Neon atom sets

The second order correlation energy component, E Ne [IVe]) calculated for the ground state of the neon atom using systematic sequences of even-tempered basis sets of Gaussian functions designed for the Ne atom and designated [2nsnp] with n = 3,4,..., 13 are also collected in Table 1. 

Ai [p/o](A e [iVe])(spd] and i Epresent work to determine accurate correlation energies. However, it is known [45] [46] [47] that the exact second order energy for the neon atom ground state is —0.3879 Hartree. The largest basis set of s- and p- type functions considered in Table 1, therefore, recovers 37.7% of the exact second order correlation energy component whilst the largest basis set of functions with s-, p- and d-symmetries considered in Table 8 corresponds to 66.8% of the exact value. 

Molecules Isoelectronic with Neon.—Another set of molecules whose structure is typical of many standard chemical environments is the set of ten-electron first row hydrides Ne, HF, H20, NH3, and CH4. On p. 281 we saw how the outer electrons of the neon atom could be described either as being in the configuration (2s)2(2p)6 or, alternatively, as occupying four tetrahedral orbitals %2, %s, and y4 orientated relative to one another in a tetrahedral manner, the orientation of the tetrahedron in space being arbitrary. The electronic structures of the other molecules of the series can now be discussed in terms of this basic system if we imagine unit positive charges to be removed successively from the nucleus. 

The chemical counterpart of the roof will be a set of valence-shell electrons, and we shall look at atomic and molecular architectures that can be hosted under such a roof when bringing in stable nuclei and corresponding core electrons. In order to see what happens with such an idea in a Chemical Aufbau approach, let us start with an octet of electrons under which we place a nucleus with atomic number Z = 10 and a K-shell with two core electrons. The result is a neon atom, an exceptionally stable architecture with spherical (three-dimensional) symmetry. The same result would happen for Z = 18 (argon) with one more "floor", and so on or the following noble gas atoms. Actually, we start with the closed electronic shells allowed by the Pauli Exclusion Principle and the "n ( Rule", and we supply the nuclei corresponding to such shells. The proof for the stability of this architecture is provided by the high ionization potential and the low electron affinity. 

Another study for the neon atom indicates that convergence of the MP series requires that the energy spectrum is well-separated (i.e. the HF reference is significantly below the first excited state), not only for the unperturbed (H = Hq) and fully perturbed (H-Ho + H0 systems, but also for the negative perturbed case (H = Hq—H ). This condition was found not to hold when a basis set containing diffuse functions was used. 

The solutions of any one-electron atom (or ion) form a complete set and so the expectation that the orbitals of, for example, the neon atom could be expanded as linear combinations of them is both physically reasonable and mathematically under-pinned. But there are some practical considerations ... 

Function counterpoise corrections for the ground state of the neon atom calculated within the matrix Hartree-Fock approximation for a systematic sequence of even-tempered basis sets of Gaussian-type functions. In this table G represents a set of ghost orbitals. The internuclear separation in the NeG system is 5.0 bour."... 

The interaction-induced dipole polarizability and second hyperpolarizability of two neon atoms was reported by Hattig et al They subsequently used the calculated values along with an accurate potential for Nc2 to estimate the refractivity and hyperpolarizability second virial coefficients of gaseous neon. The calculation of ctint, Aai t and yjnt was performed at the CCSD level of theory with a d-aug-cc-pVQZ-33211 basis set. The R-dependence of the interaction-induced electric properties was obtained at a range of internuclear separations defined by 3 < R/ao < 20. 

Figure 3 Basis set convergence errors in the (a) Hartree carbon, oxveen. and neon atoms...

Table 8 Valence Correlation Energies of the Carbon, Oxygen, and Neon Atoms (in millihartrees) from CCSD(T) Calculations with the cc-pV/tZ Basis Sets. The Estimated Valence Correlation Energies of the Atoms are from Ref. 71 (WD)...

Figure 11.1 Supramolecular MP2 correlation energies (aug-cc-pVXZ (X = 2, 3) basis set extrapolation) as an approximation to energies of dispersion interaction between a neon atom and adenine (a) and two benzene...

Before we continue, I shall give a quick illustration of the improvements from MP2-F12 theory over conventional MP2 and MP2-R12 (with a linear correlation factor). The results for a simple test case, neon atom, are shown in Fig. 3. The advantage of MP2-R12 and particularly MP2-F12 over the conventional expansion is clear-cut. A much faster convergence to the putative basis set limit is observed. 

For the neon atom, the basis-set error decreases as we go from cc-pVXZ to aug-cc-pVXZ, where it becomes stable with respect to further addition of diffuse functions. The counterpoise correction... 

Table 8 The basis-set errors and the counteipoise corrections (in mEh) of a single neon atom calculated at the Hartree-Fock and valence MP2 levels...

BasisE ib This is a library file whichcontains gaussian atomic orbital basis sets for Hydrogen - Neon. The basis sets available to choose from are ... 

Dunning, T. H., 1989, Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron Through Neon and Hydrogen , J. Chem. Phys., 90, 1007. 

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