Qualitatively Incorrect Features in the TDDFT Spectrum of Thiophene-Based Compounds

Investigation of linear and microscopic nonlinear optical responses of 1-indanone compounds in different environments based on polarity models

Molecular spectroscopic and nonlinear features can indicate positive changes by solvent molecules. In this work, DFT and spectroscopic techniques were used to study the polarity effects of different solvent environments. Polarity-based models were used for studying solvent induced interactions on the optical features of new groups of biomolecules. Despite the significant contribution of general effects on the molecular absorption spectra, there is considerable competition between general and specific environmental effects on the molecular emission properties. Under this condition, strong hydrogen bonds tend to increase molecular nonlinear responses. The same results were observed for the low order (first and second order) nonlinearity of biomolecules. Therefore, the studies on the environment effects on the biomolecules' first order nonlinearity can give valuable information about higher-order optical responses. Moreover, 1-Indanone compounds with high nonlinearity can be considered as an effective element in designing optical devices.

A multiphoton ionisation photoelectron imaging study of thiophene

Thiophene is a prototype for the excited state photophysics that lies at the heart of many technologies within the field of organic electronics. Here, we report a multiphoton ionisation photoelectron imaging study of gas-phase thiophene using a range of photon energies to excite transitions from the ground electronic state to the first two electronically excited singlet states, from the onset of absorption to the absorption maximum. Analysis of the photoelectron spectra and angular distributions reveal features arising from direct photoionisation from the ground electronic state, and resonance-enhanced photoionisation via the electronically excited singlet states. The first two ionisation energies from the ground electronic state were confirmed to be 8.8 eV (adiabatic) and 9.6 eV (vertical). The ionisation energies from the first two electronically excited singlet states were found to be 3.7 eV (adiabatic) and 4.4 eV (vertical).

From Many-Body Ab Initio to Effective Excitonic Models: A Versatile Mapping Approach Including Environmental Embedding Effects

We present an original multistate projective diabatization scheme based on Green's function formalisms that allows the systematic mapping of many-body ab initio calculations onto effective excitonic models. This method inherits the ability of the Bethe-Salpeter equation to describe Frenkel molecular excitons and intermolecular charge-transfer states equally well, as well as the possibility for an effective description of environmental effects in a QM/MM framework. The latter is found to be a crucial element in order to obtain accurate model parameters for condensed phases and to ensure their transferability to excitonic models for extended systems. The method is presented through a series of examples illustrating its quality, robustness, and internal consistency.

The "simple" photochemistry of thiophene

The static gas-phase ("simple") ultraviolet absorption spectrum of thiophene is investigated using a combination of a vibronic coupling model Hamiltonian with multi-configuration time-dependent Hartree quantum dynamics simulations. The model includes five states and all 21 vibrations, with potential surfaces calculated at the complete active space with second-order perturbation level of theory. The model includes terms up to eighth-order to describe the diabatic potentials. The resulting spectrum is in excellent agreement with the experimentally measured spectrum of Holland et al. [Phys. Chem. Chem. Phys. 16, 21629 (2014)]. The, until now not understood, spectral features are assigned, with a combination of strongly coupled vibrations and vibronic coupling between the states giving rise to a progression of triplets on the rising edge of the broad spectrum. The analysis of the underlying dynamics indicates that population transfer between all states takes place on a sub-100 fs timescale, with ring-opening occurring at longer times. The model thus provides a starting point for further investigations into the complicated photo-excited dynamics of this key hetero-aromatic molecule.

Ab initio investigation of excited state charge transfer pathways in differently capped bithiophene cages

The electronic excitations of conformationally constrained bithiophene cage systems as previously investigated by Lewis et al. (J. Am. Chem. Soc. 143, 18548 (2021)) are revisited, employing the correlated ab initio Scaled Opposite-Spin Algebraic Diagrammatic Construction Second Order electronic structure method. Quantitative descriptors are determined to assess the extent of charge transfer between the bithiophene moieties and the capping domains, represented by either phenyl or triazine groups. The investigation substantiates intrinsic differences in the photophysical behavior of these two structural variants and reveals the presence of lower-energy excited states characterized by noteworthy charge transfer contributions in the triazine cage system. The manifestation of this charge transfer character is discernible even at the Franck-Condon geometry, persisting throughout the relaxation of the excited state. By examining isolated monomer building blocks, we confirm the existence of analogous charge transfer contributions in their excitations. Employing this methodological approach facilitates the prospective identification of potential wall/cap chromophore pairs, wherein charge transfer pathways can be accessed within the energetically favorable regime.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

XPS and quantum chemical analysis of 4Me-BODIPY derivatives

The results of a X-ray photoelectron spectroscopy (XPS) and steady-state absorption spectroscopy study of the electronic structure, and cationic and excited states of a series of 1,3,5,7-tetramethyl-substituted BODIPYs (4Me,2R-BODIPYs) are presented. The experimental data were interpreted using high-level ab initio quantum chemical computations, including the algebraic diagrammatic construction method for the polarization propagator of the second order (ADC(2)), the outer-valence Green's function (OVGF) method, the density functional (DFT) approach, and the time-dependent DFT (TD-DFT) approach. Substitution effects on the XPS and absorption spectra were determined for 2,6-positions of 4Me,2R-BODIPY pyrrole nuclei (R = H, Br, Bu, benzyl). A very satisfactory performance of the DFT Koopmans theorem analogue was demonstrated with respect to the energy intervals between the electronic levels of 4Me,2R-BODIPY above 13 eV (BHHLYP functional) and the values of the HOMO-LUMO energy gap (ωB97X functional).

An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe–Salpeter equation calculations of molecules

The ab initio GW plus Bethe–Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn–Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm–Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn–Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel’s set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

Reconstruction of Nuclear Ensemble Approach Electronic Spectra Using Probabilistic Machine Learning

The theoretical prediction of molecular electronic spectra by means of quantum mechanical (QM) computations is fundamental to gain a deep insight into many photophysical and photochemical processes. A computational strategy that is attracting significant attention is the so-called Nuclear Ensemble Approach (NEA), that relies on generating a representative ensemble of nuclear geometries around the equilibrium structure and computing the vertical excitation energies (ΔE) and oscillator strengths (f) and phenomenologically broadening each transition with a line-shaped function with empirical full-width δ. Frequently, the choice of δ is carried out by visually finding the trade-off between artificial vibronic features (small δ) and over-smoothing of electronic signatures (large δ). Nevertheless, this approach is not satisfactory, as it relies on a subjective perception and may lead to spectral inaccuracies overall when the number of sampled configurations is limited due to an excessive computational burden (high-level QM methods, complex systems, solvent effects, etc.). In this work, we have developed and tested a new approach to reconstruct NEA spectra, dubbed GMM-NEA, based on the use of Gaussian Mixture Models (GMMs), a probabilistic machine learning algorithm, that circumvents the phenomenological broadening assumption and, in turn, the use of δ altogether. We show that GMM-NEA systematically outperforms other data-driven models to automatically select δ overall for small datasets. In addition, we report the use of an algorithm to detect anomalous QM computations (outliers) that can affect the overall shape and uncertainty of the NEA spectra. Finally, we apply GMM-NEA to predict the photolysis rate for HgBrOOH, a compound involved in Earth's atmospheric chemistry.

Coherent Control of Molecular Dissociation by Selective Excitation of Nuclear Wave Packets

We report on pump-probe control schemes to manipulate fragmentation product yields in p-nitrotoluene (PNT) cation. Strong field ionization of PNT prepares the parent cation in the ground electronic state, with coherent vibrational excitation along two normal modes: the C–C–N–O torsional mode at 80 cm⁻¹ and the in-plane ring-stretching mode at 650 cm⁻¹. Both vibrational wave packets are observed as oscillations in parent and fragment ion yields in the mass spectrum upon optical excitation. Excitation with 650 nm selectively fragments the PNT cation into C7H7+, whereas excitation with 400 nm selectively produces C5H5+ and C3H3+. In both cases the ion yield oscillations result from torsional wave packet excitation, but 650 and 400 nm excitation produce oscillations with opposite phases. Ab initio calculations of the ground and excited electronic potential energy surfaces of PNT cation along the C–C–N–O dihedral angle reveal that 400 nm excitation accesses an allowed transition from D₀ to D₆ at 0° dihedral angle, whereas 650 nm excitation accesses a strongly allowed transition from D₀ to D₄ at a dihedral angle of 90°. This ability to access different electronic excited states at different locations along the potential energy surface accounts for the selective fragmentation observed with different probe wavelengths. The ring-stretching mode, only observed using 800 nm excitation, is attributed to a D₀ to D₂ transition at a geometry with 90° dihedral angle and elongated C–N bond length. Collectively, these results demonstrate that strong field ionization induces multimode coherent excitation and that the vibrational wave packets can be excited with specific photon energies at different points on their potential energy surfaces to induce selective fragmentation.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange-correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Ultrafast Dynamics of Nitro-Nitrite Rearrangement and Dissociation in Nitromethane Cation

We report new insights into the ultrafast rearrangement and dissociation dynamics of nitromethane cation (NM⁺) using pump-probe measurements, electronic structure calculations, and ab initio molecular dynamics simulations. The "roaming" nitro-nitrite rearrangement (NNR) pathway involving large-amplitude atomic motion, which has been previously described for neutral nitromethane, is demonstrated for NM⁺. Excess energy resulting from initial population of the electronically excited D₂ state of NM⁺ upon strong-field ionization provides the necessary energy to initiate NNR and subsequent dissociation into NO⁺. Both pump-probe measurements and molecular dynamics simulations are consistent with the completion of NNR within 500 fs of ionization with dissociation into NO⁺ and OCH₃ occurring ∼30 fs later. Pump-probe measurements indicate that NO⁺ formation is in competition with the direct dissociation of NM⁺ to CH₃⁺ and NO₂. Electronic structure calculations indicate that a strong D₀ → D₁ transition can be excited at 650 nm when the C-N bond is stretched from its equilibrium value (1.48 Å) to 1.88 Å. On the other hand, relaxation of the NM⁺ cation after ionization into D₀ occurs in less than 50 fs and results in observation of intact NM⁺. Direct dissociation of the equilibrium NM⁺ to produce NO₂⁺ and CH₃ can be induced with 650 nm excitation via a weakly allowed D₀ → D₂ transition.

Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach

Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.

Theory of Apparent Circular Dichroism Reveals the Origin of Inverted and Noninverted Chiroptical Response under Sample Flipping

Circular dichroism (CD) finds widespread application as an optical probe for the structure of molecules and supramolecular assemblies. Its underlying chiral light-matter interactions effectively couple between photonic spin states and select quantum-mechanical degrees of freedom in a sample, implying an intricate connection with photon-to-matter quantum transduction. However, effective transduction implementations likely require interactions that are antisymmetric with respect to the direction of light propagation through the sample, yielding an inversion of the chiroptical response upon sample flipping, which is uncommon for CD. Recent experiments on organic thin films have demonstrated such chiroptical behavior, which was attributed to "apparent CD" resulting from an interference between the sample's linear birefringence and linear dichroism. However, a theory connecting the underlying optical selection rules to the microscopic electronic structure of the constituent molecules remains to be formulated. Here, we present such a theory based on a combination of Mueller calculus and a Lorentz oscillator model. The theory reaches good agreement with experimental CD spectra and allows for establishing the (supra)molecular design rules for maximizing or minimizing this chiroptical effect. It furthermore highlights that, in addition to antisymmetrically, it can manifest symmetrically such that no chiroptical response inversion occurs, which is a consequence of a helical stacking of molecules in the light propagation direction.

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Bicyclic Systems

Pursuing our efforts to define highly accurate estimates of the relative energies of excited states in organic molecules, we investigate, with coupled-cluster methods including iterative triples (CC3 and CCSDT), the vertical excitation energies of 10 bicyclic molecules (azulene, benzoxadiazole, benzothiadiazole, diketopyrrolopyrrole, furofuran, phthalazine, pyrrolopyrrole, quinoxaline, tetrathiafulvalene, and thienothiophene). In total, we provide aug-cc-pVTZ reference vertical excitation energies for 91 excited states of these relatively large systems. We use these reference values to benchmark various wave function methods, i.e., CIS(D), EOM-MP2, CC2, CCSD, STEOM-CCSD, CCSD(T)(a)*, CCSDR(3), CCSDT-3, ADC(2), ADC(2.5), and ADC(3), as well as some spin-scaled variants of both CC2 and ADC(2). These results are compared to those obtained previously on smaller molecules. It turns out that while the accuracy of some methods is almost unaffected by system size, e.g., CIS(D) and CC3, the performance of others can significantly deteriorate as the systems grow, e.g., EOM-MP2 and CCSD, whereas others, e.g., ADC(2) and CC2, become more accurate for larger derivatives.

A Computational Study of the Electronic Properties of Heterocirculenes: Oxiflowers and Sulflowers

This study investigated the relationship of electronic properties with some structural parameters of two circulene classes: Sulflowers and Oxiflowers. It is found that correlations between the HOMO-LUMO gap and some electronic properties of these circulenes are opposite to those of linear conjugated structures. Moreover, a new hybrid molecule, called an Oxisulflower, is proposed to be a potential structure for synthesizing as Sulflower. Also, a brand-new descriptor, namely, the "degree of non-planarity", is evaluated with excellent correlations with the HOMO-LUMO gap of molecules in Oxiflower and Sulflower classes. The correlations have also shown that the steric characteristic of a structure can be controlled to modulate its band gap for studying the prediction science of the electronic properties in developing organic semiconductors.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput. 17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

Tailoring CIPSI Expansions for QMC Calculations of Electronic Excitations: The Case Study of Thiophene

The perturbatively selected configuration interaction scheme (CIPSI) is particularly effective in constructing determinantal expansions for quantum Monte Carlo (QMC) simulations with Jastrow–Slater wave functions: fast and smooth convergence of ground-state properties and balanced descriptions of ground and excited states of different symmetries have been reported. In particular, accurate excitation energies have been obtained by the pivotal requirement of using CIPSI expansions with similar second-order perturbation corrections for each state, that is, a similar estimated distance to the full configuration interaction limit. Here, we elaborate on the CIPSI selection criterion for excited states of the same symmetry as the ground state, generating expansions from a common orbital set. Using these expansions in QMC as determinantal components of Jastrow–Slater wave functions, we compute the lowest, bright excited state of thiophene, which is challenging due to its significant multireference character. The resulting vertical excitation energies are within 0.05 eV of the best theoretical estimates, already with expansions of only a few thousand determinants. Furthermore, we relax the ground- and excited-state structures following the corresponding root in variational Monte Carlo and obtain bond lengths that are accurate to better than 0.01 Å. Therefore, while the full treatment at the CIPSI level of this system is quite demanding, in QMC, we can compute high-quality excitation energies and excited-state structural parameters building on affordable CIPSI expansions with relatively few, well-chosen determinants.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Using computational chemistry to design pump–probe schemes for measuring nitrobenzene radical cation dynamics

Computed potential energy surfaces of the nitrobenzene cation predict suitable excitation conditions for enhancing ion yield oscillations in time-resolved measurements.

Photoelectron spectra and electronic structure of boron diacetate formazanates

The electronic structure and cationic states of two 1,5-diphenylformazanes and two boron diacetate (B(OAc)₂) formazanates were modeled using the outer valence Green's function (OVGF) and density functional theory (DFT) methods. Comparison of data of the OVGF and ultraviolet photoelectron spectroscopy (UPS) methods made it possible to determine an effect of functional groups and complexing agents on energies of cationic states. Addition of NO₂-group at the γ-position of the chelate cycle causes stabilization of levels the five upper occupied molecular orbitals (MO) and destabilization of the bonding orbital π₃^Ph + π₃ level. The levels of MOs π₃^Ph-π₃ and n_- are stabilized due to influence of the complexing agent B(OAc)₂, with a difference in the shift of 0.67 eV. The ionization energies (I_n) changes for the π-orbitals of benzene rings are within the error of the OVGF method. Under methylation of phenyl groups, the differences between the calculated I_n, corresponding to the π-orbitals of aromatic substituents, are in good agreement with the experimental I_n shifts at transition from benzene to toluene. According to the OVGF method, in all the studied complexes the lowest unoccupied molecular orbital (LUMO) is localized mainly on the chelate cycle and has a strong acceptor character, which should contribute the low-lying charge-transfer electronic excitations. Moreover, an application of the DFT analog of the Koopmans' theorem with the BHHLYP and B2PLYP functionals made it possible to determine qualitatively a sequence of cationic states and energy intervals between them in the spectral range up to 10 eV. The DFT/wB97x/cc-pVTZ method data on the energy gap between the highest occupied molecular orbital (HOMO) and LUMO levels correlate with the OVGF/cc-pVTZ calculation results.

Simulation of time-resolved x-ray absorption spectroscopy of ultrafast dynamics in particle-hole-excited 4-(2-thienyl)-2,1,3-benzothiadiazole

To date, alternating co-polymers based on electron-rich and electron-poor units are the most attractive materials to control functionality of organic semiconductor layers in which ultrafast excited-state processes play a key role. We present a computational study of the photoinduced excited-state dynamics of the 4-(2-thienyl)-2,1,3-benzothiadiazole (BT-1T) molecule, which is a common building block in the backbone of π-conjugated polymers used for organic electronics. In contrast to homo-polymer materials, such as oligothiophene, BT-1T has two non-identical units, namely, thiophene and benzothiadiazole, making it attractive for intramolecular charge transfer studies. To gain a thorough understanding of the coupling of excited-state dynamics with nuclear motion, we consider a scenario based on femtosecond time-resolved x-ray absorption spectroscopy using an x-ray free-electron laser in combination with a synchronized ultraviolet femtosecond laser. Using Tully's fewest switches surface hopping approach in combination with excited-state calculations at the level of configuration interaction singles, we calculate the gas-phase x-ray absorption spectrum at the carbon and nitrogen K edges as a function of time after excitation to the lowest electronically excited state. The results of our time-resolved calculations exhibit the charge transfer driven by non-Born-Oppenheimer physics from the benzothiadiazole to thiophene units during relaxation to the ground state. Furthermore, our ab initio molecular dynamics simulations indicate that the excited-state relaxation processes involve bond elongation in the benzothiadiazole unit as well as thiophene ring puckering at a time scale of 100 fs. We show that these dynamical trends can be identified from the time-dependent x-ray absorption spectrum.

One- and two-photon absorption properties of quadrupolar thiophene-based dyes with acceptors of varying strengths

The one-photon (1P) and two-photon (2P) absorption properties of three quadrupolar dyes, featuring thiophene as a donor and acceptors of varying strengths, are determined by a combination of experimental and computational methods employing the density functional theory (DFT). The emission shifts in different solvents are well reproduced by time-dependent DFT calculations with the linear response and state specific approaches in the framework of the polarizable continuum model. The calculations show that the energies of both 1P- and 2P-active states decrease with an increase of the strength of the acceptor. The 2P absorption cross-sections predicted by the response theory are accounted for by considering just one intermediate state (S1) in the sum-over-states formulation. For the chromophore featuring the stronger acceptor, the energetic positions of the 1P- and 2P-active states prevent the exploitation of the theoretically predicted very high 2P activity due to the competing 1P absorption into the S1 state.

Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments

A composite of time-dependent density functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calculation of spectral properties of molecules. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approximation for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-reduction approach is also presented, which further speeds up the calculations. Our benchmark calculations show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.

Determining Orientations of Optical Transition Dipole Moments Using Ultrafast X-ray Scattering

Identification of the initially prepared, optically active state remains a challenging problem in many studies of ultrafast photoinduced processes. We show that the initially excited electronic state can be determined using the anisotropic component of ultrafast time-resolved X-ray scattering signals. The concept is demonstrated using the time-dependent X-ray scattering of N-methyl morpholine in the gas phase upon excitation by a 200 nm linearly polarized optical pulse. Analysis of the angular dependence of the scattering signal near time zero renders the orientation of the transition dipole moment in the molecular frame and identifies the initially excited state as the 3p _z Rydberg state, thus bypassing the need for further experimental studies to determine the starting point of the photoinduced dynamics and clarifying inconsistent computational results.

The screened pseudo-charge repulsive potential in perturbed orbitals for band calculations by DFT+U

The conventional linear response overestimates the U in DFT+U calculations for solids with fully occupied orbitals. Here, we demonstrate that the challenge arises from the incomplete cancellation of the electron-electron Coulomb repulsion energy under external perturbation. We applied the second charge response, denoted as the "pseudo-charge" model, to offset such residue effects. Counteracting between these two charge response-induced Coulomb potentials, the U parameters are self-consistently obtained by fulfilling the conditions for minimizing the non-Koopmans energy. Moreover, the pseudo-charge-induced repulsive potential shows a screening behavior related to the orbital occupation and is potentially in compliance with the screened exact exchange-correlation of electrons. The resultant U parameters are self-consistent solutions for improved band structure calculations by the DFT+U method. This work extends the validity of the linear response method to both partially and fully occupied orbitals and gives a reference for estimating the Hubbard U parameter prior to other advanced methods. The U parameters were determined in a transferability test using both PBE and hybrid density functional methods, and the results showed that this method is independent of the functional. The electronic structures determined from the hybrid-DFT+U^hybrid approach are provided. Comparisons are also made with the recently developed self-consistent hybrid-DFT+U_w method.

Boron difluoride dibenzoylmethane derivatives: Electronic structure and luminescence

Electronic structure and optical properties of boron difluoride dibenzoylmethanate and four of its derivatives have been studied by X-ray photoelectron spectroscopy, absorption and luminescence spectroscopy and quantum chemistry (DFT, TDDFT). The relative quantum luminescence yields have been revealed to correlate with charge transfers of HOMO-LUMO transitions, energy barriers of aromatic substituents rotation and the lifetime of excited states in the investigated complexes. The bathochromic shift of intensive bands in the optical spectra has been observed to occur when the functional groups are introduced into p-positions of phenyl cycles due to destabilizing HOMO levels. Calculated energy intervals between electronic levels correlate well with XPS spectra structure of valence and core electrons.

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.

Unusual response to environmental polarity in a nonlinear-optical benzylidene-type chromophore containing a 1,3-bis(dicyanomethylidene)indane acceptor fragment

One of the strongest known electron-accepting fragments used in the synthesis of organic dyes for applications in nonlinear optics (NLO) is 1,3-bis(dicyanomethylidene)indane (BDMI). By studying a benzylidene-type push-pull chromophore bearing a 5-carboxy-BDMI electron-acceptor and 4-(dimethylamino)aniline donor fragment, we demonstrate that this class of compounds can show unusual response to the polarity of the surrounding medium. The combined results of UV-Vis absorption spectrometry, NMR experiments and computational modeling indicate that the studied compound undergoes a geometrical transformation that involves an increase in the torsion angle ω between the aniline and indane ring systems with the rise of the polarity of the surrounding medium. This process is partly facilitated by an increased rotational freedom around ω in more polar solvents, as detected experimentally by NMR and predicted by calculations. Regarding the practical application aspects, computations predict that the solvent-polarity-induced increase of torsion ω would lead to a notable decrease in the first hyperpolarizability (β) value. This was detected experimentally, as hyper-Rayleigh scattering (HRS) data showed a drop in the compound's NLO activity from β_HRS(532)  = 513 × 10^-30 esu in toluene to β_HRS(532)  =  249 × 10^-30 esu in acetonitrile. This places limitations on the NLO applications of the studied compound and its structural analogues, as the surrounding medium (solvent of polymer matrix) with the lowest possible polarity needs to be used to maximize their NLO efficiency.

Low-Lying ππ* States of Heteroaromatic Molecules: A Challenge for Excited State Methods

The description of low-lying ππ* states of linear acenes by standard electronic structure methods is known to be challenging. Here, we broaden the framework of this problem by considering a set of fused heteroaromatic rings and demonstrate that standard electronic structure methods do not provide a balanced description of the two (typically) lowest singlet state (L_a and L_b) excitations. While the L_b state is highly sensitive to correlation effects, L_a suffers from the same drawbacks as charge transfer excitations. We show that the comparison between CIS/CIS(D) can serve as a diagnostic for detecting the two problematic excited states. Standard TD-DFT and even its spin-flip variant lead to inaccurate excitation energies and interstate gaps, with only a double hybrid functional performing somewhat better. The complication inherent to a balanced description of these states is so important that even CC2 and ADC(2) do not necessarily match the ADC(3) reference.

Theoretical investigations of the small molecular acceptor materials based on oligothiophene – naphthalene diimide in organic solar cells

The electronic transmission paths of NDI-T3DCRD with the centroid distance from core molecule to ambient molecules marked.

How does tetraphenylethylene relax from its excited states?

Photocyclization play a key role in the deactivation mechanism of tetraphenylethylene.

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.

The driving forces for twisted or planar intramolecular charge transfer

The driving forces for twisting or planarization of excited D–A (donor–acceptor)-type chromophore have been investigated.