Bonding/antibonding character of “lone pair” molecular orbitals from their energy derivatives; consequences for experimental data

Abstract

The derivative of molecular orbitals (MO) energies with respect to a bond length (dynamic orbital force [DOF]) is used to estimate the bonding/antibonding character of valence MOs along this bond, with a focus on lone pair MOs, in a series of small molecules: AH (A 5 F, Cl, Br), AH 2 (A 5 O, S, Se), AX 3 (A 5 N, P, As; X 5 H, F), and H 2 CO. The HOMO DOF agrees with the calculated variation of bond length and force constant in the corresponding ground state cation, and of bond length variation by protonation. These results also agree with available experimental data. It is worthy to note that the p-type HOMOs in AH and AH 2 are found bonding. The lone pair MO is bonding in NH 3 , while it is antibonding in PH 3 , AsH 3 , and AF 3 . K E Y W O R D S bonding/antibonding, lone pairs, molecular orbital force 1 | I N T R O D U C T I O N 1.1 | How to define the bonding/antibonding character of a MO?The bonding/antibonding character can be based on essentially two criteria, energy or force, with different possible definitions on these criteria.The IUPAC Gold Book [1] prefers the energy point of view, a bonding MO being characterized by "an increase in the total bonding." This generally corresponds also to a MO energy lower than the mean energy of the AOs constituting this MO. These definitions involve the whole molecule.Nevertheless, for the chemist, it is important to characterize local MO properties, that is, their bonding/antibonding character along a bond, or moreThe bonding/antibonding zones are, thus, characterized by a positive/negative value of the function f. They are separated by a nonbonding surface given in Figure 1 for a symmetrical A 2 molecules and the unsymmetrical HF one.On this basis, the total electron density is decomposed into MO densities and, thus, into additive orbital forces which quantify their bonding character. [3]-[5] Another concept of "orbital forces" was proposed by Tal and Katriel. [6] It is built up from the MO energy derivatives with respect to nuclear coordinates. According to the Koopmans theorem, [7] the MO energy can be expressed as Equation 2:Int J Quantum Chem. 2018;e25658. https://doi.The Table 1 indicates that 1r and 2r usually referred as r bonding MO and sp lone pair MO, respectively, are almost equally bonding. The p MOs, usually described as "purely nonbonding" have in fact a marked bonding character. This character is partly due to the presence of empty p MOs of hydrogen in an extended basis set. Nevertheless, even at the STO-3G level, this character remains (0.011 au for HF), though the overlap with the 1s AO of hydrogen is zero. It means that the pure atomic p density on atom A is intrinsically bonding, that is, exerts an attractive force on the H nucleus. It can be understood qualitatively from Figure 1: the nonbonding surface does not divide equally the 2p density which can be seen slightly more localized in the bonding region.The bonding character of p MOs agrees with the calculated bond lengths of neutral and cationic ( 2 p) species: in each case the cation HF 1 , ...

Analysis of carbon‐carbon bonding in small hydrocarbons and dicarbon using dynamic orbital forces: Bond energies and sigma/pi partition. Comparison with sila compounds

“…These MO derivatives have been also computed in small molecules as an index of a local bonding/antibonding character along a given bond . Though they do not take into account the electron correlation, these quantities agree with the variation of the bond lengths upon ionization, in a large panel of diatomic and small polyatomic molecules.…”

“…Though they do not take into account the electron correlation, these quantities agree with the variation of the bond lengths upon ionization, in a large panel of diatomic and small polyatomic molecules. A semi‐quantitative relation between the DOF and the relative bond length variation was found [2a, 5]. Moreover, it has been shown that the sum of the DOFs over occupied MOs is an index of bond strength and could be used in the interpretation of molecular properties …”

Orbital energies and nuclear forces in DFT: Interpretation and validation

“…MOs in terms of bonding or antibonding character with respect to individual bonds. [1][2][3][4][5] This technique stems from the ideas of Tal and Katriel, 6 which are based on the famed Koopmans' theorem. The main idea is captured in Eq.…”

“…Orbital forces have been used in several contexts for the individual characterization of MOs in terms of bonding or antibonding character with respect to individual bonds 1–5 . This technique stems from the ideas of Tal and Katriel, 6 which are based on the famed Koopmans' theorem.…”

Orbital Energies and Nuclear Forces in DFT: Interpretation and Validation

“…Orbital forces have been used in several contexts for the individual characterization of MOs in terms of bonding or antibonding character with respect to individual bonds. [1][2][3][4][5] This technique stems from the ideas of Tal and Katriel, 6 which are based on the famed Koopmans' theorem. The main idea is captured in Eq.…”