Orbital Hybridization in Modern Valence Bond Wave Functions: Methane, Ethylene, and Acetylene

Abstract

The concept of hybrid orbitals is one of the key theoretical concepts used by chemists to explain the structures and other properties of molecules. Recent work found that the hybrid orbitals from modern ab initio valence bond wave functions differ significantly from traditional hybrid orbitals. We report a detailed analysis of the orbitals of methane, ethylene, and acetylene from spin-coupled generalized valence bond (SCGVB) wave functions, a variationally optimized valence bond wave function that places no constraints on the orbitals and spin function. The carbon-centered orbitals in the SCGVB wave functions are found to be 2s−2p hybrid orbitals largely localized on the carbon atom and pointed directly at the hydrogen atoms to which they are bonded. However, the SCGVB orbitals for methane, ethylene, and acetylene differ markedly from the sp 3 , sp 2 , and sp hybrid orbitals traditionally associated with these molecules. It is now clear that the orbitals in modern valence bond wave functions do not follow the hybridization rules of traditional valence bond theory. These findings imply that, in modern valence bond theories, other factors are responsible for the structures and properties of molecules that are traditionally attributed to orbital hybridization.

Pauling’s Conceptions of Hybridization and Resonance in Modern Quantum Chemistry

“…Contrary to skepticism that is sometimes expressed [ 45 , 54 , 58 ], we believe that the present results confirm the essential correctness and usefulness of Pauling’s hybridization and resonance concepts, as consistently found in NBO/NRT analysis of wavefunctions from the best currently available quantum chemical methods. If anything, improved quantitative accuracy of the wavefunction tends to enhance admiration of Pauling’s powerful intuitions, developed long before numerically reliable solutions of Schrödinger’s equation became routinely available.…”

“…Even for HBr, which exhibits the largest λ variation (from 6.82 at the RHF level to 7.81 for SCGVB), the percent p -character changes by only 1.4% (from 87.2% to 88.6%). Note specifically that the SCGVB hybrid descriptors of Table 1 are generally in line with the near-Pauling results that are found both at higher and lower computational levels, contrary to the conclusions of [ 57 , 58 ]. Thus, the NBO user can be confident that the hybrid description offered at one level of theory will be largely consistent with that obtained using nearly any other level, particularly for densities from correlated or density functional calculations.…”

“…Similarly, the Group 14 hydrides (XH 4 , X = C, Si, Ge) are tetrahedral with sp 3 -like hybrids (75% p), consistent with Pauling's original inferences from molecular symmetry. [57,58]. Thus, the NBO user can be confident that the hybrid description offered at on level of theory will be largely consistent with that obtained using nearly any other leve particularly for densities from correlated or density functional calculations.…”

“…However, more general questioning of hybridization and resonance concepts can be attributed to the complex mathematical forms of modern wavefunctions and density functionals that no longer allow chemists to easily “see” the hybridization and resonance features that appear explicitly in VB-based formulations. Ironically, even some advocates of modern SCGVB theory have expressed skepticism about Pauling’s hybridization concepts [ 57 , 58 ], because the final orbital shapes no longer resemble localized VB-inspired forms. Related attempts to obtain directed hybrids of localized chemical bonding in the MO/DFT framework by transforming canonical MOs to localized LMO form [ 59 , 60 , 61 , 62 , 63 ] are similarly frustrated, because the localization procedure can be chosen rather arbitrarily to yield a virtually unlimited variety of orbital energies and shapes, with no effect on the calculated total energy or other measurable properties of the system.…”

Attempting AG-Doped Diamond-Like Carbon Film to Improve Seal Performance of Hydraulic Servo-Actuator

“…On the other hand, Ag doping may alter the C-C covalent bond angle and the distribution of carbon particles. According to the molecular orbital hybridization theory [23], the atomic orbitals start to overlap to form molecular orbitals (MO) as atoms get closer. Ag has six filled d-orbitals, and the orbitals overlap with those of carbon, increasing the bond angle and minimizing the bond energy make the local area stable [24].…”