Quasi-diabatic States from Active Space Decomposition

The Localized Active Space Method with Unitary Selective Coupled Cluster

We introduce a hybrid quantum-classical algorithm, the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. Derived from the localized active space unitary coupled cluster (LAS-UCCSD) method, LAS-USCCSD first performs a classical LASSCF calculation, then selectively identifies the most important parameters (cluster amplitudes used to build the multireference UCC ansatz) for restoring interfragment interaction energy using this reduced set of parameters with the variational quantum eigensolver method. We benchmark LAS-USCCSD against LAS-UCCSD by calculating the total energies of (H2)2, (H2)4, and trans-butadiene, and the magnetic coupling constant for a bimetallic compound [Cr2(OH)3(NH3)6]3+. For these systems, we find that LAS-USCCSD reduces the number of required parameters and thus the circuit depth by at least 1 order of magnitude, an aspect which is important for the practical implementation of multireference hybrid quantum-classical algorithms like LAS-UCCSD on near-term quantum computers.

Accurate and interpretable representation of correlated electronic structure via Tensor Product Selected CI

The task of computing wavefunctions that are accurate, yet simple enough mathematical objects to use for reasoning, has long been a challenge in quantum chemistry. The difficulty in drawing physical conclusions from a wavefunction is often related to the generally large number of configurations with similar weights. In Tensor Product Selected Configuration Interaction (TPSCI), we use a locally correlated tensor product state basis, which has the effect of concentrating the weight of a state onto a smaller number of physically interpretable degrees of freedom. In this paper, we apply TPSCI to a series of three molecular systems ranging in separability, one of which is the first application of TPSCI to an open-shell bimetallic system. For each of these systems, we obtain accurate solutions to large active spaces, and analyze the resulting wavefunctions through a series of different approaches including (i) direct inspection of the TPS basis coefficients, (ii) construction of Bloch effective Hamiltonians, and (iii) computation of cluster correlation functions.

Automatic State Interaction with Large Localized Active Spaces for Multimetallic Systems

The localized active space self-consistent field method factorizes a complete active space wave function into an antisymmetrized product of localized active space wave function fragments. Correlation between fragments is then reintroduced through localized active space state interaction (LASSI), in which the Hamiltonian is diagonalized in a model space of LAS states. However, the optimal procedure for defining the LAS fragments and LASSI model space is unknown. We here present an automated framework to explore systematically convergent sets of model spaces, which we call LASSI[r, q]. This method requires the user to select only r, the number of electron hops from one fragment to another, and q, the number of fragment basis functions per Hilbert space, which converges to CASCI in the limit of r, q → ∞. Numerical tests of this method on the trimetal oxo-centered complexes [Fe(III)Al(III)Fe(II)(μ3-O)(HCOO)6] and [Fe(III)2Fe(II)(μ3-O)(HCOO)6] show efficient convergence to the CASCI limit with 4-10 orders of magnitude fewer states than CASCI.

Toward Large-Scale Restricted Active Space Calculations Inspired by the Schmidt Decomposition

We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group (DMRG) method via the dynamically extended active space procedure. Benchmark calculations are compared against state-of-the-art results of C₂ and Cr₂, which are notorious for their multireference character. Our results for ground and excited states together with spectroscopic constants demonstrate that the proposed novel approach, dubbed as DMRG-RAS, which is variational and free of uncontrolled method errors, has the potential to outperfom conventional methods for strongly correlated molecules.

Localized Quantum Chemistry on Quantum Computers

Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here, we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground-state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with the system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene, and resource estimates are provided for linear chains of up to 20 H2 molecules.

Localized Active Space-State Interaction: a Multireference Method for Chemical Insight

Multireference electronic structure methods, like the complete active space (CAS) self-consistent field model, have long been used to characterize chemically interesting processes. Important work has been done in recent years to develop modifications having a lower computational cost than CAS, but typically these methods offer no more chemical insight than that from the CAS solution being approximated. In this paper, we present the localized active space-state interaction (LASSI) method that can be used not only to lower the intrinsic cost of the multireference calculation but also to improve interpretability. The localized active space (LAS) approach utilizes the local nature of the electron-electron correlation to express a composite wave function as an antisymmetrized product of unentangled wave functions in local active subspaces. LASSI then uses these LAS states as a basis from which to express complete molecular wave functions. This not only makes the molecular wave function more compact but also permits flexibility in choosing those states to be included in the basis. Such selective inclusion of states translates to the selective inclusion of specific types of interactions, thereby allowing a quantitative analysis of these interactions. We demonstrate the use of LASSI to study charge migration and spin-flip excitations in multireference organic molecules. We also compute the J coupling parameter for a bimetallic compound using various LAS bases to construct the Hamiltonian to provide insights into the coupling mechanism.

Importance of dynamical electron correlation in diabatic couplings of electron-exchange processes

We demonstrate the importance of the dynamical electron correlation effect in diabatic couplings of electron-exchange processes in molecular aggregates. To perform a multireference perturbation theory with large active space of molecular aggregates, an efficient low-rank approximation is applied to the complete active space self-consistent field reference functions. It is known that kinetic rates of electron-exchange processes, such as singlet fission, triplet-triplet annihilation, and triplet exciton transfer, are not sufficiently explained by the direct term of the diabatic couplings but efficiently mediated by the low-lying charge transfer states if the two molecules are in close proximity. It is presented in this paper, however, that regardless of the distance of the molecules, the direct term is considerably underestimated by up to three orders of magnitude without the dynamical electron correlation, i.e., the diabatic states expressed in the active space are not adequate to quantitatively reproduce the electron-exchange processes.

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe-Salpeter Equation

Herein, we present a fragment-based approach for calculating the charged and neutral excited states in molecular systems, based on the many-body Green's function method within the GW approximation and the Bethe-Salpeter equation (BSE). The implementation relies on the many-body expansion of the total irreducible polarizability on the basis of fragment molecular orbitals. The GW quasi-particle energies in complex molecular environments are obtained by the GW calculation for the target fragment plus induced polarization contributions of the surrounding fragments at the static Coulomb-hole plus screened exchange level. In addition, we develop a large-scale GW/BSE method for calculating the delocalized excited states of molecular aggregates, based on the fragment molecular orbital method and the exciton model. The accuracy of fragment-based GW and GW/BSE methods was evaluated on molecular clusters and molecular crystals. We found that the accuracy of the total irreducible polarizability can be improved systematically by including two-body correction terms, and the fragment-based calculations can reasonably reproduce the results of the corresponding unfragmented calculations with a relative error of less than 100 meV. The proposed approach enables efficient excited-state calculations for large molecular systems with reasonable accuracy.

Three States Involving Vibronic Resonance is a Key to Enhancing Reverse Intersystem Crossing Dynamics of an Organoboron-Based Ultrapure Blue Emitter

The recently developed narrow-band blue-emitting organoboron chromophores based on the multiple-resonance (MR) effect have now become one of the most important components for constructing efficient organic light emitting diodes (OLEDs). While they basically emit through fluorescence, they are also known for showing substantial thermally activated delayed fluorescence (TADF) even with a relatively large singlet-triplet gap (ΔE _ST). Indeed, understanding the reverse intersystem crossing (RISC) dynamics behind this peculiar TADF will allow judicious molecular designs toward achieving better performing OLEDs. Explaining the underlying nonadiabatic spin-flip mechanism, however, has often been equivocal, and how the sufficiently fast RISC takes place even with the sizable ΔE _ST and vanishingly small spin-orbit coupling is not well understood. Here, we show that a vibronic resonance, namely the frequency matching condition between the vibration and the electronic energy gap, orchestrates three electronic states together and this effect plays a major role in enhancing RISC in a typical organoboron emitter. Interestingly, the mediating upper electronic state is quite high in energy to an extent that its thermal population is vanishingly small. Through semiclassical quantum dynamics simulations, we further show that the geometry dependent non-Condon coupling to the upper triplet state that oscillates with the frequency ΔE _ST/ℏ is the main driving force behind the peculiar resonance enhancement. The existence of an array of vibrational modes with strong vibronic rate enhancements provides the ability to sustain efficient RISC over a range of ΔE _ST in defiance of the energy gap law, which can render the MR-emitters peculiar in comparison with more conventional donor-acceptor type emitters. Our investigation may provide a new guide for future blue emitting molecule developments.

Rational design of doubly-bridged chromophores for singlet fission and triplet–triplet annihilation

A novel multiple-bridging realizes rational molecular design for efficient singlet fission and triplet–triplet annihilation.

Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H(d), and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H(d) individually provides a starting point (seed) from which convergence of the full H(d) construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4(1)A states of phenol and the 1,2(1)A states of NH3, states which are coupled by conical intersections.