The DQ and DQΦ electronic structure diabatization methods: Validation for general applications

Fitting of Coupled Potential Energy Surfaces via Discovery of Companion Matrices by Machine Intelligence

Fitting coupled potential energy surfaces is a critical step in simulating electronically nonadiabatic chemical reactions and energy transfer processes. Analytic representation of coupled potential energy surfaces enables one to perform detailed dynamics calculations. Traditionally, fitting is performed in a diabatic representation to avoid fitting the cuspidal ridges of coupled adiabatic potential energy surfaces at conical intersection seams. In this work, we provide an alternative approach by carrying out fitting in the adiabatic representation using a modified version of the Frobenius companion matrices, whose usage was first proposed by Opalka and Domcke. Their work involved minimizing the errors in fits of the characteristic polynomial coefficients (CPCs) and diagonalizing the resulting companion matrix, whose eigenvalues are adiabatic potential energies. We show, however, that this may lead to complex eigenvalues and spurious discontinuities. To alleviate this problem, we provide a new procedure for the automatic discovery of CPCs and the diagonalization of a companion matrix by using a special neural network architecture. The method effectively allows analytic representation of global coupled adiabatic potential energy surfaces and their gradients with only adiabatic energy input and without experience-based selection of a diabatization scheme. We demonstrate that the new procedure, called the companion matrix neural network (CMNN), is successful by showing applications to LiH, H3, phenol, and thiophenol.

Predicting Solvatochromism of Chromophores in Proteins through QM/MM and Machine Learning

Solvatochromism occurs in both homogeneous solvents and more complex biological environments, such as proteins. While in both cases the solvatochromic effects report on the surroundings of the chromophore, their interpretation in proteins becomes more complicated not only because of structural effects induced by the protein pocket but also because the protein environment is highly anisotropic. This is particularly evident for highly conjugated and flexible molecules such as carotenoids, whose excitation energy is strongly dependent on both the geometry and the electrostatics of the environment. Here, we introduce a machine learning (ML) strategy trained on quantum mechanics/molecular mechanics calculations of geometrical and electrochromic contributions to carotenoids' excitation energies. We employ this strategy to compare solvatochromism in protein and solvent environments. Despite the important specifities of the protein, ML models trained on solvents can faithfully predict excitation energies in the protein environment, demonstrating the robustness of the chosen descriptors.

Fast and accurate excited states predictions: machine learning and diabatization

The efficiency of machine learning algorithms for electronically excited states is far behind ground-state applications. One of the underlying problems is the insufficient smoothness of the fitted potential energy surfaces and other properties in the vicinity of state crossings and conical intersections, which is a prerequisite for an efficient regression. Smooth surfaces can be obtained by switching to the diabatic basis. However, diabatization itself is still an outstanding problem. We overcome these limitations by solving both problems at once. We use a machine learning approach combining clustering and regression techniques to correct for the deficiencies of property-based diabatization which, in return, provides us with smooth surfaces that can be easily fitted. Our approach extends the applicability of property-based diabatization to multidimensional systems. We utilize the proposed diabatization scheme to achieve higher prediction accuracy for adiabatic states and we show its performance by reconstructing global potential energy surfaces of excited states of nitrosyl fluoride and formaldehyde. While the proposed methodology is independent of the specific property-based diabatization and regression algorithm, we show its performance for kernel ridge regression and a very simple diabatization based on transition multipoles. Compared to most other algorithms based on machine learning, our approach needs only a small amount of training data.

Quantum Dynamics of Photodissociation: Recent Advances and Challenges

Recent advances in constructing accurate potential energy surfaces and nonadiabatic couplings from high-level ab initio data have revealed detailed potential landscapes in not only the ground electronic state but also excited ones. They enabled quantitatively accurate characterization of photoexcited reactive systems using quantum mechanical methods. In this Perspective, we survey the recent progress in quantum mechanical studies of adiabatic and nonadiabatic photodissociation dynamics, focusing on initial state control and product energy disposal. These new insights helped to understand quantum effects in small prototypical systems, and the results serve as benchmarks for developing more approximate theoretical methods.

An energy decomposition and extrapolation scheme for evaluating electron transfer rate constants: a case study on electron self-exchange reactions of transition metal complexes

A simple approach to the analysis of electron transfer (ET) reactions based on energy decomposition and extrapolation schemes is proposed. The present energy decomposition and extrapolation-based electron localization (EDEEL) method represents the diabatic energies for the initial and final states using the adiabatic energies of the donor and acceptor species and their complex. A scheme for the efficient estimation of ET rate constants is also proposed. EDEEL is semi-quantitative by directly evaluating the seam-of-crossing region of two diabatic potentials. In a numerical test, EDEEL successfully provided ET rate constants for electron self-exchange reactions of thirteen transition metal complexes with reasonable accuracy. In addition, its energy decomposition and extrapolation schemes provide all the energy values required for activation-strain model (ASM) analysis. The ASM analysis using EDEEL provided rational interpretations of the variation of the ET rate constants as a function of the transition metal complexes. These results suggest that EDEEL is useful for efficiently evaluating ET rate constants and obtaining a rational understanding of their magnitudes.

Linearized Pair-Density Functional Theory

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-SCF multireference method that has been successful at computing ground- and excited-state energies. However, MC-PDFT is a single-state method in which the final MC-PDFT energies do not come from diagonalization of a model-space Hamiltonian matrix, and this can lead to inaccurate topologies of potential energy surfaces near locally avoided crossings and conical intersections. Therefore, in order to perform physically correct ab initio molecular dynamics with electronically excited states or to treat Jahn-Teller instabilities, it is necessary to develop a PDFT method that recovers the correct topology throughout the entire nuclear configuration space. Here we construct an effective Hamiltonian operator, called the linearized PDFT (L-PDFT) Hamiltonian, by expanding the MC-PDFT energy expression to first order in a Taylor series of the wave function density. Diagonalization of the L-PDFT Hamiltonian gives the correct potential energy surface topology near conical intersections and locally avoided crossings for a variety of challenging cases including phenol, methylamine, and the spiro cation. Furthermore, L-PDFT outperforms MC-PDFT and previous multistate PDFT methods for predicting vertical excitations from a variety of representative organic chromophores.

Target State Optimized Density Functional Theory for Electronic Excited and Diabatic States

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.

Permutation invariant polynomial neural network based diabatic ansatz for the (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller systems

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of H₃ ⁺ is studied, which is an (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. The adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

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.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

Extended Mulliken-Hush Method with Applications to the Theoretical Study of Electron Transfer

A novel adiabatic-to-diabatic (ATD) transformation strategy, namely, the extended Mulliken-Hush (XMH) method, is proposed to evaluate diabatic properties including electronic couplings, potential energy surfaces, and their crossings. The XMH method is developed by adopting our recently proposed ATD transformation formula of a general vectorial physical observable, in which a useful ATD transformation is further determined by using an auxiliary dipole between localized frontier orbitals as a simple approximation of the diabatic transition dipole. The XMH method is simple and practical that provides a flexible way to construct diabatic states. To some extent, it can be regarded as an extension of the generalized Mulliken-Hush (GMH) method since the latter takes a stronger approximation, in which the diabatic transition dipole is assumed to be vanishing. Test calculations on the HeH₂⁺ system show that the electronic couplings predicted by the XMH method are closer to the ones calculated by the valence bond block-diagonalization approach than the GMH ones since the XMH method takes into account both the magnitude and direction of the diabatic transition dipole, which is consistent with the properties of this molecule. In the study of electron transfer in the two kinds of donor-bridge-acceptor systems, the XMH method maintains the simplicity of the GMH method and gives reasonable results even when the latter fails, wherein the diabatic transition dipole is nearly perpendicular to the difference of the initial and final adiabatic dipoles. More importantly, the XMH method can be easily combined with high-level electronic structure methods, in which the properties of the ground and excited states may be more accurately calculated, and hence, one may expect that further development of the XMH method would result in a general computational model for studying electron transfer reactions.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Simulation of UV absorption spectra and relaxation dynamics of uracil and uracil-water clusters

Despite many studies, the mechanisms of nonradiative relaxation of uracil in the gas phase and in aqueous solution are still not fully resolved. Here we combine theoretical UV absorption spectroscopy with nonadiabatic dynamics simulations to identify the photophysical mechanisms that can give rise to experimentally observed decay time constants. We first compute and theoretically assign the electronic spectra of uracil using the second-order algebraic-diagrammatic-construction (ADC(2)) method. The obtained electronic states, their energy differences and state-specific solvation effects are the prerequisites for understanding the photodynamics. We then use nonadiabatic trajectory-surface-hopping dynamics simulations to investigate the photoinduced dynamics of uracil and uracil-water clusters. In contrast to previous studies, we found that a single mechanism - the ethylenic twist around the C[double bond, length as m-dash]C bond - is responsible for the ultrafast component of the nonradiative decay, both in the gas phase and in solution. Very good agreement with the experimentally determined ultrashort decay time constants is obtained.

Electronic Couplings for Photoinduced Charge Transfer and Excitation Energy Transfer Based on Fragment Particle-Hole Densities

A new scheme is proposed to calculate the electronic couplings for photoinduced charge transfer and excitation energy transfer for both singlet and triplet states. In this scheme, the locally excited and charge-transfer states are constructed from the adiabatic ones by maximally localizing the particle (i.e., electron) and hole densities in terms of predefined molecular fragments. The construction process, after which the electronic couplings are directly obtained, is highly efficient and can be combined with various kinds of preliminary electronic structure calculations as long as the adiabatic excitation energies and transition densities are available. The method also applies to the systems with multiple charge or excitation centers. Its validity is demonstrated by the applications to the 6,13-dichloropentacene dimer and tetramer and the C₆₀-Zn porphyrin dyad. The results reveal that the environment has a strong impact on the electronic couplings and can even enlarge those for long-range charge transfer by several orders of magnitude.

Block-Localized Excitation for Excimer Complex and Diabatic Coupling

We describe a block-localized excitation (BLE) method to carry out constrained optimization of block-localized orbitals for constructing valence bond-like, diabatic excited configurations using multistate density functional theory (MSDFT). The method is an extension of the previous block-localized wave function method through a fragment-based ΔSCF approach to optimize excited determinants within a molecular complex. In BLE, both the number of electrons and the electronic spin of different fragments in a whole system can be constrained, whereas electrostatic, exchange, and polarization interactions among different blocks can be fully taken into account of. To avoid optimization collapse to unwanted states, a ΔSCF projection scheme and a maximum overlap of wave function approach have been presented. The method is illustrated by the excimer complex of two naphthalene molecules. With a minimum of eight spin-adapted configurational state functions, it was found that the inversion of L_a^- and L_b^- states near the optimal structure of the excimer complex is correctly produced, which is in quantitative agreement with DMRG-CASPT2 calculations and experiments. Trends in the computed transfer integrals associated with excited-state energy transfer both in the singlet and triplet states are discussed. The results suggest that MSDFT may be used as an efficient approach to treat intermolecular interactions in excited states with a minimal active space (MAS) for interpretation of the results and for dynamic simulations, although the selection of a small active space is often system dependent.

Exclusive Neural Network Representation of the Quasi-Diabatic Hamiltonians Including Conical Intersections

We propose a numerically simple and straightforward, yet accurate and efficient neural networks-based fitting strategy to construct coupled potential energy surfaces (PESs) in a quasi-diabatic representation. The fundamental invariants are incorporated to account for the complete nuclear permutation inversion symmetry. Instead of derivative couplings or interstate couplings, a so-called modified derivative coupling term is fitted by neural networks, resulting in accurate description of near degeneracy points, such as the conical intersections. The adiabatic energies, energy gradients, and derivative couplings are well reproduced, and the vanishing of derivative couplings as well as the isotropic topography of adiabatic and diabatic energies in asymptotic regions are automatically satisfied. All of these features of the coupled global PESs are requisite for accurate dynamics simulations. Our approach is expected to be very useful in developing highly accurate coupled PESs in a quasi-diabatic representation in an efficient machine learning-based way.

Reactivities of singlet oxygen: open-shell or closed-shell?

This work explores the reactivity of singlet oxygen with respect to two typical reactions: cycloaddition to anthracene and excitation energy transfer (EET) to a carotenoid using diabatic states with multistate density functional theory (MSDFT). Noticeably, the degenerate state 1Δg has distinct open-shell (OS) and closed-shell (CS) components, and the closed-shell component showed more reactivity than the open-shell one due to the strong diabatic couplings to the product diabatic states. The diabatic perspective presented in this work could also apply to general singlet fission processes.

Construction of Quasi-diabatic Hamiltonians That Accurately Represent ab Initio Determined Adiabatic Electronic States Coupled by Conical Intersections for Systems on the Order of 15 Atoms. Application to Cyclopentoxide Photoelectron Detachment in the Full 39 Degrees of Freedom

We present, for systems of moderate dimension, a fitting framework to construct quasi-diabatic Hamiltonians that accurately represent ab initio adiabatic electronic structure data including the effects of conical intersections. The framework introduced here minimizes the difference between the fit prediction and the ab initio data obtained in the adiabatic representation, which is singular at a conical intersection seam. We define a general and flexible merit function to allow arbitrary representations and propose a representation to measure the fit-ab initio difference at geometries near electronic degeneracies. A fit Hamiltonian may behave poorly in insufficiently sampled regions, in which case a machine learning theory analysis of the fit representation suggests a regularization to address the deficiency. Our fitting framework including the regularization is used to construct the full 39-dimensional coupled diabatic potential energy surfaces for cyclopentoxy relevant to cyclopentoxide photoelectron detachment.

Two-Dimensional Analysis of the Diabatic Transition of a General Vectorial Physical Observable Based on Adiabatic-to-Diabatic Transformation

We present a full analysis of the magnitude and orientation of the diabatic transition matrix element of a general vectorial physical observable during the adiabatic-to-diabatic transformation. The diabatic transition is a function of the adiabatic-to-diabatic transformation angle and the two basic vectors of the adiabatic states, which are the off-diagonal matrix element and the difference between the two diagonal matrix elements. To the best of our knowledge, this is the first time that the transformation has been accomplished in a more general two-dimensional scale for a vectorial physical observable. All possible extreme values of a diabatic transition are deduced for systems with different features. By using an approximate diabatic transition dipole, the pilot implementation of the analysis produces an electronic coupling curve nearly identical to that obtained by the generalized Mulliken-Hush method for the testing molecule. Evidently, this complete analysis of a diabatic transition will be very useful in determining the adiabatic-to-diabatic transformation angle by using a physical observable and can also be used to evaluate the quality of various approximations for constructing the diabatic states.

Modeling Charge Flux by Interpolating Atomic Partial Charges

Although the charge flux effect or the geometric dependence of the atomic partial charges have been known for a long time, how it can be effectively handled is not yet established. Here, we present a charge interpolation scheme as a new general tool for representing the charge flux in an analytically well-defined manner. By applying it to the anionic GFP chromophore with the diabatically represented atomic charges, we show that the charge interpolation provides a substantial improvement on the accuracy of the geometry-dependent changes in the molecular dipole moments in the gas phase. We also test the scheme toward describing the electrostatic term in the solvation energy in the aqueous environment and observe that it is also improved but that the extent of the improvement is somewhat limited. We show that the remaining errors can be largely corrected by introducing atomic polarizabilities. Overall, our results show that charge interpolation is an amenable approach for describing the charge flux effect and that its description in the condensed phase should be accompanied by proper treatments of polarization effects.

Representation of coupled adiabatic potential energy surfaces using neural network based quasi-diabatic Hamiltonians: 1,2 2A′ states of LiFH

A general algorithm for determining diabatic representations from adiabatic energies, energy gradients and derivative couplings using neural networks is introduced.

Determining whether diabolical singularities limit the accuracy of molecular property based diabatic representations: The 1,21A states of methylamine

An efficient, easily implemented method for locating singularities attributable to the failure of the defining equations in a molecular property based diabatization, termed diabolical singular points, is reported. For two state diabatizations, the singular points form a seam of dimension N ^int - 2, where N ^int is the number of internal degrees of freedom. The dynamical outcomes of nuclear trajectories that reach the region of this seam are flawed. The algorithm easily identifies these otherwise hard to anticipate regions of fallaciously large derivative coupling. The fact that the algorithm is easily incorporated into a two state diabatization code based on molecular properties makes it a practical tool for determining whether the existence of diabolical singularities is relevant to the problem being considered. The algorithm is illustrated using a multireference single and double excitation configuration interaction description of the 1,2¹A states of CH₃NH_2.

A Simple Phase Correction Makes a Big Difference in Nonadiabatic Molecular Dynamics

The outcomes of nonadiabatic molecular dynamics (NA-MD) calculations are modulated by the parameters entering the time-dependent Schrödinger equation (TD-SE). The adiabatic states are commonly used as the basis in which the TD-SE is integrated. However, the phase inconsistencies of such states along the nuclear trajectories obtained in NA-MD simulations may render the wave function and other relevant properties ill-behaving, adversely affecting the dynamics. This work illustrates the consequence of adiabatic state phase inconsistencies in nonadiabatic Ehrenfest dynamics. A simple phase-correction approach is proposed and is demonstrated to alter the dynamics to make it consistent with the reference calculations done in the phase-consistent diabatic representation.

Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition

A procedure, called generalized diabatic-at-construction (GDAC), is presented to transform adiabatic potential energy surfaces into a diabatic representation by generalized singular value decomposition. First, we use a set of localized, valence bond-like configuration state functions, called DAC, as the basis states. Then, the adiabatic ground and relevant excited states are determined using multistate density functional theory (MSDFT). GDAC differs in the opposite direction from traditional approaches based on adiabatic-to-diabatic transformation with certain property restraints. The method is illustrated with applications to a model first-order bond dissociation reaction of CH₃OCH₂Cl polarized by a solvent molecule, the ground- and first-excited-state potential energy surfaces near the minimum conical intersection for the ammonia dimer photodissociation, and the multiple avoided curve crossings in the dissociation of lithium hydride. The GDAC diabatization method may be useful for defining charge-localized states in studies of electron transfer and proton-coupled electron transfer reactions in proteins.

Photophysical properties of acetylene-linked syn bimane oligomers: a molecular photonic wire

Computational studies using correlated wave function methods and density functional theory were carried out on a series of acetylene-linked bimane oligomers with particular emphasis on their excitonic properties and implications for intra-chain excitation energy transfer (EET). The low energy barriers found for the rotation of bimane subunits about the longitudinal axis are such that the π-conjugation is easily disrupted. Nevertheless, a distinctive feature of the oligomer lies in the parallel alignment of the S₁ transition dipole along the longitudinal axis, which sustains electronic coupling between adjacent bimane subunits over a range of torsional angles and is crucial for driving intra-chain EET. Using a model that comprises hexameric donor and acceptor fragments, we evaluated electronic couplings and spectral overlaps, and applied Fermi's golden rule (in the weak electronic coupling regime) to approximate the lower limit of intra-chain EET in an acetylene-linked bimane photonic wire.

Direct diabatization based on nonadiabatic couplings: the N/D method

We propose a new diabatization method that is direct, orbital-free, and adiabatic-equivalent based on directly calculated nonadiabatic couplings of states and the adiabatic energy gradients.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Accurate nonadiabatic dynamics

This Perspective addresses the use of coupled diabatic potential energy surfaces (PESs) together with rigorous quantum dynamics in full or reduced dimensional coordinate spaces to obtain accurate solutions to problems in nonadiabatic dynamics.