A diabatization protocol that includes spin-orbit coupling

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

A vibrational electronic-thermofield coupled cluster (VE-TFCC) approach is developed to calculate thermal properties of non-adiabatic vibronic coupling systems. The thermofield (TF) theory and a mixed linear exponential ansatz based on second-quantized Bosonic construction operators are introduced to propagate the thermal density operator as a "pure state" in the Bogoliubov representation. Through this compact representation of the thermal density operator, the approach is basis-set-free and scales classically (polynomial) as the number of degrees of freedoms (DoF) in the system increases. The VE-TFCC approach is benchmarked with small test models and a real molecular compound (CoF4- anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF3 + F- → CoF4-. Results shows that the VE-TFCC approach, in conjunction with vibronic models, provides an effective protocol for calculating thermodynamic properties of vibronic coupling systems.

Adiabat-to-Diabat Angle in Seam Space: Renner-Teller-Type and Pseudo-Jahn-Teller-Type Problems

In this study, we examine the adiabat-to-diabat (ATD) angles for trajectories in 2-dimensional vibrational subspace of the seam space of two degenerate states. In circulating around the tangential touching degeneracy center, the ATD angle is changed by2 π ${2\pi }$ or 0, similar to the Renner-Teller problem and the pseudo-Jahn-Teller problem, respectively. These ATD angle profiles may be indistinguishable from those of circulating multiple conical intersections or a pseudo-Jahn-Teller center. Methods to discern those seemingly indistinguishable cases are proposed. A sharp zigzag variation of the ATD angle is seen as a feature for trajectories that graze a pseudo-Jahn-Teller-type tangential touching center, in contrast to the monotonic steep variation for grazing a conical intersection or a Renner-Teller-type tangential touching center.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

The Lack of Triplet Fusion for an Intramolecular Singlet Fission Chromophore: The Expected, the Unexpected, and a Reconciliation

Singlet fission (SF) has the potential to play a key role in photovoltaics since it generates a larger number of longer-lived triplet excitons after photoabsorption. Intramolecular SF (iSF) is of special interest since it enables tuning of SF efficiency by adjusting interchromophore configuration through covalent interaction. However, as elaborated in the present work, iSF chromophores are doomed to dissatisfy one general thermodynamic criterion for all SF chromophores, intramolecular or not: E(T2) ≥ 2E(T1), and therefore, the fusion of two triplet excitons to one triplet exciton is thermodynamically favorable. In our nonadiabatic quantum dynamics simulation for a model iSF chromophore, this expected fusion does not occur, because of the inefficient intersystem crossing hidden under the cover of internal conversion of the triplet fusion. A reconciliation is achieved between the dissatisfaction of E(T2) ≥ 2E(T1) and the large tetraradical character for general iSF chromophores.

Triplet Separation after the Fastest Intramolecular Singlet Fission in the Smallest Chromophore

Singlet fission is of key importance in harvesting solar energy in solar cells, as it generates a pair of triplet excitons on the incidence of a photon. This phenomenon is not yet widely employed in the organic photovoltaics industry mostly because of the rarity of singlet fission chromophores. Pyrazino[2,3-g]quinoxaline-1,4,6,9-tetraoxide was recently designed as the smallest intramolecular singlet fission chromophore, and it undergoes the fastest singlet fission with a 16 fs time scale. The subsequent separation of the generated triplet-pair is of likewise importance as their efficient generation. Through quantum chemistry calculations and quantum dynamics simulations, we show that the triplet-pair separates to residing on two chromophores with an ∼80% probability on each collision between a chromophore with the triplet-pair and a ground state chromophore. Avoided crossing, instead of conical intersection, is involved in the efficient exciton separation.

Design of the Smallest Intramolecular Singlet Fission Chromophore with the Fastest Singlet Fission

We designed an intramolecular singlet fission (iSF) chromophore, pyrazino[2,3-g]quinoxaline-1,4,6,9-tetraoxide. Appropriate substitutions into anthracene enhance the tetraradical character, so that the molecule accommodates a pair of triplet excitons in its lowest singlet excited state. Our simulation showed a 16 fs fast iSF of the design, which is a new record. The design also sets a new record of small size iSF chromophore and high exciton density. The design can be synthesized by oxidizing the tertiary N centers of the existent pyrazino[2,3-g]quinoxaline.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in tetrahedral and octahedral symmetries

Heavy element compounds with high symmetries often feature both spin-orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be three-fold degenerate and experience complicated Jahn-Teller and pseudo-Jahn-Teller interactions. To accurately describe these interactions, high quality spin-orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin-orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes, and generates Hamiltonian expansion formulas of arbitrarily high order.

Theoretical analysis of the role of complex transition dipole phase in XUV transient-absorption probing of charge migration

We theoretically investigate the role of complex dipole phase in the attosecond probing of charge migration. The iodobromoacetylene ion (ICCBr⁺) is considered as an example, in which one can probe charge migration by accessing both the iodine and bromine ends of the molecule with different spectral windows of an extreme-ultraviolet (XUV) pulse. The analytical expression for transient absorption shows that the site-specific information of charge migration is encoded in the complex phase of cross dipole products for XUV transitions between the I-4d and Br-3d spectral windows. Ab-initio quantum chemistry calculations on ICCBr⁺ reveal that there is a constant π phase difference between the I-4d and Br-3d transient-absorption spectral windows, irrespective of the fine-structure energy splittings. Transient absorption spectra are simulated with a multistate model including the complex dipole phase, and the results correctly reconstruct the charge-migration dynamics via the quantum beats in the two element spectral windows, exhibiting out-of-phase oscillations.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries

Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C₁ to D_∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.

Analyzing Grid-Based Direct Quantum Molecular Dynamics Using Non-Linear Dimensionality Reduction

Grid-based schemes for simulating quantum dynamics, such as the multi-configuration time-dependent Hartree (MCTDH) method, provide highly accurate predictions of the coupled nuclear and electronic dynamics in molecular systems. Such approaches provide a multi-dimensional, time-dependent view of the system wavefunction represented on a coordinate grid; in the case of non-adiabatic simulations, additional information about the state populations adds a further layer of complexity. As such, wavepacket motion on potential energy surfaces which couple many nuclear and electronic degrees-of-freedom can be extremely challenging to analyse in order to extract physical insight beyond the usual expectation-value picture. Here, we show that non-linear dimensionality reduction (NLDR) methods, notably diffusion maps, can be adapted to extract information from grid-based wavefunction dynamics simulations, providing insight into key nuclear motions which explain the observed dynamics. This approach is demonstrated for 2-D and 9-D models of proton transfer in salicylaldimine, as well as 8-D and full 12-D simulations of cis-trans isomerization in ethene; these simulations demonstrate how NLDR can provide alternative views of wavefunction dynamics, and also highlight future developments.

Enabling a Unified Description of Both Internal Conversion and Intersystem Crossing in Formaldehyde: A Global Coupled Quasi-Diabatic Hamiltonian for Its S0, S1, and T1 States

In our recent work, a diabatic Hamiltonian that couples the S₀ and S₁ states of formaldehyde was constructed using a robust fitting-and-diabatizing procedure with artificial neural networks, which is capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, based on the diabatization of S₀ and S₁, the spin-orbit couplings between singlet states (S₀, S₁) and triplet state T₁ are also determined in the same diabatic representation. The diabatized spin-orbit couplings are then fit with a symmetrized neural-network functional form. The ab initio spin-orbit couplings are well reproduced in large configuration space. Together with the neural-network-based potential energy surface for T₁, the full quasi-diabatic Hamiltonian for the S₀, S₁, and T₁ states is completed, enabling a unified description of both internal conversion and intersystem crossing in formaldehyde. The vibrational levels on the three adiabatic states are found to be in good agreement with known experimental band origins.

Accurate Neural Network Representation of the Ab Initio Determined Spin-Orbit Interaction in the Diabatic Representation Including the Effects of Conical Intersections

A method for fitting ab initio determined spin-orbit coupling interactions, in the Breit-Pauli approximation, based on quasidiabatic representations using neural network fits is reported. The algorithm generalizes our recently reported neural network approach for representing the dipole interaction. The S₀, S₁, and T₁ states of formaldehyde are used as an example. First, the two singlet states S₀ and S₁ are diabatized with a modified Boys Localization diabatization method. Second, the spin-orbit coupling between singlet and triplet states is transformed to the diabatic representation. This removes the discontinuities in the adiabatic representation. The diabatized spin-orbit couplings are then fit with smooth neural network functions. The analytic representation of spin-orbit coupling interactions in a diabatic basis by neural networks will make accurate full-dimensional quantum dynamical treatment of both internal conversion and intersystem crossing possible, which will help us to gain better understanding of both processes.

Ab initio investigation of Br-3d core-excited states in HBr and HBr+ toward XUV probing of photochemical dynamics

Ultrafast X-ray/XUV transient absorption spectroscopy is a powerful tool for real-time probing of chemical dynamics. Interpretation of the transient absorption spectra requires knowledge of core-excited potentials, which necessitates assistance from high-level electronic-structure computations. In this study, we investigate Br-3d core-excited electronic structures of hydrogen bromide (HBr) using spin-orbit general multiconfigurational quasidegenerate perturbation theory (SO-GMC-QDPT). Potential energy curves and transition dipole moments are calculated from the Franck-Condon region to the asymptotic limit and used to construct core-to-valence absorption strengths for five electronic states of HBr (Σ 1 0 + ,   3 Π 1 ,   1 Π 1 ,   3 Π 0 + ,   3 Σ 1 ) and two electronic states of HBr+ (2Π3∕2, 2Σ1∕2). The results illustrate the capabilities of Br-3d edge probing to capture transitions of the electronic-state symmetry as well as nonadiabatic dissociation processes that evolve across avoided crossings. Furthermore, core-to-valence absorption spectra are simulated from the neutralΣ 1 0 + state and the ionicΠ 2 1 / 2 , 3 / 2 states by numerically solving the time-dependent Schrödinger equation and exhibit excellent agreement with the experimental spectrum. The comprehensive and quantitative picture of the core-excited states obtained in this work allows for transparent analysis of the core-to-valence absorption signals, filling gaps in the theoretical understanding of the Br-3d transient absorption spectra.

Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

Expansion formalisms for trigonal Jahn–Teller and pseudo-Jahn–Teller vibronic Hamiltonians are developed and used to study and correctly interpret the photoelectron spectrum of CO₃⁻.

Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.

Electronegativity Seen as the Ground-State Average Valence Electron Binding Energy

We introduce a new electronegativity scale for atoms, based consistently on ground-state energies of valence electrons. The scale is closely related to (yet different from) L. C. Allen's, which is based on configuration energies. Using a combination of literature experimental values for ground-state energies and ab initio-calculated energies where experimental data are missing, we are able to provide electronegativities for elements 1-96. The values are slightly smaller than Allen's original scale, but correlate well with Allen's and others. Outliers in agreement with other scales are oxygen and fluorine, now somewhat less electronegative, but in better agreement with their chemistry with the noble gas elements. Group 11 and 12 electronegativities emerge as high, although Au less so than in other scales. Our scale also gives relatively high electronegativities for Mn, Co, Ni, Zn, Tc, Cd, Hg (affected by choice of valence state), and Gd. The new electronegativities provide hints for new alloy/compound design, and a framework is in place to analyze those energy changes in reactions in which electronegativity changes may not be controlling.

General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond

We derive general expansion formulas in vibrational coordinates for all bimodal Jahn–Teller and pseudo-Jahn–Teller Hamiltonians in tetragonal symmetry.