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Assigning Hybridization: A Tutorial
Assigning Hybridization: A Tutorial

... It is a common misconception that only the number of attachments to that atom controls hybridization of an atom. Instead, hybridization is controlled by what gives the molecule the lowest energy. This lowest energy includes not only a minimization of electron repulsion, but also accommodates electro ...
p15_11_6.pdf
p15_11_6.pdf

... action along the trajectory[5–10]; in this way semiclassical methods can capture essential quantum phenomena such as interference, zero-point energy effects, and to some extent tunneling. We present some results from an approach that uses semiclassical electron dynamics to evaluate the correlation t ...
Molecular Structure and Orbitals - Blackboard
Molecular Structure and Orbitals - Blackboard

... – Usually atomic orbitals are half-filled before bonding – Spins of the electrons are paired once bond is formed • Overlapping orbitals are on adjacent atoms and are either – Standard atomic orbitals (s, p, d, f) – Hybridized atomic orbitals made by combining individual atomic orbitals. • Each bonde ...
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Chemical Reactivity as Described by Quantum Chemical Methods
Chemical Reactivity as Described by Quantum Chemical Methods

... "modern" quantum mechanics around 1925 due to the work of Schrödinger, Heisenberg, Born, … Schrödinger's equation occupied a central position in this new theory and, although later on complemented by its relativistic analogue by Dirac, stood the test of time and has been for now 75 years the central ...
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... standard choice for the confining potential. Still, this is indeed an approximation and some efforts have been made to use a more realistic description of the whole physical situation, see e.g. Refs. [10, 14–17]. If one assumes this simplified view of the confining potential, theoretical quantum dot ...
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... eigenvalues of Dkl (kl ∈ B) can lie arbitrarily close to 0 or 1 (or to 0 or 2 when a spin-summed restricted Slater determinant is used as the low-level wavefunction). It can happen for very large basis sets (Nocc < LA ), or when the occupied core orbitals of neighbouring atoms are in practice unenta ...
A Theoretical Study of Atomic Trimers in the Critical Stability Region
A Theoretical Study of Atomic Trimers in the Critical Stability Region

... a harder task than bound state calculations. From a computational perspective such threshold states are difficult to obtain, since they lead to representations having very small and very large eigenvalues. As such, calculations of atomic halos and vdW trimers provide a challenge for any formal/numer ...
Interacting Fock spaces: central limit theorems and quantum
Interacting Fock spaces: central limit theorems and quantum

... some important properties are exposed. In particular we present the rules of commutations, namely canonical commutation relations (CCR), canonical anticommutation relations (CAR) and free commutation relations of these operators respectively in boson, fermion and free case. In the second chapter int ...
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... We enhance the recently proposed Optimized-orbital Quasi-Variational Coupled Cluster Doubles (OQVCCD) method for the calculation of ground-state molecular electronic structure by augmenting it with the standard perturbative (T) correction for the effects of connected triple excitations. We demonstra ...
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Hartree–Fock method

In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.The Hartree–Fock method often assumes that the exact, N-body wave function of the system can be approximated by a single Slater determinant (in the case where the particles are fermions) or by a single permanent (in the case of bosons) of N spin-orbitals. By invoking the variational method, one can derive a set of N-coupled equations for the N spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system.Especially in the older literature, the Hartree–Fock method is also called the self-consistent field method (SCF). In deriving what is now called the Hartree equation as an approximate solution of the Schrödinger equation, Hartree required the final field as computed from the charge distribution to be ""self-consistent"" with the assumed initial field. Thus, self-consistency was a requirement of the solution. The solutions to the non-linear Hartree–Fock equations also behave as if each particle is subjected to the mean field created by all other particles (see the Fock operator below) and hence the terminology continued. The equations are almost universally solved by means of an iterative method, although the fixed-point iteration algorithm does not always converge.This solution scheme is not the only one possible and is not an essential feature of the Hartree–Fock method.The Hartree–Fock method finds its typical application in the solution of the Schrödinger equation for atoms, molecules, nanostructures and solids but it has also found widespread use in nuclear physics. (See Hartree–Fock–Bogoliubov method for a discussion of its application in nuclear structure theory). In atomic structure theory, calculations may be for a spectrum with many excited energy levels and consequently the Hartree–Fock method for atoms assumes the wave function is a single configuration state function with well-defined quantum numbers and that the energy level is not necessarily the ground state.For both atoms and molecules, the Hartree–Fock solution is the central starting point for most methods that describe the many-electron system more accurately.The rest of this article will focus on applications in electronic structure theory suitable for molecules with the atom as a special case.The discussion here is only for the Restricted Hartree–Fock method, where the atom or molecule is a closed-shell system with all orbitals (atomic or molecular) doubly occupied. Open-shell systems, where some of the electrons are not paired, can be dealt with by one of two Hartree–Fock methods: Restricted open-shell Hartree–Fock (ROHF) Unrestricted Hartree–Fock (UHF)↑ ↑
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