Nuclear relaxation energy

Limited experimental data is available for the EAs of the DNA bases. The trend in the "estimated EAs" (obtained by correcting the HF Koopmanns EA by the calculated nuclear relaxation energy) is T > C > A > G, which is in agreement with early studies on DNA predicting that the thymine anion is the major reduction product upon irradiation [72]. Alternatively, the trend predicted through examination of the adiabatic EAs calculated with DFT (C > T > G > A) supports experimental data predicting cytosine to be the major reduction site in... 

In the presence of a field H, rotating at the precessional frequency the nuclear system can absorb energy, following which nuclear relaxation occurs. Thus, the equation of motion must include both the precessional and the relaxation contributions ... 

The static ZFS, which is present in low-symmetry complexes, affects mainly the energy level fine structure. It is described by axial and rhombic components, D and E. Its effects on nuclear relaxation depend on two angles, 9 and cj), defining the position of the nucleus with respect to the ZFS principal tensor axes. Figure 23 shows the dispersion profiles for different values of S, D, E and 9. Many such examples are reported in Chapter 2. 

Relaxation can be described in terms of the magnetization vector components. At resonance, the equilibrium magnetization M0 parallel to B0 decreases to Mz, due to the transitions between the nuclear magnetic energy levels caused by the alternating field B,. Following resonance, the equilibrium of the nuclear spins with their lattice and with each other is restored by relaxation. 

If the interaction energy fluctuates, then nuclear relaxation enhancements occur. Such relaxation enhancements are proportional to the average squared interaction energy... 

The movements capable of relaxing the nuclear spin that are of interest here are related to the presence of unpaired electrons, as has been discussed in Section 3.1. They are electron spin relaxation, molecular rotation, and chemical exchange. These correlation times are indicated as rs (electronic relaxation correlation time), xr (rotational correlation time), and xm (exchange correlation time). All of them can modulate the dipolar coupling energy and therefore can cause nuclear relaxation. Each of them contributes to the decay of the correlation function. If these movements are independent of one another, then the correlation function decays according to the product... 

In practice nuclear spin-lattice relaxation is always within the Redfield limit, i.e. the interaction energy with the lattice is always much smaller than rc-1. This is true even with paramagnetic systems, where the nuclear spin-lattice interaction eneigy is often much larger than usual. On the other hand, it is not obvious that electrons are always in the Redfield limit. When electrons are outside the Redfield limit, although nuclear relaxation is in the Redfield limit, it is not easy... 

In the limit of static fields, the nuclear relaxation contribution (from now on just vibrational ) to the polarizabilities can be computed in the double harmonic approximation, i.e. assuming that the expansions of both the potential energy and the electronic properties with respect to the normal coordinates can be limited to the quadratic and the linear terms, respectively (i.e. assuming both mechanical and electric harmonicity). 

Figure 2.2. Scheme of nuclear potentials in the ground electronic state E°(Q) and the excited electronic state E (Q). In the excited state, the frequency changes (i20->S2r) and the equilibrium point is shifted. The classical relaxation energy to the new nuclear configuration in the excited state is the Franck-Condon energy Efc and characterizes the linear exciton-vibration coupling. 

We saw in Chapter 7 that the resonance frequency of a quadrupolar nucleus is dependent on the orientation of the molecule in which it resides. Molecular tumbling now causes fluctuating electric fields, which induce transitions among the nuclear quadrupole energy levels. The resulting nuclear relaxation is observed in the NMR just as though the relaxation had occurred by a magnetic mechanism. 

Spin relaxation in a nucleus is induced by random fluctuations of local magnetic fields. These result from time-dependent modulation of the coupling energy of the resonating nuclear spin with nearby nuclear spins, electron spins, quadrupole moments, etc. Any time-dependent phenomenon able to modulate these couplings can contribute to nuclear relaxation. The distribution of the frequencies contained in these time-dependent phenomena is described by a correlation function, characterized by a parameter Tc, the correlation time. Its reciprocal can be considered as the maximum frequency produced by the fluctuations in the vicinity of the nuclear spin. If more than one process modulates the coupling between the nuclear spin and its surroundings, the reciprocal of the effective correlation time is the sum of the reciprocals of the various contributions... 

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