Neon correlation energy

Table 2 Correlation energies of the neon isoelectronic series Comparison ofE 2 tth the...

Table 2 Correlation energies of the neon isoelectronic series Comparison ofE 2 1- (4-6), with the corresponding second order Moller-Plesset (MP2) [30], RLDA [16] andPW91-GGA [8] results. In addition, AHF 1- is compared With the difference IaE, Eq. (4.9), between RHF [60] and x-only ROPM [16]...

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. 

Neon, and the elements directly below it in the periodic table or the Solid State Table, form the simplest closed-shell systems. The electronic structure of the inert-gas solid, which is face-ccntercd cubic, is essentially that of the isolated atoms, and the interactions between atoms are well described by an overlap interaction that includes a correlation energy contribution (frequently described as a Van der Waals interaction). The total interaction, which can be conveniently fitted by a two-parameter Lennard-Jones potential, describes the behavior of both the gas and the solid. Electronic excitations to higher atomic states become excitons in the solid, and the atomic ionization energy becomes the band gap. Surprisingly, as noted by Pantelides, the gap varies with equilibrium nearest-neighbor distance, d, as d... 

Perhaps the most constructive contribution to solve this problem is the study of pair-densities in hydrides of elements from lithium to fluorine by Bader and Stephens 116). One major advantage is that it is not a predetermined working hypothesis, but a quantitative test of validity of Lewis structures, which may be appropriate or not. Bader and Stephens conclude that spatially localized pairs are satisfactory in LiH, BeH2, BH3 and BHT that CH4 (among all molecules) is a border-line case, and that intra-correlated pair-functions would fail to recover a major fraction of the correlation energy in NH3, H20 and HF. It is also true for the neon atom and for N2 and F2 that most of the correlation energy comes from correlation between even the best optimized electron-pairs. There is no physical basis for the view that there are two separately localized pairs of non-bonded electrons in HzO. 

Equation (85) has been confirmed very recently for the first row atoms (Gladney and Allen later obtained similar empirical values), dementi evaluated the correlation energies of these atoms and their ions empirically using his H.F. results and estimates of relativistic effects. The additivity observed is within the empirical uncertainty of the data. Figures 1 and 2 are based on his data and show the correlation energy increments in nitrogen and neon ions and atoms as more and more electrons are added. 

Fig. 2. Correlation energies of neon ions and atom (based on the empirical data of E. Clementi, Reference 67).

The complete energy given by the many-electron theory includes R [Eqs. (78) to (80)]. These many-electron corrections are negligible compared to the total corr. of an atom or the binding energy of a stable molecule (Section XVIII). The correlation energy, Eq. (167), between two non-bonded atoms on the other hand is a very small quantity to start with. The London attraction between two neon atoms 4.0 A apart r = 3,( A) is only —1.3 X 10 ev as compared to the corr. —11 ev of a single neon atom. The R terms could then be easily comparable to 2. The examination of these R many-electron terms, therefore, becomes of particular importance in connection with inter-molecular forces. 

Figure 15.5 shows the dependence of calculated cohesive energy on volume of the unit cell. Local density approximation of the exchange-correlation energy of electrons fails for these molecular systems. Minima at curves based on improved theory (Figure 15.5, small squares) correspond well to experimental quantities (diamonds) for argon and krypton (error of the order of 9%). For neon the error of the cohesive energy calculation equals to 39%. 

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