Natural orbital function equilibrium geometries

All three states were described by a single set of SCF molecular orbitals based on the occupied canonical orbitals of the X Z- state and a transformation of the canonical virtual space known as "K-orbitals" [10] which, among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical intemuclear distances, i.e. R. (equilibrium geometry) and about 3Re,and adding to the HF... 

The natural orbitals have properties that are very stable, independently of how the wave function has been obtained. We find for all molecular systems that the NOs can be divided into three different classes One group of orbitals have occupation numbers close to 2. These orbitals may be considered as almost doubly occupied. We call them strongly occupied. There is another large group of orbitals that have occupation numbers close to zero (typically smaller than 0.02). These are the weakly occupied NOs. For stable, closed-shell molecules close to their equilibrium geometry, we shall find only these two types of NOs. However, in more complex situations (molecules far from equilibrium geometry, excited states, radicals, ions, etc.) we find a... 

At the end of the reaction we have two new bonding orbitals from the ring. They are single bonds, which typically have occupation numbers close to two. The importance of this analysis is that it is valid for the exact wave function. Whether it remains true for approximate methods depends on the method. Below we shall discuss an approach that takes these features of the electronic structure explicitly into account. But first, we shall look more closely at the situation where all occupied orbitals have occupation numbers close to two. This situation is common for most molecules in their ground electronic state, close to their equilibrium geometry. It is a natural first approximation to assume that the occupation numbers are exactly two or zero, which can be... 

The natural orbitals of this wave function will be the same, but now p and p2 will have the occupation number one. This is the crossing point shown in Figure 1. So, we have three wave functions Equation (14), valid at infinite distance Equation (15), valid at the C4H8 equilibrium geometry and Equation (16), valid in the transition-state region. How do we write a wave function that is valid for the full reaction path The obvious choice is to abandon the singleconfiguration (HF) approach and write ... 

Let us analyse the electronic state in terms of the natural-orbital occupation numbers in Table 5.4. At the equilibrium geometry, the occupation number of the lOg orbital is 1.9643, indicating that a single Slater determinant with a doubly occupied Icr orbital should provide a reasonably accurate representation of the exact wave function. With an occupation number of 0.0199, the lcr orbital (which corresponds to the antibonding Is orbital of the minimal basis) is the second most important... 

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