Ab Initio Calculation of UV-vis Absorption of Parent Mg, Fe, Co, Ni, Cu, and Zn Metalloporphyrins.

Relativistic restricted active space (RAS) second-order multireference perturbation theory (MRPT2) methods, incorporating spin-orbit (SO) coupling perturbatively via state interaction (SO-MRPT2/RASSCF), were used to reproduce the absorption spectra of parent metalloporphyrins containing the Mg2+, Zn2+, Co2+, Ni2+, Cu2+, or FeCl2+ ions in the 12,500-40,000 cm-1 region. Particular attention was paid to the interaction between the porphyrin ring and the metal 3d electrons in states of different multiplicities (we used metal 3d and double d-shell or 3d' orbitals). For this class of compounds, the N-electron valence state perturbation theory (NEVPT2) method is superior to the complete active space perturbation theory (CASPT2) and successfully reproduces the energies of all four characteristic transitions (Q, B, N, and L) of closed-shell metalloporphyrins. Inclusion of SO coupling was found to have very little effect on excitation energies and oscillator strengths. For FeCl2+ porphyrin, we treated ligand-to-metal charge-transfer (LMCT; π,d), metal ligand field (d,d), and metal-to-ligand charge-transfer (MLCT; d,π*) transitions within the same framework. The broad and intense spectral features associated with its B (Soret) band are attributed to multiconfigurational LMCT (d,π*) bands involving strong metal-ligand orbital mixing.

Inverse Design of Tetracene Polymorphs with Enhanced Singlet Fission Performance by Property-Based Genetic Algorithm Optimization.

The efficiency of solar cells may be improved by using singlet fission (SF), in which one singlet exciton splits into two triplet excitons. SF occurs in molecular crystals. A molecule may crystallize in more than one form, a phenomenon known as polymorphism. Crystal structure may affect SF performance. In the common form of tetracene, SF is experimentally known to be slightly endoergic. A second, metastable polymorph of tetracene has been found to exhibit better SF performance. Here, we conduct inverse design of the crystal packing of tetracene using a genetic algorithm (GA) with a fitness function tailored to simultaneously optimize the SF rate and the lattice energy. The property-based GA successfully generates more structures predicted to have higher SF rates and provides insight into packing motifs associated with improved SF performance. We find a putative polymorph predicted to have superior SF performance to the two forms of tetracene, whose structures have been determined experimentally. The putative structure has a lattice energy within 1.5 kJ/mol of the most stable common form of tetracene.

Structure and photophysics of indigoids for singlet fission: Cibalackrot.

We report an investigation of structure and photophysics of thin layers of cibalackrot, a sturdy dye derived from indigo by double annulation at the central double bond. Evaporated layers contain up to three phases, two crystalline and one amorphous. Relative amounts of all three have been determined by a combination of X-ray diffraction and FT-IR reflectance spectroscopy. Initially, excited singlet state rapidly produces a high yield of a transient intermediate whose spectral properties are compatible with charge-transfer nature. This intermediate more slowly converts to a significant yield of triplet, which, however, does not exceed 100% and may well be produced by intersystem crossing rather than singlet fission. The yields were determined by transient absorption spectroscopy and corrected for effects of partial sample alignment by a simple generally applicable procedure. Formation of excimers was also observed. In order to obtain guidance for improving molecular packing by a minor structural modification, calculations by a simplified frontier orbital method were used to find all local maxima of singlet fission rate as a function of geometry of a molecular pair. The method was tested at 48 maxima by comparison with the ab initio Frenkel-Davydov exciton model.

Singlet Fission Rate: Optimized Packing of a Molecular Pair. Ethylene as a Model.

A procedure is described for unbiased identification of all π-electron chromophore pair geometry choices that locally maximize the rate of conversion of a singlet exciton into a singlet biexciton (triplet pair), using a simplified version of the diabatic frontier orbital model of singlet fission (SF). The resulting approximate optimal geometries provide insight and are expected to represent useful starting points for searches by more advanced methods. The general procedure is illustrated on a pair of ethylenes as the simplest model of a π-electron system, but it is applicable to pairs of much larger molecules, with dozens of non-hydrogen atoms, and not necessarily planar. We first examine the value of |TA|2, the square of the electronic matrix element for SF with initial excitation fully localized on partner A, on a grid of several billion geometries within the six-dimensional space of physically realizable possibilities. Several of the optimized pair geometries are somewhat unexpected, but all are found to follow the qualitative guidance proposed earlier. In the neighborhood of each local maximum of |TA|2, consideration of mixing with charge-transfer configurations and of excitonic interaction between partners A and B determines the SF energy balance and yields squared matrix elements |T*|2 and |T**|2 for the lower and upper excitonic states S* and S**, respectively. Assuming Boltzmann populations of these states, the geometry is further optimized to maximize k, the sum of the SF rates obtained from Marcus theory, and this reorders the suitable geometries substantially. At 87 pair geometries, the |T*|2 and |T**|2 values are compared with those obtained from high-level ab initio nonorthogonal configuration interaction calculations and found to follow the same trend. Finally, the biexciton binding energy at the optimized geometries is calculated. Altogether, 13 significant local maxima of SF rate for a pair of ethylenes are identified in the physically relevant part of space that avoids molecular interpenetration in the hard-sphere approximation. The three best geometries are twist-stacked, slip-stacked, and L-shaped. The maxima occur at the (five-dimensional) surfaces of seven six-dimensional "parent" regions of space centered at physically inaccessible geometries at which the calculated SF rate is very large but the two ethylenes interpenetrate. The results are displayed in interactive graphics. The computer code ("Simple") written for these calculations is flexible in that it permits a choice of performing the search for local maxima in six dimensions on |TA|2, |T*|2, or k. It is available as freeware at https://cloud.uochb.cas.cz/simple .

Molecular Packing and Singlet Fission: The Parent and Three Fluorinated 1,3-Diphenylisobenzofurans.

Crystal structures, singlet fission (SF) rate constants, and other photophysical properties are reported for three fluorinated derivatives of 1,3-diphenylisobenzofuran and compared with those of the two crystal forms of the parent. The results place constraints on the notion that the effects of molecular packing on SF rates could be studied separately from effects of chromophore structural changes by examining groups of chromophores related by weakly perturbing substitution if their crystal structures are different. The results further provide experimental evidence that dimer-based models of SF are not sufficiently general and that trimer- and possibly even higher oligomer-based or many-body models need to be formulated.

An MS-CASPT2 Calculation of the Excited Electronic States of an Axial Difluoroborondipyrromethene (BODIPY) Dimer.

The previously reported ( Duman et al., J. Org. Chem . 2012 , 77 , 4516 ) calculated state energies of monomeric difluoroborondipyrromethene (BODIPY) and its axial dimer would suggest that these dyes are promising candidates for singlet fission, and the dimer was computed to have an unusual low-lying doubly excited state. We find that these results were affected by the use of an imbalanced active space in multireference calculations and are not correct. Multistate complete-active-space second-order perturbation theory (MS-CASPT2/cc-pVDZ) calculations using an [8,8] (8 electrons in 8 orbitals) active space for the monomer and a [16,16] active space for the dimer reproduce quite well the observed excitation energies of the S1 states of both, and yield T1 excitation energies well in excess of half of the S1 excitation energies. We conclude that neither BODIPY monomer nor its axial dimer would permit exothermic singlet fission and are not worthy of investigation as potentially useful candidates, and that the unusual low-energy doubly excited states of the dimer were artifacts.

Investigation of the acid-base and electromigration properties of 5-azacytosine derivatives using capillary electrophoresis and density functional theory calculations.

Capillary electrophoresis (CE) and quantum mechanical density functional theory (DFT) were applied to the investigation of the acid-base and electromigration properties of important compounds: newly synthesized derivatives of 5-azacytosine - analogs of efficient antiviral drug cidofovir. These compounds exhibit a strong antiviral activity and they are considered as potential new antiviral agents. For their characterization and application, it is necessary to know their acid-base properties, particularly the acidity constants (pKa) of their ionogenic groups (the basic N3 atom of the triazine ring and the acidic phosphonic acid group in the alkyl chain). First, the mixed acidity constants (pKamix) of these ionogenic groups and the ionic mobilities of these compounds were determined by nonlinear regression analysis of the pH dependence of their effective electrophoretic mobilities. Effective mobilities were measured by CE in a series of background electrolytes in a wide pH range (2.0-10.5), at constant ionic strength (25mM) and constant temperature (25°C). Subsequently, the pKamix values were recalculated to thermodynamic pKa values using the Debye-Hückel theory. The thermodynamic pKa value of the NH+ moiety at the N3 atom of the triazine ring was found to be in the range 2.82-3.30, whereas the pKa of the hydrogenphosphonate group reached values from 7.19 to 7.47, depending on the structure of the analyzed compounds. These experimentally determined pKa values were in good agreement with those calculated by quantum mechanical DFT. In addition, DFT calculations revealed that from the four nitrogen atoms in the 5-azacytosine moiety, the N3 atom of the triazine ring is preferentially protonated. Effective charges of analyzed compounds ranged from zero or close-to-zero values at pH 2 to -2 elementary charges at pH≥9. Ionic mobilities were in the range (-16.7 to -19.1)×10-9m2V-1s-1 for univalent anions and in the interval (-26.9 to -30.3)×10-9m2V-1s-1 for divalent anions.

Single-Step Formation of Pyrimido[4,5-d]pyridazines by a Pyrimidine-Tetrazine Tandem Reaction.

A straightforward synthesis of pyrimido[4,5-d]pyridazines from pyrimidines and tetrazines under basic conditions is reported. Deprotonated, substituted 5-halopyrimidines readily react with variously substituted tetrazines in a highly regioselective manner via a complex reaction pathway, which was supported by DFT calculations. This mechanism leads to the empirically observed regioisomers without going through the conceivable hetaryne intermediate. These results on 5-halopyrimidines led to development of the methodology for preparation of opposite regioisomers based on 6-halopyrimidines.

Electronic Spectra of the Tetraphenylcyclobutadienecyclopentadienylnickel(II) Cation and Radical.

Properties of the tetraphenylcyclobutadienecyclopentadienylnickel(II) cation 1 and its tetra-o-fluoro derivative 1a have been measured and calculated. The B3LYP/TZP optimized geometry of the free cation 1 agrees with a single-crystal X-ray diffraction structure except that in the crystal one of the phenyl substituents is strongly twisted to permit a close-packing interaction of two of its hydrogens with a nearby BF4(-) anion. The low-energy parts of the solution electronic absorption and magnetic circular dichroism (MCD) spectra of 1 and 1a have been interpreted by comparison with TD-DFT (B3LYP/TZP) results. Reduction or pulse radiolysis lead to a neutral 19-electron radical, whose visible absorption and MCD spectra have been recorded and interpreted as well. The reduction is facilitated by ∼0.1 V upon going from 1 to 1a. Unsuccessful attempts to prepare several other aryl substituted derivatives of 1 by the classical synthetic route are described in the Supporting Information .

Excitation Localization/Delocalization Isomerism in a Strongly Coupled Covalent Dimer of 1,3-Diphenylisobenzofuran.

Two isomers of both the lowest excited singlet (S1) and triplet (T1) states of the directly para, para'-connected covalent dimer of the singlet-fission chromophore 1,3-diphenylisobenzofuran have been observed. In one isomer, excitation is delocalized over both halves of the dimer, and in the other, it is localized on one or the other half. For a covalent dimer in solution, such "excitation isomerism" is extremely rare. The vibrationally relaxed isomers do not interconvert, and their photophysical properties, including singlet fission, differ significantly.

Captodatively stabilized biradicaloids as chromophores for singlet fission.

Singlet fission offers an opportunity to improve solar cell efficiency, but its practical use is hindered by the limited number of known efficient materials. We look for chromophores that satisfy the desirable but rarely encountered adiabatic energy conditions, E(T2) - E(S0) > E(S1) - E(S0) ≈ 2[E(T1) - E(S0)], and are small enough to permit highly accurate calculations. We provide a rationale for the use of captodative biradicaloids, i.e., biradicals stabilized by direct interaction between their radical centers, which carry both an acceptor and a donor group. A computation of vertical excitation energies of 14 structures of this type by time-dependent density functional theory (TD-DFT) yielded 11 promising candidates. The vertical excitation energies from S0 and T1 were recalculated by complete-active-space second-order perturbation theory (CASPT2), and five of the compounds met the above energy criteria. Their adiabatic excitation energies from the S0 into the S1, S2, T1, and T2 excited states were subsequently calculated, and three of them look promising. For 2,3-diamino-1,4-benzoquinone, adiabatic E(T1) and E(S1) energies were close to optimal (1.12 and 2.23 eV above the S0 ground state, respectively), and for its more practical N-peralkylated derivative they were even lower (0.63 and 1.06 eV above S0, respectively). PCM/CASPT2 results suggested that the relative energies can be further tuned by varying the polarity of the environment.

Toward designed singlet fission: solution photophysics of two indirectly coupled covalent dimers of 1,3-diphenylisobenzofuran.

In order to identify optimal conditions for singlet fission, we are examining the photophysics of 1,3-diphenylisobenzofuran (1) dimers covalently coupled in various ways. In the two dimers studied presently, the coupling is weak. The subunits are linked via the para position of one of the phenyl substituents, in one case (2) through a CH2 linker and in the other (3) directly, but with methyl substituents in ortho positions forcing a nearly perpendicular twist between the two joint phenyl rings. The measurements are accompanied with density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. Although in neat solid state, 1 undergoes singlet fission with a rate constant higher than 10(11) s(-1); in nonpolar solutions of 2 and 3, the triplet formation rate constant is less than 10(6) s(-1) and fluorescence is the only significant event following electronic excitation. In polar solvents, fluorescence is weaker because the initial excited singlet state S1 equilibrates by sub-nanosecond charge transfer with a nonemissive dipolar species in which a radical cation of 1 is attached to a radical anion of 1. Most of this charge transfer species decays to S0, and some is converted into triplet T1 with a rate constant near 10(8) s(-1). Experimental uncertainties prevent an accurate determination of the number of T1 excitations that result when a single S1 excitation changes into triplet excitation. It would be one if the charge-transfer species undergoes ordinary intersystem crossing and two if it undergoes the second step of two-step singlet fission. The triplet yield maximizes below room temperature to a value of roughly 9% for 3 and 4% for 2. Above ∼360 K, some of the S1 molecules of 3 are converted into an isomeric charge-transfer species with a shorter lifetime, possibly with a twisted intramolecular charge transfer (TICT) structure. This is not observed in 2.

The Loss of a Prominent Scientist: Detlef Schröder.

Schröder Special Issue: This collection of papers is dedicated to the memory of our friend and colleague Detlef Schröder, who we honor with this selection of top-quality science.

Search for a small chromophore with efficient singlet fission: biradicaloid heterocycles.

Of the five small biradicaloid heterocycles whose S(1), S(2), T(1), and T(2) adiabatic excitation energies were examined by the CASPT2/ANO-L-VTZP method, two have been found to meet the state energy criterion for efficient singlet fission and are recommended to the attention of synthetic chemists and photophysicists.

HCB11(CF3)(n)F(11-n)-: inert anions with high anodic oxidation potentials.

Cs salts of four of the title anions were prepared by fluorination of salts of partly methylated (n = 11, 10) or partly methylated and partly iodinated (n = 6, 5) CB(11)H(12)(-) anions. The CH vertex is acidic, and in the unhindered anion with n = 6 it has been alkylated. Neat Cs(+)[1-H-CB(11)(CF(3))(11)](-) is as treacherously explosive as Cs(+)[CB(11)(CF(3))(12)](-), but no explosions occurred with the salts of the other three anions. BL3YP/6-31G* gas-phase electron detachment energies of the title anions are remarkably high, 5-8 eV. Treated with NiF(3)(+) in anhydrous liquid HF at -60 °C, anions with n = 11 or 10 resist oxidation, whereas anions with n = 6 or 5 are converted to colored EPR-active species, presumably the neutral radicals [HCB(11)(CF(3))(n)F(11-n)](•). These are stable for hours at -60 °C after extraction into cold perfluorohexane or perfluorotri-n-butylamine solutions. On warming to -20 °C in a Teflon or quartz tube, the color and EPR activity disappear, and the original anions are recovered nearly quantitatively, suggesting that the radicals oxidize the solvent.

Toward designed singlet fission: electronic states and photophysics of 1,3-diphenylisobenzofuran.

Single crystal molecular structure and solution photophysical properties are reported for 1,3-diphenylisobenzofuran (1), of interest as a model compound in studies of singlet fission. For the ground state of 1 and of its radical cation (1(+*)) and anion (1(-*)), we report the UV-visible absorption spectra, and for neutral 1, also the magnetic circular dichroism (MCD) and the decomposition of the absorption spectrum into purely polarized components, deduced from fluorescence polarization. These results were used to identify a series of singlet excited states. For the first excited singlet and triplet states of 1, the transient visible absorption spectra, S(1) --> S(x) and sensitized T(1) --> T(x), and single exponential lifetimes, tau(F) = approximately 5.3 ns and tau(T) = approximately 200 micros, are reported. The spectra and lifetimes of S(1) --> S(0) fluorescence and sensitized T(1) --> T(x) absorption of 1 were obtained in a series of solvents, as was the fluorescence quantum yield, Phi(F) = 0.95-0.99. No phosphorescence has been detected. The first triplet excitation energy of solid 1 (11,400 cm(-1)) was obtained by electron energy loss spectroscopy, in agreement with previously reported solution values. The fluorescence excitation spectrum suggests an onset of a nonradiative channel at approximately 37,000 cm(-1). Excitation energies and relative transition intensities are in agreement with those of ab initio (CC2) calculations after an empirical 3000 cm(-1) adjustment of the initial state energy to correct differentially for a better quality description of the initial relative to the terminal state of an absorption transition. The interpretation of the MCD spectrum used the semiempirical PPP method, whose results for the S(0) --> S(x) spectrum require no empirical adjustment and are otherwise nearly identical with the CC2 results in all respects including the detailed nature of the electronic excitation. The ground state geometry of 1 was also calculated by the MP2, B3LYP, and CAS methods. The calculations provided a prediction of changes of molecular geometry upon excitation or ionization and permitted an interpretation of the spectra in terms of molecular orbitals involved. Computations suggest that 1 can exist as two nearly isoenergetic conformers of C(2) or C(s) symmetry. Linear dichroism measurements in stretched polyethylene provide evidence for their existence and show that they orient to different degrees, permitting a separation of their spectra in the region of the purely polarized first absorption band. Their excitation energies are nearly identical, but the Franck-Condon envelopes of their first transition differ to a surprising degree.

Molecular design of specific metal-binding peptide sequences from protein fragments: theory and experiment.

A novel strategy is presented for designing peptides with specific metal-ion chelation sites, based on linking computationally predicted ion-specific combinations of amino acid side chains coordinated at the vertices of the desired coordination polyhedron into a single polypeptide chain. With this aim, a series of computer programs have been written that 1) creates a structural combinatorial library containing Zi-(X)n-Zj sequences (n=0-14; Z: amino acid that binds the metal through the side chain; X: any amino acid) from the existing protein structures in the non-redundant Protein Data Bank; 2) merges these fragments into a single Z1-(X)n1 -Z2-(X)n2 -Z3-(X)n3 -...-Zj polypeptide chain; and 3) automatically performs two simple molecular mechanics calculations that make it possible to estimate the internal strain in the newly designed peptide. The application of this procedure for the most M2+-specific combinations of amino acid side chains (M: metal; see L. Rulísek, Z. Havlas J. Phys. Chem. B 2003, 107, 2376-2385) yielded several peptide sequences (with lengths of 6-20 amino acids) with the potential for specific binding with six metal ions (Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Hg2+). The gas-phase association constants of the studied metal ions with these de novo designed peptides were experimentally determined by MALDI mass spectrometry by using 3,4,5-trihydroxyacetophenone as a matrix, whereas the thermodynamic parameters of the metal-ion coordination in the condensed phase were measured by isothermal titration calorimetry (ITC), chelatometry and NMR spectroscopy methods. The data indicate that some of the computationally predicted peptides are potential M2+-specific metal-ion chelators.

Substituent effect on exo stereoselectivity in the 1,3-Dipolar cycloaddition reaction of tulipalin A with nitrile ylides.

1,3-Dipolar cycloaddition reactions of dihydro-3-methylene-2(3H)-furanone (tulipalin A) with various benzonitrile(p-X-benzylide) ylides prefer formation of exo-cycloadducts in the extent corresponding to an increasing electron donor character of the substituent X in the para-position of the benzylide phenyl ring of the 1,3-dipolar reagent. The substituent effect on diastereoselectivity of the 1,3-DC reaction is rationalized in terms of CH/pi interaction between the dipole and the dipolarophile in an exo-transition state. The determining role of such an interaction is demonstrated by the correlation of the observed diastereoselectivities with substituent Hammett sigma constants, which shows a small negative rho value. A certain contribution of CO/pi interaction between the lactone carbonyl and the substituted phenyl ring to mediation of the substituent effect is also discussed. The energy profiles of both reaction pathways were analyzed using DFT and RI-MP2 theoretical approaches. Calculated energy and structural differences between located transition states are consistent with reaction diastereoselectivities.

The sixteen CB(11)H(n)Me(12-n)(-) anions with fivefold substitution symmetry: anodic oxidation and electronic structure.

The 15 symmetrically methylated derivatives of the CB11H12(-) anion (1a) have been synthesized and found to vary greatly in ease of oxidation. Cyclic voltammetry in liquid SO2 yielded fully reversible oxidation potentials for five of those that have no adjacent unsubstituted vertices in positions 7-12; three others showed some indication of reversibility. The anions 1a-16a and the Jahn-Teller distorted neutral radicals 1r-16r have been characterized by ab initio and density functional theory calculations. In the state average CASSCF(13,12)/6-31+G* approximation, the ground state potential energy surface of 1r contains five symmetry-related pairs of minima. The computational results account for the reversible redox potentials very well when the solvent is included explicitly (RI-DFT(BP)/TZVP, COSMO). For display and for a semiquantitative understanding of methyl substituent effects in terms of perturbation theory, the molecular orbitals of 1a have been expressed in the symmetry-adapted cluster basis. The results serve as an underpinning for a set of additive empirical increments for redox potential prediction. Relative to the usual hydrogen standard, a single methyl group facilitates oxidation by approximately 50, 70, 70, and 10 mV in positions 1, 2, 7, and 12, respectively. This electron donor effect on the redox potential is due to a contribution, whereas those of (inductive and direct field) type are negligible.