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Radical ions with nearly degenerate ground state: Correlation between the rate of spin-lattice relaxation and the structure of adiabatic potential energy surface
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Image of FIG. 1.
FIG. 1.

Pseudorotation scheme, SOMO images and designations of stationary structures for cyclohexane radical cation (to the left). Pseudorotation coordinate is shown at the center of the scheme. The plot to the right shows the PES cross-sections along the pseudorotation trough (B3LYP). Since the trough has a cyclic shape, it is convenient to use the angle ϕ (0 < ϕ < 360°) as the pseudorotation coordinate.

Image of FIG. 2.
FIG. 2.

Pseudorotation scheme and SOMOs of stationary structures for staggered conformation of ethylcyclohexane radical cation. The ethyl fragment is attached to the cyclohexane ring at atom 1 as labeled in Fig. 1.

Image of FIG. 3.
FIG. 3.

The PES sections along the pseudorotation trough (B3LYP) for the cycloalkane RCs studied. Here the angle ϕ is the pseudorotation coordinate, ϕ = 0 corresponds to A(0) structures. The dashed line added to the plot e) denotes BHHLYP calculations for Pr-cH+•. Note that the plots show the different vertical scale.

Image of FIG. 4.
FIG. 4.

TR MFE curves for 0.03 M solutions of cH (1), t-DEC (2), Et-cH (3), 1,4-Me2-cH (4), nPr-cH (5), cyclohexane-d 12 (6), Me-cH (7), 1,1-Me2-cH (8), iPr-cH (9), c-DEC (10), and tBu-cH (11) in n-hexane with the addition of 3 μM pTP at 293 K (B = 1 T).

Image of FIG. 5.
FIG. 5.

Correlation between spin-lattice relaxation time, T 1, of cycloalkane RCs (Table III) and the pseudorotation barrier height E B according to unrestricted B3LYP calculations (Table I). A smooth line is constructed for convenience of perception. The cross indicates probable position of the point for nPr-cH (see the text).

Image of FIG. 6.
FIG. 6.

The dependence of the spin-lattice relaxation time on magnetic induction squared for cH+• (1) and Et-cH+• (2) in n-hexane solution at 293 K. Straight lines show the approximation by means of Eq. (3) at τ c ≈ 0.16 ps, Δ ≈ 106 mT (1), and τ c ≈ 0.3 ps, Δ ≈ 50 mT (2).

Image of FIG. 7.
FIG. 7.

The rate of spin-lattice relaxation in cH+• (1), t-DEC+• (2), Et-cH+• (3), 1,4-Me2-cH+• (4), nPr-cH+• (5), Me-cH+• (6) at B = 1 T for various temperatures. Straight lines show the exponential approximation by A·exp(–E a /RT) functions. The values of A and E a are listed in Table III.

Image of FIG. 8.
FIG. 8.

Correlation between the effective activation energy of the spin-lattice relaxation rate and the pseudorotation barrier height at PES for cycloalkane RCs, with T 1 < 100 ns (except for nPr-cH). Straight line is given to guide eyes.

Image of FIG. 9.
FIG. 9.

A scheme of the crossing of the Zeeman sublevels of vibronic states. The dashed line indicates the feasible way of system evolution with electron spin flip. δ is the characteristic value of the splitting of vibronic states due to the interaction with the solvent.


Generic image for table
Table I.

Relative energies (kcal/mol) for the stationary PES structures of alkyl-cyclohexane radical cations, R-cH+•, and total energies for the global minima (E min, a.u.).a

Generic image for table
Table II.

Experimental (matrix isolation) and calculated HFC constantsa a H for alkyl-cyclohexane radical cations, R-cH+•.

Generic image for table
Table III.

Spin-lattice relaxation time T 1 at B= 1 T (293 K, values are averaged over 2–4 experiments) and the parameters of the approximation of the temperature dependences of cycloalkane RC relaxation rate.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Radical ions with nearly degenerate ground state: Correlation between the rate of spin-lattice relaxation and the structure of adiabatic potential energy surface