Theoretic-numerical approach

XIV. A Theoretic-Numeric Approach to Calculate the Electronic Non-Adiabatic Coupling Terms... 

XrV. A THEORETIC-NUMERIC APPROACH TO CALCULATE THE ELECTRONIC NON-ADIABATIC COUPLING TERMS... 

In this chapter, we discuss three theoretical-numerical approaches for studying heat flow in molecular systems. The different methods were developed in order to focus on various aspects of heat flow at the nanoscale, and are applicable at different parameters regimes quantum, semiclassical and classical. Ultimately, developing a unified approach is of great interest [16,17]. 

Steric descriptors and/or -> size descriptors representing the volume of a molecule. The volume of a molecule can be derived from experimental observation such as the volume of the unit cell in crystals or the molar volume of a solution or from theoretical calculations. In fact, analytical and numerical approaches have been proposed for the calculation of molecular volume where the measure depends directly on the definition of - molecular surface-, -> van der Waals volume and -> solvent-excluded volume are two volume descriptors based on van der Waals surface and solvent-accessible surface, respectively. 

The first theoretical QSAR/QSPR approaches date back to the endofl940s and are those relating biological activities and physico-chemical properties to theoretical numerical indices derived from the molecular stmcture. 

Many theoretical models have been developed to describe the electrical polarizability of polyelectrolytes [2-4,13-40], The problem is, however, extremely complex and difficult, even if simple models are assumed for the geometry of the polyions [37]. This is because many fields are involved concentrations of small ions, the electrical potential, and the solvent velocity, to be determined as functions of space and time, which are coupled with each other through essentially nonlinear equations. Our numerical approach, however, need not introduce, as in most of the theories, somewhat ad hoc approximations such that counterions are classified into free and bound ions, only the latter contributing to the polarizability, nor neglect interactions between counterions. 

The development of somatic gene therapy is still in its infancy. A number of theoretical risks of gene therapy have been listed, and numerous approaches and gene transfer methods are being developed in the clinic, even more in preclinical experiments. 

The LICS, produced by an idealized Continuous-Wave (CW) laser (steady amplitude and single-frequency laser), can differ substantially from the structure produced by a pulsed laser, since the AC Stark shifts produce time-dependent detunings relative to one- and two-photon resonance. The time-dependent pulse and frequency effects in population trapping in LICS have received attention in theoretical works [93]. Using numerical approaches, as well as approximate analytical solution, it was shown that the trapped population in realistic atomic systems can be sufficiently decreased, to the point when no population remains in the system, by the increase in laser energies. Furthermore, the use of properly chirped laser pulses not only helps to increase the trapped population but also makes the system more stable against increases in the pulse energy. 

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