDFT Using the Cholesky Decomposition

Range-separated hybrid functionals making use of a smooth separation of the Coulomb operator in terms of the error function and its complement have proven to be a valuable tool for improving Kohn-Sham density functional theory (DFT) calculations. This holds in particular for obtaining accurate excitation energies from linear-response time-dependent DFT. Evaluating the long-range exchange contributions represents one of the most time-consuming tasks in such calculations. Prefitted auxiliary basis sets can be employed to speed up this step. Here, we present a way to generate auxiliary basis sets optimized to fit the long-range exchange contributions only, contrary to the common optimization strategies on the basis of the full Coulomb operator. For this purpose, we use the atomic Cholesky decomposition technique. The basis sets are generated on-the-fly using the specific range-separation parameter defined in the exchange-correlation functional. We obtain excitation energies and oscillator strengths which are of similar or better accuracy than those obtained with conventional resolution-of-the-identity auxiliary basis sets while drastically reducing the number of auxiliary functions required. This is demonstrated for the QUESTDB#5 benchmark set. In addition, we outline the benefits of this approach in sequences of calculations employing varying range-separation parameters, as is the case in the optimally tuned range-separation strategy. Finally, we illustrate the efficiency of this approach for real-world examples, namely, a chlorophyll tetramer from photosystem II and a carotenoid-porphyrin-C₆₀ triad.

Low-Scaling Excited State Calculation Using the Block Interaction Product State

We develop an automatic and efficient scheme for the accurate construction of the bases for excitonic models, which can enable "black-box" excited state structure calculations for large molecular systems. These new and optimized bases, which are named the block interaction product state (BIPS), can be expressed as the direct products of the local states for each chromophore. Each chromophore's local states are selected by diagonalization of its reduced density matrix, which is obtained by quantum chemical calculation of the small subsystem composed of the chromophore and its nearest neighbors. We implemented the BIPS framework with fragment-based calculations considering two- and three-body interactions. Test calculations for eight different molecular aggregates demonstrate that this framework provides an accurate description of not only the excitation energies but also the first-order wave function properties (dipole moment and transition dipole moment) of the low-lying excited states at a low-scaling computational cost.

Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning

Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.