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One of the conceptual advantages of deriving the theory of an atom in a molecule from Schwinger's principle is that it yields both Schrödinger's equation and the Heisenberg equation of motion in a single unified approach, by combining the action principle with Dirac's transformation theory.
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One of the conceptual advantages of deriving the theory of an atom in a molecule from Schwinger's principle is that it yields both Schrödinger's equation and the Heisenberg equation of motion in a single unified approach, by combining the action principle with Dirac's transformation theory.
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9
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Bader, R. F. W.; Cheeseman, J. R.; Laidig, K. E.; Breneman, C.; Wiberg, K. B. J. Am. Chem. Soc. 1990, 112, 6530-6536.
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Cremer, D.; Kraka, E.; Slee, T. S.; Bader, R. F. W.; Lau, C. D. H.; Nguyen-Dang, T. T.; MacDougall, P. J. J. Am. Chem. Soc. 1983, 105, 5069-5075.
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Cremer, D.; Childs, R. F.; Kraka, E. In The Chemistry of the Cyclopropyl Group; John Wiley & Sons Ltd: New York, NY 1995; 2, pp 339-409.
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Cremer, D.; Childs, R. F.; Kraka, E. In The Chemistry of the Cyclopropyl Group; John Wiley & Sons Ltd: New York, NY 1995; Vol. 2, pp 339-409.
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0012828820
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Atoms in Molecules
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34548188148
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20 for a readable account.
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20 for a readable account.
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28
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34548182441
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Any trajectory traced out by the gradient of the density satisfies the zero-flux condition at every point with the exception of those that terminate at a nuclear position where the density exhibits a cusp and its gradient is not defined.29 The only trajectories that define a two-dimensional manifold and satisfy the zero-flux condition at every point are those that terminate at a bond critical point where the gradient vector of the density vanishes
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29 The only trajectories that define a two-dimensional manifold and satisfy the zero-flux condition at every point are those that terminate at a bond critical point where the gradient vector of the density vanishes.
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30
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34548184565
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In a nonequilibrium geometry, the atomic statement of the virial theorem is again in accord with the statement for the total molecule, the kinetic energy now containing a component from the atom's share of the virial of the Feynman forces acting on the nuclei, the quantity W(Ω)31, to yield -T(Ω, T(Ω, V(Ω, W(Ω, E(Ω, WΩ, Thus the energy of an atom in a molecule is always defined and, like all atomic properties, is additive
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In a nonequilibrium geometry, the atomic statement of the virial theorem is again in accord with the statement for the total molecule, the kinetic energy now containing a component from the atom's share of the virial of the Feynman forces acting on the nuclei, the quantity W(Ω)31, to yield -T(Ω) = T(Ω) + V(Ω) + W(Ω) = E(Ω) + W(Ω). Thus the energy of an atom in a molecule is always defined and, like all atomic properties, is additive.
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31
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79960895355
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Matta, C. F, Boyd, R. J, Eds, Wiley-VCH: Weinheim, Germany
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