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

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.

A new architecture for high spin organics based on Baird's rule of 4n electron triplet aromatics

This work reports triplet aromatic high spin ground states of cyclopentadienyl cation polyads as alternative to high spin polyradicals or polycarbenes.

Theoretical rationalization of the singlet-triplet gap in OLEDs materials: impact of charge-transfer character

New materials for OLED applications with low singlet-triplet energy splitting have been recently synthesized in order to allow for the conversion of triplet into singlet excitons (emitting light) via a Thermally Activated Delayed Fluorescence (TADF) process, which involves excited-states with a non-negligible amount of Charge-Transfer (CT). The accurate modeling of these states with Time-Dependent Density Functional Theory (TD-DFT), the most used method so far because of the favorable trade-off between accuracy and computational cost, is however particularly challenging. We carefully address this issue here by considering materials with small (high) singlet-triplet gap acting as emitter (host) in OLEDs and by comparing the accuracy of TD-DFT and the corresponding Tamm-Dancoff Approximation (TDA), which is found to greatly reduce error bars with respect to experiments thanks to better estimates for the lowest singlet-triplet transition. Finally, we quantitatively correlate the singlet-triplet splitting values with the extent of CT, using for it a simple metric extracted from calculations with double-hybrid functionals, that might be applied in further molecular engineering studies.

Intramolecular vibrational redistribution in the non-radiative excited state decay of uracil in the gas phase: an ab initio molecular dynamics study

We report a study of intramolecular vibrational distribution (IVR) occurring in the electronic ground state of uracil (S0) in the gas phase, following photoexcitation in the lowest energy bright excited state (Sπ) and decay through the ethylene-like Sπ/S0 Conical Intersection (CI-0π). To this aim we have performed 20 independent ab initio molecular dynamics simulations starting from CI-0π (ten of them with 1 eV kinetic energy randomly distributed over the different molecular degrees of freedom) and 10 starting from the ground state minimum (Franck-Condon, FC, point), with the excess kinetic energy equal to the energy gap between CI-0π and the FC point. The simulations, exploiting PBE0/6-31G(d) calculations, were performed over an overall period of 10 ps. A thorough statistical analysis of the variation of the geometrical parameters of uracil during the simulation time and of the distribution of the kinetic energy among the different vibrational degrees of freedom provides a consistent picture of the IVR process. In the first 0-200 fs the structural dynamics involve mainly the recovery of the average planarity. In the 200-600 fs time range, a substantial activation of CO and NH degrees of freedom is observed. After 500-600 fs most of the geometrical parameters reach average values similar to those found after 10 ps, though the system cannot be considered to be in equilibrium yet.

Description of Conical Intersections with Density Functional Methods

Conical intersections are perhaps the most significant mechanistic features of chemical reactions occurring through excited states. By providing funnels for efficient non-adiabatic population transfer, conical intersections govern the branching ratio of products of such reactions, similar to what the transition states do for ground-state reactivity. In this regard, intersections between the ground and the lowest excited states play a special role, and the correct description of the potential energy surfaces in their vicinity is crucial for understanding the mechanism and dynamics of excited-state reactions. The methods of density functional theory, such as time-dependent density functional theory, are widely used to describe the excited states of large molecules. However, are these methods suitable for describing the conical intersections or do they lead to artifacts and, consequently, to erroneous description of reaction dynamics? Here we address the first part of this question and analyze the ability of several density functional approaches, including the linear-response time-dependent approach as well as the spin-flip and ensemble formalisms, to provide the correct description of conical intersections and the potential energy surfaces in their vicinity. It is demonstrated that the commonly used linear-response time-dependent theory does not yield a proper description of these features and that one should instead use alternative computational approaches.

Identifying and tracing potential energy surfaces of electronic excitations with specific character via their transition origins: application to oxirane

We show that the transition origins of electronic excitations identified by quantified natural transition orbital (QNTO) analysis can be employed to connect potential energy surfaces (PESs) according to their character across a wide range of molecular geometries.

Theoretical spectroscopy and photodynamics of a ruthenium nitrosyl complex

Photoactive transition-metal nitrosyl complexes are particularly interesting as potential drugs that deliver nitric oxide (NO) upon UV-light irradiation to be used, e.g., in photodynamic therapy. It is well-recognized that quantum-chemical calculations can guide the rational design and synthesis of molecules with specific functions. In this contribution, it is shown how electronic structure calculations and dynamical simulations can provide a unique insight into the photodissociation mechanism of NO. Exemplarily, [Ru(PaPy3)(NO)](2+) is investigated in detail, as a prototype of a particularly promising class of photoactive metal nitrosyl complexes. The ability of time-dependent density functional theory (TD-DFT) to obtain reliable excited-state energies compared with more sophisticated multiconfigurational spin-corrected calculations is evaluated. Moreover, a TD-DFT-based trajectory surface-hopping molecular dynamics study is employed to reveal the details of the radiationless decay of the molecule via internal conversion and intersystem crossing. Calculations show that the ground state of [Ru(PaPy3)(NO)](2+) includes a significant admixture of the Ru(III)(NO)(0) electronic configuration, in contrast to the previously postulated Ru(II)(NO)(+) structure of similar metal nitrosyls. Moreover, the lowest singlet and triplet excited states populate the antibonding metal d → πNO* orbitals, favoring NO dissociation. Molecular dynamics show that intersystem crossing is ultrafast (<10 fs) and dissociation is initiated in less than 50 fs. The competing relaxation to the lowest S1 singlet state takes place in less than 100 fs and thus competes with NO dissociation, which mostly takes place in the higher-lying excited triplet states. All of these processes are accompanied by bending of the NO ligand, which is not confined to any particular state.

Configuration Interaction-Corrected Tamm-Dancoff Approximation: A Time-Dependent Density Functional Method with the Correct Dimensionality of Conical Intersections

Linear response (LR) Kohn-Sham (KS) time-dependent density functional theory (TDDFT), or KS-LR, has been widely used to study electronically excited states of molecules and is the method of choice for large and complex systems. The Tamm-Dancoff approximation to TDDFT (TDDFT-TDA or KS-TDA) gives results similar to KS-LR and alleviates the instability problem of TDDFT near state intersections. However, KS-LR and KS-TDA share a debilitating feature; conical intersections of the reference state and a response state occur in F - 1 instead of the correct F - 2 dimensions, where F is the number of internal degrees of freedom. Here, we propose a new method, named the configuration interaction-corrected Tamm-Dancoff approximation (CIC-TDA), that eliminates this problem. It calculates the coupling between the reference state and an intersecting response state by interpreting the KS reference-state Slater determinant and linear response as if they were wave functions. Both formal analysis and test results show that CIC-TDA gives similar results to KS-TDA far from a conical intersection, but the intersection occurs with the correct dimensionality. We anticipate that this will allow more realistic application of TDDFT to photochemistry.

Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model

In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn-Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties.

Theoretical calculation of reorganization energy for electron self-exchange reaction by constrained density functional theory and constrained equilibrium thermodynamics

Within the framework of constrained density functional theory (CDFT), the diabatic or charge localized states of electron transfer (ET) have been constructed. Based on the diabatic states, inner reorganization energy λin has been directly calculated. For solvent reorganization energy λs, a novel and reasonable nonequilibrium solvation model is established by introducing a constrained equilibrium manipulation, and a new expression of λs has been formulated. It is found that λs is actually the cost of maintaining the residual polarization, which equilibrates with the extra electric field. On the basis of diabatic states constructed by CDFT, a numerical algorithm using the new formulations with the dielectric polarizable continuum model (D-PCM) has been implemented. As typical test cases, self-exchange ET reactions between tetracyanoethylene (TCNE) and tetrathiafulvalene (TTF) and their corresponding ionic radicals in acetonitrile are investigated. The calculated reorganization energies λ are 7293 cm(-1) for TCNE/TCNE(-) and 5939 cm(-1) for TTF/TTF(+) reactions, agreeing well with available experimental results of 7250 cm(-1) and 5810 cm(-1), respectively.

Isomerization mechanism of the HcRed fluorescent protein chromophore

To understand how the protein achieves fluorescence, the isomerization mechanism of the HcRed chromophore is studied both under vacuum and in the solvated red fluorescent protein. Quantum mechanical (QM) and quantum mechanical/molecular mechanical (QM/MM) methods are applied both for the ground and the first excited state. The photoinduced processes in the chromophore mainly involve torsions around the imidazolinone-bridge bond (τ) and the phenoxy-bridge bond (φ). Under vacuum, the isomerization of the cis-trans chromophore essentially proceeds by τ twisting, while the radiationless decay requires φ torsion. By contrast, the isomerization of the cis-trans chromophore in HcRed occurs via simultaneous τ and φ twisting. The protein environment significantly reduces the barrier of this hula twist motion compared with vacuum. The excited-state isomerization barrier via the φ rotation of the cis-coplanar conformer in HcRed is computed to be significantly higher than that of the trans-non-coplanar conformer. This is consistent with the experimental observation that the cis-coplanar-conformation of the chromophore is related to the fluorescent properties of HcRed, while the trans-non-planar conformation is weakly fluorescent or non-fluorescent. Our study shows how the protein modifies the isomerization mechanism, notably by interactions involving the nearby residue Ile197, which keeps the chromophore coplanar and blocks the twisting motion that leads to photoinduced radiationless decay.

Progress in time-dependent density-functional theory

The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in Volume 55 of the Annual Review of Physical Chemistry left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Because doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis is placed on the problem of going beyond or around the TD-DFT adiabatic approximation, which limits TD-DFT calculations to nominally singly-excited states.

Unravelling the details of vitamin D photosynthesis by non-adiabatic molecular dynamics simulations

We investigate the photodynamics of vitamin D derivatives by a fully analytical implementation of the linear response time-dependent density functional theory surface hopping method (LR-TDDFT-SH). Our study elucidates the dynamics of the processes involved in vitamin D formation at the molecular level and with femtosecond resolution. We explain the major experimental findings and provide new insights that cannot directly be obtained from experiments: firstly, we investigate the dynamics of the photoinduced ring-opening of provitamin D (Pro) and cyclohexadiene (CHD) and the subsequent rotational isomerization. In agreement with recent experiments and CC2 calculations, only the bright S(1) state is involved in the ring-opening reaction. Our calculations confirm the experimentally reported 5 : 1 ratio between the excited state lifetimes of Pro and CHD. The longer lifetimes of Pro are attributed to steric constraints of the steroid skeleton and to temperature effects, both emerging directly from our simulations. For CHD and Pro, we present an explanation of the biexponential decay recently reported by Sension and coworkers [Tang et al., J. Phys. Chem., 2011, 134, 104503]: our calculations suggest that the fast and slow components arise from a reactive and an unreactive reaction pathway, respectively. Secondly, we assess the wavelength dependent photochemistry of previtamin D (Pre). Using replica exchange molecular dynamics we sample the Pre conformers present at thermal equilibrium. Based on this ensemble we explain the conformation dependent absorption and the essential features of Pre photochemistry. Consistent with the experiments, we find ring-closure to occur mostly after excitation of the cZc conformers and at lower energies, whereas Z/E isomerization of the central double bond preferably occurs after excitation at higher energies. For the isomerization we provide the first theoretical evidence of the proposed hula-twist mechanism. Our results show that LR-TDDFT-SH is a highly valuable tool for studying the photochemistry of moderately large systems, even though challenges remain in the vicinity of conical intersections.

Influence of Triplet Instabilities in TDDFT

Singlet and triplet vertical excitation energies from time-dependent density functional theory (TDDFT) can be affected in different ways by the inclusion of exact exchange in hybrid or Coulomb-attenuated/range-separated exchange-correlation functionals; in particular, triplet excitation energies can become significantly too low. To investigate these issues, the explicit dependence of excitation energies on exact exchange is quantified for four representative molecules, paying attention to the effect of constant, short-range, and long-range contributions. A stability analysis is used to verify that the problematic TDDFT triplet excitations can be understood in terms of the ground state triplet instability problem, and it is proposed that a Hartree-Fock stability analysis should be used to identify triplet excitations for which the presence of exact exchange in the TDDFT functional is undesirable. The use of the Tamm-Dancoff approximation (TDA) significantly improves the problematic triplet excitation energies, recovering the correct state ordering in benzoquinone; it also affects the corresponding singlet states, recovering the correct state ordering in naphthalene. The impressive performance of the TDA is maintained for a wide range of molecules across representative functionals.

Excited-State Electronic Structure with Configuration Interaction Singles and Tamm-Dancoff Time-Dependent Density Functional Theory on Graphical Processing Units

Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm–Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).

Excitation energies from spin-restricted ensemble-referenced Kohn-Sham method: a state-average approach

A time-independent density functional approach to the calculation of excitation energies from the ground states of molecules typified by the strong nondynamic electron correlation is suggested. The new method is based on the use of the spin-restricted ensemble-referenced Kohn-Sham formalism [Filatov, M.; Shaik, S. Chem. Phys. Lett. 1999, 304, 429] for the calculation of the ground state. In the new method, the average energy of the ground state and a state created by a single excitation thereof is minimized with respect to the Kohn-Sham orbitals and their fractional occupation numbers. The lowest singlet excitation energies obtained with the help of the new formalism for a number of model systems, such as the hydrogen molecule with stretched bond, twisted ethylene, and twisted hexa-1,3,5-triene, are compared with the results of the time-dependent density functional theory, with the results of ab initio CASSCF/CASPT2 calculations, and with the experimental data. Applicability of the new method to the description of photochemical reactions is discussed.