Ab initio electronic ground state energies of the ozone molecule in 4D representation illustrating the grid density of nuclear geometrical configurations for our AV5Z and AV6Z calculations. The calculations are essentially focused on the main potential well and on the way towards the dissociation transition state. Left-hand side corresponds to X = 5 and right-hand side to X = 6 AVXZ calculations. Horizontal axes correspond to bond lengths r 1 and r 2 (in a.u.), vertical axe to the apex angle (in degrees), and the scale of the electronic energy E-E0 (in cm−1) is given in color.
(a)-(c) Harmonic frequencies versus the cardinal number X of the atomic basis set with the setup of Table I .
Barrier (B) of the reef structure, van der Waals well point (vdW), and dissociation threshold (D) versus the cardinal number X. All quantities are calculated with respect to E0 on the MEP with θ fixed to 117° (Table I ).
1D r 1-cuts of two PES versions with r 2 = 2.28 a.u. and θ = 117°. Magenta-dots and green-diamond points refer to icMR-CISD+QD ab initio calculations with a1 and a5 ansätze correspondingly; the range r ∼ 4.5-5.5 a.u. corresponds to a1/a5 smoothing (see the text). Panels (a and b): Dashed curve for R_PES with reef structure (one electronic state optimisation). Panels (c and d): Continuous curve for NR_PES without reef structure. The latter is removed using the 1D MEP correction due to Dawes et al. 9 accounting for two reference functions in the ic-MRCI calculations along with orbitals from full-valence 13-state DWSA-CASSCF. Panels (e and f): Comparison of R_PES and NR_PES at the TS range. The fit of these two PES versions to ab initio points is described in Sec. V .
Non-symmetrized MEP as obtained by simple “drag” method with one bond length successively fixed step-by-step and with another bond relaxed in order to minimise the potential energy. Bond lengths are given in a.u. and energy on the vertical scale in cm−1. Red curve corresponds to the function .
2D representation of the non-symmetrized μ-path (red dashed curves) superposed with the contour plots for two versions of the potential: (panel (a)) for the R_PES and (panel (b)) for the NR_PES. (Panel (c)) The symmetrized MEP (solid black curve) for the NR_PES.
Scatter of ab initio points fitted with the MEP analytical model for two versions of the PES. Fit residuals are given in vertical scale for the R_PES (panel (a)) and for the NR_PES (panel (b)) in the 2D representation versus the apex angle (from 90° to 145°) and versus increasing energy up to 9200 cm−1. Panels (c) and (d): the fit residuals shown in blue (R_PES) and gray (NR_PES) cycles are plotted for two regions: main C 2V well (E-E0 < 5000 cm−1) and up to “dynamical” range above the dissociation (E-E0 < 9500 cm−1).
The stretch-stretch cut of the ozone ground electronic transition state range towards the dissociation for two versions of PES: left-side panels (a), (c): for R_PES and right-side panels (b), (d) for NR_PES. The MEP on the overall view from the C 2V equilibrium up to D e is shown in red on the upper panels. The blown up scale of the lower panels gives a comparison of the analytical surfaces with ab initio energies: (a1) calculations for red points and (a5) calculations for green points. The apex angle if fixed to 117° (near equilibrium value). The bond lengths r 1 and r 2 are given in a.u. and the PES values in cm−1 on the vertical scale.
Stretch-stretch cut (for θ = 117°) and stretch-bend cut (for r 2 = 2.4 a.u.) of the NR_PES and sample grids of ab initio configurations used in the fit.
Comparison of the analytical NR_PES with ab initio points for the stretch-bend cut (one bond fixed to the equilibrium value 2.4 a.u.): (a) in the main C 2V well; (b) on the way from the main well towards the dissociation. Ab initio calculations using a1 ansatz are denoted in magenta and those using a5 ansatz for r > 4.5 in green.
Global shape of the NR_PES with ab initio points: stretch-stretch cut for A = 117° in the main well, in the dissociation and channels and for the bisector range towards O − O − O fragmentation. Ab initio calculations using a1 ansatz are denoted in magenta and those using a5 ansatz for r > 4.5 in green.
4D representation of the global shape of the NR_PES.
Harmonic normal mode frequencies (ω i ), stretching force constant (f rr ), TS characteristic points, and dissociation energy calculated for 16O3 using ic-MRCI-QD/AVXZ with one electronic state optimization. a
Root-mean-square deviations of the PES fit to ab initio points using the analytical model ((3)-(12)) versus the energy cut-off E max . a
Vibration band centres of 16O3 predicted from NR_PES using atomic masses. a
Comparison of 16O3 band centres observed in high-resolution spectra with ab initio predictions using NR_PES. a
Comparison of 16O3 band centres obtained from low resolution spectra and “dark state” analyses with ab initio predictions using NR_PES. a
Article metrics loading...
Full text loading...