Abstract
Stationarity of electron probability distribution within the resolution of atomic orbitals is considered involving some concepts from Orbital Communication Theory and the theory of Markov Processes. A new method of evaluating electron conditional probabilities based on natural orbitals is proposed and briefly discussed.
Highlights
In the last half-century the electron population analyses (EPA) turned out to be very useful and commonly used tools in probing the electronic structure and chemical reactivity of molecules
EPA-procedures give rise to partition the electron density of the whole molecule between atoms, chemical bonds, molecular fragments, etc. Such partition can be performed within either physical or Hilbert space of molecular orbitals (MO) and there is a multitude of diverse EPA-procedures among which the most commonly used are those proposed by: Mulliken [1,2], Löwdin [3,4], Weinhold [5], Bader [6], Hirshfeld [7] and Merz-Kollman [8]. This is a field of research that seems to be regarded by some scientists as exhausted, in this short paper we would like to address some of the general issues respecting stationarity and uniqueness of electron probability distributions within the framework of MO theory and resolution of atomic orbitals (AO)
For the hypothetical conditional probability matrix P obtained from appropriate renormalization of each row of matrix of elements {Γμ2,ν} its stationary distribution p differs from p and lim pP = p = p. To solve this problem we propose in this paper the following alternative definition of conditional probability Pν|μ, by means of natural orbitals and their occupation numbers: n
Summary
In the last half-century the electron population analyses (EPA) turned out to be very useful and commonly used tools in probing the electronic structure and chemical reactivity of molecules. Such partition can be performed within either physical or Hilbert space of molecular orbitals (MO) and there is a multitude of diverse EPA-procedures among which the most commonly used are those proposed by: Mulliken [1,2], Löwdin [3,4], Weinhold [5], Bader [6], Hirshfeld [7] and Merz-Kollman [8] This is a field of research that seems to be regarded by some scientists as exhausted, in this short paper we would like to address some of the general issues respecting stationarity and uniqueness of electron probability distributions within the framework of MO theory and resolution of atomic orbitals (AO). The main purpose of this article is to briefly introduce a new method of determining stationary electron probability distributions, based on natural orbitals (NO) and involving some concepts from the Orbital Communication Theory (OCT) of the chemical bond [10,11,12] and the theory of Markov Processes [13]
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