Effective bond orders

We present in Table 3 the excitation energies needed to produce a valence state with all orbitals singly occupied. The largest excitation energy is for Ac. The price to pay for forming a triple bond between two Ac atoms is 2.28 eV for Th, only 1.28 eV is needed, which can then, in principle, form a quadruple bond. Note that in these two cases only 7s and 6d orbitals are involved. For Pa, 1.67eV is needed, which results in the possibility of a quintuple bond. The uranium case was already described above where we saw that, despite six unpaired atomic orbitals, only a quintuple bond is formed with an effective bond order that is closer to four than five. 

Lewis dot diagrams of nitric oxide compared to the nitrosonium ion and molecular nitrogen. Each bond contains one electron from each atom. These simple diagrams fail to properly account for the effective bond order of 2.5 predicted by molecular orbital theory and must be only considered as illustrative. The dimer of two nitric oxide molecules has five bonds, which is the same as two individual molecules. Thus, nitric oxide remains dissociated at room temperatures. 

This y value is called an instability value of a chemical bond (or diradical character) [29]. In case of the spin-restricted or spin-adapted (SA) calculations, the y value should be zero. However, if a couple of electrons tend to localize on each atom, in other words the chemical bond becomes unstable with the strong static correlation effect, the y value becomes larger and finally becomes 1.0. So, the y value can be applied for the analyses of di- or polyradical species, and it is often useful to discuss the stability (or instability) of chemical bonds. The idea of effective bond order b), which defined by the difference in occupation numbers of occupied NO (n) and unoccupied NO ( ) as... 

More elaborate calculations have yielded an effective bond order of 3.2 for [Re2Cl8p, recommended as an alternative label to a weak quadruple bond. See L. GagUardi, B. O. Roos, Inorg. Chem., 2003,42,1599. 

In this chapter, we reviewed different quantum chemical approaches to determine local quantities from (multireference) wave functions in order to provide a qualitative interpretation of the chemical bond in open-shell molecules. Chemical bonding in open-shell systems can be described by covalent interactions and electron-spin coupling schemes. For different definitions of the (effective) bond order as well as various decomposition schemes of the total molecular spin expectation value into local contributions, advantages and shortcomings have been pointed out. For open-sheU systems, the spin density distribution is an essential ingredient in the... 

The choice of the active space is the challenging aspect of these calculations. An appropriate active space should include the metal-metal bonding and antibonding orbitals and also the necessary hgand orbitals that interact with the metal d- and s-type orbitals. This active space comprises at least all the nd (n= 3, 4 or 5) and ( +l)s orbitals forming the M-M multiple bond, namely, 12 orbitals. From a G SSCF wavefunction it is possible to compute the effective bond order (EBO) [10, 11] which quantifies the formation of a chemical bond. For a single bond the EBO is defined as ... 

Table 9.1 Formal and effective bond orders for Crj, Moj and Wj, together with their calculated dissociation energy (eV) and equilibrium bond distance (A).

Table 7.2 Effective bond order, total bond order, Tc-Tc and Tc-X bond distances (A) for the TcjXg (X = Cl, Br) calculated at the CASPT2/VTZP level of theory.

Theoretical calculations were performed, initially with SCF-Xa-SW methods on a truncated model [16], and later with the complete active space self-consistent field (CASSCF) and mul-ticonfigurational complete active space second-order perturbation theory (CASPT2) methods on the full molecule [15]. The electronic structures from the two calculations were remarkably similar. The CASSCF/PT2 calculations predicted a single, dominant configuration (73%) with (a) (x) (x ) (a ) (8) (5 ). Although the formal bond order is 1.5, the effective bond order, which considers minor configurations that contribute to the ground-state wavefunction, is lower at 1.15. 

The complex has a magnetic moment of 7.95 pg, which is largely invariant from 150 to 300 K. CASSCF/PT2 calculations predict the ground spin state to be high spin, or S = 3. The calculations yield an effective bond order (EBO) of 1.19, suggesting a modest amount of multiple bonding despite the experimentally short Fe-Fe bond. The Mossbauer spectrum shows one quadrupole doublet with IS of 0.44 mm s and QS of 2.39 mm s". ... 

Maurice R, Real F, Gomes ASP, Vallet V, Montavon G et al (2015) Effective bond orders from two-step spin-orbit coupling approaches The I2, At2, lO, and AtO case studies. J Chem Phys 142 094305-094309... 

The Wiberg bond orders (WBO) in the U2 diatom is 3.408, very close to the effective bond order (EBO) of 4.2 estimated by Roos et al. [83] at a high level of theory. Such a WBO value indicates qualitatively the formation of a strong triple bond involving fully occupied and 6dn bonding MOs shown in Figure 18.1. 

Computing Accurate Net Atomic Charges, Atomic Spin Moments, and Effective Bond Orders in Complex Materials... 

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