Molecular extended density functions

Key words Hartree-Fock, Density functional theory, Extended Hiickel, Molecular mechanics, Quantum mechanics/molecular mechanics... 

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

Chapter 1 of Volume 15 deals with density functional theory (DFT). As with many quantum mechanical calculations, it is easy to become wrapped up in the theory and lose sight of the chemical phenomena we are trying to explain with the calculations. Equally important to how the numerical calculations are done is how the results can be interpreted to gain chemical insight. Dr. F. Matthias Bickelhaupt and Professor Evert Jan Baerends show how the results of DFT calculations can be analyzed to open up chemical understanding. This chapter illustrates that the plain numbers from a quantum mechanical calculation can be interpreted to be conceptually useful to chemists. In many ways, this chapter evokes memories of the famous way Professor Roald Hoffmann has extracted information from extended Hiickel molecular orbital calculations. 

In order to overcome the limitations of currently available empirical force field param-eterizations, we performed Car-Parrinello (CP) Molecular Dynamic simulations [36]. In the framework of DFT, the Car-Parrinello method is well recognized as a powerful tool to investigate the dynamical behaviour of chemical systems. This method is based on an extended Lagrangian MD scheme, where the potential energy surface is evaluated at the DFT level and both the electronic and nuclear degrees of freedom are propagated as dynamical variables. Moreover, the implementation of such MD scheme with localized basis sets for expanding the electronic wavefunctions has provided the chance to perform effective and reliable simulations of liquid systems with more accurate hybrid density functionals and nonperiodic boundary conditions [37]. Here we present the results of the CPMD/QM/PCM approach for the three nitroxide derivatives sketched above details on computational parameters can be found in specific papers [13]. 

The QM theory of chemical shielding was originally developed many years ago [22,23], but only later have ab initio methods and density functional theories (DFT) been reliably used for the prediction of NMR properties of isolated molecular systems, and finally of solvated systems. The latter step has been achieved by extending the gas-phase theoretical methods to continuum solvation models (see Ref. [11] for a sufficiently updated list of papers). 

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