Visualizing Complex-Valued Molecular Orbitals

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

Efficient Quantum Analytic Nuclear Gradients with Double Factorization

Efficient representations of the Hamiltonian such as double factorization drastically reduce circuit depth or number of repetitions in error corrected and noisy intermediate scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically-simulated examples with up to 327 quantum and 18470 total atoms in QM/MM simulations, with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver (VQE) in case studies such as transition state optimization, ab initio molecular dynamics simulation and energy minimization of large molecular systems.Comment: 22 pages, 5 figure

Spin-state energetics of iron(II) porphyrin from the particle-particle random phase approximation

The particle-particle random phase approximation (pp-RPA) has been deployed to study the spin-state energetics of transition metal (TM) complexes for the first time in this work. Namely, we designed and implemented a non-canonical reference pp-RPA protocol that is capable of capturing the singlet low-spin (LS) – triplet intermediate-spin (IS) excitation process of iron(II) complexes; herein we applied this method to iron-porphyrin related heme derivatives with clearly defined LS and IS electronic states. Coupled to the CAM-B3LYP functional and to Dunning-type basis sets, we utilized both the active-space and Davidson methods to solve the pp-RPA equation effectively to obtain vertical singlet–triplet excitation energies. Correcting these vertical metrics with a structural relaxation factor for each species, we evaluated the relative stability of LS and IS electronic states. Comparison of the pp-RPA results to established ab initio data revealed that pp-RPA describes well excitation energies and related relative spin state stabilities if the transition is based on non-bonding d-orbitals, such as complexes without an axial ligand in the investigated set of molecules. But it notably overestimates the stability of the singlet LS state to the triplet IS state in complexes, where the d-orbitals at which the excitation is centered have bonding or antibonding character

Accurate Treatment of Charge-Transfer Excitations and Thermally Activated Delayed Fluorescence Using the Particle–Particle Random Phase Approximation

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 (S₁) and triplet (T₁) excited states (Δ<i>E</i>(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 S₁ and T₁ 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<i>E</i>(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 S₁ and T₁ 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<i>E</i>(ST) = ¹CT – ³CT). For experimentally known TADF molecules with a small (<0.2 eV) Δ<i>E</i>(ST) in this data set, a high accuracy is demonstrated for the prediction of both the S₁ (MAD = 0.18 eV) and T₁ (MAD = 0.20 eV) excitation energies as well as Δ<i>E</i>(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

Accurate Treatment of Charge-Transfer Excitations and Thermally Activated Delayed Fluorescence Using the Particle–Particle Random Phase Approximation

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 (S₁) and triplet (T₁) excited states (Δ<i>E</i>(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 S₁ and T₁ 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<i>E</i>(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 S₁ and T₁ 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<i>E</i>(ST) = ¹CT – ³CT). For experimentally known TADF molecules with a small (<0.2 eV) Δ<i>E</i>(ST) in this data set, a high accuracy is demonstrated for the prediction of both the S₁ (MAD = 0.18 eV) and T₁ (MAD = 0.20 eV) excitation energies as well as Δ<i>E</i>(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

Diverse Optimal Molecular Libraries for Organic Light-Emitting Diodes

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

Oxidation of Cymantrene Analogues of Ferrocifen: Electrochemical, Spectroscopic, and Computational Studies of the Parent Complex 1,1′-Diphenyl-2-cymantrenylbutene

The oxidative electrochemical behavior of 1,1′-diphenyl-2-cymantrenylbutene (<b>1</b>), a cymantrene analogue of the breast cancer drug ferrocifen, was shown to involve the sequential electron-transfer series <b>1</b>/<b>1</b>⁺/<b>1</b>²⁺ in dichloromethane/0.05 M [NBu₄]­[B­(C₆F₅)₄] (<i>E</i>_1/2 values 0.78 and 1.18 V vs ferrocene). By a combination of spectroscopic and computational techniques, it was shown that the cymantrene functionality plays an important role in dissipating the positive charges in the oxidized compounds and is therefore an active participant in the redox events. The redox-active orbital goes from roughly equal degrees of organometallic and π-organic (diphenylolefin) makeup in <b>1</b> to increasingly organic based fractions in <b>1</b>⁺ and <b>1</b>²⁺. Structural changes mimicking those of oxidized tetrakis­(aryl)­ethylenes accompany the one-electron oxidations. There is sufficient unpaired electron density on the manganese center in <b>1</b>⁺ to allow for oxidatively induced ligand exchange of one or more of the carbonyl ligands with donor ligands, including phosphites and pyridine. The complex Mn­(CO)₂P­(OPh)₃(η⁵-C₅H₄(Et)­CC­(C₆H₅)₂) was prepared by the “electrochemical switch” method, wherein [Mn­(CO)₂P­(OPh)₃(η⁵-C₅H₄(Et)­CC­(C₆H₅)₂)]⁺, produced by the oxidation of <b>1</b> in the presence of P­(OPh)₃, was reduced back to the neutral CO-substituted complex