THE ORIGIN OF THE CHEMICAL BOND
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Publisher:Ohio State University
“It is known that (1) by virtue of the virial theorem the molecular binding energy $\Delta E$ results from the potential energy drop $\Delta V = 2 \Delta E < 0$ , and. in spite of the kinetic energy increase $\Delta T=|\Delta E| > 0$; (2) bond formation is closely connected with the overlap of atomic wavefunctions in the bond region. Current opinion, fashionable in quantumchemical textbooks, regards the facts (1) and (2) as demonstrating that the quantummechanical overlap effect accumulates in the bond extra charge (as compared with a classical model) and that this extra charge, being attracted by both nuclei, gives rise to the negative potential $\Delta V$. A Quantitative analysis shows this inference to be invalid. In actual fact, the overlap accumulation of charge leads to a considerable increase in potential energy. It furnishes, however, a decrease in kinetic energy. The resulting low kinetic energy density in the bond region permits a high kinetic energy density near the nuclei without undue increase of the total kinetic energy. As a consequence, the valence electrons can cluster more tightly around the nuclei than in the free atoms before being held back by virtue of the uncertainty principle in the form of the virial theorem. In doing so they acquire the negative potential energy $\Delta V$. Thus the chemical bond owes its existence to a lowering of the kinetic energy in the bond region which, indirectly, creates the possibility of a closer approach of the valence electrons to the nuclei with a concomittant lowering of the potential energy.”
Author Institution: Institute for Atomic Research, Departments of Chemistry and Physics, Iowa State University
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