H2O: geometry

Table 11.1. H2O geometry as a function of basis set at the HF level of theory ...

Ion Ref. Basis set1) Uncontracted Contracted H2O geometry2) unperturbed Interaction energy2) with rigid H2O -AE Complex geometry2) with H2O geometry relaxed Optimized2) -AE... 

Table 11.4 H2O geometry as a function of basis set at the MP2 level of theory including all electrons in the correlation-----------------------...

Structural parameters derived for six cases A...D use the six nondeuterated isotopic species and E...F use all isotopic species. The constraints are as follows the H2O geometry is fixed for all cases as is CO2 except for case C. (A) Planar (B) planar except H20(456) rotated about C2V axis by an amount Ti (C) same as B but CO2 geometry varied (bent) (D) planar except H(5) and H(8) are symmetrically out of plane by 7 rotation about two OH bonds (E) the same as D with all isotopes (scheme I, see original paper) and (F) the same as E (scheme II used). 

For an application to the vibrational spectroscopy analysis, we took an H2O molecule in liquid water [42]. Initially, the structure of the H2O molecule in water was optimized by the standard FEG method for the H2O geometry to satisfy the zero-FEG condition (cf. Eq. (8.19)) using the FE-Hessian matrix (cf. Eq. 8.10). Then, to estimate INM-Hessian matrices for the vibrational frequency analysis (VFA) at the optimized stmcture q on FES, we executed ab initio QM/MM-MD simulation to apply the dual VFA (cf. Sect. 8.2.2.3) approach to the present H2O system. 

Uranium hexafluoride [7783-81-5], UF, is an extremely corrosive, colorless, crystalline soHd, which sublimes with ease at room temperature and atmospheric pressure. The complex can be obtained by multiple routes, ie, fluorination of UF [10049-14-6] with F2, oxidation of UF with O2, or fluorination of UO [1344-58-7] by F2. The hexafluoride is monomeric in nature having an octahedral geometry. UF is soluble in H2O, CCl and other chlorinated hydrocarbons, is insoluble in CS2, and decomposes in alcohols and ethers. The importance of UF in isotopic enrichment and the subsequent apphcations of uranium metal cannot be overstated. The U.S. government has approximately 500,000 t of UF stockpiled for enrichment or quick conversion into nuclear weapons had the need arisen (57). With the change in pohtical tides and the downsizing of the nation s nuclear arsenal, debates over releasing the stockpiles for use in the production of fuel for civiUan nuclear reactors continue. 

Chlorides. The oHve-green trichloride [10025-93-1], UCl, has been synthesized by chlorination of UH [13598-56-6] with HCl. This reaction is driven by the formation of gaseous H2 as a reaction by-product. The stmcture of the trichloride has been deterrnined and the central uranium atom possesses a riine-coordinate tricapped trigonal prismatic coordination geometry. The solubiUty properties of UCl are as follows soluble in H2O, methanol, glacial acetic acid insoluble in ethers. 

Uranium tetrachloride [10026-10-5], UCl, has been prepared by several methods. The first method, which is probably the best, involves the reduction/chlorination of UO [1344-58-7] with boiling hexachloropropene. The second consists of heating UO2 [1344-57-6] under flowing CCl or SOCI2. The stmcture of the dark green tetrachloride is identical to that of Th, Pa, and Np, which all show a dodecahedral geometry of the chlorine atoms about a central actinide metal atom. The tetrachloride is soluble in H2O, alcohol, and acetic acid, but insoluble in ether, and chloroform. Industrially the tetrachloride has been used as a charge for calutrons. 

Bromides and Iodides. The red-brown tribromide, UBr [13470-19-4], and the black tniodide, Ul [13775-18-3], may both be prepared by direct interaction of the elements, ie, uranium metal with X2 (X = Br, I). The tribromide has also been prepared by interaction of UH and HBr, producing H2 as a reaction product. The tribromide and tniodide complexes are both polymeric soflds with a local bicapped trigonal prismatic coordination geometry. The tribromide is soluble in H2O and decomposes in alcohols. 

These features are illustrated for H2O in Figure 2.5, where the exact form is taken firom a parametric fit to a large number of spectroscopic data. The simple harmonic approximation (P2) is seen to be accurate to about 20° from the equilibrium geometry and the cubic approximation (P3) up to 40°. Enforcing the cubic polynomial to have a zero derivative at 180° (P3 ) gives a qualitative correct behaviour, but reduces the overall fit, although it still is better than a simple harmonic approximation. 

In this chapter we will illustrate some of the methods described in the previous sections. It is of course impossible to cover all types of bonding and geometries, but for highlighting the features we will look at the H2O molecule. This is small enough that we can employ the full spectrum of methods and basis sets. 

The experimental geometry for H2O has a bond length of 0.9578 A and an angle of 104.48°. Let us investigate how the calculated geometry change as a function of theoretical sophistication. 

Here /, are the three moments of inertia. The symmetry index a is the order of the rotational subgroup in the molecular point group (i.e. the number of proper symmetry operations), for H2O it is 2, for NH3 it is 3, for benzene it is 12 etc. The rotational partition function requires only information about the atomic masses and positions (eq. (12.14)), i.e. the molecular geometry. 

The similar species Ir(PMe3)4 likewise shows tetrahedral distortion from square planar geometry (P-Ir—P 152.6-158.9°). It undergoes some remarkable oxidative addition reactions with species like H2O and H2S (Figure 2.72). 

Figure 18. Contour plots of the potential energy surfaces of the first three electronic states of H2O. The polar plots depict the movement of one H atom around OH with an OH bond length fixed at 1.07 A. Energies are in electron volts relative to the ground electronic state. The X and B states are degenerate at the conical intersection (denoted by (g)) in the (a) H—OH geometry and (b) H—HO geometry. Reprinted fix)m [75] with permission from the American Association for the Advancement of Science.

---