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At least 19 records

Improved Methods for Modeling Functional Transition Metal Compounds in Complex Environments: Ground States, Excited States, and Spectroscopies

Rapid advances in energy applications require new theory and computational models to provide guidance for interpretation of experimental results and mechanistic understanding. New theory development is necessary to treat systems of increasing complexity, size, and relevance to real applications. Functional transition metal compounds, including molecules, clusters, nanoparticles, surfaces, and solids, provide particular promise for magnetic, optical, and catalytic applications. However, such systems can be exceptionally challenging to model. To make progress in understanding and designing transition metal compounds for energy applications, theory must be able to simulate such systems in complex environments, as well as simulate the spectra of such complex systems to provide direct connections with experiment. Leveraging the independent expertise of the team’s members, this project aimed to make inroads to the theoretical and computational challenges associated with studying transition metal compounds, their reaction chemistry, photophysics and photochemistry, and response to spectroscopic interrogation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Support of the Third Summer School and Workshop Focused on Theory and Applications of Time-Dependent Density Functional Theory, Electronic Excited States, and Excited State Dynamics

To create a community of scholars with a deep understanding of TDDFT and excited state methods, both their capabilities and limitations, and how they can be used to model the excited state properties and charge transfer in materials and molecules, we are planning the third iteration of a summer school and workshop focusing on theory and applications of TDDFT, Excited States, and Excited State Dynamics to be offered in the summer of 2023. The two iterations of the US-based school that we previously organized have been very successful with overwhelmingly positive feedback. There is a high level of engagement, enthusiasm, and active participation and networking amongst the students of the school and the scientists of the workshop.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using ground state and excited state density functional theory to decipher 3d dopant defects in GaN

Abstract Using ground state density functional theory (DFT) and implementing an occupation-constrained DFT (occ-DFT) for self-consistent excited state calculations, we decipher the electronic structure of the Mn dopant and other 3 d defects in GaN across the band gap. Our analysis, validated with broad agreement with defect levels (ground-state calculations) and photoluminescence data (excited-state calculations), mandates reinterpretation and reassignment of 3 d defect data in GaN. The Mn Ga defect is determined to span stable charge states from (1−) in n -type GaN through (2+) in p -type GaN. The Mn(2+) is predicted to be a d 2 ground state spin triplet defect with a singlet excited state, isoelectronic with the defect associated with the 1.19 eV photoluminescence in n -type GaN. The combined analysis of defect levels and excited states invites reassessment of all d 2 -capable dopants in GaN. We demonstrate that the 1.19 eV defect, a candidate defect for optically controlled quantum applications, cannot be the Cr(1+) assumed in literature and instead must be the V(0). The combined ground-state/excited-state DFT analysis is shown to be able to chemically fingerprint defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Vibrationally resolved ionization cross sections for the ground state and electronically excited states of the hydrogen molecule and its isotopomeres

An existing set of vibrationally resolved ionization cross section for the ground state and the first excited states of the hydrogen molecule, based on the Gryzinski method, is extended by cross sections for the isotopomeres of H{sub 2} (i.e. D{sub 2}, T{sub 2}, HD, HT, and DT), both for non-dissociative and dissociative ionizations. The comparison of cross sections for non-dissociative ionization of H{sub 2} with results obtained by the Molecular Convergent Close-Coupling method gives a very good agreement. The compiled tables give non-dissociative and dissociative cross sections for the ground state and the five energetically lowest electronically excited states of H{sub 2} and its isotopomeres, in each case for the first 9 vibrational levels. Data for all vibrational levels of the excited states is available online.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantum Davidson algorithm for excited states

Abstract Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace through real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

97 MATHEMATICS AND COMPUTING↗

Adaptive variational quantum eigensolvers for highly excited states

Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In this work, we explore the potential of variational quantum algorithms to approximate such states. We propose an adaptive variational quantum eigensolver (VQE) for excited states (X) that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian H by attempting to minimize the energy variance with respect to H. We benchmark the method by applying it to an Ising spin chain with integrable and nonintegrable regimes, where we calculate various quantities of interest, including the total energy, magnetization density, and entanglement entropy. We also compare the performance of adaptive VQE-X to an adaptive variant of the folded-spectrum method. For both methods, we find a strong dependence of the algorithm's performance on the choice of operator pool used for the adaptive construction of the ansatz. In particular, an operator pool including long-range two-body gates accelerates the convergence of both algorithms in the nonintegrable regime. Here, we also study the scaling of the number of variational parameters with system size, finding that an exponentially large number of parameters may be necessary to approximate individual highly excited states. Nevertheless, we argue that these methods lay a foundation for the use of quantum algorithms to study finite-energy-density properties of many-body systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observation of a dipole-bound excited state in 4-ethynylphenoxide and comparison with the quadrupole-bound excited state in the isoelectronic 4-cyanophenoxide

Negative ions do not possess Rydberg states, but can have Rydberg-like nonvalence excited states near the electron detachment threshold, including dipole-bound states (DBSs) and quadrupole-bound states (QBSs). While DBSs have been studied extensively, quadrupole-bound excited states have been more rarely observed. 4-cyanophenoxide (4CP – ) was the first anion observed to possess a quadrupole-bound exited state 20 cm-1 below its detachment threshold. Here we report the observation of a DBS in the isoelectronic 4-ethynylphenoxide anion (4EP – ), providing a rare opportunity to compare the behaviors of a dipole-bound and a quadrupole-bound excited state in a pair of very similar anions. Photodetachment spectroscopy (PDS) of cryogenically-cooled 4EP – reveals a DBS 76 cm -1 below its detachment threshold. Photoelectron spectroscopy (PES) at 266 nm shows that the electronic structure of 4EP – and 4CP – are nearly identical. The observed vibrational features in both the PDS and PES, as well as autodetachment from the nonvalence excited states, are also found to be similar for both anions. However, resonant two-photon detachment (R2PD) from the bound vibrational ground state is observed to be very different for the DBS in 4EP – and the QBS in 4CP – . The R2PD spectra reveal that decays take place from both the DBS and QBS to the respective anion ground electronic states within the 5 ns detachment laser pulse due to internal conversion followed by intramolecular vibrational redistribution (IVR), but the decay mechanisms appear to be very different. In the R2PD spectrum of 4EP – , we observe strong threshold electron signals, which are due to detachment, by the second photon, of highly rotationally excited anions resulted from the decay of the DBS. On the other hand, in the R2PD spectrum of 4CP – we observe well-resolved vibrational peaks due to the three lowest-frequency vibrational modes of 4CP – , which are populated from the decay of the QBS. Here, the different behaviors of the R2PD spectra suggest unexpected differences between the relaxation mechanisms of the dipole-bound and quadrupole-bound excited states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Vibrational Spin-Orbit Coupling Contributions to Excited State Decay of Ligand-to-Ligand Charge Transfer States

Controlling excited state relaxation processes is important in a variety of photochemical and photophysical processes, including the generation of ground and excited state spin polarization for quantum information science applications. Here, we address how specific static distortions – based on vibrational spin-orbit active modes at C2v symmetry determined by group theory – in a series of low-symmetry ligand-to-ligand charge transfer complexes enable direct spin-orbit coupling contributions to T1 → S0 excited state decay. These results are used to address spin-vibronic coupling contributions to T1 → S0 decay in a high-symmetry (tBu2bpy)Pt(S,S) (tBu2bpy = 4,4’-di-tert-butyl-2,2’-bipyridine and S,S = benzene-1,2-dithiolate) ligand-to-ligand charge transfer complex with effective C2v symmetry, where T1 relaxation is both spin- and orbitally forbidden due to the direct spin-orbit coupling matrix element being zero by symmetry. Low-frequency vibrations that involve a pyridine-pyridine twisting motion within the bpy ligand generate large ∂/∂Qi values that will contribute significantly to T1 → S0 relaxation. The work advances ligand design strategies for the generation of tailored T1 → S0 relaxation rates, which can be utilized to optimize the generation of electron spin polarization in radical-elaborated ligand-to-ligand charge transfer complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum Orbital Minimization Method for Excited States Calculation on a Quantum Computer

Herein we propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parametrized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts a classical optimizer to minimize the objective function with respect to the parameters in ansatz circuits. The objective function has an orthogonality constraint implicitly embedded, which allows qOMM to apply a different ansatz circuit to each input reference state. We carry out numerical simulations that seek to find excited states of H 2 , LiH, and a toy model consisting of four hydrogen atoms arranged in a square lattice in the STO-3G basis with UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.

97 MATHEMATICS AND COMPUTING↗

A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states

We extend our hybrid linear-method/accelerated-descent variational Monte Carlo optimization approach to excited states and investigate its efficacy in double excitations. In addition to showing a superior statistical efficiency when compared to the linear method, our tests on small molecules show good energetic agreement with benchmark methods. We also demonstrate the ability to treat double excitations in systems that are too large for a full treatment by using selected configuration interaction methods via an application to 4-aminobenzonitrile. Finally, we investigate the stability of state-specific variance optimization against collapse to other states’ variance minima and find that symmetry, Ansatz quality, and sample size all have roles to play in achieving stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Watching Excited State Dynamics with Optical and X-ray Probes: The Excited State Dynamics of Aquocobalamin and Hydroxocobalamin

Femtosecond time-resolved X-ray absorption (XANES) at the Co K-edge, X-ray emission (XES) in the Co Kβ and valence-to-core regions, and broadband UV–vis transient absorption are combined to probe the femtosecond to picosecond sequential atomic and electronic dynamics following photoexcitation of two vitamin B12 compounds, hydroxocobalamin and aquocobalamin. Polarized XANES difference spectra allow identification of sequential structural evolution involving first the equatorial and then the axial ligands, with the latter showing rapid coherent bond elongation to the outer turning point of the excited state potential followed by recoil to a relaxed excited state structure. Time-resolved XES, especially in the valence-to-core region, along with polarized optical transient absorption suggests that the recoil results in the formation of a metal-centered excited state with a lifetime of 2–5 ps. In conclusion, this combination of methods provides a uniquely powerful tool to probe the electronic and structural dynamics of photoactive transition-metal complexes and will be applicable to a wide variety of systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elucidation of complex triplet excited state dynamics in Pd(ii) biladiene tetrapyrroles

Pd(II) biladienes have been developed over the last five years as non-aromatic oligotetrapyrrole complexes that support a rich triplet photochemistry. In this work, we have undertaken the first detailed photophysical interrogation of three homologous Pd(II) biladienes bearing different combinations of methyl- and phenyl-substituents on the frameworks’ sp 3 -hybridized meso-carbon (i.e., the 10-position of the biladiene framework). These experiments have revealed unexpected excited-state dynamics that are dependent on the wavelength of light used to excite the biladiene. More specifically, transient absorption spectroscopy revealed that higher-energy excitation (λ exc ~ 350–500 nm) led to an additional lifetime (i.e., an extra photophysical process) compared to experiments carried out following excitation into the lowest-energy excited states (λ exc = 550 nm). Each Pd(II) biladiene complex displayed an intersystem crossing lifetime on the order of tens of ps and a triplet lifetime of ~20 μs, regardless of the excitation wavelength. However, when higher-energy light is used to excite the complexes, a new lifetime on the order of hundreds of ps is observed. The origin of the ‘extra’ lifetime observed upon higher energy excitation was revealed using density functional theory (DFT) and time-dependent DFT (TDDFT). These efforts demonstrated that excitation into higher-energy metal-mixed-charge-transfer excited states with high spin–orbit coupling to higher energy metal-mixed-charge-transfer triplet states leads to the additional excitation deactivation pathway. Furthermore, the results of this work demonstrate that Pd(II) biladienes support a unique triplet photochemistry that may be exploited for development of new photochemical schemes and applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Methods to Calculate Electronic Excited-State Dynamics for Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase

Here, we present an efficient set of methods for propagating excited-state dynamics involving a large number of configuration interaction singles (CIS) or Tamm-Dancoff approximation (TDA) single-reference excited states. Specifically, (i) following Head-Gordon et al., we implement an exact evaluation of the overlap of singly-excited CIS/TDA electronic states at different nuclear geometries using a biorthogonal basis and (ii) we employ a unified protocol for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states, where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reductive Dynamic and Static Excited State Quenching of a Homoleptic Ruthenium Complex Bearing Aldehyde Groups

A new homoleptic Ru polypyridyl complex bearing two aldehyde groups on each bipyridine ligand, [Ru(dab) 3 ](PF 6 ) 2 , where dab is 4,4′-dicarbaldehyde-2,2′-bipyridine, was synthesized, characterized, and utilized for iodide photo-oxidation studies. In acetonitrile (CH 3 CN) solution, the complex displayed an intense metal-to-ligand charge transfer (MLCT) absorbance maximum at 475 nm (ε = 22,000 M –1 cm –1 ) and an infrared (IR) band at 1712 cm –1 assigned to the pendent aldehyde groups. Visible light excitation in air-saturated solution resulted in room temperature photoluminescence (PL) with a maximum at 675 nm, a quantum yield, ϕ PL = 0.048, and an excited state lifetime, τ ο = 440 ns, from which radiative and nonradiative relaxation rate constants were extracted, k r = 9.1 × 10 4 s –1 and knr = 1.8 × 10 6 s –1 . Pulsed visible light excitation yielded transient UV–vis and IR absorption spectra consistent with an MLCT excited state; relaxation occurred with the maintenance of two isosbestic points in the visible region, and a lifetime that agreed with that measured by time-resolved PL. Cyclic voltammetry studies in a CH 3 CN solution with 0.1 M TBAPF 6 electrolyte revealed a quasi-reversible oxidation, E°(Ru III/II ) = +1.25 V vs. Fc +/0 , and three sequential one-electron reductions at −1.10, −1.25, and −1.54 V vs. Fc +/0 . Here, an excited state reduction potential of E°(Ru *2+/+ ) = +0.89 V vs. Fc +/0 was estimated with the Rehm–Weller expression. Titration of tetrabutylammonium iodide, TBAI, into a CD 3 CN solution of [Ru(dab) 3 ](PF 6 ) 2 resulted in significant shifts in the aldehyde H atom and 3,3′-biypridyl resonances that were analyzed with a 1:1 equilibrium model, from which K eq = 460 M –1 was extracted, increasing to 5800 M –1 when the solvent was changed to acetone-d 6 . Iodide titrations resulted in a significant quenching of the [Ru(dab) 3 ] *2+ lifetime and quantum yield in both CH 3 CN and acetone solvents. In CH 3 CN, the quenching was mainly dynamic and well described by the Stern–Volmer model, from which a quenching rate constant, k q , of 4.5 × 10 10 M –1 s –1 and an equilibrium constant, K eq , of 8.3 × 10 3 M –1 were obtained. In acetone, the static quenching pathway by iodide was greatly enhanced, with a K eq of 1.2 × 10 4 M –1 and a higher k q of 9.2 × 10 10 M –1 s –1 .

Aldehydes↗

Excited state electron transfer in A 2 and A 2 B 2 functionalized zinc porphyrins carrying rigid and flexible β -pyrrole π-extended substituents

Optical absorption and emission, electrochemical, and photochemical properties of peripherally functionalized with flexible and rigid π-extended substituents on A 2 and A 2 B 2 type zinc porphyrins is investigated. The significance of rigid π-substituents over flexible ones in governing the spectral properties is unraveled. Flexible π-substituents on the porphyrin ring caused appreciable spectral broadening compared to porphyrin carrying rigid π-substituents. Further, supramolecular dyads are formed by coordinating phenyl imidazole functionalized fullerene, C 60 Im. Here, the calculated binding constants for the 1:1 complexes is in the order of 2–7 × 10 5 M −1 suggesting stable complex formation. Free-energy calculations performed according to the Rehm–Weller approach suggested possibility of excited state electron transfer in these dyads. Femtosecond transient absorption studies of the dyads performed in o-dichlorobenzene showed evidence of occurrence of electron transfer from the singlet-excited state that was in competition with the intersystem crossing process to populate the triplet-excited state of porphyrins.

A2 and A2B2 functionalized zinc↗

Radiative properties of quantum emitters in boron nitride from excited state calculations and Bayesian analysis

Abstract Point defects in hexagonal boron nitride (hBN) have attracted growing attention as bright single-photon emitters. However, understanding of their atomic structure and radiative properties remains incomplete. Here we study the excited states and radiative lifetimes of over 20 native defects and carbon or oxygen impurities in hBN using ab initio density functional theory and GW plus Bethe-Salpeter equation calculations, generating a large data set of their emission energy, polarization and lifetime. We find a wide variability across quantum emitters, with exciton energies ranging from 0.3 to 4 eV and radiative lifetimes from ns to ms for different defect structures. Through a Bayesian statistical analysis, we identify various high-likelihood charge-neutral defect emitters, among which the native V N N B defect is predicted to possess emission energy and radiative lifetime in agreement with experiments. Our work advances the microscopic understanding of hBN single-photon emitters and introduces a computational framework to characterize and identify quantum emitters in 2D materials.

Chemistry↗