Calculating Molecular Properties Using ab initio Quantum Mechanics

7 Calculating Molecular Properties Using ab initio Quantum Mechanics 

The traditional way to provide the nuclear coordinates to a quantum mechanical program is via a Z-matrix, in which the positions of the nuclei are defined in terms of a set of internal coordinates (see Section 1.2). Some programs also accept coordinates in Cartesian format, which can be more convenient for large systems. It can sometimes be important to choose an appropriate set of internal coordinates, especially when locating minima or transition points or when following reaction pathways. This is discussed in more detail in Section 5.7. 

The correction due to electron correlation would be expected to be greater for the unionised state than for the ionised state, as the former has more electrons. Fortunately, therefore, the effect of electron correlation often opposes the effect of the frozen orbitals, resulting in many cases in good agreement between experimentally determined ionisation potentials and calculated values. 

A Hartree-Fock SCF calculation with K basis functions provides K molecular orbitals, but many of these will not be occupied by any electrons they are the virtual spin orbitals. If we were to add an electron to one of these virtual orbitals then this should provide a means of calculating the electron affinity of the system. Electron affinities predicted by Koopman s theorem are always positive when Hartree-Fock calculations are used, because the virtual orbitals always have a positive energy. However, it is observed experimentally that many neutral molecules will accept an electron to form a stable anion and so have negative electron affinities. This can be understood if one realises that electron correlation would be expected to add to the error due to the frozen orbital approximation, rather than to counteract it as for ionisation potentials. 

Some of the most important properties that a quantum mechanical calculation provides are the electric multipole moments of the molecule. The electric multipoles reflect the distribution of charge in a molecule. The simplest electric moment (apart from the total net charge on the molecule) is the dipole. The dipole moment of a distribution of charges located at positions r, is given by ij r/. If there are just two charges +q and -q separated by a distance 

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