Water localized orbitals

There is always a transformation between symmetry-adapted and localized orbitals that can be quite complex. A simple example would be for the bonding orbitals of the water molecule. As shown in Figure 14.1, localized orbitals can... 

Localized orbitals, see bond orbitals and group orbitals Lone pairs, 9, 39, 42, 49 cyclopropanone, 37 methyl fluoride, 42 pyrazine, 28 water, 42... 

A new reservoir of comets may have formed at around 5 AU in a local orbit around Jupiter or at least perturbed by its gravitational attraction. A comet close to Jupiter would simply have been captured, delivering its chemical payload to the ever-increasing gas giant. Some comets would merely have been deflected towards the inner terrestrial planets, delivering a similar payload of water and processed molecules. Cometary impacts such as the spectacular collision of the comet Shoemaker-Levy 9 with Jupiter would have been common in the early formation phase of the solar system but with a much greater collision rate. Calculations of the expected collision rate between the Earth and potential small comets deflected from the snow line may have been sufficient to provide the Earth with its entire... 

In this study, we have chosen the supermolecule approach and have used the semi-empirical quantum mechanical method called PCILO (Perturbative Configuration Interaction using Localized Orbitals) (16) to calculate intermolecular interactions. This method has recently been used successfully to calculate the intermolecular energies and geometries of hydrogen-bonded dimers of hydrocarbons and water (17,18). H-bonded complexes are particularly well characterized by this method (19). 

Localized orbitals have also been used as a tool to extract the infrared spectrum of a solute in solution [194,195,202] or to decompose the IR spetrum in intramolecular and intermolecular contributions [202]. Model electrostatics of solute molecules was also based on localized orbitals [242, 243], not only at the dipolar level [244]. As an extension we also defined molecular states from localized orbitals to study the electronic states of liquid water [245], or of solvated ions [47]. It is also possible to perform CP-MD propagating the Wannier orbitals, by constraining the Kohn-Sham orbitals to stay in a Wannier gauge [246]. 

The water molecules forming the hydration shell can be divided into clusters by inspection of their geometrical positions. The clusters are chosen in such a way that the intracluster interaction should be larger than the intercluster ones. As a next step ab initio calculations have to be performed for each water cluster. The resulting canonical Hartree-Fock orbitals are transformed to localized ones. To find a suitable representation of the electron distribution of the teg clusters by point charges first ghe electrostatic potential each localized orbital of the Nth... 

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

---