The Density-Functional Theory (DFT) description of equilibria in both the externally closed and open molecules, controlled by the system overall number of electrons N or the system/reservoir chemical potential μ, respectively, is used to explore within the Born–Oppenheimer approximation the compliance constants reflecting the coupling between molecular electronic and geometric degrees-of-freedom. The ground-state interaction between the electronic and geometrical parameters-of-state in both the externally closed and open molecular systems is explored within the so-called geometrical representations, which use the explicit dependence of the Legendre-transforms of the system Born–Oppenheimer potential-energy-surface on the Cartesian (R) or internal (Q) nuclear positions or their energy conjugates, the forces FR or FQ acting on nuclei. The principal second derivatives of the system electronic energy with respect to both the electronic and nuclear state-variables in the canonical, say, (N, Q) representation define the system generalized, electronic-nuclear Hessian matrix, including the electronic hardness and geometric force constants as diagonal blocks, as well as the nuclear Fukui function indices determining the coupling between these two aspects of the molecular structure. Its partial or complete inversion subsequently determines the associated compliant matrices in alternative Legendre-transformed representations, in which these principal state-variables have been partly or totally replaced by their respective energy conjugates. Specific coupling-constant descriptors measuring the interplay between molecular electronic and nuclear state-parameters in the geometrically rigid or relaxed systems, are identified and discussed. Their numerical values resulting from the standard ab initio calculations (HF, CISD, MP2), with the N-derivatives estimated by finite differences, are compared and discussed for several representative molecules. The minimum-energy coordinates are introduced and discussed within such a combined electronic-nuclear treatment of molecular systems. Other compliant descriptors of the molecule as a whole, generated within the complementary Electron Following (EF) and Electron Preceding (EP) perspectives on the system global equilibrium, are also reported for illustrative molecules. These compliant quantities are advocated as reactivity criteria, since they directly reflect the system electronic (or geometric) conditions required for the molecule to undergo specific nuclear (or electronic) displacements responsible for the chemical reaction of interest.
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Apr 18, 2011
Serdal Kirmizialtin + 1
Open Access
