Direct diabatization of electronic states by the fourfold way. II. Dynamical correlation and rearrangement processes

Synergetic Effects of Triplet-Triplet Annihilation and Directional Triplet Exciton Migration in Organic Crystals for Photon Upconversion

In condensed solids, triplet exciton migration and succeeding triplet-triplet annihilation (TTA) are major bottleneck processes for efficient photon upconversion (UC) using sunlight excitation. We theoretically investigated the reaction times of TTA and the triplet-triplet energy transfer (TTET) as the elementary processes of triplet exciton migration in organic crystals of two molecular species: 9,10-diphenylanthracene (DPA) and its double-strapped alkyl  derivative (C7-sDPA) as the models of a recently reported crystalline system of TTA-UC by Kamada et al. The reaction times calculated based on Marcus theory clarified that the dimensionality of TTET and synergetic effects of TTA and TTET are responsible for the high UC quantum yield as well as their triplet lifetimes.

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.

Intramolecular Singlet Fission: Insights from Quantum Dynamical Simulations

We investigate the dynamics of intramolecular singlet fission in a dimer consisting of two pentacene-based chromophores covalently bonded to a phenylene spacer using an approach that combines high-level ab initio multireference perturbation theory methods and quantum dynamical simulations. The results show that the population of the multiexcitonic state, corresponding to the first step of singlet fission, is facilitated by the existence of higher-lying doubly excited and charge transfer states that participate in a superexchange-like way. The important role played by high-frequency ring-breathing molecular vibrations in the process is also discussed.

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.

Electronic spectrum and characterization of diabatic potential energy surfaces for thiophenol

We present an accurate simulation of the UV spectrum and a diabatization of three singlet potential surfaces along four coordinates.

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.

Unified model for singlet fission within a non-conjugated covalent pentacene dimer

When molecular dimers, crystalline films or molecular aggregates absorb a photon to produce a singlet exciton, spin-allowed singlet fission may produce two triplet excitons that can be used to generate two electron–hole pairs, leading to a predicted ∼50% enhancement in maximum solar cell performance. The singlet fission mechanism is still not well understood. Here we report on the use of time-resolved optical and electron paramagnetic resonance spectroscopy to probe singlet fission in a pentacene dimer linked by a non-conjugated spacer. We observe the key intermediates in the singlet fission process, including the formation and decay of a quintet state that precedes formation of the pentacene triplet excitons. Using these combined data, we develop a single kinetic model that describes the data over seven temporal orders of magnitude both at room and cryogenic temperatures.

Singlet fission is an important process occurring in solar cells, however the mechanism is not well understood. Here the authors reveal intermediates during singlet fission of a non-conjugated pentacene dimer, developing a single kinetic model to describe the data over seven temporal orders of magnitude at room and cryogenic temperatures.

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.

Diabatization for Time-Dependent Density Functional Theory: Exciton Transfers and Related Conical Intersections

Intermolecular exciton transfers and related conical intersections are analyzed by diabatization for time-dependent density functional theory. The diabatic states are expressed as a linear combination of the adiabatic states so as to emulate the well-defined reference states. The singlet exciton coupling calculated by the diabatization scheme includes contributions from the Coulomb (Förster) and electron exchange (Dexter) couplings. For triplet exciton transfers, the Dexter coupling, charge transfer integral, and diabatic potentials of stacked molecules are calculated for analyzing direct and superexchange pathways. We discuss some topologies of molecular aggregates that induce conical intersections on the vanishing points of the exciton coupling, namely boundary of H- and J-aggregates and T-shape aggregates, as well as canceled exciton coupling to the bright state of H-aggregate, i.e., selective exciton transfer to the dark state. The diabatization scheme automatically accounts for the Berry phase by fixing the signs of reference states while scanning the coordinates.

A Direct Mechanism of Ultrafast Intramolecular Singlet Fission in Pentacene Dimers

Interest in materials that undergo singlet fission (SF) has been catalyzed by the potential to exceed the Shockley-Queisser limit of solar power conversion efficiency. In conventional materials, the mechanism of SF is an intermolecular process (xSF), which is mediated by charge transfer (CT) states and depends sensitively on crystal packing or molecular collisions. In contrast, recently reported covalently coupled pentacenes yield ∼2 triplets per photon absorbed in individual molecules: the hallmark of intramolecular singlet fission (iSF). However, the mechanism of iSF is unclear. Here, using multireference electronic structure calculations and transient absorption spectroscopy, we establish that iSF can occur via a direct coupling mechanism that is independent of CT states. We show that a near-degeneracy in electronic state energies induced by vibronic coupling to intramolecular modes of the covalent dimer allows for strong mixing between the correlated triplet pair state and the local excitonic state, despite weak direct coupling.

Solution-based intramolecular singlet fission in cross-conjugated pentacene dimers

We show unambiguous and compelling evidence by means of pump-probe experiments, which are complemented by calculations using ab initio multireference perturbation theory, for intramolecular singlet fission (SF) within two synthetically tailored pentacene dimers with cross-conjugation, namely XC1 and XC2. The two pentacene dimers differ in terms of electronic interactions as evidenced by perturbation of the ground state absorption spectra stemming from stronger through-bond contributions in XC1 as confirmed by theory. Multiwavelength analysis, on one hand, and global analysis, on the other hand, confirm that the rapid singlet excited state decay and triplet excited state growth relate to SF. SF rate constants and quantum yields increase with solvent polarity. For example, XC2 reveals triplet quantum yields and rate constants as high as 162 ± 10% and (0.7 ± 0.1) × 10(12) s(-1), respectively, in room temperature solutions.

Diabatic Population Matrix Formalism for Performing Molecular Mechanics Style Simulations with Multiple Electronic States

An accurate description of nonbonded interactions is important in investigating dynamics of molecular systems. In many situations, fixed point charge models are successfully applied to explaining various chemical phenomena. However, these models with conventional formulations will not be appropriate in elucidating the detailed dynamics during nonadiabatic events. This is mainly because the chemical properties of any molecule, especially its electronic populations, significantly change with respect to molecular distortions in the vicinity of the surface crossing. To overcome this issue in molecular simulations yet within the framework of the fixed point charge model, we define a diabatic electronic population matrix and substitute it for the conventional adiabatic partial charges. We show that this matrix can be readily utilized toward attaining more reliable descriptions of Coulombic interactions, in combination with the interpolation formalism for obtaining the intramolecular interaction potential. We demonstrate how the mixed formalism with the diabatic charges and the interpolation can be applied to molecular simulations by conducting adiabatic and nonadiabatic molecular dynamics trajectory calculations of the green fluorescent protein chromophore anion in aqueous environment.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Nonintuitive Diabatic Potential Energy Surfaces for Thioanisole

Diabatization of potential energy surfaces is a technique that enables convenient molecular dynamics simulations of electronically nonadiabatic processes, but diabatization itself is nonunique and can be inconvenient; the best methods to achieve diabatization are still under study. Here, we present the diabatization of two electronic states of thioanisole in the S-CH3 bond stretching and C-C-S-C torsion two-dimensional nuclear coordinate space containing a conical intersection. We use two systematic methods: the (orbital-dependent) 4-fold way and the (orbital-free) Boys localization diabatization method. These very different methods yield strikingly similar diabatic potential energy surfaces that cross at geometries where the adiabatic surfaces are well separated and do not exhibit avoided crossings, and the contours of the diabatic gap and diabatic coupling are similar for the two methods. The validity of the diabatization is supported by comparing the nonadiabatic couplings calculated from the diabatic matrix elements to those calculated by direct differentiation of the adiabatic states.

The requisite electronic structure theory to describe photoexcited nonadiabatic dynamics: nonadiabatic derivative couplings and diabatic electronic couplings

Electronically photoexcited dynamics are complicated because there are so many different relaxation pathways: fluorescence, phosphorescence, radiationless decay, electon transfer, etc. In practice, to model photoexcited systems is a very difficult enterprise, requiring accurate and very efficient tools in both electronic structure theory and nonadiabatic chemical dynamics. Moreover, these theoretical tools are not traditional tools. On the one hand, the electronic structure tools involve couplings between electonic states (rather than typical single state energies and gradients). On the other hand, the dynamics tools involve propagating nuclei on multiple potential energy surfaces (rather than the usual ground state dynamics). In this Account, we review recent developments in electronic structure theory as directly applicable for modeling photoexcited systems. In particular, we focus on how one may evaluate the couplings between two different electronic states. These couplings come in two flavors. If we order states energetically, the resulting adiabatic states are coupled via derivative couplings. Derivative couplings capture how electronic wave functions change as a function of nuclear geometry and can usually be calculated with straightforward tools from analytic gradient theory. One nuance arises, however, in the context of time-dependent density functional theory (TD-DFT): how do we evaluate derivative couplings between TD-DFT excited states (which are tricky, because no wave function is available)? This conundrum was recently solved, and we review the solution below. We also discuss the solution to a second, pesky problem of origin dependence, whereby the derivative couplings do not (strictly) satisfy translation variance, which can lead to a lack of momentum conservation. Apart from adiabatic states, if we order states according to their electronic character, the resulting diabatic states are coupled via electronic or diabatic couplings. The couplings between diabatic states |ΞA⟩ and |ΞB⟩ are just the simple matrix elements, ⟨ΞA|H|ΞB⟩. A difficulty arises, however, because constructing exactly diabatic states is formally impossible and constructing quasi-diabatic states is not unique. To that end, we review recent advances in localized diabatization, which is one approach for generating adiabatic-to-diabatic (ATD) transformations. We also highlight outstanding questions in the arena of diabatization, especially how to generate multiple globally stable diabatic surfaces.

Chemical bonding: the orthogonal valence-bond view

Chemical bonding is the stabilization of a molecular system by charge- and spin-reorganization processes in chemical reactions. These processes are said to be local, because the number of atoms involved is very small. With multi-configurational self-consistent field (MCSCF) wave functions, these processes can be calculated, but the local information is hidden by the delocalized molecular orbitals (MO) used to construct the wave functions. The transformation of such wave functions into valence bond (VB) wave functions, which are based on localized orbitals, reveals the hidden information; this transformation is called a VB reading of MCSCF wave functions. The two-electron VB wave functions describing the Lewis electron pair that connects two atoms are frequently called covalent or neutral, suggesting that these wave functions describe an electronic situation where two electrons are never located at the same atom; such electronic situations and the wave functions describing them are called ionic. When the distance between two atoms decreases, however, every covalent VB wave function composed of non-orthogonal atomic orbitals changes its character from neutral to ionic. However, this change in the character of conventional VB wave functions is hidden by its mathematical form. Orthogonal VB wave functions composed of orthonormalized orbitals never change their character. When localized fragment orbitals are used instead of atomic orbitals, one can decide which local information is revealed and which remains hidden. In this paper, we analyze four chemical reactions by transforming the MCSCF wave functions into orthogonal VB wave functions; we show how the reactions are influenced by changing the atoms involved or by changing their local symmetry. Using orthogonal instead of non-orthogonal orbitals is not just a technical issue; it also changes the interpretation, revealing the properties of wave functions that remain otherwise undetected.

Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born–Oppenheimer breakdown corrections

Analytical and numerical solutions describing Born–Oppenheimer breakdown in a simple, widely applicable, model depict shortcomings in modern computational methods.

Tuning spin-states of carbynes and silylynes: a long jump with one leg

The challenge motivating this paper is to induce, by chemical substitution, a silylyne, SiR, or a congeneric carbyne, CR, to adopt the high-spin quartet rather than the low-spin doublet as its ground state. The difficulty is seen in the preference for the doublet of the parent SiH (doublet-quartet energy difference ∼39 kcal/mol, favoring the doublet) or CH (∼17 kcal/mol). Strategies for having high-spin ground state parallel those for silylenes and carbenes: greater electropositivity (σ-donation) and π-acceptance of the single substituent favor the high-spin state. The electronegativity trend can be understood from an ions in molecules way of thinking already present in the literature in the works of Boldyrev and Simons, and of Mavridis and Harrison; i.e., the quartet ground state spin of some CR/SiR species is largely determined by the ground state spin of C(-)/Si(-). In this study, we provide a diabatization analysis that solidly confirms the ions in molecules picture and explains the difference in the equilibrium internuclear distances for the two spin states. In general, electronegativity dominates the ordering of spin states. π-Acceptors also help to lower the quartet state energy of the many carbynes (silylynes) examined, whose range of doublet-quartet differences calculated is impressive, 120 (100) kcal/mol. The qualitative understanding gained leads to the prediction of some quartet-ground state carbynes (CMgH, CAlH2, CZnH, CSiH3, CSiF3, etc.) and a smaller number of silylynes (SiMgH, SiMgF, SiBeH, etc.). A beginning is made on the energetics of approach geometries of the fragments in the highly exoergic dimerization of CH to acetylene; it should proceed for the ground state doublet CH through C2h-like trajectories, with no activation energy.