Open spin density distributions

The dimerisation energy for derivatives of 2 (ca. 35 kJ mol-1) is considerable, particularly in relation to the strength of intermolecular forces and some persistence is required in order to isolate derivatives of 2 which do not form 7T —7r dimers in the solid state. A survey of the monomeric derivatives has been published recently.26 Since the spin density distribution in 2 is rather insensitive to chemical tuning, approaches to inhibit dimerisation rely exclusively on structural modifications, which affect the nature of the intermolecular forces. Inclusion of sterically demanding groups, such as 13, 14 and 15 has proved partially successful (in the case of the diradical 14 one ring is involved in formation of a dimer, while the other retains its open shell character). 

Other properties in magnetic resonance may be mentioned here, for example, hyperfine couplings. As the isotropic hyperfine coupling also depends crucially on the spherical spin-density distribution around the nucleus in question, s-character in bonding and, thus, hybridization defects will be important. Obviously, for open-shell radicals the s-character of the singly occupied MO(s) is the most cmcial aspect, but spin polarization of doubly occupied MOs with core or valence s-character may also be relevant (e.g., when the singly occupied molecular orbital is of pure p-character at the given atom). 

So far, we have encountered the spin density as a variable both in the description of electronic structures of open-shell character and in the analysis of local quantities such as local spins or bond orders. For an accurate treatment of open-shell molecules, spin-spin interactions and chemical bonding, reliable spin densities are thus mandatory. However, the determination of rehable spin density distributions can be a difficult task in quantum chemistry [199, 200]. Examples of such difficult cases are iron nitrosyl complexes containing salen or porphyrin ligands for which DFT spin densities considerably depend on the approximate exchange-correlation functional [87,199]. 

In this chapter, we reviewed different quantum chemical approaches to determine local quantities from (multireference) wave functions in order to provide a qualitative interpretation of the chemical bond in open-shell molecules. Chemical bonding in open-shell systems can be described by covalent interactions and electron-spin coupling schemes. For different definitions of the (effective) bond order as well as various decomposition schemes of the total molecular spin expectation value into local contributions, advantages and shortcomings have been pointed out. For open-sheU systems, the spin density distribution is an essential ingredient in the... 

As an example of an open-shell transition-metal complex we discussed some of the pitfalls of present-day DFT and CASSCF calculations in determining accurate spin density distributions in open-shell transition-metal complexes. An accurate description of the spin density and of the electronic structure is mandatory for a subsequent qualitative analysis of the chemical bonding. This could only be accomplished by employing the DMRG algorithm to produce an accurate CASCI-type electronic wave function. 

The situation is still more complicated for open-shell (radical) conjugated oligomers. In neutral polyene radicals, even the most precise and expensive ab initio correlated methods, such as CCSD(T), can give at best a qualitative prediction of the spin density distributions, and the behavior of common DFT schemes is also mediocre [42]. The problems with exchange and correlation are augmented in this case by the spin-restricted/umestricted ansatz dilemma discussed above. An efficient practical solution is, somewhat unexpectedly, provided by correlated semiempirical methods with a simple Hamiltonian, such as PPP [53]. We therfore also often use semiempirical methods in our studies of conjugated oligomer radical-ions. 

Semiempirical calculations have been carried out by an unparameterized SCF-MO method with integral approximations [5], various versions of the CNDO [37 to 42] and INDO [6, 38, 43 to 45] methods, the MNDO [46, 47] and MINDO [48] methods, the extended Hiickel method [3, 4, 49, 50] (presumably also [51 ]), a Pariser-Parr-Pople-type open-shell method [49] (presumably also [51]), and a simple MO approach [52]. Besides some other molecular properties, the charge distribution (atomic charges and/or overlap populations) [5, 38,40,41,43,49 to 51] and the spin density distribution (and thus, the hyperfine coupling constants, compare above and p. 241) [3 to 6, 46, 48] have been the subjects of many of these studies. 

Despite the advanced formulation that have been put forward, we must emphasize that the treatment of nonlocality in chemistry is still an open problem calling for accurate representations (i.e., beyond the simple local ansatz) for the nonlocal reactivity kernels as well as suitable approximations to the higher-order responses of the electron and/or spin density distribution. Further work of implementation and computational testing on this important topic remain a challenge in thefield of both spin-free and spin-polarized versions of conceptual DFT. As a result of the complex nature of these quantities, almost no applications of these indices in practical chemical problems have been presented yet. 

For closed-shell molecules (in which all electrons are paired), the spin density is zero everywhere. For open-shell molecules (in which one or more electrons are unpaired), the spin density indicates the distribution of unpaired electrons. Spin density is an obvious indicator of reactivity of radicals (in which there is a single unpaired electron). Bonds will be made to centers for which the spin density is greatest. For example, the spin density isosurface for allyl radical suggests that reaction will occur on one of the terminal carbons and not on the central carbon. 

The summations in Equations (3.3) and (3 4) are over the occupied orbitals with a and (3 spin as appropriate. Thus, cnocc + Pocc equals the total number of electrons in the system. In a closed-shell Hartree-Fock wavefunction the distribution of electron spin is zero everywhere because the electrons are paired. In an open-shell system, however, there is an excess of electron spin, which can be expressed as the spin density, analogous to the electron density The spin density p (r) at a point r is given by ... 

From the above definition of the spin density, it is clear that in regions of space where there is a higher probability of finding an electron of a spin than there is of finding an electron of p spin the spin density is positive. Alternatively, the spin density is negative in regions of space where electrons off spin are most prevalent. The individual densities p" and p are, of course positive everywhere. The spin density is a convenient way of describing the distribution of spins in an open-shell system. 

In natural population analysis (NPA) of open-shell species (see, for example, 1/0-3.10), the natural spin density is evaluated for each NAO, then summed over NAOs on each atom to give and finally over all atoms to give net overall spin density of the species (as measured hy ESR spectroscopy see Chapter 7). This provides a very detailed picture of spin charge and spin polarization distributions throughout the molecule, allowing one to quantify (or rationally design) specific magnetic properties of interest. 

Ru(tap)3] and [Ru(tap)2(phen)] with guanosine-5-monophosphate or N-acetyl-tyrosine gives rise to photo-CIDNP signals [125], that is, non-Boltzmann nuclear spin state distributions that has been detected by NMR spectroscopy as enhanced absorption or emission signals. However, the interpretation framework must be confirmed. In order to validate the experimental predictions. Density Functional Theory (DFT) calculations can be performed. These calculations are based on the determination of the electronic structure of the mono-reduced form of Ru(II) complexes in gas phase and aqueous solution. Recently, some of us showed that the electron spin density and the isotropic Fermi contact contribution to the hyperfine interactions with the nuclei agree remarkably well with the observed photo-CIDNP enhancements [34]. Thus, combined photo-CIDNP experiments and DFT calculations open up new important perspectives for the study of polyazaaromatic Ru(II) complexes photoreactions. 

The electron density increase in bonding areas appears by positive Ap values (blue color in the figures) while antibonding areas show negative Ap values (red color). Finally, for open-shell systems, spin density, defined by subtracting p density to the a density, brings information on the unpaired electron distribution in the system. 

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