Water natural orbitals

Fig. 1, Eight natural orbitals for the water molecule. They were obtained from a complete active spare self-consistent-field calculation using a basis set of the size (OAs2>p2d/ms2p)...

The diagonalization of the one-particle density matrix P on the Cl level yields the natural orbitals (NOs) and the occupation numbers of the molecule. In an RHF-SCF calculation, all occupation numbers are either 0 or 2, which means that an MO is either doubly occupied by 2 electrons or not occupied. If we invoke a Cl calculation, the mixing of configurations results in fractional occupation numbers of the NOs. Still in a normal molecule, such as ethane, water, ammonia, etc., the occupation numbers for the ground state will be close to 0 or 2. The occupation numbers of at least two NOs of excited states usually deviate from the values 0 and 2. In a biradicaloid structure occupation numbers will change and typically two of them will be close to 1. However, this method cannot characterize zwitterions since occupation numbers should be close to 0 and 2, respectively, in this case. The approach by Jug and Poredda yields both zwitterionic and diradical character of species, based on the valence criterion of Gopinathan and Jug. The valence is defined according to equation (5), which can be reformulated as equation (6). 

For nonlinear geometries, the most recent calculations on excited potential energy surfaces of water find the A A state to be repulsive. These calculations, which employed a double zeta basis set augmented by polarization functions and Rydberg orbitals coupled with an iterative natural orbital procedure, also find the state ( A" in Cs symmetry) to be totally repulsive. The repulsive nature of the Cg pathways is in agreement with earlier results obtained by Miller et at the SCF level. The latter authors... 

Table 5 The FCl energy (fpci)- the weight of the Hartree-Fock determinant in the FCI wave function OVhf) and the FC3 natural-orbital occupation numbers for the C2, water molecule in the cc-pVDZ basis for various OH bond distances R (atomic units). The HOH bond angle is fixed at 110.565° and / ref = L84345ao- Orbitals that are doubly occupied at all geometries are shaded dark grey and wbitals with variable occupancies — which participate directly in the OH bond breaking - are shaded light grey...

Table 5.8 The cc-pVDZ natural-orbital occupation numbers of the valence (3,0,1,2) CASSCF wave function for the 2 water molecule at various intemuclear separations R. The HOH bond angle is fixed at llO-SfiS" and = l-84345flo...

Dinitrogen has a dissociation energy of 941 kj/mol (225 kcal/mol) and an ionisation potential of 15.6 eV. Both values indicate that it is difficult to either cleave or oxidize N2. For reduction, electrons must be added to the lowest unoccupied molecular orbital of N2 at —7 eV. This occurs only in the presence of highly electropositive metals such as lithium. However, lithium also reacts with water. Thus, such highly energetic interactions ate unlikely to occur in the aqueous environment of the natural enzymic system. Even so, highly reducing systems have achieved some success in N2 reduction even in aqueous solvents. 

The development of molecular orbital theory (MO theory) in the late 1920s overcame these difficulties. It explains why the electron pair is so important for bond formation and predicts that oxygen is paramagnetic. It accommodates electron-deficient compounds such as the boranes just as naturally as it deals with methane and water. Furthermore, molecular orbital theory can be extended to account for the structures and properties of metals and semiconductors. It can also be used to account for the electronic spectra of molecules, which arise when an electron makes a transition from an occupied molecular orbital to a vacant molecular orbital. 

AEba = —45 kJ mol 1 for the HO + SiH4 reaction and AEba = —43 kJ mol-1 in the reaction of hydrogen atom with water. The repulsion of the electron orbitals of the atoms forming the reaction center AER plays an important role in all the radical abstraction reactions. In the interaction of radicals with molecules the contribution of this repulsion ranges from 25 to 46 kJ mol-1. In reactions of molecules with hydrogen atoms the contribution is naturally smaller, varying from 8 to 16kJ mol-1. 

The quantum mechanical polarizability is calculated using the DFT, with B3P86 (Becke s three-parameter functional [53] with the non-local correlation provided by Perdew [54]). The basis set used for the water molecules is 6-311 + +G. Because of the very diffuse nature of the anion F, the basis set used is the specially designed, and very extensive, fully uncontracted 14s 9p 6d 2f Gaussian-type orbitals [55]. All the QM calculations were made with the Gaussian98 program [56]. 

Two different mechanisms have been proposed for the ROP of (di)lactones depending on the nature of the organometalhc derivatives. Metal halides, oxides, and carboxylates would act as Lewis acid catalysts in an ROP actually initiated with a hydroxyl-containing compound, such as water, alcohol, or co-hydroxy acid the later would result more hkely from the in-situ hydrolysis of the (di)lac-tone [11]. Polymerization is assumed to proceed through an insertion mechanism, the details of which depends on the metal compound (Scheme la). The most frequently encountered Lewis acid catalyst is undoubtedly the stannous 2-ethylhexanoate, currently referred to as stannous octoate (Sn(Oct)2). On the other hand, when metal alkoxides containing free p-, d-, or f- orbitals of a favo-... 

It is never found in its free, pure form in nature. Although less reactive than the metals with fewer electrons in their outer orbits, boron is usually compounded with oxygen and sodium, along with water, and in this compound, it is referred to as borax. It is also found as a hard, brittle, dark-brown substance with a metallic luster, as an amorphous powder, or as shiny-black crystals. 

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