Physics And Chemistry Basis Of Biotechnology - De Cuyper - tiera.ru

Radiation-induced bioradicals: technologies and research
determined with a (near) experimental accuracy, erroneous results can be produced in
those cases where the incorporation of electron correlation, the instantaneous
interaction of the electrons, is quintessential. This is particularly true for the calculation
of magnetic properties of radicals such as hyperfine coupling constants. The electron
correlation can be accounted for by so-called post-Hartree-Fock approaches that are
however characterised by a dramatic increase of the computational work involved.
Consequently, their use is limited to small molecular systems, even with the formidable
computer power currently available. Therefore, resort has to be sought to other methods
if one is interested in routinely calculating properties to a high degree of accuracy in
systems that are of true interest to a biologist or chemist such as radicals derived from
biomolecules.
Density functional calculations have proved valuable in this respect over the last
few years. The basis for density functional theory (DFT) is the proof by Hohenberg and
Kohn (1964) that the ground state electronic energy of an atomic or molecular species
is completely determined by the electron density r. This means that there exists a oneto-one
correspondence between the electron density of the system and the energy. The
problem is that although it has been proven that each different density yields a different
ground-state energy, the functional 2 connecting these two quantities is unknown. The
goals of DFT methods is to design functionals that connect the electron density with the
energy.
In analogy with the wave function approach, the energy functional can be divided
into three parts, kinetic energy, T[ρ ], attraction between the nuclei and electrons,
E ne[ρ], and electron-electron repulsion, E ee[r]. The E ee[ρ] term may be hrther divided
into a Coulomb and exchange part, J [r] and K[r], respectively. The exchange energy is
a correction that should be made to the Coulomb energy to take into account the effect
of spin correlation . 3 Thus the energy functional is written as
E[r] = T[r] +Ene[r]+ J[r] +K[r]*
The key for the practical use of DFT methods in computational chemistry lies in the
Kohn-Sham theory. Central in this theory is the calculation of the kinetic energy Ts[r]
assuming that the electrons are not interacting (in the same way as non-interacting
electrons are described in wave mechanics by the HF method). In reality, the electrons
are interacting, so the Kohn-Sham kinetic energy does not provide the total kinetic
energy. However, the difference between the exact kinetic energy and that calculated
2 A functional is a prescription for producing a number from a function which in turn
depends on variables. The electron density p is a function (of spatial and spin coordinates)
whereas an energy dependirig on the density is a functional, denoted with
brackets, E[ρ].
3 Spin correlation refers to the quantum mechanical effect that gives electrons of
opposite spin an increased probability of being found near to each other, whereas those
of the same spin are preferentially kept apart.
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