A combined ab initio and Franck–Condon factor simulation study on the photodetachment spectrum of HfO2−

Daniel K. W. Mok; Edmond P. F. Lee; Foo-tim Chau; John M. Dyke

doi:10.1039/B809863H

A combined ab initio and Franck–Condon factor simulation study on the photodetachment spectrum of HfO₂⁻

Daniel K. W. Mok,^a Edmond P. F. Lee,†^ab Foo-tim Chau^a and John M. Dyke^b

^a Department of Applied Biology and Chemical Technology, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
E-mail: epl@soton.ac.uk; bcdaniel@polyu.edu.hk

^b School of Chemistry, University of Southampton, Highfield, Southampton, UK

Abstract

Restricted-spin coupled-cluster single-double plus perturbative triple excitation {RCCSD(T)} potential energy functions (PEFs) of the [X with combining tilde] ¹A₁ state of HfO₂ and the ²A₁ state of HfO₂⁻ were computed, employing the quasi-relativistic effective core potential, ECP60MWB, and an associated contracted [13s6p6d4f3g2h] basis set designed for Hf, and the augmented correlation-consistent polarized valence quadruple-zeta (aug-cc-pVQZ) basis set for O. Based on the differences between the computed r₀ and r_e geometrical parameters obtained from the PEF, and available experimentally derived r₀ geometrical parameters of the [X with combining tilde] ¹A₁ state of HfO₂, the experimental r_e geometrical parameters of the ¹A₁ state of HfO₂ were estimated as:−r_e(HfO) = 1.7751 Å and θ_e(OHfO) = 107.37°.

In addition, Franck–Condon factors for the HfO₂ ( [X with combining tilde] ¹A₁) + e← HfO₂⁻ ( ²A₁) electron detachment process, which include allowance for Duschinsky rotation and anharmonicity, were calculated using the computed RCCSD(T) PEFs, and were used to simulate the HfO₂ ( ¹A₁) + e← HfO₂⁻ ( ²A₁) photodetachment band of HfO₂⁻. Employing the estimated experimental r_e geometrical parameters of the [X with combining tilde] ¹A₁ state of HfO₂ obtained in this work, the iterative Franck–Condon analysis (IFCA) procedure was carried out to optimize the geometrical parameters of the ²A₁ state of HfO₂⁻ until the simulated spectrum matched best with the experimental 355 nm photodetachment spectrum of W. Zheng, et. al., J. Phys. Chem. A, 1998, 102, 9129. The equilibrium geometrical parameters of [X with combining tilde] ²A₁ state of HfO₂⁻ derived via the IFCA procedure are r_e(HfO) = 1.823 Å and θ_e(OHfO) = 111.5°.

Further calculations on low-lying triplet states of HfO₂ gave adiabatic electronic energies (T_e’s) of, and vertical excitation energies (T_vert’s) to, the ã ³B₂, [b with combining tilde] ³B₁, [c with combining tilde] ³A₁ and [d with combining tilde] ³A₂ states of HfO₂ (from the [X with combining tilde] ¹A₁ state of HfO₂), as well as electron affinities (EAs) and vertical detachment energies (VDEs) to these neutral states from the ²A₁ state of HfO₂⁻.