Path Integral Monte Carlo Simulation on Molecular Systems with Multiple Electronic Degrees of Freedom

We present an imaginary time path-integral formalism for molecular systems including nuclear and electronic degrees of freedom based on the previous work of [Schmidt, J. R.; Tully, J. C. J. Chem. Phys. 2007, 127, 094103]. To sample the resulting path integral expression efficiently, a path integral Monte Carlo scheme is proposed, allowing the computation of finite temperature equilibrium properties of molecular systems including multiple low-lying electronic states directly from ab initio potential energy surfaces. Finally, we show how this generalized approach in combination with the Monte Carlo scheme can reproduce exact results for a simple model system including nonadiabatic couplings as well as thermodynamic equilibrium properties of H2 and C2. Our implementation of the algorithm is available as an open-source code.

Indium Imidazo[4,5,-b]porphyrins as Photocatalysts for Oxidation of Sulfides

Over the past two decades, the application of photocatalytic reactions in organic synthesis has increased remarkably. Porphyrins, renowned for their exceptional photophysical properties, photostability, and prevalence in natural catalytic processes, are attracting significant attention as promising photocatalysts for reactions proceeding through energy transfer and one-electron transfer. In this work, we synthesized the indium(III) complex of 2-[4-(diethoxyphosphoryl)phenyl]-1H-imidazo[4,5-b]-5,10,15,20-tetramesitylporphyrin (InTMPIP) and explored its application as a photocatalyst for the oxidation of sulfides by dioxygen or air. Complex InTMPIP was found to generate singlet oxygen with quantum yield of 0.92 (toluene) and enables efficient photooxidation of sulfides to sulfoxides by dioxygen in "green" acetonitrile/water (4:1 v/v) or methanol/chloroform (2:1 v/v) solvent mixtures with almost quantitative yield. Furthermore, InTMPIP was grafted onto hydrated mesoporous titania and materials InTMPIP/TiO2-1 and InTMPIP/TiO2-2 with different In/Ti ratios were obtained and investigated. The composition and structure of the materials were studied using a combination of elemental analysis, various spectroscopic methods, gas adsorption measurements, and SEM imaging. Finally, the photocatalytic efficiency of InTMPIP/TiO2-2 was explored in aerobic photooxidation of sulfides. The heterogenized complex enables selective synthesis of sulfoxides under "green" conditions; however, it is prone to leaching into the solution when irradiated with both blue and red LEDs.

The development and applications of multidimensional biomolecular spectroscopy illustrated by photosynthetic light harvesting

The parallel and synergistic developments of atomic resolution structural information, new spectroscopic methods, their underpinning formalism, and the application of sophisticated theoretical methods have led to a step function change in our understanding of photosynthetic light harvesting, the process by which photosynthetic organisms collect solar energy and supply it to their reaction centers to initiate the chemistry of photosynthesis. The new spectroscopic methods, in particular multidimensional spectroscopies, have enabled a transition from recording rates of processes to focusing on mechanism. We discuss two ultrafast spectroscopies - two-dimensional electronic spectroscopy and two-dimensional electronic-vibrational spectroscopy - and illustrate their development through the lens of photosynthetic light harvesting. Both spectroscopies provide enhanced spectral resolution and, in different ways, reveal pathways of energy flow and coherent oscillations which relate to the quantum mechanical mixing of, for example, electronic excitations (excitons) and nuclear motions. The new types of information present in these spectra provoked the application of sophisticated quantum dynamical theories to describe the temporal evolution of the spectra and provide new questions for experimental investigation. While multidimensional spectroscopies have applications in many other areas of science, we feel that the investigation of photosynthetic light harvesting has had the largest influence on the development of spectroscopic and theoretical methods for the study of quantum dynamics in biology, hence the focus of this review. We conclude with key questions for the next decade of this review.

Analytic Evaluation of Nonadiabatic Couplings within the Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method

We present the theory for the evaluation of nonadiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motion can facilitate transitions between different resonances and between resonances and bound states. These nonadiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the NAC between bound states and pseudocontinuum states, between bound states and resonances, and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate, whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate.

Modeling Excited-State Proton Transfer Using the Lindblad Equation: Quantification of Time-Resolved Spectroscopy with Mechanistic Insights

The quantum dynamics of excited-state intramolecular proton transfer (ESIPT) is studied using a multilevel vibronic Hamiltonian and the Lindblad master equation. We simulate time-resolved fluorescence spectroscopy of 2-(2'-hydroxyphenyl) benzothiazole (HBT) and 10-hydroxybenzo[h]quinoline (HBQ), which suggests that the underlying mechanism behind the initial ultrafast rise and decay in the spectra is electronic state population that evolves simultaneously with proton wave packet dynamics. The results predict that the initial rise and decay signals at different wavelengths vary significantly with system properties in terms of their shape, the time, and the intensity of the maximum. These findings provide clues for data interpretation, mechanism validation, and control of the dynamics, and the model serves as an attempt toward clarifying ESIPT by direct comparison to time-resolved spectroscopy.

Interference of nuclear wavepackets in a pair of proton transfer reactions

Quantum mechanics revolutionized chemists' understanding of molecular structure. In contrast, the kinetics of molecular reactions in solution are well described by classical, statistical theories. To reveal how the dynamics of chemical systems transition from quantum to classical, we study femtosecond proton transfer in a symmetric molecule with two identical reactant sites that are spatially apart. With the reaction launched from a superposition of two local basis states, we hypothesize that the ensuing motions of the electrons and nuclei will proceed, conceptually, in lockstep as a superposition of probability amplitudes until decoherence collapses the system to a product. Using ultrafast spectroscopy, we observe that the initial superposition state affects the reaction kinetics by an interference mechanism. With the aid of a quantum dynamics model, we propose how the evolution of nuclear wavepackets manifests the unusual intersite quantum correlations during the reaction.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

High-level ab initio quartic force fields and spectroscopic characterization of C2N. Phys Chem Chem Phys 2021;23:26227-26240. [PMID: 34787132 DOI: 10.1039/d1cp03505c]

While it is now well established that large carbon chain species and radiative electron attachment (REA) are key ingredients triggering interstellar anion chemistry, the role played by smaller molecular anions, for which REA appears to be an unlikely formation pathway, is as yet elusive. Advancing this research undoubtedly requires the knowledge (and modeling) of their astronomical abundances which, for the case of C₂N^-, is largely hindered by a lack of accurate spectroscopic signatures. In this work, we provide such data for both ground -CCN^-(³Σ^-) and low-lying c-CNC^-(¹A₁) isomers and their singly-substituted isotopologues by means of state-of-the-art rovibrational quantum chemical techniques. Their quartic force fields are herein calibrated using a high-level composite energy scheme that accounts for extrapolations to both one-particle and (approximate) -particle basis set limits, in addition to relativistic effects, with the final forms being subsequently subject to nuclear motion calculations. Besides standard spectroscopic attributes, the full set of computed properties includes fine and hyperfine interaction constants and can be readily introduced as guesses in conventional experimental data reduction analyses through effective Hamiltonians. On the basis of benchmark calculations performed anew for a minimal test set of prototypical triatomics and limited (low-resolution) experimental data for -CCN^-(³Σ^-), the target accuracies are determined to be better than 0.1% of experiment for rotational constants and 0.3% for vibrational fundamentals. Apart from laboratory investigations, the results here presented are expected to also prompt future astronomical surveys on C₂N^-. To this end and using the theoretically-predicted spectroscopic constants, the rotational spectra of both -CCN^-(³Σ^-) and c-CNC^-(¹A₁) are derived and their likely detectability in the interstellar medium is further explored in connection with working frequency ranges of powerful astronomical facilities. Our best theoretical estimate places c-CNC^-(¹A₁) at about 15.3 kcal mol^-1 above the ground-state -CCN^-(³Σ^-) species.

Dynamics near a conical intersection-A diabolical compromise for the approximations of ab initio multiple spawning

Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.

Spontaneous electron emission vs dissociation in internally hot silver dimer anions

Referring to a recent experiment, we theoretically study the process of a two-channel decay of the diatomic silver anion (Ag₂ ^-), namely, the spontaneous electron ejection giving Ag₂ + e^- and the dissociation leading to Ag^- + Ag. The ground state potential energy curves of the silver molecules of diatomic neutral and negative ions were calculated using proper pseudo-potentials and atomic basis sets. We also estimated the non-adiabatic electronic coupling between the ground state of Ag₂ ^- and the ground state of Ag₂ + e^-, which, in turn, allowed us to estimate the minimal and mean values of the electron autodetachment lifetimes. The relative energies of the rovibrational levels allow the description of the spontaneous electron emission process, while the description of the rotational dissociation is treated with the quantum dynamics method as well as time-independent methods. The results of our calculations are verified by comparison with the experimental data.

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings entirely-the resulting "quasidiabatic" states are still coupled by smaller but nonvanishing residual nonadiabatic couplings, which are typically neglected. Here, we propose a general method for assessing the validity of this potentially drastic approximation by comparing quantum dynamics simulated either with or without the residual couplings. To make the numerical errors negligible to the errors due to neglecting the residual couplings, we use the highly accurate and general eighth-order composition of the implicit midpoint method. The usefulness of the proposed method is demonstrated on nonadiabatic simulations in the cubic Jahn-Teller model of nitrogen trioxide and in the induced Renner-Teller model of hydrogen cyanide. We find that, depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can result in wrong dynamics. In contrast, simulations with the exact quasidiabatic Hamiltonian, which contains the residual couplings, always yield accurate results.

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Exploring the write-in process in molecular quantum cellular automata: a combined modelingand first-principle approach

The molecular quantum cellular automata paradigm (m-QCA) offers a promising alternative framework to current CMOS implementations. A crucial aspect for implementing this technology concerns the construction of a device which effectively controls intramolecular charge-transfer processes. Tentative experimental implementations have been developed in which a voltage drop is created generating the forces that drive a molecule into a logic state. However, important factors such as the electric field profile, its possible time-dependency and the influence of temperature in the overall success of charge-transfer are relevant issues to be considered in the design of a reliable device. In this work, we theoretically study the role played by these processes in the overall intramolecular charge-transfer process. We have used a Landau-Zener (LZ) model, where different time-dependent electric field profiles have been simulated. The results have been further corroborated employing density functional tight-binding method. The role played by the nuclear motions in the electron-transfer process has been investigated beyond the Born-Oppenheimer approximation by computing the effect of the external electric field in the behavior of the potential energy surface. Hence, we demonstrate that the intramolecular charge-transfer process is a direct consequence of the coherent LZ nonadiabatic tunneling and the hybridization of the diabatic vibronic states which effectively reduces the trapping of the itinerant electron at the donor group.

Corresponding Orbitals Derived from Periodic Bloch States for Electron Transfer Calculations of Transition Metal Oxides

An approach for modeling electron transfer in solids and at surfaces of iron-(oxyhydr)oxides and other redox active solids has been developed for electronic structure methods (i.e., plane-wave density functional theory) capable of performing calculations with periodic cells and large system sizes efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, V _AB, and the electron transfer transmission factor, κ_el. This method is an extension of the valence bond theory electron transfer method for molecules and clusters implemented by Dupuis and others and used extensively by Rosso and co-workers in which scaled corresponding orbitals derived from the Bloch states are used to calculate the off-diagonal matrix elements H _AB and S _AB. A key development of the present work is the formulation of algorithms to improve the accuracy of the integration of the exact exchange integral in periodic boundary conditions. This method is demonstrated on model systems for electron small polaron transfer in iron-(oxyhydr)oxides, including bare Fe²⁺-Fe³⁺ ions, and in [Fe³⁺(OH₂)₂ (OH^-)₂)] _nⁿ⁺ chains representing the common edge-sharing Fe octahedral motif in these materials.

Coherent wavepackets in the Fenna-Matthews-Olson complex are robust to excitonic-structure perturbations caused by mutagenesis

Femtosecond pulsed excitation of light-harvesting complexes creates oscillatory features in their response. This phenomenon has inspired a large body of work aimed at uncovering the origin of the coherent beatings and possible implications for function. Here we exploit site-directed mutagenesis to change the excitonic level structure in Fenna-Matthews-Olson (FMO) complexes and compare the coherences using broadband pump-probe spectroscopy. Our experiments detect two oscillation frequencies with dephasing on a picosecond timescale-both at 77 K and at room temperature. By studying these coherences with selective excitation pump-probe experiments, where pump excitation is in resonance only with the lowest excitonic state, we show that the key contributions to these oscillations stem from ground-state vibrational wavepackets. These experiments explicitly show that the coherences-although in the ground electronic state-can be probed at the absorption resonances of other bacteriochlorophyll molecules because of delocalization of the electronic excitation over several chromophores.

Coherence Spectroscopy in the Condensed Phase: Insights into Molecular Structure, Environment, and Interactions

The role of coherences, or coherently excited superposition states, in complex condensed-phase systems has been the topic of intense interest and debate for a number of years. In many cases, coherences have been utilized as spectators of ultrafast dynamics or for identifying couplings between electronic states. In rare cases, they have been found to drive excited state dynamics directly. Interestingly though, the utilization of coherences as a tool for high-detail vibronic spectroscopy has largely been overlooked until recently, despite their encoding of key information regarding molecular structure, electronically sensitive vibrational modes, and intermolecular interactions. Furthermore, their detection in the time domain makes for a highly comprehensive spectroscopic technique wherein the phase and dephasing times are extracted in addition to amplitude and intensity, an element not afforded in analogous frequency domain "steady-state" measurements. However, practical limitations arise in disentangling the large number of coherent signals typically accessed in broadband nonlinear spectroscopic experiments, often complicating assignment of the origin and type of coherences generated. Two-dimensional electronic spectroscopy (2DES) affords an avenue by which to disperse and decompose the large number of coherent signals generated in nonlinear experiments, facilitating the assignment of various types of quantum coherences. 2DES takes advantage of the broad bandwidth necessary for achieving the high time resolution desired for ultrafast dynamics and coherence generation by resolving the excitation axis to detect all excitation channels independently. This feature is beneficial for following population dynamics such as electronic energy transfer, and 2DES has become the choice method for such studies. Simultaneously, coherences arise as oscillations at well-defined coordinates across the 2D map often atop those evolving population signals. By isolating the coherent contribution to the 2DES data and Fourier transforming along the population time, a 3D spectral representation of the coherent 2D data is generated, and coherences are then ordered by their oscillation frequency, ν₂. Individual coherences can then be selected by their frequency and evaluated via their distinct "2D coherence" spectra, yielding a significantly more distinctive set of spectroscopic signatures over other 1D methodologies and single-point 2DES analysis. Given that coherences of different origin result in unique 2D coherence spectra, these characteristics can be catalogued and compared directly against experiment for prompt assignment, a strategy not afforded by traditional 2DES analysis. In this Account, a structure-driven time-independent spectral model is discussed and employed to compare the 2D fingerprints of various coherences to experimental 2D coherence spectra. The frequency-domain approach can easily integrate ab initio derived vibronic parameters, and its correspondence with experimental coherence spectra of a model compound is demonstrated. Several examples and applications are discussed herein, from 2D Franck-Condon analysis of a model compound, to identifying the signatures of interpigment vibronic coupling in a photosynthetic light-harvesting complex. The 3D spectral approach to 2DES provides remarkable spectroscopic detail, in turn leading to new insights in molecular structure and interactions, which complement the time-resolved dynamics simultaneously recorded. The approach presented herein has the potential to distill down the convoluted set of nonlinear signals appearing in 2D coherent spectra, making the technique more amenable to high-detail vibronic spectroscopy in inherently complex condensed phase systems.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Electron-vibration entanglement in the Born-Oppenheimer description of chemical reactions and spectroscopy

Entanglement is sometimes regarded as the quintessential measure of the quantum nature of a system and its significance for the understanding of coupled electronic and vibrational motions in molecules has been conjectured. Previously, we considered the entanglement developed in a spatially localized diabatic basis representation of the electronic states, considering design rules for qubits in a low-temperature chemical quantum computer. We extend this to consider the entanglement developed during high-energy processes. We also consider the entanglement developed using adiabatic electronic basis, providing a novel way for interpreting effects of the breakdown of the Born-Oppenheimer (BO) approximation. We consider: (i) BO entanglement in the ground-state wavefunction relevant to equilibrium thermodynamics, (ii) BO entanglement associated with low-energy wavefunctions relevant to infrared and tunneling spectroscopies, (iii) BO entanglement in high-energy eigenfunctions relevant to chemical reaction processes, and (iv) BO entanglement developed during reactive wavepacket dynamics. A two-state single-mode diabatic model descriptive of a wide range of chemical phenomena is used for this purpose. The entanglement developed by BO breakdown correlates simply with the diameter of the cusp introduced by the BO approximation, and a hierarchy appears between the various BO-breakdown correction terms, with the first-derivative correction being more important than the second-derivative correction which is more important than the diagonal correction. This simplicity is in contrast to the complexity of BO-breakdown effects on thermodynamic, spectroscopic, and kinetic properties. Further, processes poorly treated at the BO level that appear adequately treated using the Born-Huang adiabatic approximation are found to have properties that can only be described using a non-adiabatic description. For the entanglement developed between diabatic electronic states and the nuclear motion, qualitatively differently behavior is found compared to traditional properties of the density matrix and hence entanglement provides new information about system properties. For chemical reactions, this type of entanglement simply builds up as the transition-state region is crossed. It is robust to small changes in parameter values and is therefore more attractive for making quantum qubits than is the related fragile ground-state entanglement, provided that coherent motion at the transition state can be sustained.

On the synthesis of functionalized porphyrins and porphyrin conjugates via β-aminoporphyrins

A two-step methodology to prepare a series ofmeso-tetraarylporphyrin conjugates bearing water-soluble moieties, anchoring groups and receptor subunits.

A unified diabatic description for electron transfer reactions, isomerization reactions, proton transfer reactions, and aromaticity

A way is found for describing general chemical reactions using diabatic multi-state and “twin-state” models. (Image adapted with permission from https://www.flickr.com/photos/cybaea/64638988/).

Bond angle variations in XH3 [X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

The origins of the observed bond angles in XH₃ and XH₃⁺ are explained using high-level calculations and a simple diabatic model.