Troubleshooting time-dependent density-functional theory for photochemical applications: Oxirane

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Thiocarbonyl-Bridged N-Heterotriangulenes for Energy Efficient Triplet Photosensitization: A Theoretical Perspective

Structurally-rigid metal-free organic molecules are of high demand for various triplet harvesting applications. However, inefficient intersystem crossing (ISC) due to large singlet-triplet gap (Δ E S - T ${\Delta {E}_{S-T}}$ ) and small spin-orbit coupling (SOC) between lowest excited singlet and triplet often limits their efficiency. Excited electronic states, fluorescence and ISC rates in several thiocarbonyl-bridged N-heterotriangulene ( m ${m}$ S-HTG) with systematically increased thione content (m = ${m=}$ 0-3) are investigated implementing polarization consistent time-dependent optimally-tuned range-separated hybrid. All m ${m}$ S-HTGs are dynamically stable and also thermodynamically feasible to synthesize. Relative energies of several low-lying singlets (S n ${{S}_{n}}$ ) and triplets (T n ${{T}_{n}}$ ), and their excitation nature (i. e.,n π * ${n{\pi }^{^{\ast}}}$ orπ π * ${\pi {\pi }^{^{\ast}}}$ ) and SOC are determined for these m ${m}$ S-HTGs in dichloromethane. Low-energy optical peak displays gradual red-shift with increasing thione content due to relatively smaller electronic gap resulted from greater degree of orbital delocalization. Significantly large SOC due to different orbital-symmetry and heavy-atom effect produces remarkably high ISC rates (k I S C ${{k}_{ISC}}$ ~1012 s-1) for enthalpically favouredS 1 n π * → T 2 ${{S}_{1}\left(n{\pi }^{^{\ast}}\right)\to {T}_{2}}$ (π π * ${\pi {\pi }^{^{\ast}}}$ ) channel in these m ${m}$ S-HTGs, which outcompete radiative fluorescence rates (~108 s-1) even directly from higher lying optically brightπ π * ${\pi {\pi }^{^{\ast}}}$ singlets. Importantly, high energy triplet excitons of ~1.7 eV resulting from such significantly large ISC rates from non-fluorescentS 1 n π * ${{S}_{1}\left(n{\pi }^{^{\ast}}\right)}$ make these thiocarbonylated HTGs ideal candidates for energy efficient triplet harvest including triplet-photosensitization.

Nature and energetics of low-lying excited singlets/triplets and intersystem crossing rates in selone analogs of perylenediimide: A theoretical perspective

The structural rigidity and chemical diversity of the highly fluorescent perylenediimide (PDI) provide wide opportunities for developing triplet photosensitizers with sufficiently increased energy efficiency. Remarkably high intersystem crossing (ISC) rates with a complete fluorescence turn-off reported recently for several thione analogs of PDI due to substantially large spin-orbit coupling garners huge attention to develop other potential analogs. Here, several selone analogs of PDI, denoted as mSe-PDIs (m = 1-4) with varied Se content and positions, are investigated to provide a comprehensive and comparative picture down the group-16 using density functional theory (DFT) and time-dependent DFT implementing optimally tuned range-separated hybrid in toluene dielectric. All mSe-PDIs are confirmed to be dynamically stable and also thermodynamically feasible to synthesize from their oxygen and thione congeners. The first excited-state singlet (S1) of mSe-PDI with relatively low Se-content (m = 1, 2) is of nπ* character with an expected fluorescence turn-off. Whereas, the ππ* nature of the S1 for 3Se-PDI and 4Se-PDI suggests a possible fluorescence turn-on in the absence of any other active nonradiative deactivation pathways. However, ∼4-6 orders greater ISC rates (∼1012-1014 s-1) than the fluorescence ones (∼108 s-1) for all mSe-PDIs signify highly efficient triplet harvest. Importantly, significantly higher ISC rates for these mSe-PDIs than their thione congeners render them efficient triplet photosensitizers.

Solvent-Dependent Emissions Properties of a Model Aurone Enable Use in Biological Applications

Fluorophores are powerful visualization tools and the development of novel small organic fluorophores are in great demand. Small organic fluorophores have been derived from the aurone skeleton, 2-benzylidenebenzofuran-3(2H)-one. In this study, we have utilized a model aurone derivative with a methoxy group at the 3' position and a hydroxyl group at the 4' position, termed vanillin aurone, to develop a foundational understanding of structural factors impacting aurone fluorescence properties. The fluorescent behaviors of the model aurone were characterized in solvent environments differing in relative polarity and dielectric constant. These data suggested that hydrogen bonding or electrostatic interactions between excited state aurone and solvent directly impact emissions properties such as peak emission wavelength, emission intensity, and Stokes shift. Time-dependent Density Functional Theory (TD-DFT) model calculations suggest that quenched aurone emissions observed in water are a consequence of stabilization of a twisted excited state conformation that disrupts conjugation. In contrast, the calculations indicate that low polarity solvents such as toluene or acetone stabilize a brightly fluorescent planar state. Based on this, additional experiments were performed to demonstrate use as a turn-on probe in an aqueous environment in response to conditions leading to planar excited state stabilization. Vanillin aurone was observed to bind to a model ATP binding protein, YME1L, leading to enhanced emissions intensities with a dissociation equilibrium constant equal to ~ 30 µM. Separately, the aurone was observed to be cell permeable with significant toxicity at doses exceeding 6.25 µM. Taken together, these results suggest that aurones may be broadly useful as turn-on probes in aqueous environments that promote either a change in relative solvent polarity or through direct stabilization of a planar excited state through macromolecular binding.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Does the Intersystem Crossing Rate of β-Iodinated Phosphorus Corrole Depend on Iodine Numbers and/or Positions?

The heavy-atom effect is known to enhance the intersystem crossing (ISC) in organic molecular systems. Effects of iodine numbers and positions on the ISC rate of a few meso-difluorophenyl substituted β-iodinated phosphorus corroles (PCs) with axially ligated fluorine atoms (mI-FPC; m = 1-4) are studied using a time-dependent optimally tuned range-separated hybrid. Solvent effects are accounted for through a polarizable continuum model with a toluene dielectric. Calculations suggest similar thermodynamic stability for all mI-FPCs and also reproduce the experimentally measured 0-0 energies for some of the freebase phosphorus corrole (FPC) systems studied here. Importantly, our results reveal that all mI-FPCs display 10 times larger ISC rate (∼109 s-1) than the fluorescence rate (∼108 s-1), and the higher ISC rate stems from the improved spin-orbit coupling (SOC) introduced by lighter heteroatoms like central P and biaxial F rather than the I heavy-atom effect. However, an enhanced SOC is found with increasing I content for El-Sayed forbidden ISC channels. Research findings reported in this study unveil the impact of light heteroatoms and heavy atoms in promoting ISC in several iodinated PCs, which help in designing visible-light-driven efficient triplet photosensitizers.

Size-dependent errors in real-time electron density propagation

Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Electronic Structures and Charge Mobilities of Several Regioisomeric B2N2-Substituted Perylenediimides

Tunable and rich electronic properties of perylenediimide (PDI), an n-type semiconductor together with its synthetic ease and processibility, make it suitable for various optoelectronic and field-effect transistor applications. The electronic structures, spectroscopic properties, and charge mobilities for a few isoelectronic BN-substituted PDIs (B₂N₂-PDIs) with varied BN-patterning are studied using density functional theory (DFT) and time-dependent DFT employing optimally tuned range-separated hybrid. Two substitutional doping patterns, namely, BNNB and NBBN with zero dipole and also BNBN, the one with a finite dipole, are considered to explore the changes in the PDI properties due to different B₂N₂-substitutions. All three B₂N₂-PDIs are found to be dynamically stable and lie within a small energy window of ca. ∼1.7 kcal mol^-1. An increased electronic gap due to charge localization produces a similar but slightly blue-shifted low-lying optical peak compared to the pristine PDI, in good agreement with the experimental observations. Additionally, differently considered BN patterns result in only slightly varied charge mobilities due to mainly differences in electronic couplings with larger electron mobilities found for the experimentally synthesized BNNB-PDI crystal. On the other hand, small reorganization energy and relatively large coupling for the hole transport produce greater hole mobilities for the NBBN-PDI. Varied nuclear reorganization and electronic coupling are understood by analyzing Huang-Rhys factors associated with normal modes and frontier molecular orbitals, respectively. These results serve as complementary to understanding the recently reported experimental findings and also provide new insights into the impact of different BN patterns on modulating the PDI electronic and charge-transport properties.

Optimization Stability in Excited-State-Specific Variational Monte Carlo

We investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

Rational Design of Asymmetric Polymethines to Attain NIR(II) Bioimaging at >1100 nm

Organic molecules having emission in the NIR(II) region are emergent and receiving enormous attention. Unfortunately, attaining accountable organic emission intensity around the NIR(II) region is hampered by the dominant internal conversion operated by the energy gap law, where the emission energy gap and the associated internal reorganization energy λ_int play key roles. Up to the current stage, the majority of the reported organic NIR(II) emitters belong to those polymethines terminated by two symmetric chromophores. Such a design has proved to have a small λ_int that greatly suppresses the internal conversion. However, the imposition of symmetric chromophores is stringent, limiting further development of organic NIR(II) dyes in diversity and versatility. Here, we propose a new concept where as far as the emissive state of the any asymmetric polymethines contains more or less equally transition density between two terminated chromophores, λ_int can be as small as that of the symmetric polymethines. To prove the concept, we synthesize a series of new polymethines terminated by xanthen-9-yl-benzoic acid and 2,4-diphenylthiopyrylium derivatives, yielding AJBF1112 and AEBF1119 that reveal emission peak wavelength at 1112 and 1119 nm, respectively. The quantum yield is higher than all synthesized symmetric polymethines of 2,4-diphenylthiopyrylium derivatives (SC1162, 1182, 1185, and 1230) in this study. λ_int were calculated to be as small as 6.2 and 7.3 kcal/mol for AJBF1112 and AEBF1119, respectively, proving the concept. AEBF1119 was further prepared as a polymer dot to demonstrate its in vitro specific cellular imaging and in vivo tumor/bone targeting in the NIR(II) region.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Analytical gradients and derivative couplings for the TDDFT-1D method

We derive and implement analytic gradients and derivative couplings for time-dependent density functional theory plus one double (TDDFT-1D) which is a semiempirical configuration interaction method whereby the Hamiltonian is diagonalized in a basis of all singly excited configurations and one doubly excited configuration as constructed from a set of reference Kohn-Sham orbitals. We validate the implementation by comparing against finite difference values. Furthermore, we show that our implementation can locate both optimized geometries and minimum-energy crossing points along conical seams of S₁/S₀ surfaces for a set of test cases.

Tailoring intersystem crossing of perylenediimide through chalcogen-substitution at bay-position: A theoretical perspective

Molecular-scale design strategies for promoting intersystem crossing (ISC) in small organic molecules are ubiquitous in developing efficient metal-free triplet photosensitizers with high triplet quantum yield (Φ_T). Air-stable and highly fluorescent perylenediimide (PDI) in its pristine form displays very small ISC compared to the fluorescence due to the large singlet-triplet gap (ΔE_S-T) and negligibly small spin-orbit coupling (SOC) between the lowest singlet (S₁) and triplet state (T₁). However, its Φ_T can be tuned by different chemical and mechanical means that are capable of either directly lowering the ΔE_S-T and increasing SOC or introducing intermediate low-lying triplet states (T_n, n = 2, 3, …) between S₁ and T₁. To this end, herein, a few chalcogen (X = O, S, Se) bay-substituted PDIs (PDI-X₂) are computationally modeled aiming at introducing geometrical-strain at the PDI core and also mixing nπ* orbital character to ππ* in the lowest singlet and triplet excited states, which altogether may reduce ΔE_S-T and also improve the SOC. Our quantum-chemical calculations based on optimally tuned range-separated hybrid reveal the presence of intermediate triplet states (T_n, n = 2, 3) in between S₁ and T₁ for all three PDI-X₂ studied in dichloromethane. More importantly, PDI-X₂ shows a significantly improved ISC rate than the pristine PDI due to the combined effects stemming from the smaller ΔE_S-T and the larger SOC. The calculated ISC rates follow the order as PDI-O₂ < PDI-S₂ < PDI-Se₂. These research findings will be helpful in designing PDI based triplet photosensitizers for biomedical, sensing, and photonic applications.

Can domain-based local pair natural orbitals approaches accurately predict phosphorescence energies?

Since the discovery of the peculiar conducting and optical properties of aromatics, many efforts have been made to characterize and predict their phosphorescence. This physical process is exploited in modern Organic Emitting Light Diodes (OLEDs), and it is also one of the processes decreasing the efficiency of Dye-sensitized solar cells (DSSCs). Herein, we propose a computational strategy for the accurate calculation of singlet-triplet gaps of aromatic compounds, which provides results that are in excellent agreement with available experimental data. Our approach relies on the domain-based local pair natural orbital (DLPNO) variant of the "gold standard" CCSD(T) method. The convergence of our results with respect to the key technical parameters of the calculation, such as the basis set used, the approximations employed in the perturbative triples correction, and the dimension of the PNOs space, was thoroughly discussed.

Mechanistic photophysics and photochemistry of unnatural bases and sunscreen molecules: insights from electronic structure calculations

Photophysics and photochemistry are basic subjects in the study of light-matter interactions and are ubiquitous in diverse fields such as biology, energy, materials, and environment. A full understanding of mechanistic photophysics and photochemistry underpins many recent advances and applications. This contribution first provides a short discussion on the theoretical calculation methods we have used in relevant studies, then we introduce our latest progress on the mechanistic photophysics and photochemistry of two classes of molecular systems, namely unnatural bases and sunscreens. For unnatural bases, we disclose the intrinsic driving forces for the ultrafast population to reactive triplet states, impacts of the position and degree of chalcogen substitutions, and the effects of complex environments. For sunscreen molecules, we reveal the photoprotection mechanisms that dissipate excess photon energy to the surroundings by ultrafast internal conversion to the ground state. Finally, relevant theoretical challenges and outlooks are discussed.

In Silico Discovery of Multistep Chemistry Initiated by a Conical Intersection: The Challenging Case of Donor-Acceptor Stenhouse Adducts

Detailed mechanistic understanding of multistep chemical reactions triggered by internal conversion via a conical intersection is a challenging task that emphasizes limitations in theoretical and experimental techniques. We present a discovery-based, hypothesis-free computational approach based on first-principles molecular dynamics to discover and refine the switching mechanism of donor-acceptor Stenhouse adducts (DASAs). We simulate the photochemical experiment in silico, following the "hot" ground state dynamics for 10 ps after photoexcitation. Using state-of-the-art graphical processing units-enabled electronic structure calculations we performed in total ∼2 ns of nonadiabatic ab initio molecular dynamics discovering (a) critical intermediates that are involved in the open-to-closed transformation, (b) several competing pathways which lower the overall switching yield, and (c) key elements for future design strategies. Our dynamics describe the natural evolution of both the nuclear and electronic degrees of freedom that govern the interconversion between DASA ground-state intermediates, exposing significant elements for future design strategies of molecular switches.

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiff base C5H6NH2. J Chem Phys 2021;155:124111. [PMID: 34598550 DOI: 10.1063/5.0062757]

Nonadiabatic trajectory surface hopping simulations are reported for trans-C₅H₆NH₂ ⁺, a model of the rhodopsin chromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C₅H₆NH₂ ⁺, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S₁/S₀ conical intersections is immaterial to the photodynamics.

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.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Ultrafast Photo-ion Probing of the Ring-Opening Process in Trans-Stilbene Oxide

The ultrafast photo‐induced ring opening of the oxirane derivative trans‐stilbene oxide has been studied through the use of ultrafast UV/UV pump‐probe spectroscopy by using photo‐ion detection. Single‐ and multiphoton probe paths and final states were identified through comparisons between UV power studies and synchrotron‐based vacuum ultraviolet (VUV) single‐photon ionization studies. Three major time‐dependent features of the parent ion (sub‐450 fs decay, (1.5±0.2) ps, and >100 ps) were observed. These decays are discussed in conjunction with the primary ring‐opening mechanism of stilbene oxide, which occurs through C−C dissociation in the oxirane ring. The appearance of fragments relating to the masses of dehydrogenated diphenylmethane (167 amu) and dehydrogenated methylbenzene (90 amu) were also investigated. The appearance of the 167 amu fragment could suggest an alternative ultrafast ring‐opening pathway via the dissociation of one of the C−O bonds within the oxirane ring.

Structure-Photochemical Function Relationships in the Photobasicity of Aromatic Heterocycles Containing Multiple Ring Nitrogen Atoms

Photobases are compounds that become more basic when promoted to an excited electronic state. Previous experimental and computational studies have demonstrated that several quinoline and quinoline-derived compounds are strong photobases (pK_a^* > 14). Moreover, the strength of photobasicity was shown to depend strongly on the identity and position of the substituent group(s), with the strongest photobases having multiple electron-donating substituents on a fused benzene ring as opposed to the ring containing the photobasic nitrogen atom. These electron-donating substituents build up electron density on one side of the molecule that shifts onto the nitrogen-containing ring in the electronic transition. This shift in electron density produces an increase in negative charge on the ring nitrogen atom responsible for the photobasicity. In this paper, we expand on our previous investigation to study the effect of an additional ring nitrogen atom on photobasicity in aromatic heterocycles. In particular, we consider how the thermodynamic driving force for excited-state protonation can be tuned by changing the relative placement of the ring nitrogen atoms and varying the position and number of electron-donating substituents. In the set of 112 molecules screened, we identified 42 strong photobases with generally comparable pK_a^* but lower vertical excitation energies than the quinoline derivatives with only a single ring nitrogen atom. We additionally explored photobasicity in substituted azaindole and carboline derivatives, identifying 76 strongly photobasic compounds with pK_a^* as large as 22.6 out of the 155 compounds that we considered. Overall, this work provides new insights into the design principles necessary to develop next-generation photocatalysts that employ photobasicity.

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

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

Analytic gradients and derivative couplings for configuration interaction with all single excitations and one double excitation-En route to nonadiabatic dynamics

We present analytic gradients and derivative couplings for the simplest possible multireference configuration interaction method, CIS-1D, an electronic structure Ansatz that includes all single excitations and one lone double excitation on top of a Hartree-Fock reference state. We show that the resulting equations are numerically stable and require the evaluation of a similar number of integrals as compared to standard CIS theory; one can easily differentiate the required frontier orbitals (h and l) with minimal cost. The resulting algorithm has been implemented within the Q-Chem electronic structure package and should be immediately useful for understanding photochemistry with S₀-S₁ crossings.

Photochemical Ring Opening of Oxirane Modeled by Constrained Density Functional Theory

A constrained density functional theory/classical trajectory surface hopping study of the photochemical dissociation of oxirane (CH₂)₂O is presented. The calculations confirm the Gomer-Noyes mechanism for the initial reaction and agree largely with experimental photolysis data including reaction yields. The calculated yields, however, depend both on temperature and its modeling. The timescales of the various reaction steps are well below 100 fs, similar to previous time-dependent density functional calculations. At variance with those, however, the present calculations obey Kasha's rule, i.e., the photoreaction is initiated in the energetically lowest excited state.

Combining Graphics Processing Units, Simplified Time-Dependent Density Functional Theory, and Finite-Difference Couplings to Accelerate Nonadiabatic Molecular Dynamics

Starting from our recently published implementation of nonadiabatic molecular dynamics (NAMD) on graphics processing units (GPUs), we explore further approaches to accelerate ab initio NAMD calculations at the time-dependent density functional theory (TDDFT) level of theory. We employ (1) the simplified TDDFT schemes of Grimme et al. and (2) the Hammes-Schiffer-Tully approach to obtain nonadiabatic couplings from finite-difference calculations. The resulting scheme delivers an accurate physical picture while virtually eliminating the two computationally most demanding steps of the algorithm. Combined with our GPU-based integral routines for SCF, TDDFT, and TDDFT derivative calculations, NAMD simulations of systems of a few hundreds of atoms at a reasonable time scale become accessible on a single compute node. To demonstrate this and to present a first, illustrative example, we perform TDDFT/MM-NAMD simulations of the rhodopsin protein.

Structure-Photochemical Function Relationships in Nitrogen-Containing Heterocyclic Aromatic Photobases Derived from Quinoline

Photobases are compounds that become strong bases after electronic excitation. Recent experimental studies have highlighted the photobasicity of the 5-R quinoline compounds, demonstrating a strong substituent dependence to the pK_a^*. In this paper, we describe our systematic study of how the thermodynamic driving force for photobasicity is tuned through substituents in four families of nitrogen-containing heterocyclic aromatics. We show that substituent position and identity both significantly impact the pK_a^*. We demonstrate that the substituent effects are additive and identify many disubstituted compounds with substantially greater photobasicity than the most photobasic 5-R quinoline compound identified previously. We show that the addition of a second fused benzene ring to quinoline, along with two electron-donating substituents, lowers the S₀ → S_PBS vertical excitation energy into the visible region while still maintaining a pK_a^* > 14. Overall, the structure-function relationships developed in this study provide new insights to guide the development of new photocatalysts that employ photobasicity.

Nonadiabatic Molecular Dynamics on Graphics Processing Units: Performance and Application to Rotary Molecular Motors

Nonadiabatic molecular dynamics (NAMD) simulations of molecular systems require the efficient evaluation of excited-state properties, such as energies, gradients, and nonadiabatic coupling vectors. Here, we investigate the use of graphics processing units (GPUs) in addition to central processing units (CPUs) to efficiently calculate these properties at the time-dependent density functional theory (TDDFT) level of theory. Our implementation in the FermiONs++ program package uses the J-engine and a preselective screening procedure for the calculation of Coulomb and exchange kernels, respectively. We observe good speed-ups for small and large molecular systems (comparable to those observed in ground-state calculations) and reduced (down to sublinear) scaling behavior with respect to the system size (depending on the spatial locality of the investigated excitation). As a first illustrative application, we present efficient NAMD simulations of a series of newly designed light-driven rotary molecular motors and compare their S1 lifetimes. Although all four rotors show different S1 excitation energies, their ability to rotate upon excitation is conserved, making the series an interesting starting point for rotary molecular motors with tunable excitation energies.

What Is the Accuracy Limit of Adiabatic Linear-Response TDDFT Using Exact Exchange-Correlation Potentials and Approximate Kernels?

Calculation of vertical excitation energies by the adiabatic linear-response time-dependent density-functional theory (TDDFT) requires static Kohn-Sham potentials and exchange-correlation kernels. When these quantities are derived from standard density-functional approximations (DFA), mean absolute errors (MAE) of the method are known to range from 0.2 eV to over 1 eV, depending on the functional and type of excitation. We investigate how the performance of TDDFT varies when increasingly accurate exchange-correlation potentials derived from Hartree-Fock (HF) and post-HF wavefunctions are combined with different approximate kernels. The lowest MAEs obtained in this manner for valence excitations are about 0.15-0.2 eV, which appears to be the practical limit of the accuracy of TDDFT that can be achieved by improving the Kohn-Sham potentials alone. These findings are consistent with previous reports on the benefits of accurate exchange-correlation potentials in TDDFT, but provide new insights and afford more definitive conclusions.

Isomerization of cyanopropyne in solid argon

Cyanopropyne, CH3-C[triple bond, length as m-dash]C-CN, is a simple molecule whose photochemistry is still unexplored. Here we investigate the UV photolysis of this astrophysically significant nitrile trapped in solid argon. The FTIR study was assisted with 15N-isotopic substitution data and with DFT-level computations including the analyses of ground- and excited-state potential energy surfaces. Cyanopropyne was found to decay mainly via a two-step isomerization process. Infrared absorption spectra evolved to show signals from allenyl cyanide, CH2[double bond, length as m-dash]C[double bond, length as m-dash]CH-CN, which then further convert into propargyl cyanide, H-C[triple bond, length as m-dash]C-CH2-CN. Some evidence for the presence of allenyl isocyanide, propargyl isocyanide, 3-cyanocyclopropene, and 1,2,3-butatrien-1-imine under particular experimental conditions was also observed. Although cyano/isocyano interconversion has been observed during photolysis of other closely related species in solid argon matrices, including H-C[triple bond, length as m-dash]C-CN, no evidence could be found for production of 1-isocyano-1-propyne, CH3-C[triple bond, length as m-dash]C-NC for these experiments.

Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations

HF/DFT orbitals spin-polarize when single bonds are stretched past the Coulson–Fischer point. We report unphysical features in the excited state potential energy surfaces predicted by CIS/TDDFT in this regime, and characterize their origin.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

On the applicability of a wavefunction-free, energy-based procedure for generating first-order non-adiabatic couplings around conical intersections

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.

Fast and slow excited-state intramolecular proton transfer in 3-hydroxychromone: a two-state story?

The photodynamics of 3-hydroxychromone in its first-excited singlet electronic state (bright state of ππ* character) is investigated with special emphasis given to two types of reaction pathways: the excited-state intramolecular-proton-transfer coordinate and the hydrogen-torsion coordinate linking the excited cis and trans isomers. A newly-found conical intersection with the second-excited singlet electronic state (dark state of nπ* character) is suspected to be, to some extent, the reason for the slower rate constant. This hypothesis based on quantum-chemistry calculations is supported by quantum-dynamics simulations in full dimensionality. They show significant transfer of electronic population and provide consistently a vibronic interpretation for the forbidden band in the UV absorption spectrum.

Ab Initio Nonadiabatic Dynamics with Coupled Trajectories: A Rigorous Approach to Quantum (De)Coherence

We report the first nonadiabatic molecular dynamics study based on the exact factorization of the electron-nuclear wave function. Our approach (a coupled-trajectory mixed quantum-classical, CT-MQC, scheme) is based on the quantum-classical limit derived from systematic and controlled approximations to the full quantum-mechanical problem formulated in the exact-factorization framework. Its strength is the ability to correctly capture quantum (de)coherence effects in a trajectory-based approach to excited-state dynamics. We show this by benchmarking CT-MQC dynamics against a revised version of the popular fewest-switches surface-hopping scheme that is able to fix its well-documented overcoherence issue. The CT-MQC approach is successfully applied to investigation of the photochemistry (ring-opening) of oxirane in the gas phase, analyzing in detail the role of decoherence. This work represents a significant step forward in the establishment of the exact factorization as a powerful tool to study excited-state dynamics, not only for interpretation purposes but mainly for nonadiabatic ab initio molecular dynamics simulations.

Shedding new light on an old molecule: quinophthalone displays uncommon N-to-O excited state intramolecular proton transfer (ESIPT) between photobases

Excited state dynamics of common yellow dye quinophthalone (QPH) was probed by femtosecond transient absorption spectroscopy. Multi-exponential decay of the excited state and significant change of rate constants upon deuterium substitution indicate that uncommon nitrogen-to-oxygen excited state intramolecular proton transfer (ESIPT) occurs. By performing density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations, we found that adiabatic surface crossing between the S₁ and S₂ states takes place in the photoreaction. Unlike most cases of ESIPT, QPH does not exhibit tautomer emission, possibly due to internal conversion or back-proton transfer. The ESIPT of QPH presents a highly interesting case also because the moieties participating in ESIPT, quinoline and aromatic carbonyl, are both traditionally considered as photobases.

Intermolecular Singlet and Triplet Exciton Transfer Integrals from Many-Body Green's Functions Theory

A general approach to determine orientation and distance-dependent effective intermolecular exciton transfer integrals from many-body Green's functions theory is presented. On the basis of the GW approximation and the Bethe-Salpeter equation (BSE), a projection technique is employed to obtain the excitonic coupling by forming the expectation value of a supramolecular BSE Hamiltonian with electron-hole wave functions for excitations localized on two separated chromophores. Within this approach, accounting for the effects of coupling mediated by intermolecular charge transfer (CT) excitations is possible via perturbation theory or a reduction technique. Application to model configurations of pyrene dimers shows an accurate description of short-range exchange and long-range Coulomb interactions for the coupling of singlet and triplet excitons. Computational parameters, such as the choice of the exchange-correlation functional in the density-functional theory (DFT) calculations that underly the GW-BSE steps and the convergence with the number of included CT excitations, are scrutinized. Finally, an optimal strategy is derived for simulations of full large-scale morphologies by benchmarking various approximations using pairs of dicyanovinyl end-capped oligothiophenes (DCV5T), which are used as donor material in state-of-the-art organic solar cells.