Fig 1.
UHF/6-31G** [(H2O)2-5] and UHF/6-31G*[(H2O)6] optimized geometries of the water cluster isomers selected for this study.
When two or more isomers of a given water cluster are considered, they are depicted/listed in the order of increasing energy; the first depicted/listed isomer is the lowest-energy isomer in its whole known series with the present theory [e.g. 6a is the lowest-energy (H2O)6 structure out of 12 known (H2O)6 isomers[34]]. 6a and 6b are the prism and cage isomers of (H2O)6.
Fig 2.
H+ + (H2O)1-6 initial conditions.
A given water cluster (not depicted for clarity’s sake) is placed at rest with its center of mass at the origin of the coordinate axes and with its major (pseudo-)plane of symmetry with maximum coincidence with the x-y plane. The H+ projectile is initially prepared with position and momentum and
and with impact parameter b (Panel I). Different projectile-target relative orientations Ω = (α, β, γ) are generated by rotating
and
through the extrinsic Euler angles γ (Panel I), β (Panel II), and α (Panel III) around the space-fixed z, y, and z axes, respectively. The definite initial conditions of the H+ projectile to start the simulations,
and
, are shown in Panel IV (cf. text for more details).
Table 1.
Grids for the projectile impact parameter b for the SLEND simulations.
[b]1 = grids for short-time simulations to calculate 1-electron-transfer total integral cross sections; [b]2 = grids for long-time simulations to predict fragmentation processes. Grid data are given as [bMin, bMax, Δb] ⇒ b = bMin, bMin + Δb, bMin + 2Δb … bMax. All units are in a.u.
Table 2.
Water-to-proton 1-electron-transfer total integral cross sections (ICSs) σ1−ET for H+ + H2O at ELab = 100 keV from experiments, SLEND theory and alternative theories: basis generator method (BGM) and continuum distorted wave-eikonal initial state (CDW-EIS) approximation.
Fig 3.
SLEND/6-31G* and /6-31G** target-to-proton total 1-ET ICSs σ1−ET for H+ + (H2O)1-6 vs. the water cluster size n.
Current data are in comparison with available experimental and theoretical σ1−ET for n = 1 [Exp.: A [70], B [71], C [72] and D [73], Theory A: basis generator method (BGM) [23], Theory B: continuum distorted wave-eikonal initial state (CDW-EIS) approximation [22]]. SLEND values are fit to the scaling formula σ1−ET (x) = cn2/3. The error of the SLEND ICSs is ± 0.005 Ä. The errors from the Theory A and B results compared herein were not reported.
Table 3.
SLEND cluster-to-proton 1-electron-transfer integral cross sections σ1−ET for H+ + (H2O)n, n = 2–6, at ELab = 100 keV.
Cf. Fig 1 for the structures of the water cluster isomers. The error of the SLEND integral cross sections is ± 0.005 Ä.
Fig 4.
Orientation-averaged target-to-proton 1-ET probabilities at the SLEND/6-31G* (left panel) and /6-31G** (right panel) levels vs. the impact parameter b for the investigated (H2O)1-6.
Water cluster isomers are denoted with the number code in Fig 1 (1, 2 … 6b, 6c).
Fig 5.
Orientation-averaged impact-parameter-weighted target-to-proton 1-ET probabilities at the SLEND/6-31G* (left panel) and /6-31G** (right panel) levels vs. b for the investigated (H2O)1-6.
Water cluster isomers are denoted with the number code in Fig 1 (1, 2 … 6b, 6c).
Fig 6.
Example of a SLEND/6-31G* simulation of H+ + H2O leading H2O to fragment into H2 and O.
Panels 1 to 5 are frames of this simulation animation, where colored spheres represent the nuclei (white = H and red = O) and colored clouds represent selected electron density iso-surfaces (from red = lowest density to blue = highest density). Panel 6 shows the Mulliken populations of the projectile Hproj. and of the O and H2 moieties of/from H2O vs. time in a.u. Mulliken populations at final time indicate that with q1 = 1−N1 = +1, q2 = 2−N2 = 0 and q3 = 8−N3 = 0.
Fig 7.
Target fragments from individual SLEND/6-31G* simulations of H+ + (H2O)2..
Colored spheres represent the nuclei (white = H and red = O) and brown clouds represent selected electron density iso-surfaces. The predicted fragments from (H2O)2 are labeled and identified as 1: H2O + HO + H, 2: H3O + O + H, 3: H2O + 2H + O, and 4: H3O + OH.