The Helium Dimer

Experiments carried out on He gas cooled to temperatures below 10 Khave demonstrated the presence of bound atom pairs with an average internuclear distance of 6200 1000 pm, nearly one hundred times larger than the bond distance in H2 Calculations indicate that there is just one vibrational level below the dissociation energy threshold and that Do is about 0.01 kJmoP [9]. Sinceis about 300 pm, the huge average internuclear distance suggests that vibrations allow the internuclear distance to increase to more than 10000 pm before the atoms must turn back. 

The study of the interactions among closed shell systems (van der Waals forces) represents a benchmark for theories of electron correlation. We report here the results of our variational MO-VB study of the interaction between two helium atoms [70]. Up to n=10 optimal virtuals are calculated and employed to generate MO-VB final wavefunctions of higher and higher accuracy, in the usual MO-VB form  

The energy of such wavefunctions is calculated by solving the final secular problem by means of usual standard VB techniques [20]. 

The results obtained are in acceptable agreement with Aziz s potential [72] which possesses a well of 34.7 pEh at 5.60 a.u. These calculations suggest that a complete accordance with the experimental and accurate theoretical results of Korona et al. [73] can be reached by the improved MO-VB wave function, once the appropriate number of virtuals is included and a more extended basis set with h functions is employed. Work is in progress in our laboratory on this problem. 

In this review, research in the field of van der Waals molecules accomplished by our group in the last few years was summarised. On the basis of the results obtained so far, it appears that the modification of the Roothaan equations to avoid basis set superposition error at the Hartree-Fock level of theory is a promising approach. The fundamental development of the SCF-MI strategy to deal with electron correlation treatments in the framework of the valence bond theory has been described. A compact multistructure and size 

Laguna et al. (Eds.). Quantum Systems in Chemistry and Physics vol. 1 Basic Problems and Model Systems, Kluwer Academic Publishers, Dordrecht, p. 361 

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Fig. 1. Counterpoise-corrected and uncorrected for the helium dimer. The dashed lines represent the estimated CBS limit.

A particularly interesting group of reactions that fall in this category are those of the helium dimer ion, He (Ar22 ). It was suggested some time ago that reaction of this species with nitrogen,... 

Fig. 17. The calculated MO-VB interaction potential (JiEh) for the helium dimer system.

Calculations of the third-order exchange contributions have not been performed thus far. The results reported in Ref. (81) for the total third-order exchange effect for the helium dimer suggest that they quench a large part of the third-order polarization contribution. 

A symmetry-adapted perturbation theory approach for the calculation of the Hartree-Fock interaction energies has been proposed by Jeziorska et al.105 for the helium dimer, and generalized to the many-electron case in Ref. (106). The authors of Refs. (105-106) developed a basis-set independent perturbation scheme to solve the Hartree-Fock equations for the dimer, and analyzed the Hartree-Fock interaction energy in terms of contributions related to many-electron SAPT reviewed in Section 7. Specifically, they proposed to replace the Hartree-Fock equations for the... 

The scalar spin-spin coupling has been calculated by Pecul for the helium dimer using full configuration interaction and EOM-CCSD methods. The... 

Hesselmann, A. and Jansen, G. (2003). The helium dimer potential from a combined density functional theory and symmetry-adapted perturbation theory approach using an exact exchange-correlation potential. Phys. Chem. Chem. Phys., 5, 5010-14. 

Total energy (Etotai) and full Cl correlation energy (Ecorr) for the beryllium atom and the helium dimer (Rt = 5.6 bohr) obtained with the numerical molecular basis sets. All energies are in Hartree. 

Recently, the convergence of the many-body sapt expansion for the interaction-induced dipole moment of He-H2 (24) and the polarizability of He2 (24, 32). has been checked by comparison with fci results in the same basis set. The numerical results for the helium dimer are summarized in Table 1 where we consider the anisotropy 7 and the trace a 7 = Aa — Aasx and a = (Act, + 2Aazz)/3, in which the z-axis is the molecular axis. An inspection of Table 1 shows that for all distances considered in Ref. (32) the many-body SAPT expansion reproduces the fci results to... 

B. Liu and A. D. McLean, ]. Chem. Phys., 91, 2348 (1989). The Interacting Correlated Fragments Model for Weak Interactions, Basis Set Superposition Error, and the Helium Dimer Potential. 

One of the simplest van der Waals complexes is the helium dimer. The small size of the system has made it possible to evaluate the He- He spin-spin coupling constant in an accurate manner, at the full configuration interaction level The Fermi-contact term has been found to have non-negligible value of 1.3 Hz at R=5.6 a.u. (dose to the energy minimum), while the other contributions are practically zero. The coupling decreases very fast, in an exponential manner, with the intemuclear distance R. For R equal to 4 a.u. it is over 22 Hz, while for R over 7 a.u. it falls below... 

By exciting a pair of metastable He atoms in the metastable state 2 5 1 with a narrow-band laser at X = 1083 nm, bound vibrational levels of the helium dimer He in the electronic 0 state (2 S + 2 Pq) could be populated in a magnetic trap [619]. The inner turning point at R = ISOao and the outer turning point at 1150 0 = 57.5 nm show that these excited dimers are indeed giant molecules in terms of their size. 

Moszynski et al. calculated the interaction-induced polarizability of the helium dimer for the internuclear separations 3computational approach relied on spin-adapted perturbation theory (SAPT) calculations with a large basis set of [5s4p3d2f] size. Subsequently, they determined the polarized and depolarized Raman spectrum of the dimer. The computed polarized spectrum displays fair agreement with experiment. Most important, the computed intensities of the depolarized spectrum agree quite well with the experimental data reported by Proffitt et al7 ... 

Unit 6 The helium dimer and trimer (van der Waals interactions, three body effects)... 

Recently, impressive calculations using Hylleraas wave functions have been done for the H2 molecule by the Hylleraas method [44,63], the Iterative Complement Iteration (ICI) [36], and Explicitly Correlated Gaussian (ECG) [12] methods. Few molecules have yet been calculated using Hylleraas-type wave functions HeH+ and some other species [72] using the Hylleraas method, the helium dimer He2 interaction energy [46] and the ground state of the BH molecule [7], both using the ECG method. 

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