Calculating rate constants for intersystem crossing and internal conversion in the Franck-Condon and Herzberg-Teller approximations

Effective and fast algorithms for calculating rate constants for internal conversion (IC) and intersystem crossing (ISC) in the Franck-Condon and Herzberg-Teller approximations have been developed and implemented. The methods have been employed for calculating IC and ISC rate constants for the pyrromethene-567 dye (PM567), hetero[8]circulene (4B) and free-base porphyrin (H2P). The fluorescence quantum yields obtained by comparing calculated rate constants for the radiative and non-radiative processes are in good agreement with experimental data.Peer reviewe

Integration of global ring currents using the Ampere-Maxwell law

Magnetically induced ring currents are calculated from the magnetic shielding tensor by employing the Ampere-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the shielding tensor along the symmetry axis of highly symmetric ring-shaped aromatic, antiaromatic and nonaromatic molecules. The calculated ring-current strengths agree perfectly with the ones obtained by integrating the current-density flux passing through a plane cutting half the molecular ring. The method can be used in combination with all electronic structure codes capable of calculating nuclear magnetic resonance (NMR) shielding tensors in general points in space. We also show that nucleus independent chemical shifts (NICS) along the symmetry axis are related to the spatial derivative of the strength of the global ring-current along the z axis.Peer reviewe

Fast estimation of the internal conversion rate constant in photophysical applications

An efficient method for estimating non-adiabatic coupling matrix elements (NACME) and rate constants for internal conversion (k(IC)) is presented. The method, based on Plotnikov's theory, requires only calculations of the electronic wave functions and the corresponding electronic excitation energies. Computationally expensive calculations of the derivatives of the electronic wave function with respect to the nuclear coordinates are avoided. When the main accepting modes of the electronic excitation energy are X-H vibrations, the present method can be used for estimating the efficiency of the energy transfer between donor and acceptor molecules. It can also be used in studies of the influence of hydrogen bonding or solvent effect on fluorescence quenching, in studies of vibronic effects of TADF (thermally activated delayed fluorescence) emitters, and for calculating k(IC). Here, k(IC) and NACME are calculated for free-base porhyrin, magnesium porphyrin, azulene, naphthalene, pyrene and fluorenone interacting with a solvent molecule. Reverse k(IC) and NACME are further calculated for the T-1 -> T-2 transition of dibenzothiophene-S,S-dioxide (PTZ-DBTO2), which is used in TADF applications. Finally, we estimate the efficiency of the energy transfer between two large porphyrinoid dimers.Peer reviewe

Aromaticity of Even-Number Cyclo[n]carbons (n=6-100)

The recently synthesized cyclo[18]carbon molecule has been characterized in a number of studies by calculating electronic, spectroscopic, and mechanical properties. However, cyclo[18] carbon is only one member of the class of cyclo[n]carbons-standalone carbon allotrope representatives. Many of the larger members of this class of molecules have not been thoroughly investigated. In this work, we calculate the magnetically induced current density of cyclo[n]carbons in order to elucidate how electron delocalization and aromatic properties change with the size of the molecular ring (n), where n is an even number between 6 and 100. We find that the Hiickel rules for aromaticity (4k + 2) and antiaromaticity (4k) become degenerate for large C-n rings (n > 50), which can be understood as a transition from a delocalized electronic structure to a nonaromatic structure with localized current density fluxes in the triple bonds. Actually, the calculations suggest that cyclo[n]carbons with n > 50 are nonaromatic cyclic polyalkynes. The influence of the amount of nonlocal exchange and the asymptotic behavior of the exchange-correlation potential of the employed density functionals on the strength of the magnetically induced ring current and the aromatic character of the large cyclo[n]carbons is also discussed.Peer reviewe

When are Antiaromatic Molecules Paramagnetic?

Magnetizabilities and magnetically induced current densities have been calculated and analyzed for a series of antiaromatic cyclo[4k]carbons (k = 2-11), iso[n]phlorins (n = 4-8), expanded porphyrinoids, and meso-meso, beta-beta,beta-beta triple-linked porphyrin and isophlorin arrays. The cyclo[4k]carbons with k = 2-6 are predicted to be closed-shell paramagnetic molecules due to the very strong paratropic ring current combined with its large radius. Larger cyclo[4k]carbons with k = 6-11 are diamagnetic because they sustain a paratropic ring current whose strength is weaker than -20 nA T-1, which seems to be the lower threshold value for closed-shell paramagnetism. This holds not only for cyclo[4k]carbons but also for other organic molecules like expanded porphyrinoids and oligomers of porphyrinoids. The present study shows that meso-meso, beta-beta, beta-beta triple-linked linear porphyrin and isophlorin arrays have a domainlike distribution of alternating diatropic and paratropic ring currents. The strength of their local paratropic ring currents is weaker than -20 nA T-1 in each domain. Therefore, linear porphyrin and isophlorin arrays become more diamagnetic with increasing length of the ribbon. For the same reason, square-shaped meso-meso, beta-beta, beta-beta triple-linked free-base porphyrin and isophlorin tetramers as well as the Zn(II) complex of the porphyrin tetramer are diamagnetic. We show that closed-shell molecules with large positive magnetizabilities can be designed by following the principle that a strong paratropic current ring combined with a large ring-current radius leads to closed-shell paramagnetism.Peer reviewe

Influence of perhalophenyl groups in the TADF mechanism of diphosphino gold(I) complexes

New perhalophenyl three-coordinated gold(i) complexes using the chelate ligand 1,2-bis(diphenyl-phosphino)benzene (dppBz) and [AuR(tht)] (R = C6F5 (1), o-C6BrF4 (2), p-C6BrF4 (3), o-C6F4I (4), p-C6F4I (5); tht = tetrahydrothiophene) have been prepared. The crystal structures of compounds 1 and 2 consist of distorted three-coordinated Au(i) complexes displaying different Au-P distances at the same gold atom. The complexes show intense photoluminescent emission in the solid state at room temperature (RT) and at 77 K. The study of the dependence of the emission lifetime with temperature suggests the existence of thermally activated delayed fluorescence (TADF) processes at RT. We have computed the rate constants for intersystem crossing and reverse intersystem crossing of the photophysical processes through first-principle calculations, supporting the experimental observations with very good agreement.Peer reviewe

Gold(i)-containing light-emitting molecules with an inverted singlet-triplet gap

Delayed fluorescence from molecules with an inverted singlet-triplet gap (DFIST) is the consequence of the unusual reverse order of the lowest excited singlet (S-1) and triplet (T-1) states of thermally activated delayed fluorescence (TADF) emitters. Heptazine (1,3,4,6,7,9,9b-heptaazaphenalene) derivatives have an inverted singlet-triplet gap thanks to the combination of multiple resonance (MR) effects and a significant double excitation character. Here, we study computationally the effect of gold(I) metalation and coordination on the optical properties of heptazine (molecule 4) and the phosphine-functionalized 2,5,8-tris(dimethylphosphino)heptazine derivatives (molecules 1-3). Ab initio calculations at the approximate second-order coupled cluster (CC2) and extended multiconfigurational quasi degenerate perturbation theory at the second order (XMC-QDPT2) levels show that molecules 1-4 have an inverted singlet- triplet gap due to the alternating spatial localization of the electron and hole of the exciton in the heptazine core. A non-vanishing one-electron spin-orbit coupling operator matrix element between T-1 and S-1((S-1|H-SO|T-1)) and a fast S-1? T(1 )intersystem crossing rate constant (k(ISC)) calculated at the XMC-QDPT2(12,12) level of theory for molecule 4 suggest that this new family of complexes may be the first organometallic DFIST emitters reported.Peer reviewe

Vibronic spectra of bifluorene and terfluorene

Using the method of the density functional theory (DFT/B3LYP/6-31G(d,p)), the vibrational absorption and emission spectra of bifluorene and terfluorene molecules are calculated. A good agreement is obtained between the model and experimental spectra. The vibrational promoting modes forming a vibronic progression in the emission bands are determined

Experimental and computational studies of the optical properties of 2,5,8-tris(phenylthiolato)heptazine with an inverted singlet-triplet gap

Photophysical properties of the three-fold symmetric 2,5,8-tris(phenylthiolato)heptazine molecule (1) are studied from combined experimental and computational viewpoints. The intense blue photoemission of 1 in the solid state and in toluene solution is proposed to have a fluorescent origin on the basis of a relatively short emission lifetime and no detectable triplet decay. Calculations at correlated ab initio levels of theory also show that 1 has a large inverted singlet-triplet (IST) gap, a non-vanishing spin-orbit coupling matrix element between the first excited singlet and triplet states, and a fast intersystem crossing rate constant that leads to singlet population from the higher-lying triplet state. The IST gap implies that the first excited singlet state is the lowest excited one, agreeing with the measured fluorescent behaviour of 1. IST gaps are also obtained for the oxygen-containing (2) and selenium-containing (3) analogues of 1 at the ADC(2) level of theory, but not for the tellurium one (4). Calculations of the magnetically induced current density demonstrate that the heptazine core of 1 is globally non-aromatic due to the alternation of carbon and nitrogen atoms along its external rim.The calculated energy inversion of the first excited states of a heptazine phenylthiolate molecule is consistent with the intense blue fluorescence in the solid state and in toluene solution.Peer reviewe