Abstract
Chemical bonding is the stabilization of a molecular system by charge- and spin-reorganization processes in chemical reactions. These processes are said to be local, because the number of atoms involved is very small. With multi-configurational self-consistent field (MCSCF) wave functions, these processes can be calculated, but the local information is hidden by the delocalized molecular orbitals (MO) used to construct the wave functions. The transformation of such wave functions into valence bond (VB) wave functions, which are based on localized orbitals, reveals the hidden information; this transformation is called a VB reading of MCSCF wave functions. The two-electron VB wave functions describing the Lewis electron pair that connects two atoms are frequently called covalent or neutral, suggesting that these wave functions describe an electronic situation where two electrons are never located at the same atom; such electronic situations and the wave functions describing them are called ionic. When the distance between two atoms decreases, however, every covalent VB wave function composed of non-orthogonal atomic orbitals changes its character from neutral to ionic. However, this change in the character of conventional VB wave functions is hidden by its mathematical form. Orthogonal VB wave functions composed of orthonormalized orbitals never change their character. When localized fragment orbitals are used instead of atomic orbitals, one can decide which local information is revealed and which remains hidden. In this paper, we analyze four chemical reactions by transforming the MCSCF wave functions into orthogonal VB wave functions; we show how the reactions are influenced by changing the atoms involved or by changing their local symmetry. Using orthogonal instead of non-orthogonal orbitals is not just a technical issue; it also changes the interpretation, revealing the properties of wave functions that remain otherwise undetected.
Highlights
We analyze four chemical reactions by transforming the multi-configurational self-consistent field (MCSCF) wave functions into orthogonal valence bond (VB) wave functions; we show how the reactions are influenced by changing the atoms involved or by changing their local symmetry
Slater pointed to the fact that orthogonalization of atomic orbitals (AO) prevents constructive interference in ΨoHL, and we showed that all OVB-configuration state functions (CSF) have the same one-particle density
The spin distribution is not as isotropic as it is on a sphere, and the maxima of the spin distributions must be calculated with appropriate methods; e.g., quantum Monte Carlo (QMC) methods. Such calculations were made by Scemama et al [69] and Lüchow [70]; the combination of OVB and QMC methods seems to be very promising for investigating the processes of chemical bonding
Summary
In a composite system composed of two or more subsystems, the subsystems do not initially interact if they are spatially well separated. The system’s state of minimum energy is called the equilibrium state; it is well characterized by properties, such as equilibrium geometry, equilibrium dipole moment, etc Both stabilization and destabilization of the composite system are defined relative to the state of non-interacting subsystems, which one might call the canonical reference state. Atoms approach each other, the electron densities gradually change due to contraction and polarization, but the implausible reference state is constructed as if the completely separated atoms can be brought to the equilibrium distance, where they instantly change from the electron densities of the free atoms to the molecular electron density In this model reaction, the interaction between the free atoms can be switched on at a certain geometry. I shall use the word “debonding” to describe the destabilization of a composite system; the word “bond” will only be used to describe elements in a structural formula, e.g., a C–H bond or a C=C double bond
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