Real‐Space In Situ Bond Energies: Toward A Consistent Energetic Definition of Bond Strength

Abstract

A rigorous definition of intrinsic bond strength based on the partitioning of a molecule into real-space fragments is presented. Using the domains provided by the quantum theory of atoms-in-molecules (QTAIM) together with the interacting quantum atoms (IQA) energetic decomposition, we show how an in situ bond strength, matching all the requirements of an intrinsic bond energy, can be defined between each pair of fragments. Total atomization or fragmentation energies are shown to be equal to the sum of these in situ bond energies (ISBEs) if the energies of the fragments are measured with respect to their in-the-molecule state. These energies usually lie above the ground state of the isolated fragments by quantities identified with the standard fragment relaxation or deformation energies, which are also provided by the protocol. Deformation energies bridge dissociation energies with ISBEs, and can be dissected by using well-known tools of real-space theories of chemical bonding. Similarly, ISBEs can be partitioned into ionic and covalent contributions, and this feature adds to the chemical appeal of the procedure. All the energetic quantities examined are observable and amenable, in principle, to experimental determination. Several systems, exemplifying the role of each energetic term presented herein, are used to show the power of the approach.

Real space bond orders are energetic descriptors

“…We have recently shown that total interaction energies E AB int behave as intrinsic bond energies, 21 and can be used to solve several longstanding problems in the appropriate definition of these important quantities. E int 's fullfil all the requisites to be used as rigorous energetic descriptors of bond strength.…”

On Electrostatics, Covalency, and Chemical Dashes: Physical Interactions versus Chemical Bonds

“…This is nothing but the textbook Born–Haber cycle, which can be restated in terms of atomic self‐energies. Promoting the free Li and F atoms into their in‐the‐molecule states in diatomic LiF costs 132.1 and −55.7 kcal mol −1 , respectively . These add to a 76.4 kcal mol −1 global penalty that is more than compensated for by the mutual −170.3 kcal mol −1 electrostatic attraction between the formed ions.…”

“…The electrostatic contribution is destabilizing, which it must be if two neutral nonoverlapping charge distributions interact . In contrast, a CCSD calculation for LiF provides an opposite energetic partition of =−208.1 kcal mol −1 , with =−28.8 and =−179.3 kcal mol −1 . Interestingly, assuming point net QTAIM charges for LiF provides a very good approximation to : Q A Q B / R AB =−184.5 kcal mol −1 (this is only the case in very ionic compounds).…”

“…[8] In contrast, aC CSD calculation for LiF provides an opposite energetic partition of E LiF int = À208.1 kcal mol À1 ,w ith E LiF cov = À28.8 and E LiF els = À179.3 kcal mol À1 . [25] Interestingly, assuming point net QTAIM charges for LiF provides a very good approximation to E LiF els : Q A Q B /R AB = À184.5 kcal mol À1 (this is only the case in very ionic compounds). Thus, in these two paradigmatic cases, the interatomic interaction energies are consistentw ith the computed dissociation energies: À105.9 kcal mol À1 in H 2 and À131.7 kcal mol À1 in LiF.A se xpected, D e in H 2 is dominated by covalency, and by electrostaticsi n LiF.…”

“…Promoting the free Li and Fa toms into their in-the-molecule states in diatomic LiF costs 132.1 and À55.7 kcal mol À1 ,r espectively. [25] These add to a7 6.4 kcal mol À1 global penaltyt hat is more than compensated for by the mutual À170.3 kcal mol À1 electrostatic attraction between the formedi ons. Similarly,t he full Madelung energy is essential to account for the total lattice energy of the LiF crystal.…”