Neon dimer

T. Jahnke, A. Czasch, M.S. Schoffler, S. Schossler, A. Knapp, M. Kasz, J. Titze, C. Wimmer, K. Kreidi, R.E. Grisenti, A. Staudte, O. Jagutzki, U. Hergenhahn, H. Schmidt-Bocking, R. Dorner, Experimental observation of interatomic Coulombic decay in neon dimers, Phys. Rev. Lett. 93 (2004) 163401. 

The extended geminal models are reviewed with emphasis both on their conceptual structure and computational feasibility. A new numerical model which drastically reduced the computation time at the cost of a very small reduction in accuracy, is introduced. A review of the applications of the extended geminal models to studies of intermolecular interactions is given, and the neon dimer is considered in more detail to illustrate the properties of these models. 

In this work we shall review the essential features of the extended geminal models, sketch some numerical refinements of the models, consider some important applications and present some new numerical results on the neon dimer. 

In this section we shall briefly comment on previous works based on extended geminal models (Sect. 3.1) and present a case study of the neon dimer (Sect. 3.2). 

Fig. 1. Intersection between the xy-plane and the charge ellipsoids of the localized orbitals of the neon dimer. Relative interatomic distance twice as large as on figure. Charge centroids are marked with a cross and nuclear positions with a dot. The numbering of the ellipsoids is utilized in Table 3.

In Table 4 we present results from the calculation on the neon dimer. The equilibrium distance of the potential is not determined in this work. But based on previous experience with extended geminal models, say on the He2 dimer [45] and the Be2 dimer [47], we can safely assume that the equilibrium distance obtained by a geometry optimization, is close to the experimental value. Hence, the quantity —U (R = 5.84 au), where U(R) is the interatomic... 

Table 3. Intersystem valence double pair correction terms for the neon dimer as a function of the dimension of the truncated virtual spacea,b,c ...

The extended geminal models have two main advantages. First, the conceptual structure which facilitates interpretation. This property is utilized in several studies on intermolecular interactions where energy decomposition schemes illuminate the character of the bonding. Second, the models are highly accurate. This feature is related to the FCI corrections on which the models are based. The reported calculations on few-electron systems illustrate this point. However, as demonstrated by the calculation on the neon dimer reported in this work, a high accuracy of a calculation on larger systems, require that at least triple pair corrections are included. 

A step in the right direction was made by Engel et al. [136] who obtained reasonable results for the helium and neon dimers. In [137], Bartlett and... 

The Diels-Alder reaction produced on the lighter noble gas dimer compounds (i.e. He2 Ceo and Ne2 C6o) presents reaction and activation barriers that are close to the ones obtained for free Ceo- I-e., the reaction energies for the most reactive bond 1 are compared to the free fullerene 0.2 and 2.4 kcal moP more favorable for the helium and neon dimer compounds, respectively. Likewise, the activation barrier for the addition to bond 1 is 12.8 and 11.9 kcal moP for the He2 C6o and Ne2 Ceo cases, respectively. The other [6,6] bonds present similar reaction and activation energies, whereas [5,6] bonds are much more less reactive. It is important to remark that the addition of 1,3-butadiene produces a rotation of the noble gas dimer which is reoriented during the course of the reaction from the initial position to face the attacked bond. 

Eggenberger R, Gerber S, Huber H et al (1994) A new ab initio potential for the neon dimer and its application in molecular dynamics simulations of the condensed phase. Mol Phys 82 689-699... 

Within the framework of the Born-Oppenheimer approximation the initial state, that is, the ground state of neutral neon dimer, is given by... 

Here r(i ) = r[2 S+Ne ](jR) is the local electronic decay width of inner-valence ionized neon dimer and R) is the phase of the resonance width amplitude. 

Finally, we recall the two van der Waals systems of Section 8.5. For the neon dimer, we obtained a CCSD(T) interaction energy of —132 pEh, in good agreement with the experimental energy of — 134 pEh. For the water dimer, we obtained at the CCSD(T) level an interaction eneigy of —7.9 mEh, again in agreement with the experimental value of —8.6(11) mEh. 

Depending on the nature of the interaction, molecular interaction energies vary considerably in magnitude. Typically, the interactions are 100-500 mEh for covalent bonds, 1-10 mEi, for hydrogen-bonded complexes and 50-5(X) pEh for complexes bound by dispersion. The BSSE is present in all cases but is more important for weakly bound van der Waals ctnnplexes than for chemically bonded molecules. In the following, we shall investigate the importance of BSSE at the Hartree-Fock and correlated levels for three systems, selected to represent the three cases of interaction listed above the BH molecule, the water dimer and the neon dimer. 

In the neon dimer, the closed-shell, nonpolar neon atoms are held together by dispersion forces alone. This very weak interaction is a pure correlation effect and cannot be described by the Hartree-Fock model, which, in the limit of a complete basis, gives rise to a purely repulsive interaction between the two atoms. An empirical potential-energy curve for the neon dimer gives an interaction energy of —134 pEh with a minimum at a separation of 5.84oo [29]. Because of the extreme weakness of this interaction (it constitutes less than a millionth of the total energy of the system), we must carefully consider the effects of BSSE. 

Hartree-Fock interaction is attractive at the experimental minimum. The origin of this interaction is BSSE, whose spurious stabilization of the neon dimer outweighs the Pauli repulsion for small basis sets. These effects are illustrated on the left in Figure 8.24, where we have plotted the (uncorrected) Hartree-Fock potential-energy curve for various doubly augmented basis sets. As the cardinal number increases, the spurious Hartree-Fock minimum becomes shallower and located further out. We note that the potential-energy curve may contain several such spurious minima. Thus, the d-aug-cc-pVDZ curve has a minimum of —73 pEh at a separation of 6.1oo a shallower minimum of —14 pEh at a separation of 8.5ao-... 

Fig. 8.24. The interaction energy of the neon dimer (in pEh) plotted as a function of the intemuclear separation (in oq). On the left, we have plotted the interaction energies calculated at the Hartree-Fock level in a complete basis (lull line) and using the d-aug-cc-pVXZ sets with X < 4 (with the number of consecutive dots indicating the cardinal number). No counterpoise correction has been applied to any of the Hartree-Fock curves. On the right, we have plotted the (counterpoise-corrected) interaction energies for different ab initio models at the frozen-core d-aug-cc-pV5Z level the Hartree-Fock model (full line), the MP2 model (longer dashes), the CCSD model (shorter dashes) and the CCSD(T) model (dots). The thick grey line represents the potential-energy curve extracted from experiment [29].

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