Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way, and therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field (MCSCF) theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces (PES). This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections, and on-the-fly photodynamics simulations; both depend heavily on the ability of the method to properly explore the PES. Since such applications require the nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly improves the utility of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. To motivate the readers, we first summarize the notable applications of multireference electron correlation methods to mainstream chemistry, including geometry optimizations and on-the-fly dynamics. Subsequently, we review the analytical nuclear gradient and derivative coupling theories for these methods, and the software infrastructure that allows one to make use of these quantities in applications. The future prospects are discussed at the end of this review.
We report the analytical nuclear gradient theory for complete active space second-order perturbation theory (CASPT2) with imaginary shift, which is commonly used to avoid divergence of the perturbation expression. Our formulation is based on the Lagrangian approach and is an extension of the algorithm for CASPT2 nuclear gradients with real shift. The working equations are derived and implemented into an efficient parallel program. Numerical examples are presented for the ground-and excited-state geometries and conical intersections of a green fluorescent protein model chromophore, p−HBDI − . We also report timing benchmarks with adenine, p−HBDI − , and iron porphyrin. It is demonstrated that the energies and geometries obtained with the imaginary shift improve accuracy at a minor additional cost which is mainly associated with evaluating the effective density matrix elements for the imaginary shift term.
We report an implementation of a program for visualizing complex-valued molecular orbitals. The orbital phase information is encoded on each of the vertices of triangle meshes using the standard color wheel. Using this program, we visualized the molecular orbitals for systems with spin-orbit couplings, external magnetic fields, and complex absorbing potentials. Our work has not only created visually attractive pictures, but also clearly demonstrated that the phases of the complex-valued molecular orbitals carry rich chemical and physical information of the system, which has often been unnoticed or overlooked.
Thermally activated delayed florescence (TADF) is a mechanism that increases the electroluminescence efficiency in organic light-emitting diodes by harnessing both singlet and triplet excitons. TADF is facilitated by a small energy difference between the first singlet (S) and triplet (T) excited states (Δ E(ST)), which is minimized by spatial separation of the donor and acceptor moieties. The resultant charge-transfer (CT) excited states are difficult to model using time-dependent density functional theory (TDDFT) because of the delocalization error present in standard density functional approximations to the exchange-correlation energy. In this work we explore the application of the particle-particle random phase approximation (pp-RPA) for the determination of both S and T excitation energies. We demonstrate that the accuracy of the pp-RPA is functional dependent and that, when combined with the hybrid functional B3LYP, the pp-RPA computed Δ E(ST) have a mean absolute deviation (MAD) of 0.12 eV for the set of examined molecules. A key advantage of the pp-RPA approach is that the S and T states are characterized as CT states for all of experimentally reported TADF molecules examined here, which allows for an estimate of the singlet-triplet CT excited state energy gap (Δ E(ST) = CT -CT). For experimentally known TADF molecules with a small (<0.2 eV) Δ E(ST) in this data set, a high accuracy is demonstrated for the prediction of both the S (MAD = 0.18 eV) and T (MAD = 0.20 eV) excitation energies as well as Δ E(ST) (MAD = 0.05 eV). This result is attributed to the consideration of correct antisymmetry in the particle-particle interaction leading to the use of full exchange kernel in addition to the Coulomb contribution, as well as a consistent treatment of both singlet and triplet excited states. The computational efficiency of this approach is similar to that of TDDFT, and the cost can be reduced significantly by using the active-space approach.
Organic light-emitting diodes (OLEDs) have wide-ranging applications, from lighting to device displays. However, the repertoire of organic molecules with efficient blue emission is limited. To address this limitation, we have developed a strategy to design property-optimized, diversity-oriented libraries of structures with favorable fluorescence properties. This approach identifies novel diverse candidate organic molecules for blue emission with strong oscillator strengths and low singlet-triplet energy gaps that favor thermally activated delayed fluorescence (TADF) emission.
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