Spin Alternation Rule in USCF for Through-Bond Magnetic Coupling─A New Look: Why and When Does It Arise and How To See It.

This work takes a new look at the spin alternation rule in unrestricted self-consistent-field (USCF) calculations in terms of structural characteristics such as periodicity, impurity location, and Coulomb exchange. For clarity, the systems considered are biradicals produced from linear conjugated hydrocarbons. Both site-parametrized Hamiltonian models for theoretical analysis and spin unrestricted density functional theory (DFT) calculations are used. Theoretical analysis leads to the following conclusions: (1) The diradical state is an excited state of a linear chain of N conjugated carbon atoms (when N is about ≤ 10). Spin alternation is a consequence of the (truncated) periodic symmetry combined with filling each closed-shell pi orbital with two electrons and each singly occupied molecular orbital (SOMO) with one electron. Spin polarization is evident in triplet (T) and broken symmetry (BS) solutions for an odd N and only in the T solution for an even N. Spin alternation is visible in the BS for an odd N and always remains muted in the calculated T. (2) For a doped chain with two radical centers, spin alternation is generally visible in the BS for an odd N. The sign of spin population on the radical centers in the BS indicates the stable spin. For radical centers separated by an odd (even) number of pz electrons, spin alternation favors T (S) state with FM (AFM) interaction. Spin oscillation remains less transparent for an even N without exchange. (3) In an unrestricted treatment with exchange, spin alternation becomes observable. Without SCF iterations, the more stable state can be identified from a clear spin oscillation in the BS. An irregular oscillation indicates a possible singlet ground state. These observations are supported by density functional calculations using the B3LYP functional and the 6-311+g(d,p) basis set on linear decapentaene diradicals with nitronyl nitroxide moieties substituted on two sets of conjugated atoms, (3,9) and (3,10). Because of the SCF procedure, one finds spin alternation in the T (BS) solution and erratic oscillation in the BS (T) solution of the 3,9 (3,10) diradical in respective equilibrium geometries. The ground state is T (S). DFT adiabatic coupling constants, SOMO energies, spin population plots, and SOMO lobe diagrams compare well with molecular electronic characteristics from theoretical analysis using Hamiltonian parameters.

Quantum Chemical Investigation of Light-Activated Spin State Change in Pyrene Coupled to Oxoverdazyl Radical Center.

Low-spin ground states and low-lying excited states of higher spin were investigated for four pyrene oxoverdazyl monoradicals 1-4 and eight pyrene dioxoverdazyl diradicals 5-12. The ground states for quartet and quintet spin symmetries that are in reality excited states were found in the region of 565-775 nm above the respective electronic ground states. We calculated the "adiabatic" magnetic exchange coupling constant in the electronic ground state of each isolated biradical (5-12) by unrestricted density functional theory. A number of hybrid functionals such as B3LYP, PBE0, M06, and M06-2X were used. We also used range-separated functionals such as LC-ωPBE and ωB97XD to compare their effects on the coupling constant and the relative energy of the high-spin state. Molecular geometries were optimized for the doublet and quartet spin states of every monoradical (1-4), and the broken symmetry and triplet solutions were optimized for every biradical (5-12), by systematically using 6-311G, 6-311G(d,p), and 6-311++G(d,p) basis sets with each functional. The geometry of each quintet diradical (5-12) was optimized using 6-311G basis set. B3LYP produced the best spin values. The excited state (quartet or quintet)-ground state energy difference (ΔE) increases in the presence of para-phenylene connectors. These energy differences were predicted here. The nature of spin coupling and consequently the ground state spin agree with spin alternation rule and the calculated atomic spin population. The adiabatic coupling constants were predicted for the biradicals (5-12) in their electronic ground states. Electron paramagnetic resonance parameters were determined at 6-311++G** level for the ground state and the quartet state of 1 and compared with the available experimental data. Low-lying excited states were found for the radical center (oxoverdazyl), pyrene, molecule 1, and diradical 5 by time-dependent density functional theory (TDDFT) method using B3LYP hybrid, 6-311++G(d,p) basis set, and the molecular geometry in the electronic ground state. Data from these calculations were used to discuss possible mechanisms for the achievement of the high-spin (excited) states in 1 and 5 and to predict a similar outcome for radicals 2-4 and 6-12 upon excitation. A comprehensive mechanism for the first excitation is proposed here. In particular, we show that the initial excitation of 1 involves large contributions from mixed transitions between pyrene and oxoverdazyl moieties, whereas the initial excitation of 5 is basically that of only the pyrene fragment. Subsequent internal conversion and intersystem crossing are likely to lead to the high-spin states of lower energy. Sample spin-flip TDDFT calculations were also done to confirm the energetic location and composition of the quartet state of 1 and the quintet state of 5.

Quantum chemical investigation of meta-xylylene based one-dimensional polymer chain.

We have investigated unsubstituted and methyl substituted polyradical chains of meta-xylylene by using density functional theory-broken symmetry methodology (DFT-BS). Optimization of geometry in the high-spin and low-spin states have been done at B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) levels in unrestricted methodology. Single-point calculations on the high-spin optimized geometries have been done by using the 6-311G(d,p) basis set. Each polyradical has been found to be nonplanar with a high-spin ground state. Each has a coupling constant larger than thermal energy. For each group of polyradicals, the coupling constant has been found to exponentially decrease with increase in the number of phenylene groups. The B3LYP infinite chain limit has been estimated for both the unsubstituted and substituted polyradicals. The individual inter-radical-site coupling constants have been estimated for the triradicals and tetraradicals using HDVV Hamiltonian in ORCA 3.0.1 code. These are also generally large and positive, revealing a strong intersite ferromagnetic interaction. The intersite coupling constant too decreases with increasing distance between the radical centers. Finally, we have used CRYSTAL09 package for calculations on the infinitely long one-dimensional and periodic polyradical chains. The coupling constants estimated from the periodic calculations are quite large at about 500 cm(-1) and somewhat greater than the limiting values calculated for the polyradicals with an increasing number of phenylene groups. This happens as the individual polyradicals of increasing size progressively deviate from periodicity, and thereby lessens the strength of through-bond spin-spin coupling. The calculated band gap of ∼4.5 eV indicates that the infinitely long one-dimensional chains must be ferromagnetic and electron insulators.

Solvation of CO2 in water: effect of RuBP on CO2 concentration in bundle sheath of C4 plants.

An understanding of the temperature-dependence of solubility of carbon dioxide (CO2) in water is important for many industrial processes. Voluminous work has been done by both quantum chemical methods and molecular dynamics (MD) simulations on the interaction between CO2 and water, but a quantitative evaluation of solubility remains elusive. In this work, we have approached the problem by considering quantum chemically calculated total energies and thermal energies, and incorporating the effects of mixing, hydrogen bonding, and phonon modes. An overall equation relating the calculated free energy and entropy of mixing with the gas-solution equilibrium constant has been derived. This equation has been iteratively solved to obtain the solubility as functions of temperature and dielectric constant. The calculated solubility versus temperature plot excellently matches the observed plot. Solubility has been shown to increase with dielectric constant, for example, by addition of electrolytes. We have also found that at the experimentally reported concentration of enzyme RuBP in bundle sheath cells of chloroplast in C4 green plants, the concentration of CO2 can effectively increase by as much as a factor of 7.1-38.5. This stands in agreement with the observed effective rise in concentration by as much as 10 times.

The Triplet-Singlet Gap in the m-Xylylene Radical: A Not So Simple One.

Meta-benzoquinodimethane (MBQDM) or m-xylylene provides a model for larger organic diradicals, the triplet-singlet gap being the key property. In the present work this energy difference has been the object of a systematic study by means of several density functional theory-based methods including B3LYP, M06, M06-2X, HSE and LC-ωPBE potentials and a variety of wave function-based methods such as complete active space self consistent field (CASSCF), Multireference second-order Møller-Plesset (MRMP), difference dedicated configuration interaction (DDCI), and Multireference configuration interaction (MRCI). In each case various basis sets of increasing quality have been explored, and the effect of the molecular geometry is also analyzed. The use of the triplet and broken symmetry (BS) solutions for the corresponding optimized geometries obtained from B3LYP and especially M06-2X functionals provide the value of the adiabatic triplet-singlet gap closer to experiment when compared to the reported value of Wenthold, Kim, and Lineberger, (J. Am. Chem. Soc. 1997, 119, 1354) and also for the electron affinity. The agreement further improves using the full π-valence CASSCF(8,8) optimized geometry as an attempt to correct for the spin contamination effects on the geometry of the BS state. The CASSCF, MRMP, and MRCI, even with the full π valence CAS(8,8) as reference and relatively large basis set, systematically overestimate the experimental value indicating either that an accurate description must go beyond this level of theory, including σ electrons and higher order polarization functions, or perhaps that the measured value is affected by the experimental conditions.

Metaphenylene-based nitroxide diradicals: a protocol to calculate intermolecular coupling constant in a one-dimensional chain.

Intramolecular magnetic exchange coupling constants are determined for seven isolated metaphenylene-based dinitroxide diradicals by unrestricted density functional methodology (UDFT) using a number of hybrid functionals such as B3LYP, B3LYP-D3, M06-2X, HSE, and LC-ωPBE. Geometry optimizations for both triplet and broken symmetry solutions are performed with the 6-311G(d,p) basis set for all the molecules. In all cases, B3LYP somewhat overestimates the coupling constant, and M06-2X produces a more realistic value. The range-separated HSE and LC-ωPBE functional yield large deviations from experiment. The nature of spin coupling agrees with the spin alternation rule and the calculated spin densities, in conjunction with the McConnell rule. It can also be explained in terms of the nondisjoint Single Occupied Molecular Orbital effect. Furthermore, it correlates with the calculated NICS(1) isotropic and zz and hyperfine coupling constants. We also put forward a method for the determination of the intramolecular (J) and intermolecular (J') coupling constants from quantum chemical calculations on a one-dimensional chain of weakly bound diradicals. Two expressions are derived for the energies of different spin states in terms of J and J'. Exemplary UDFT computations are done on the N-mers (N = 2-6) of two diradicals for which the crystal coordinates are available. The intramolecular and intermolecular coupling constants are determined from the calculated UDFT energies. These are indeed in general agreement with the measured coupling constants.

Theoretical investigation of photomagnetic properties of oxoverdazyl-substituted pyrenes.

We have investigated the ground state spin of 10 pairs of possible photochromic diradical isomers by quantum chemical methods. Dihydrogen pyrenes and dinitrile pyrenes have been chosen as spacers with radical centers attached at (1,7) and (1,8) locations. Oxoverdazyl has served as a radical center, and both C and N linkages have been investigated. Triplet molecular geometries have been optimized at the UB3LYP/6-311G(d,p) level. Single-point calculations on triplet and broken symmetry states have been performed using the 6-311++G(d,p) basis set. Careful designs have led to the prediction of strongly coupled dihydropyrene (DHP) isomers, and the cyclophenadiene (CPD) isomers have always been found as weakly coupled. The effect of the functional M06-2X has been investigated. Calculated TDDFT spectra have been sufficient to guarantee photochromism of the designed diradicals. It has been estimated that compounds of diradicals with large coupling constants in the DHP form would show a pronounced change in molar susceptibility on photoconversion. This has led us to identify two molecules that can serve as a photomagnetic switch at room temperature.

Theoretical investigation of stilbene as photochromic spin coupler.

Density functional theory (DFT) based calculations are used here to investigate the magnetic behavior, spectroscopic transitions, and possible photomagnetic properties of stilbene derivatives using photochromicity of cis- and trans-forms of the parent molecule. Nitronyl nitroxide (NN), iminonitroxide (IN), tetrathiafulvalene cation (TTF), and verdazyl (VER) are used as monoradical centers at the p, p' positions. The B3LYP functional with the usual broken symmetry approach and a sufficiently large basis set is chosen to obtain reliable estimates of the intramolecular exchange coupling constants (J). It is found that, with stilbene as a spacer, the coupling of TTF with NN, IN, and VER is always antiferromagnetic with J being generally large and negative. Although J values obtained for cis- and trans-forms are both negative, the difference in J values is quite large. Spectroscopic transition energies and corresponding oscillator strengths of cis- and trans-stilbene diradicals are estimated by time-dependent (TD)-DFT calculations using the same functional. Interestingly, the spectral features of the diradicals are similar to those of cis- and trans-stilbene, which suggests that stilbene diradicals would have good photoswitching properties. Finally, we show that, when these diradicals are placed in a matrix, photochromicity would be accompanied by a significant change in paramagnetic susceptibility.

High magnetic exchange coupling constants: a density functional theory based study of substituted Schlenk diradicals.

The Schlenk diradical has been known since 1915. After a detailed experimental work by Rajca, its magnetic nature has remained more or less unexplored. We have investigated by quantum chemical calculations the nature of magnetic coupling in 11 substituted Schlenk diradicals. Substitution has been considered at the fifth carbon atom of the meta-phenylene moiety. The UB3LYP method has been used to study 12 diradicals including the original one. The 6-311G(d,p) basis set has been employed for optimization of molecular geometry in both singlet and triplet states for each species. The singlet optimization has led to the optimization of the broken-symmetry structure for 10 species including the unsubstituted one. This development makes it possible to carry out further broken symmetry calculations in two ways. The triplet calculation has been done using 6-311++G(d,p) basis set and the optimized triplet geometry in both procedures. The broken symmetry calculations have used the optimized geometries of either the triplet states or the broken symmetry solutions. The first method leads to the prediction of electron paramagnetic resonance (EPR) compatible magnetic exchange coupling constant (J) in the range 517-617 cm(-1). A direct optimization of the broken symmetry geometry gives rise to a lower estimate of J, in the range of 411-525 cm(-1) and compatible with macroscopic Curie studies. The calculated J for the unsubstituted Schlenk diradical is 512 cm(-1) that can be compared with 455 cm(-1) estimated by Rajca. In both cases, introduction of groups with +M and +I effects (Ingold's notation) decreases the J value from that for the unsubstituted Schlenk diradical while -I and -M groups at the same position increases J. These trends have been explained in terms of Hammett constants, atomic spin densities, and dihedral angles.

On the photomagnetism of nitronyl nitroxide, imino nitroxide, and verdazyl-substituted azobenzene.

The cis- and trans-azobenzenes are known as photochromic isomers with the trans- converting into the cis-form and vice versa upon irradiation with specific wavelengths. We have quantum chemically investigated the cis- and trans-forms of substituted azobenzene diradicals, with two nitronyl nitroxides, imino nitoxides, or verdazyls at para positions and serving as monoradical centers, to determine whether they can exhibit a photoassisted magnetic crossover. Geometries of both substituted and unsubstituted molecules have been optimized by density functional (DF) method UB3LYP using the 6-311G(d,p) basis set. Optimization of the geometry of the cis isomers has required special care. Single point singlet, triplet, and broken symmetry calculations have been done using 6-311++G(3df, 3pd) basis set. The magnetic exchange coupling constants have been estimated from the broken symmetry calculations. Absorption wavelengths have been estimated for both substituted and unsubstituted species from time-dependent DF treatment using restricted spin-polarized methodology RB3LYP and 6-311++G(3df, 3pd) basis set. From the similarity in the calculated absorption wavelengths for the unsubstituted and substituted azobenzenes, and the increased oscillator strengths (f) for the substituted species, we predict that the diradical isomers would be strongly photochromic. From our triplet state and broken symmetry calculations, we predict that both the cis- and the trans-diradicals are antiferromagnetically coupled. This prediction is consistent with the spin alternation rule, and the possibility of a magnetic crossover is nonexistent for these species.