Assessment of density functional theory based ΔSCF (self-consistent field) and linear response methods for longest wavelength excited states of extended π-conjugated molecular systems

Spin-Vibronic Control of Intersystem Crossing in Iodine-Substituted Heptamethine Cyanines

Spin-orbit coupling between electronic states of different multiplicity can be strongly coupled to molecular vibrations, and this interaction is becoming recognized as an important mechanism for controlling the course of photochemical reactions. Here, we show that the involvement of spin-vibronic coupling is essential for understanding the photophysics and photochemistry of heptamethine cyanines (Cy7), bearing iodine as a heavy atom in the C3' position of the chain and/or a 3H-indolium core, as potential triplet sensitizers and singlet oxygen producers in methanol and aqueous solutions. The sensitization efficiency was found to be an order of magnitude higher for the chain-substituted than the 3H-indolium core-substituted derivatives. Our ab initio calculations demonstrate that while all optimal structures of Cy7 are characterized by negligible spin-orbit coupling (tenths of cm^-1) with no dependence on the position of the substituent, molecular vibrations lead to its significant increase (tens of cm^-1 for the chain-substituted cyanines), which allowed us to interpret the observed position dependence.

Double Hybrid Density Functionals for the Electronic Excitation Energies of Linear Cyanines

The lowest bright electronic excitations of seven model linear cyanines (CN3-CN15) using 28 double-hybrid (DH) density functionals are benchmarked against accurate and recent CC3 results. Some of these DH functionals are recently designed specifically for excited electronic state calculations. In addition, CIS, CIS(D), SCS-CIS(D), and SOS-CIS(D) were also tested. Four different basis sets were used for the vertical electronic excitation calculations: cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis. Augmented basis sets (e.g. aug-cc-pVDZ and aug-cc-pVTZ) are found to be required for accurate and consistent results using DH functionals. The DH functionals tested in this work are classified into four main groups: global double-hybrids (GDH), range-separated double-hybrids (RSDH), spin-component and spin-opposite scaling global double-hybrids (SCS/SOS-GDH), and spin-component and spin-opposite scaling range-separated double-hybrids (SCS/SOS-RSDH). Within these groups, the SCS/SOS-RSDH group of functionals is found to provide the lowest mean absolute error (MAE) values (in the range 0.020-0.148 eV) in comparison with the GDH group (0.195-0.441 eV), the RSDH group (0.186-0.511 eV), and the SCS/SOS-GDH group (0.079-0.461 eV). Of all the DH functionals and ab initio methods investigated in the present contribution, the following functionals are found to be the most accurate and consistent: SCS-ωB2GPPLYP (MAE = 0.036 eV), SOS-ωB2GPPLYP (MAE = 0.020 eV), SOS-ωB88PP86 (MAE = 0.035 eV), and SOS-ωPBEPP86 (MAE = 0.037 eV). In general, the ab initio methods tested here show mediocre performance as compared to many DH functionals.

Reference Excitation Energies of Increasingly Large Molecules: A QMC Study of Cyanine Dyes

We revisit here the lowest vertical excitations of cyanine dyes using quantum Monte Carlo and leverage recent developments to systematically improve on previous results. In particular, we employ a protocol for the construction of compact and accurate multideterminant Jastrow-Slater wave functions for multiple states, which we have recently validated on the excited-state properties of several small prototypical molecules. Here, we obtain quantum Monte Carlo excitation energies in excellent agreement with high-level coupled cluster for all the cyanines where the coupled cluster method is applicable. Furthermore, we push our protocol to longer chains, demonstrating that quantum Monte Carlo is a viable methodology to establish reference data at system sizes which are hard to reach with other high-end approaches of similar accuracy. Finally, we determine which ingredients are key to an accurate treatment of these challenging systems and rationalize why a description of the excitation based on only active π orbitals lacks the desired accuracy for the shorter chains.

Description of Sudden Polarization in the Excited Electronic States with an Ensemble Density Functional Theory Method

Sudden polarization (SP) is one of the manifestations of electron transfer in the electronically excited states of molecules. Proposed initially to explain the unusual reactivity of photoexcited olefins, SP often occurs in the excited states of molecules possessing strongly correlated diradical ground state. Theoretical description of SP involves mixing between the singly excited and the doubly excited zwitterionic states, which makes it inaccessible with the use of the popular linear-response time-dependent density functional theory methods. In this work, an extended variant of the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS, or SSR) method is applied to study SP in a number of organic diradical systems. To this end, the analytical derivative formalism is derived and implemented for the SSR(3,2) method (see the main text for explanation of the acronym), which enables the automatic geometry optimization and obtains the relaxed density matrices as well as the electron binding energies and respective Dyson's orbitals. Application of the new method to SP in the lowest singlet excited state of ethylene agrees with the results obtained previously with the use of multireference methods of wavefunction theory. A number of interesting manifestations of SP are observed, such as the charge transfer in photoexcited tetramethyleneethene (TME) diradical mediated by the vibrational motion and conductivity switching in the excited state of a donor-acceptor dyad placed in an external electric field.

Donor acceptor fluorophores: synthesis, optical properties, TD-DFT and cytotoxicity studies

Donor-π-acceptor (D-π-A) fluorophores consisting of a donor unit, a π linker, and an acceptor moiety have attracted attention in the last decade. In this study, we report the synthesis, characterization, optical properties, TD-DFT, and cytotoxicity studies of 17 near infrared (NIR) D-π-A analogs which have not been reported so far to the best of our knowledge. These fluorophores have chloroacrylic acid as the acceptor unit and various donor units such as indole, benzothiazole, benzo[e]indole, and quinoline. The fluorophores showed strong absorption in the NIR (700-970 nm) region due to their enhanced intramolecular charge transfer (ICT) between chloroacrylic acid and the donor moieties connected with the Vilsmeier-Haack linker. The emission wavelength maxima of the fluorophores were in between 798 and 870 nm. Compound 20 with a 4-quinoline donor moiety showed an emission wavelength above 1000 nm in the NIR II window. The synthesized fluorophores were characterized by 1H NMR and 13C NMR, and their optical properties were studied. Time dependent density functional theory (TD-DFT) calculations showed that the charge transfer occurs from the donor groups (indole, benzothiazole, benzo[e]indole, and quinoline) to the acceptor chloroacrylic acid moiety. Fluorophores with [HOMO] to [LUMO+1] transitions were shown to possess a charge separation character. The cytotoxicity of selected fluorophores, 4, 7, 10 and 12 was investigated against breast cancer cell lines and they showed better activity than the anti-cancer agent docetaxel.

Sensing mechanism of a ratiometric near-infrared fluorescent chemosensor for cysteine hydropersulfide: Intramolecular charge transfer

Previous studies have shown that the cysteine hydropersulfide (Cys-SSH) as the sulfur donor is crucial to sulfur-containing cofactors synthesis. Recently, a selective and sensitive near-infrared ratiometric fluorescent chemosensor Cy-DiSe has been designed and synthesized to detect Cys-SSH spontaneously. Herein, by means of the density functional theory (DFT) and time-dependent density functional theory (TD-DFT) approaches, the sensing mechanism has been thoroughly explored. According to our calculations, the experimental data have been reproduced. The results indicate the intramolecular charge transfer (ICT) is the reason for changes in fluorescence wavelengths. Compared with the chemosensor Cy-DiSe, the larger energy gap of Cy induced by ICT mechanism leads to the blue-shift of the absorption and emission spectra, which guarantees that Cy-DiSe can become a ratiometric fluorescent chemosensor to detect Cys-SSH.

Description of ground and excited electronic states by ensemble density functional method with extended active space

An extended variant of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, the REKS(4,4) method, designed to describe the ground electronic states of strongly multireference systems is modified to enable calculation of excited states within the time-independent variational formalism. The new method, the state-interaction state-averaged REKS(4,4), i.e., SI-SA-REKS(4,4), is capable of describing several excited states of a molecule involving double bond cleavage, polyradical character, or multiple chromophoric units. We demonstrate that the new method correctly describes the ground and the lowest singlet excited states of a molecule (ethylene) undergoing double bond cleavage. The applicability of the new method for excitonic states is illustrated with π stacked ethylene and tetracene dimers. We conclude that the new method can describe a wide range of multireference phenomena.

The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges

We review the Bethe–Salpeter formalism and analyze its performances for the calculation of the excited state properties of molecular systems.

Rationalisation of the optical signatures of nor-dihydroxanthene-hemicyanine fused near-infrared fluorophores by first-principle tools

The perfect pair towards more effective nor-DXH-hemicyanine fused NIR fluoroohores.

Singlet La and Lb Bands for N-Acenes (N = 2-7): A CASSCF/CASPT2 Study

In this work CASPT2 calculations of polyacenes (from naphthalene to heptacene) were performed to find a methodology suitable for calculations of the absorption spectra, in particular of the L_a (B_2u state) and L_b (B_3u state) bands, of more extended systems. The effect of the extension of the active space and of freezing σ orbitals was investigated. The MCSCF excitation energy of the B_2u state is not sensitive to the size of the active space used. However, the CASPT2 results depend strongly on the amount of σ orbitals frozen reflecting the ionic character of the B_2u state. On the other hand, the excitation energies of the B_3u state are much more sensitive to the size of the active space used in the calculations reflecting its multiconfigurational character. We found a good agreement with experimental data for both bands by including 14 electrons in 14 π orbitals in the active space followed by the CASPT2(14,14) perturbation scheme in which both σ and π orbitals are included.

Bethe-Salpeter study of cationic dyes: Comparisons with ADC(2) and TD-DFT

We present a theoretical investigation of the excited-state properties of a large series of structurally diverse arylcarbonium derivatives that are known to be challenging for theoretical models. More specifically, we compare the pros and cons of TD-DFT (TD-M06-2X), ADC(2), and BSE/GW approaches for a large panel of compounds, using two different solvent models. Both 0-0 and vertical transition energies are considered and compared to the experimental values. All approaches reasonably reproduce the auxochromic and acidochromic shifts, although in most cases both TD-DFT and BSE/GW return larger correlation with experimental values than ADC(2) for these shifts. In contrast, the absolute transition energies obtained with ADC(2) tend to be closer to the measurements, TD-DFT using the M06-2X functional largely overestimating the experimental references (by ca. 0.5 eV), and BSE/GW providing intermediate values. In addition, we show that the selected solvent model has a significant impact on the results, the corrected linear-response approach providing larger transition energies than its linear-response counterpart.

Constricted variational density functional theory for spatially clearly separated charge-transfer excitations

Constricted Variational Density Functional Theory (CV-DFT) is known to be one of the successful methods in predicting charge-transfer excitation energies. In this paper, we apply the CV-DFT method to the well-known model systems ethylene-tetrafluoroethylene (C₂H₄ × C₂F₄) and the zincbacteriochlorin-bacteriochlorin complex (ZnBC-BC). The analysis of the CV-DFT energies enables us to understand the -1/R charge-transfer behaviour in CV-DFT for large separation distances R. With this we discuss the importance of orbital relaxations using the relaxed version of CV(∞)-DFT, the R-CV(∞)-DFT method. Possible effects of the optimization of the transition matrix for the relaxed self-consistent field version of CV(∞)-DFT, RSCF-CV(∞)-DFT in the case of large fragment separations are shown and we introduce two possible gradient restrictions to avoid the unwanted admixing of other transitions.

Using the GVB Ansatz to develop ensemble DFT method for describing multiple strongly correlated electron pairs

Ensemble density functional theory (DFT) furnishes a rigorous theoretical framework for describing the non-dynamic electron correlation arising from (near) degeneracy of several electronic configurations. Ensemble DFT naturally leads to fractional occupation numbers (FONs) for several Kohn-Sham (KS) orbitals, which thereby become variational parameters of the methodology. The currently available implementation of ensemble DFT in the form of the spin-restricted ensemble-referenced KS (REKS) method was originally designed for systems with only two fractionally occupied KS orbitals, which was sufficient to accurately describe dissociation of a single chemical bond or the singlet ground state of biradicaloid species. To extend applicability of the method to systems with several dissociating bonds or to polyradical species, more fractionally occupied orbitals must be included in the ensemble description. Here we investigate a possibility of developing the extended REKS methodology with the help of the generalized valence bond (GVB) wavefunction theory. The use of GVB enables one to derive a simple and physically transparent energy expression depending explicitly on the FONs of several KS orbitals. In this way, a version of the REKS method with four electrons in four fractionally occupied orbitals is derived and its accuracy in the calculation of various types of strongly correlated molecules is investigated. We propose a possible scheme to ameliorate the partial size-inconsistency that results from perfect spin-pairing. We conjecture that perfect pairing natural orbital (NO) functionals of reduced density matrix functional theory (RDMFT) should also display partial size-inconsistency.

0-0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/GW formalisms for 80 Real-Life Compounds

The 0-0 energies of 80 medium and large molecules have been computed with a large panel of theoretical formalisms. We have used an approach computationally tractable for large molecules, that is, the structural and vibrational parameters are obtained with TD-DFT, the solvent effects are accounted for with the PCM model, whereas the total and transition energies have been determined with TD-DFT and with five wave function approaches accounting for contributions from double excitations, namely, CIS(D), ADC(2), CC2, SCS-CC2, and SOS-CC2, as well as Green's function based BSE/GW approach. Atomic basis sets including diffuse functions have been systematically applied, and several variations of the PCM have been evaluated. Using solvent corrections obtained with corrected linear-response approach, we found that three schemes, namely, ADC(2), CC2, and BSE/GW allow one to reach a mean absolute deviation smaller than 0.15 eV compared to the measurements, the two former yielding slightly better correlation with experiments than the latter. CIS(D), SCS-CC2, and SOS-CC2 provide significantly larger deviations, though the latter approach delivers highly consistent transition energies. In addition, we show that (i) ADC(2) and CC2 values are extremely close to each other but for systems absorbing at low energies; (ii) the linear-response PCM scheme tends to overestimate solvation effects; and that (iii) the average impact of nonequilibrium correction on 0-0 energies is negligible.

Taking up the cyanine challenge with quantum tools

Cyanine derivatives, named from the Greek word kyanos meaning dark-blue, were discovered more than 150 years ago and remain one of the most widely used classes of organic dyes with contemporary applications in photography (panchromatic emulsions), information storage (CD-R and DVD-R media) and biochemistry (DNA and protein labeling) fields. Cyanine chromogens consist of a charged π-conjugated segment containing an odd number of sp(2) carbon atoms with the chain capped at the extremities by two electronegative centers, typically nitrogen or oxygen atoms. Cyanines are characterized by a vanishing bond length alternation indicating nearly equal carbon-carbon bond lengths, as well as a very intense and sharp absorption band presenting a shoulder. This hallmark band undergoes a strong red shift when the chain is extended. This so-called vinyl shift is extremely large (ca. 100 nm for each pair of carbon atoms added in the π-conjugated path), making cyanines ideal building blocks for the design of devices with near-infrared applications. Numerous cyanines also exhibit emission bands with large quantum yields. These exceptional optical properties explain why both canonical cyanines and the corresponding fluoroborates (e.g., boron-dipyrromethene, BODIPY) remain the focus of an ever-growing body of experimental work. In turn, this popularity has stimulated quantum mechanical investigations aiming, on the one hand, at probing the specific electronic nature of cyanine dyes and, on the other hand, at helping to design new dyes. However, the adiabatic approximation to time-dependent density functional theory, the most widespread ab initio model for electronically excited states, fails to accurately reproduce the absorption spectra of cyanine derivatives: it yields a systematic and large underestimation of the experimental wavelengths irrespective of the details of the computational protocol. In contrast, highly correlated wave function approaches provide accurate transition energies for model systems but are hardly applicable to real-life cyanines and BODIPY. This indicates that setting up a computationally tractable theoretical protocol that provides both robust and accurate optical spectra for cyanine-based dyes is a major challenge that has only been taken up lately. In this Account, we compile the most recent advances in the field by considering both compact streptocyanines and large fluoroborates. For the former, we summarize the key results obtained with a large panel of theoretical approaches, allowing us not only to understand the origin of the cyanine challenge but also to pinpoint the schemes presenting the most promising accuracy/effort ratio. For the latter, we show via selected examples how theoretical models can be used to reproduce simultaneously experimental band shapes and transition energies, thus paving the way to an efficient in silico design of new compounds.

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.

Ensemble DFT Approach to Excited States of Strongly Correlated Molecular Systems

Ensemble density functional theory (DFT) is a novel time-independent formalism for obtaining excitation energies of many-body fermionic systems. A considerable advantage of ensemble DFT over the more common Kohn-Sham (KS) DFT and time-dependent DFT formalisms is that it enables one to account for strong non-dynamic electron correlation in the ground and excited states of molecular systems in a transparent and accurate fashion. Despite its positive aspects, ensemble DFT has not so far found its way into the repertoire of methods of modern computational chemistry, probably because of the perceived lack of practically affordable implementations of the theory. The spin-restricted ensemble-referenced KS (REKS) method is perhaps the first computationally feasible implementation of the ideas behind ensemble DFT which enables one to describe accurately electronic transitions in a wide class of molecular systems, including strongly correlated molecules (biradicals, molecules undergoing bond breaking/formation), extended π-conjugated systems, donor-acceptor charge transfer adducts, etc.