Assignment of the 6,6'-dioxo-3,3'-biverdazyl ground state by using broken symmetry and spectroscopy oriented configuration interaction techniques.

The singlet-triplet energy differences (DeltaE(ST)) and the Heisenberg-Dirac-van-Vleck exchange parameter (J) of 6,6'-dioxo-3,3'-biverdazyl (BVD) have been studied by hybrid density functional (HDF), broken symmetry (BS), and spectroscopy oriented configuration interaction (SORCI) methods. Energy surface scans as a function of the dihedral angle between the two verdazyl rings (phi(N2C3C3'N2')) have been performed. The BS computations predict an antiferromagnetic ground state. However, the diradical index (R(BS)) ranges from 97.5 to 99.9%, implying that the interactions between the two unpaired electrons are very weak. To calculate J and DeltaE(ST), the multireference character introduced by these weak spin-spin interactions must be taken into account. Consequently, multireference difference dedicated configuration interaction (MRDDCI) methods, as implemented in the SORCI procedure, are used. The in-plane pi (IPpi), out-of-plane pi (OPpi), and sigma configurations are included in the CI expansions in a balanced fashion. The OPpi-OPpi and OPpi-IPpi overlaps are the predominant factors that influence the J and DeltaE(ST) as a function of phi(N2C3C3'N2') and cause them to peak around 40 and 140 degrees. In these regions, the antiferromagnetic interactions are minimal, and the MRDDCI methods predict a triplet ground state. At phi(N2C3C3'N2') = 0, DeltaE(ST)[MRDDCI3(14,12)] is in excellent agreement with that of 1,1',5,5'-tetramethyl-6,6'-dioxo-3,3'-biverdazyl determined experimentally from electron paramagnetic resonance (EPR) spectroscopy and differs only by 2.3%. Furthermore, DeltaE(ST)[MRDDCI3(14,12)] is consistently smaller than J(Y) as the verdazyl rings rotate with respect to each other. This corroborates the theory that the HDF-BS technique increases the singlet-triplet energy gap and favors the singlet state. Because the SORCI method is specifically designed for large molecules, the present very good results open the way for the computation of the magnetic properties of larger molecules by the SORCI method. To the best of our knowledge, this is the first time that DeltaE(ST) has been computed by the MRDDCI3 method by utilizing such a large CI reference space for a molecule of this size.

Calculation of the 4,5-dihydro-1,3,2-dithiazolyl radical g tensor components by the coupled-perturbed Kohn-Sham hybrid density functional and configuration interaction methods: a comparative study.

The g tensor components of the 4,5-dihydro-1,3,2-dithiazolyl (H2DTA•) radical, which is a basic building block for molecular magnets and spintronic devices, is calculated by the coupled-perturbed Kohn-Sham (CPKS) hybrid density functional (HDF) and multireference configuration interaction-sum over states (MRCI-SOS) techniques. In both methods, the diagonalized g tensor principal axes are found to be aligned with the radical's inertial axes. The tensor components are in very good agreement with those determined experimentally by electron paramagnetic resonance (EPR) spectroscopy. The MRCI technique produced g tensor components that are more accurate than those obtained by the CPKS-HDF method. Nonetheless, to get reasonable MRCI results, one must include the in-plane and out-of-plane interactions in an unbiased way. The minimum reference space that satisfies these conditions is generated from a complete active space of nine electrons in six orbitals [CAS(9,6)] and contains a(1), a(2), b(1) and b(2) type orbitals. In addition, the number of roots in the MRCI-SOS g tensor expansion should include all excited states that range from 0 to 56,000 cm(-1). The most accurate results are obtained using an MRCI-SOS/CAS(13,9) calculation. These g tensor components are within the experimental accuracy range of 1000 ppm. The one- and two-electron contributions to the g tensor components are separated and individually analyzed. The very good agreement with experiment opens the door for further accurate calculations of spin Hamiltonian tensors of larger DTA• radicals.

Magneto-structural relationships for radical cation and neutral pyridinophane structures with intrabridgehead nitrogen atoms. An integrated experimental and quantum mechanical study.

An integrated experimental and computational approach was used to compare the properties of representative molecules containing intrabridgehead nitrogen atoms with those of the corresponding radical cations issuing from one-electron oxidation with the aim of unraveling the characteristics of the three-electron sigma-bonds formed in the open-shell species. From a quantitative point of view, last-generation density functional methods coupled with proper basis sets and, when needed, continuum models for describing bulk solvent effects confirm their reliability for the computation of structures and magnetic properties of organic free radicals. From an interpretative point of view, different hybridizations of nitrogen atoms tuned by their chemical environment lead to markedly different magnetic properties that represent reliable and sensitive probes of structural and electronic characteristics.

Effects of restricted rotations and dynamic averaging on the calculated isotropic hyperfine coupling constants of the bis-dimethyl and bis-Di(trifluoromethyl) nitroxide radicals.

The rotational effects of the CH(3) and CF(3) groups on the electronic structure and nuclear hyperfine coupling constants (HFCCs) in dimethylnitroxide (DMNO*) and ditrifluoro-methynitroxide (TFMNO*) are investigated using the UB1LYP hybrid density functional method. The CH(3) and CF(3) HFCCs of both radicals are found to obey the McConnell relation during rotation. The two CH(3) groups of the DMNO* do not gear with each other, but the rotation of the first CH(3) group induces only a small rocking effect ( approximately 7 degrees ) in the second group. However, in TFMNO*, the fluorine atoms from different CF(3) groups are close enough so that the steric repulsion between them causes them to act as two interlocked gears, where one drives the other. Therefore, both CF(3) groups undergo full rotation. To the best of our knowledge, this is only the second example of "gearing" to be studied. Stabilization due to hyperconjugation is also a major factor that affects the magnitudes of the HFCCs of the CF(3) groups during rotational averaging. Stable configurations at specific CF(3) group orientations have a large overlap with the NO pi-electron cloud because the lobes of the hybridized p(sigma)(F(2)), p(sigma)(F(3)), p(sigma)(F(5)), and p(sigma)(F(6)) orbitals along the F-C bonds have cylindrical symmetry and are of the correct phases for hyperconjugation to occur. The calculated TFMNO* C(1)-N and C(2)-N bond orders range from 0.91 to 0.95 as the CF(3) groups are rotated. Therefore, the C-N bonds are essentially single bonds. This, in conjunction with the low rotational energy barrier of approximately 50 cm(-1), explains why the EPR intensities of the (19)F hyperfine splittings, in the range of 163-297 K, are characteristic of six equivalent rapidly rotating fluorine atoms. The TFMNO* out-of-plane NO vibrations induce additional s character at the (14)N nucleus. This increases the magnitude of the (14)N HFCC and decreases the (19)F HFCCs. As the temperature increases and because of mixing of the first excited out-of-plane vibrational state, the NO vibrational amplitudes also increase. This leads to an increased (14)N HFCC and decreased (19)F HFCCs, which is in agreement with experiment.

Role of the geometry, restricted rotations and solvents on the computed 2,2'-diphenyl-1-picrylhydrazyl hyperfine tensors.

The nuclear hyperfine tensor (A) components of the 2,2'-diphenyl-1-picrylhydrazyl neutral radical are computed using the UB1LYP hybrid density functional method. Solvent interactions via hydrogen bonding are found to play a crucial role in the position of the two phenyl rings relative to the picryl moiety. Under these conditions, the calculated isotropic hyperfine tensor components of the N 1 and N 2 hydrazyl backbone are within approximately 1.3 Gauss (G) of the experimental values determined by EPR and ENDOR spectroscopy. Just as important are the effects of restricted rotations of the phenyl rings on these tensors. Rotational averaging using a Maxwell-Boltzmann type distribution improves the agreement between theory and experiment to less than 1.0 G. In addition, rotational averaging of the twelve isotropic proton coupling constants has also been performed. They come within 0.3 G of the experimental values. Thus, for the first time, all the nuclear hyperfine tensor components of this large class of molecules are accurately calculated without resorting to post Hartree-Fock techniques.

Evolution of the pseudo-1,3-dipolar cycloaddition chemistry of SNSMF6 (M = As, Sb) leading to 2,5-dihydroxybenzo-1,3,2-dithiazolylium and 2,7-dicarbonylnaphtha-1,3,2-dithiazolylium salts and their corresponding radicals.

We report the unprecedented formation of a benzo-fused 1,3,2-dithiazolylium [AsF6-] salt by a one step, quantitative, cycloaddition of SNSAsF6 with 1,4-benzoquinone. In contrast, the reaction of SNSSbF6 with 1,4-naphthaquinone results in 2,7-dicarbonylnaphtha-1,3,2-dithiazolylium [SbF6-]. Both were reduced to the corresponding 7pi radicals.

General expressions for the coupling coefficient, quality and filling factors for a cavity with an insert using energy coupled mode theory.

A cavity (CV) with a dielectric resonator (DR) insert forms an excellent probe for the use in electron paramagnetic resonance (EPR) spectrometers. The probe's coupling coefficient, κ, the quality factor, Q, and the filling factor, η are vital in assessing the EPR spectrometer's performance. Coupled mode theory (CMT) is used to derive general expressions for these parameters. For large permittivity the dominating factor in κ is the ratio of the DR and CV cross sectional areas rather than the dielectric constant. Thus in some cases, resonators with low dielectric constant can couple much stronger with the cavity than do resonators with a high dielectric constant. When the DR and CV frequencies are degenerate, the coupled η is the average of the two uncoupled ones. In practical EPR probes the coupled η is approximately half of that of the DR. The Q of the coupled system generally depends on the eigenvectors, uncoupled frequencies (ω1,ω2) and the individual quality factors (Q1,Q2). It is calculated for different probe configurations and found to agree with the corresponding HFSS® simulations. Provided there is a large difference between the Q1, Q2 pair and the frequencies of DR and CV are degenerate, Q is approximately equal to double the minimum of Q1 and Q2. In general, the signal enhancement ratio, Iwithinsert/Iempty, is obtained from Q and η. For low loss DRs it only depends on η1/η2. However, when the DR has a low Q, the uncoupled Qs are also needed. In EPR spectroscopy it is desirable to excite only a single mode. The separation between the modes, Φ, is calculated as a function of κ and Q. It is found to be significantly greater than five times the average bandwidth. Thus for practical probes, it is possible to excite one of the coupled modes without exciting the other. The CMT expressions derived in this article are quite general and are in excellent agreement with the lumped circuit approach and finite numerical simulations. Hence they can also be applied to a loop-gap resonator in a cavity. For the design effective EPR probes, one needs to consider the κ, Q and η parameters.

Coupled modes, frequencies and fields of a dielectric resonator and a cavity using coupled mode theory.

Probes consisting of a dielectric resonator (DR) inserted in a cavity are important integral components of electron paramagnetic resonance (EPR) spectrometers because of their high signal-to-noise ratio. This article studies the behavior of this system, based on the coupling between its dielectric and cavity modes. Coupled-mode theory (CMT) is used to determine the frequencies and electromagnetic fields of this coupled system. General expressions for the frequencies and field distributions are derived for both the resulting symmetric and anti-symmetric modes. These expressions are applicable to a wide range of frequencies (from MHz to THz). The coupling of cavities and DRs of various sizes and their resonant frequencies are studied in detail. Since the DR is situated within the cavity then the coupling between them is strong. In some cases the coupling coefficient, κ, is found to be as high as 0.4 even though the frequency difference between the uncoupled modes is large. This is directly attributed to the strong overlap between the fields of the uncoupled DR and cavity modes. In most cases, this improves the signal to noise ratio of the spectrometer. When the DR and the cavity have the same frequency, the coupled electromagnetic fields are found to contain equal contributions from the fields of the two uncoupled modes. This situation is ideal for the excitation of the probe through an iris on the cavity wall. To verify and validate the results, finite element simulations are carried out. This is achieved by simulating the coupling between a cylindrical cavity's TE011 and the dielectric insert's TE01δ modes. Coupling between the modes of higher order is also investigated and discussed. Based on CMT, closed form expressions for the fields of the coupled system are proposed. These expressions are crucial in the analysis of the probe's performance.

Optimal dielectric and cavity configurations for improving the efficiency of electron paramagnetic resonance probes.

An electron paramagnetic resonance (EPR) spectrometer's lambda efficiency parameter (Λ) is one of the most important parameters that govern its sensitivity. It is studied for an EPR probe consisting of a dielectric resonator (DR) in a cavity (CV). Expressions for Λ are derived in terms of the probe's individual DR and CV components, Λ1 and Λ2 respectively. Two important cases are considered. In the first, a probe consisting of a CV is improved by incorporating a DR. The sensitivity enhancement depends on the relative rather than the absolute values of the individual components. This renders the analysis general. The optimal configuration occurs when the CV and DR modes are nearly degenerate. This configuration guarantees that the probe can be easily coupled to the microwave bridge while maintaining a large Λ. It is shown that for a lossy CV with a small quality factor Q2, one chooses a DR that has the highest filling factor, η1, regardless of its Λ1 and Q1. On the other hand, if the CV has a large Q2, the optimum DR is the one which has the highest Λ1. This is regardless of its η1 and relative dielectric constant, ɛr. When the quality factors of both the CV and DR are comparable, the lambda efficiency is reduced by a factor of 2. Thus the signal intensity for an unsaturated sample is cut in half. The second case is the design of an optimum shield to house a DR. Besides preventing radiation leakage, it is shown that for a high loss DR, the shield can actually boost Λ above the DR value. This can also be very helpful for relatively low efficiency dielectrics as well as lossy samples, such as polar liquids.

Analysis of two stacked cylindrical dielectric resonators in a TE102 microwave cavity for magnetic resonance spectroscopy.

The frequency, field distributions and filling factors of a DR/TE102 probe, consisting of two cylindrical dielectric resonators (DR1 and DR2) in a rectangular TE102 cavity, are simulated and analyzed by finite element methods. The TE(+++) mode formed by the in-phase coupling of the TE01(δ)(DR1), TE01(δ)(DR2) and TE102 basic modes, is the most appropriate mode for X-band EPR experiments. The corresponding simulated B(+++) fields of the TE(+++) mode have significant amplitudes at DR1, DR2 and the cavity's iris resulting in efficient coupling between the DR/TE102 probe and the microwave bridge. At the experimental configuration, B(+++) in the vicinity of DR2 is much larger than that around DR1 indicating that DR1 mainly acts as a frequency tuner. In contrast to a simple microwave shield, the resonant cavity is an essential component of the probe that affects its frequency. The two dielectric resonators are always coupled and this is enhanced by the cavity. When DR1 and DR2 are close to the cavity walls, the TE(+++) frequency and B(+++) distribution are very similar to that of the empty TE102 cavity. When all the experimental details are taken into account, the agreement between the experimental and simulated TE(+++) frequencies is excellent. This confirms that the resonating mode of the spectrometer's DR/TE102 probe is the TE(+++) mode. Additional proof is obtained from B1(x), which is the calculated maximum x component of B(+++). It is predominantly due to DR2 and is approximately 4.4 G. The B1(x) maximum value of the DR/TE102 probe is found to be slightly larger than that for a single resonator in a cavity because DR1 further concentrates the cavity's magnetic field along its x axis. Even though DR1 slightly enhances the performance of the DR/TE102 probe its main benefit is to act as a frequency tuner. A waveguide iris can be used to over-couple the DR/TE102 probe and lower its Q to ≈150. Under these conditions, the probe has a short dead time and a large bandwidth. The DR/TE102 probe's calculated conversion factor is approximately three times that of a regular cavity making it a good candidate for pulsed EPR experiments.

Accurate calculation of the phenyl radical's magnetic inequivalency, relative orientations of its spin hamiltonian tensors, and its electronic spectrum.

The phenyl radical's electronic structure, magnetic inequivalency, spin Hamiltonian tensor components, and the relative orientation of their principal axes are computed by Neese's coupled-perturbed Kohn-Sham hybrid density functional (CPKS-HDF) technique in a moderate amount of time without resorting to expensive post-Hartree-Fock techniques. The g tensor component values are in excellent agreement with those determined experimentally and differ by less than 370 ppm. The computed hydrogen nuclear hyperfine tensors, A(1H), are also found to be in very good agreement with their experimental counterparts. The correlation of the radical's electronic structure with its g and A numerical values corroborates that it has a 2A(1) ground state. In accordance with our previous studies on the equivalency of planar radicals that possess C(2v) symmetry, the in-plane g and A(1H) principal axes should not be parallel to one another. Consequently, the spatially equivalent ortho (1H(2), 1H(6)) and meta (1H(3), 1H(5)) proton pairs should be magnetically inequivalent. This was confirmed in both the present computations and the simulation of the EPR solid-state spectrum. To the best of our knowledge, this is the first aromatic in-plane sigma-type radical whose magnetic inequivalency is studied both computationally and experimentally. To properly interpret the radical's electronic excitation spectra, the spectroscopy-oriented dedicated difference configuration interaction (SORCI) procedure was employed. Aside from a slight overestimation, the method seems to be capable of reproducing the C(6)H(5)* electronic vertical excitation energies in the range of 0-50,000 cm(-1). These vertical excitations, in conjunction with the corresponding orbit and spin orbit matrix elements, were also used to compute the g tensor components, employing the sum-over-states technique. Due to the limited number of computed roots and excited states, the results were marginally inferior to those obtained using the CPKS-HDF method.

Toward a more general synthetic route to paramagnetic solids containing RCNSSS*+ radical cations. A structure-property correlation for RCNSSS*+ (R = F5C2, Cl3C).

Reaction of Cl3CN and F5C2CN with a 1:1 mixture of S4(AsF6)2 and S8(AsF6)2 affords the paramagnetic solids Cl3CNSSSAsF6 (1CCl3AsF6) and F5C2CNSSSAsF6 (1C2F5AsF6). Isotropic electron paramagnetic resonance spectra of 1CCl3AsF6 and 1C2F5AsF6 in SO2 consist of a single line with g = 2.01675 and 2.01580, respectively. The structure of 1CCl3AsF6 contains chains of radical cations with relatively close interchain interactions. In contrast, chains are isolated in 1C2F5AsF6. The magnetic behavior of both compounds was interpreted as that of 1D Heisenberg antiferromagnetic chains (1CCl3AsF6, J = -34 cm(-1), theta = -9 cm(-1), TIP = 0.00082, rho = 0.012; 1C2F5AsF6, J = -21 cm(-1), theta = -4.2 cm(-1), TIP = 0.00092, rho = 0.065). Density functional theory calculated and experimental magnetic coupling constants were in good agreement. The correlation between intermolecular S...S contacts and the strength of magnetic couplings was established.