Hartree−Fock−Heitler−London Method. 2. First and Second Row Diatomic Hydrides

Abstract

The Hartree-Fock-Heitler-London, HF-HL, method is a new ab initio approach which variationally combines the Hartree-Fock, HF, and the Heitler-London, HL, approximations, yielding correct dissociation products. Furthermore, the new method accounts for nondynamical correlation and explicitly considers avoided crossing. With the HF-HL model we compute the ground-state potential energy curves for H2 [1Sigma+g], LiH [X 1Sigma+], BeH [2Sigma+], BH [1Sigma+], CH [2Pi], NH [3Sigma-], OH [2Pi], and FH [1Sigma+], obtaining in average 80% of the experimental binding energy with a correct representation of bond breaking. Inclusion of ionic configurations improves the computed binding energy. The computed dipole moment is in agreement with laboratory data. The dynamical and nondynamical correlation energies for atomic and molecular systems with 2-10 electrons are analyzed. For BeH the avoided crossing of the two lowest [2Sigma+] states is considered in detail. The HF-HL function is proposed as the zero-order reference wave function for molecular systems. To account for the dynamical correlation energy a post-HF-HL technique based on multiconfiguration expansions is presented. We have computed the potential energy curves for H2 [1Sigma+g], HeH [2Sigma+], LiH [X1Sigma+], LiH [A1Sigma+], and BeH [2Sigma+]. The corresponding computed binding energies are 109.26 (109.48), 0.01 (0.01), 57.68 (58.00), 24.19 (24.82), and 49.61 (49.83) kcal/mol, with the experimental values given in parentheses. The corresponding total energies are -1.1741, -3.4035, -8.0695, -7.9446, and -15.2452 hartrees, respectively, the best ab initio variational published calculations, H2 excluded.

From atomic and molecular orbitals to chemical orbitals

“…from a 249 term wave function with elliptic type basis set, yielding the accurate binding energy of 109.48 kcal/mol, computed from large internuclear distances to 0.2 bohr. In the figure, to the Kolos et al landmark we add the potential energy computations 33–35 from the Heitler‐London, the Hartree‐Fock, and the HF‐HL, the latter with two ionic structures, HF‐HL‐ i ‐(2), related to this work and obtained with a basis set large enough to reach the accuracy limit of the corresponding models 33.…”

“…The HF‐HL function in its simplest form yields qualitatively correct binding energies, accounts for the nondynamical correlation energy 14, 38–41, and yields—by construction—correct dissociation; these features make the HF‐HL model superior to both HF and HL. In addition, the inclusion into the HF‐HL function of a few HL ionic structures 34, 35, leading to the “HF‐HL‐ i ” model, yields nearly accurate binding energies not only in heteropolar 35 but also in homopolar 33, 35 molecules. This somewhat surprising computational result calls for a physical interpretation.…”

“…The recent HF‐HL approach is documented in Refs. 32–36. We recall the Hartree‐Fock and the Heitler‐London wave functions, Ψ HF , and Ψ HL for a n electron molecule: The Φ i defines the i ‐th molecular orbital 12, 13 in the HF function.…”

“…To account for near‐degeneracy 14, 34, 38–41 (e.g., 2s/2p near degeneracy in the Be, B, and C atoms) and/or avoided state crossing 4 short linear expansions are introduced, ∑ s a s Ψ HF (s) and ∑ t b t Ψ HL (t), where the a s and b t are variational coefficients. When there is no near degeneracy in the component atoms the Ψ HF‐HL wave‐function is defined 32–36 as: and for molecules composed by atoms with near degeneracy and/or for state crossing configurations the Ψ HF‐HL is The first summation is often limited to one term 36, whereas the second summation includes all the structures formed with the near‐degenerate atomic configurations. For a given state, the HL function includes all the possible spin couplings 53, therefore the solution of Eq.…”

“…The observation that MOs provide a particularly valid representation near the equilibrium internuclear distances, whereas the AOs are often superior particularly near molecular dissociation, provides a hint that a more general one‐electron function should exist, containing both MO‐like and AO‐like characterization. These requirements are preliminarily satisfied with the recently introduced Hartree‐Fock‐Heitler‐London, HF‐HL, model 32–36, but only indirectly, because the model explicitly requires the use of both the usual MOs and the AOs.…”