Orbital imaging and assessment of different orbital models for the valence shell of methanol: Comparison of electron momentum spectroscopy measurements with near-Hartree–Fock limit, MRSD-CI, localized valence bond and density functional theory

Abstract

The momentum distributions of the valence orbitals of methanol have been studied by electron momentum spectroscopy (EMS) and Hartree–Fock (HF), multi-reference singles and doubles configuration interaction (MRSD-CI), localized valence bond (VB) and density functional theory (DFT) calculations. The experiment was performed using a multichannel EMS spectrometer at a total energy of 1200 eV plus the binding energy. Binding-energy spectra measured in the energy range of 6–47 eV are presented for the azimuthal angles φ=0° and φ=8°. Synthetic binding-energy spectra from Green's function and HF calculations for the azimuthal angles φ=0° and φ=8° in the 6–47 eV energy region are also compared to experiment. In the inner valence region strong splitting of the 4a′ and 3a′ ionization is observed due to final-state electron correlation effects. The measured momentum profiles are compared with HF calculations at the level of the target HF approximation using basis sets ranging from simple (STO-3G) to large (110-GTO and Trun-pV5Z). DFT calculations at the level of the target Kohn–Sham approximation employing the local density approximation or hybrid functional methods and the large Trun-pV5Z basis set are also compared to experiment. The effects of electron correlation and relaxation are also investigated in the outer valence region by MRSD-CI calculations of the full ion–neutral overlap amplitude using the 110-G(CI) basis set. The shapes of all momentum profiles are well predicted by higher level theory. Some small discrepancy still exists between all theoretical treatments and experiment in the low-momentum region for the HOMO 2a″ orbital. MRSD-CI or DFT (i.e. correlated) methods are needed to adequately describe the shape of the 7a′ and (6a′+1a″) momentum profiles. The s-type character in the 5a′ momentum profile is underestimated by HF theory and overemphasized by density functional theory (DFT). The 110-G(CI) calculation best predicts the shape for the 5a′ momentum profile. The shapes of the experimental momentum profiles for the 4a′ and 3a′ are well-reproduced by large basis set HF and DFT calculations. In addition, nearly all the inner valence 4a′ pole strength is found in the 20–28 eV region while the high-energy 28–47 eV region contains virtually all of the 3a′ pole strength. Lastly, the HOMO and NHOMO momentum profiles are compared to the corresponding localized molecular orbitals (LMO) (i.e. the `lone-pair' orbitals of VSEPR or qualitative VB theory), the canonical molecular orbitals (CMO) of molecular orbital (MO) theory and the Kohn–Sham orbitals (KSO) of DFT used in the present work. The experimental results unequivocally support the delocalized CMO and KSO models and are very different from the LMO description. Although electron correlation effects are also important at low momenta in the 7a′ NHOMO this orbital is also basically a CMO or KSO in character as shown by the CI and DFT calculations. It is noteworthy that the KSOs of DFT, often described as fictitious mathematical concepts, in fact very closely fit the experimental results and are very similar to the CMOs given by HF or CI calculations of the full ion–neutral overlap where necessary. These conclusions have profound implications for computer-aided molecular design, molecular modelling and molecular recognition.