CCL: Case Studies of QM Computational Chemistry in Reactivity



Stefan,
 You wrote: "the HK theorems simply do not apply here."
 You are very incorrect!
 The Hohenberg-Kohn theorems always apply to a non-degenerate,
 non-relativistic chemical ground state.
 That is the whole point of these theorems! They establish that there is a
 one-to-one mapping between the
 system's Hamiltonian (up to an arbitrary constant potential offset) and its
 ground state electron density distribution.
 Because the system's Hamiltonian determines its wavefunction, this
 establishes that all physical properties of the system, not just its energy
 are functionals of the ground state electron density distribution.
 It is true that there is some flexibility in how to define net atomic
 charges, but owing to the Hohenberg-Kohn theorems all methods that are not
 functionals of the electron density distribution are ruled out up front.
 This means that Mulliken and Lowdin populations cannot represent physical
 properties, because they are not functionals of the ground state electron
 distribution. This does not mean that net atomic charges are not physical
 properties, because it is possible to construct definitions of net atomic
 charges that are functionals of the electron density distribution.
 Sincerely,
 Tom
 On Fri, Sep 11, 2015 at 2:54 AM, Stefan Grimme grimme*|*thch.uni-bonn.de <
 owner-chemistry(_)ccl.net> wrote:
 >
 > Sent to CCL by: "Stefan  Grimme" [grimme^thch.uni-bonn.de]
 > Dear Tom,
 > to this:
 > >I wanted to address one more of your comments. You wrote:  "I
 don't want
 > to defend orbital based partitionings (I prefer observables) but making the
 > mathematical limit to the encompassing requirement seem nonsense to
 me."
 > Actually, this has already been proved in Nobel prize winning work. In
 > 1998, Walter Kohn received the Nobel prize in chemistry for his development
 > of density functional theory. This theory proved that all ground state
 > properties of a non-relativistic, non-degenerate quantum chemical system
 > can be represented as a functional of the ground state electron density
 > distribution. A direct corollary is that since net atomic charges are a
 > property of a chemical system, for a non-degenerate chemical ground state
 > the net atomic charges have to be a functional of the ground state electron
 > distribution. When I and others say that the net atomic charges should
 > approach a well-defined basis set limit, because they are functionals of
 > the electron density distribution, we!
 >   are simply stating a direct corollary of the Hohenberg-Kohn theorems.
 > This has already been proved and received a Nobel prize.
 >
 > the HK theorems simply do not apply here. They establish a relation
 > between two observables in a strict QM sense (energy and density). Because
 > there is no atomic charge operator as I already said, the statement
 > "atomic charges are a functional of the ground state density"
 > is just empty.
 > What you probably mean is that some operational definitions
 > of atomic charge like AIM or Hirshfeld are functionals of the density.
 > This is true but does not eliminate the arbitrariness in their definition
 > (usually artificial boundaries in the molecule).
 >
 > Best wishes
 > Stefan>
 >
 >