Calculation of One-Photon and Two-Photon Absorption Spectra of Porphyrins Using Time-Dependent Density Functional Theory

Ultrafast Evaluation of Two-Photon Absorption with Simplified Time-Dependent Density Functional Theory

This work presents the theoretical background to evaluate two-photon absorption (2PA) cross-sections in the framework of simplified time-dependent density functional theory (sTD-DFT). Our new implementation allows the ultrafast evaluation of 2PA cross-sections for large molecules based on a regular DFT ground-state determinant as well as a variant employing our tight-binding sTD-DFT-xTX flavor for very large systems. The method is benchmarked against higher-level calculations for trans-stilbene and typical fluorescent protein chromophores. For eGFP, a quadrupolar chromophore and its branched version, the flavine mono-nucleotide, and the iLOV protein, we compare sTD-DFT 2PA spectra to experimental ones. This includes extension and testing of our all-atom quantum chemistry methodology for the evaluation of 2PA for a system of ∼2000 atoms, providing striking agreement with the experimental spectrum.

Calculated linear and nonlinear optical absorption spectra of phosphine-ligated gold clusters

Although prediction of optical excitations of ligated gold clusters by time-dependent density functional theory (TDDFT) is relatively well-established, limitations still exist, for example in the choice of the exchange-correlation functional....

Application of TD-DFT Theory to Studying Porphyrinoid-Based Photosensitizers for Photodynamic Therapy: A Review

An important focus for innovation in photodynamic therapy (PDT) is theoretical investigations. They employ mostly methods based on Time-Dependent Density Functional Theory (TD-DFT) to study the photochemical properties of photosensitizers. In the current article we review the existing state-of-the-art TD-DFT methods (and beyond) which are employed to study the properties of porphyrinoid-based systems. The review is organized in such a way that each paragraph is devoted to a separate aspect of the PDT mechanism, e.g., correct prediction of the absorption spectra, determination of the singlet-triplet intersystem crossing, and interaction with molecular oxygen. Aspects of the calculation schemes are discussed, such as the choice of the most suitable functional and inclusion of a solvent. Finally, quantitative structure-activity relationship (QSAR) methods used to explore the photochemistry of porphyrinoid-based systems are discussed.

Push-pull quinoidal porphyrins

A family of push-pull quinoidal porphyrin monomers has been prepared from a meso-formyl porphyrin by bromination, thioacetal formation, palladium-catalyzed coupling with malononitrile and oxidation with DDQ. Attempts at extending this synthesis to a push-pull quinoidal/cumulenic porphyrin dimer were not successful. The crystal structures of the quinoidal porphyrins indicate that there is no significant contribution from singlet biradical or zwitterionic resonance forms. The crystal structure of an ethyne-linked porphyrin dimer shows that the torsion angle between the porphyrin units is only about 3°, in keeping with crystallographic results on related compounds, but contrasting with the torsion angle of about 35° predicted by computational studies. The free-base quinoidal porphyrin monomers form tightly π-stacked layer structures, despite their curved geometries and bulky aryl substituents.

Two-Photon Absorbing Phosphorescent Metalloporphyrins: Effects of π-Extension and Peripheral Substitution

The ability to form triplet excited states upon two-photon excitation is important for several applications of metalloporphyrins, including two-photon phosphorescence lifetime microscopy (2PLM) and two-photon photodynamic therapy (PDT). Here we analyzed one-photon (1P) and degenerate two-photon (2P) absorption properties of several phosphorescent Pt (II) porphyrins, focusing on the effects of aromatic π-extension and peripheral substitution on triplet emissivity and two-photon absorption (2PA). Our 2PA measurements for the first time made use of direct time-resolved detection of phosphorescence, having the ability to efficiently reject laser background through microsecond time gating. π-Extension of the porphyrin macrocycle by way of syn-fusion with two external aromatic fragments, such as in syn-dibenzo- (DBP) and syn-dinaphthoporphyrins (DNP), lowers the symmetry of the porphyrin skeleton. As a result, DBPs and DNPs exhibit stronger 2PA into the one-photon-allowed B (Soret) and Q states than fully symmetric (D4h) nonextended porphyrins. However, much more 2P-active states lie above the B state and cannot be accessed due to the interfering linear absorption. Alkoxycarbonyl groups (CO2R) in the benzo-rings dramatically enhance 2PA near the B state level. Time-dependent density functional theory (TDDFT) calculations in combinations with the sum-over-states (SOS) formalism revealed that the enhancement is due to the stabilization of higher-lying 2P-active states, which are dominated by the excitations involving orbitals extending onto the carbonyl groups. Furthermore, calculations predicted even stronger stabilization of the 2P-allowed gerade-states in symmetric Pt octaalkoxycarbonyl-tetrabenzoporphyrins. Experiments confirmed that the 2PA cross-section of PtTBP(CO2Bu)8 near 810 nm reaches above 500 GM in spite of its completely centrosymmetric structure. Combined with exceptionally bright phosphorescence (ϕphos = 0.45), strong 2PA makes Pt(II) complexes of π-extended porphyrins a valuable class of chromophores for 2P applications. Another important advantage of these porphyrinoids is their compact size and easily scalable synthesis.

A systematic theoretical study of the electronic structures of porphyrin dimers: DFT and TD-DFT calculations on diporphyrins linked by ethane, ethene, ethyne, imine, and azo bridges

Theoretical calculations of the geometries, electronic structures and electronic absorption spectra of a series of covalently-linked porphyrin dimers are reported. The diporphyrins comprise 5,10,15-triphenylporphyrinatozinc(II) (ZnTriPP) units linked through the meso carbons by two-atom bridges, namely 1,2-ethanediyl (1), trans-1,2-ethenediyl (2), ethynediyl (3), 1,2-iminomethenediyl (4), and transdiazenediyl (5). The structures were optimised in toluene solvent by Density Functional Theory (DFT), using the integral equation formalism variant of the polarizable continuum model. The calculations were performed using the B3LYP functional and the 6-31G(d,p) basis set. The complete molecules were modelled, with no substitution of smaller groups on the periphery. In parallel, the compounds 2–5 were prepared by known or novel synthetic routes, to enable comparisons of experimental electronic absorption spectra with those calculated using time dependent-DFT at the same level of theory. As the ethane dimer 1 is not yet synthetically accessible, the model monomer meso-2-phenylethylZnTriPP was used for comparisons with the theoretical predictions. The results form a self-consistent set, enabling for the first time legitimate comparisons of the electronic structures of the series, especially regarding the degree to which the porphyrin p-systems interact by conjugation across the bridges. The theoretical calculations of the electronic transitions match the observed spectra in toluene to a remarkable degree, especially with respect to the peak maximum of the Q band, which represents to a large degree the energy of the HOMO–LUMO transition. The imine 4 is intrinsically polar due to the asymmetric bridge, and the HOMO is located almost exclusively on the ZnTriPP unit attached to the nitrogen of the imine, and the LUMO on the C-attached ring. Thus the Q-band transition is mapped as a comprehensive charge-transfer from the former ring to the latter. This may have consequences for the non-linear optical properties of the system. The azoporphyrin 5 exhibits the largest splittings between the interacting MOs via the conjugated bridge, vindicating a prediction by Anderson and co-workers in 2002, and confirmed experimentally by our synthesis of 5. The collected results also indicate that this level of theory is more thanadequate as a model with which to handle these large delocalised molecules.

The assessment and application of an approach to noncovalent interactions: the energy decomposition analysis (EDA) in combination with DFT of revised dispersion correction (DFT-D3) with Slater-type orbital (STO) basis set

An assessment study is presented about energy decomposition analysis (EDA) in combination with DFT including revised dispersion correction (DFT-D3) with Slater-type orbital (STO) basis set. There has been little knowledge about the performance of the EDA + DFT-D3 concerning STOs. In this assessment such an approach was applied to calculate noncovalent interaction energies and their corresponding components. Complexes in S22 set were used to evaluate the performance of EDA in conjunction with four representative types of GGA-functionals of DFT-D3 (BP86-D3, BLYP-D3, PBE-D3 and SSB-D3) with three STO basis sets ranging in complexity from DZP, TZ2P to QZ4P. The results showed that the approach of EDA + BLYP-D3/TZ2P has a better performance not only in terms of calculating noncovalent interaction energy quantitatively but also in analyzing corresponding energy components qualitatively. This approach (EDA + BLYP-D3/TZ2P) was thus applied further to two representative large-system complexes including porphine dimers and fullerene aggregates to gain a better insight into binding characteristics.

Reversible, opto-mechanically induced spin-switching in a nanoribbon-spiropyran hybrid material

It has recently been shown that electronic transport in zigzag graphene nanoribbons becomes spin-polarized upon application of an electric field across the nanoribbon width. However, the electric fields required to experimentally induce this magnetic state are typically large and difficult to apply in practice. Here, using both first-principles density functional theory (DFT) and time-dependent DFT, we show that a new spiropyran-based, mechanochromic polymer noncovalently deposited on a nanoribbon can collectively function as a dual opto-mechanical switch for modulating its own spin-polarization. These calculations demonstrate that upon mechanical stress or photoabsorption, the spiropyran chromophore isomerizes from a closed-configuration ground-state to a zwitterionic excited-state, resulting in a large change in dipole moment that alters the electrostatic environment of the nanoribbon. We show that the electronic spin-distribution in the nanoribbon-spiropyran hybrid material can be reversibly modulated via noninvasive optical and mechanical stimuli without the need for large external electric fields. Our results suggest that the reversible spintronic properties inherent to the nanoribbon-spiropyran material allow the possibility of using this hybrid structure as a resettable, molecular-logic quantum sensor where opto-mechanical stimuli are used as inputs and the spin-polarized current induced in the nanoribbon substrate is the measured output.

Optoelectronic and Excitonic Properties of Oligoacenes: Substantial Improvements from Range-Separated Time-Dependent Density Functional Theory

The optoelectronic and excitonic properties in a series of linear acenes (naphthalene up to heptacene) are investigated using range-separated methods within time-dependent density functional theory (TDDFT). In these rather simple systems, it is well-known that TDDFT methods using conventional hybrid functionals surprisingly fail in describing the low-lying L(a) and L(b) valence states, resulting in large, growing errors for the L(a) state and an incorrect energetic ordering as a function of molecular size. In this work, we demonstrate that the range-separated formalism largely eliminates both of these errors and also provides a consistent description of excitonic properties in these systems. We further demonstrate that reoptimizing the percentage of Hartree-Fock exchange in conventional hybrids to match wave function-based benchmark calculations still yields serious errors, and a full 100% Hartree-Fock range separation is essential for simultaneously describing both of the L(a) and L(b) transitions. From an analysis of electron-hole transition density matrices, we finally show that conventional hybrid functionals over-delocalize excitons and underestimate quasiparticle energy gaps in the acene systems. The results of our present study emphasize the importance of both a range-separated and asymptotically correct contribution of exchange in TDDFT for investigating optoelectronic and excitonic properties, even for these simple valence excitations.