Exponentially correlated Gaussian functions in variational calculations. Momentum space properties of the ground state helium dimer

Komasa, Jacek

doi:10.1063/1.1373428

Cited by 20 publications

(16 citation statements)

References 74 publications

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“…A CP calculation using the CCSD(T) method predicts with a d-AV6Z basis set a binding energy of −10.58 K, while Table 2 and Fig. 4 show that a similar accuracy is achieved at a lower cost via (T, Q) or [31] b From symmetry adapted perturbation theory [57] c Variational upper bounds using exponentially correlated Gaussian functions [35] d Variational upper bound [36] e From Quantum Monte Carlo [29] [26] h MRCI results from Ref. [25] i From r 12 -MR-ACPF calculations [24] j Extrapolated results from CCSD(T) and FCI calculations in orbital bases [32] k From supermolecular Gaussian geminal calculations [37] l From supermolecular Gaussian geminal calculations [38] m From this work by direct extrapolation of the total interaction energy using Eqs.…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, Klopper [32] reported an accurate extrapolation of the He 2 potential to the limit of a complete basis using CC methods, both including single and double excitations (CCSD [33]) as well as perturbative corrections for connected triple excitations [CCSD(T) [34]]. Most of such accurate works, either directly [24,35,36] or indirectly (i.e., correcting the result for basis set unsaturation, as has been done in Refs. [25,26]) make use of explicitly correlated methods.…”

Section: Introductionmentioning

confidence: 99%

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Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Varandas

2008

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Configuration interaction and coupled cluster calculations are reported for He 2 using various orbital basis sets of the d-aug-AVX Z type, with the results being extrapolated to the one electron basis set limit both with counterpoise and without counterpoise correction. A generalized uniform singlet-and triplet-pair extrapolation scheme has been utilized for such a purpose. Using appropriate corrections to mimic full configuration interaction, the energies were predicted in excellent agreement with the best available estimates. The results also suggest that extrapolation to the complete basis set limit may be a general alternative to the counterpoise correction that yields a more accurate potential energy while being more economical.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Varandas

2008

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“…1). It is because of these exotic properties that "as the hydrogen molecule in the past, the helium dimer today became a test case for the development of new computational methods and tools" [5] in quantum chemistry. Despite this fundamental nature of the diffuse helium dimer wave function, it has escaped direct experimental observation until now, as the diffraction grating experiment measure the mean value and not the shape of the wave function itself.…”

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confidence: 99%

Single Photon Double Ionization of the Helium Dimer

et al. 2010

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We show that a single photon can ionize the two helium atoms of the helium dimer in a distance up to 10 Å . The energy sharing among the electrons, the angular distributions of the ions and electrons, as well as comparison with electron impact data for helium atoms suggest a knockoff type double ionization process. The Coulomb explosion imaging of He 2 provides a direct view of the nuclear wave function of this by far most extended and most diffuse of all naturally existing molecules. DOI: 10.1103/PhysRevLett.104.153401 PACS numbers: 36.40.Àc, 34.80.Dp The helium dimer ( 4 He 2 ) is an outstanding example of a fragile molecule whose existence was disputed for a long time because of the very weak interaction potential [1] (see black curve in Fig. 1). Unequivocal experimental evidence for 4 He 2 was first provided in 1994 in diffraction experiments [2] by a nanostructured transmission grating. Subsequently, the average dimer bond length and dimer binding energy could be determined to be 52 Å and 10 À7 eV (0:9 Â 10 À3 cm À1 or 1.3 mK) [3]. This very large bond length, a factor 100 larger than the hydrogen bond length, goes along with a prediction of very widely delocalized wave function, unseen in any other molecule [4] (see R 2 É 2 i function in Fig. 1). It is because of these exotic properties that ''as the hydrogen molecule in the past, the helium dimer today became a test case for the development of new computational methods and tools '' [5] in quantum chemistry. Despite this fundamental nature of the diffuse helium dimer wave function, it has escaped direct experimental observation until now, as the diffraction grating experiment measures the mean value and not the shape of the wave function itself. Our experiment provides a direct view of this diffuse object.The large distance between the two helium atoms and the minuscule binding energy make the helium dimer a unique model system to explore electron correlations over large distances. The most sensitive tool for such studies is multiple photoionization. Since photoabsorption is described by a single electron operator the photon energy and angular momentum is best thought of as being initially given to one electron of the atom only. In the absence of electron correlation the ejection of a single electron would be the only possible outcome of the photoabsorption process. Because of the ubiquity of electron correlation, however, the ejection of electron pairs by a single photon is a wide spread phenomenon seen in atoms [6], molecules [7,8], and solids [9]. This two electron process poses at least two central questions: what is the correlation mechanism by which the photon energy is distributed among the two electrons and over which distance are such correlations active? In the present Letter we report the surprising observation that a single photon can lead to nonsequential ejection of two electrons from two atoms which are separated by many atomic radii and where the overlap of the electronic wave functions is negligible. By measuring the internuclear dist...

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“…The values of E 0 represent strict upper bounds to the exact nonrelativistic interaction energy. The lowest one, ÿ10:9953 K, is significantly more accurate than the best previously published variational result, ÿ10:981 K [13], but still too small in magnitude to fit within the error bars established in Ref. [6]: ÿ11:009 0:008 K. The convergence of the relativistic properties, calculated directly from Eqs.…”

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confidence: 86%

Relativistic Correction to the Helium Dimer Interaction Energy

et al. 2005

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The lowest-order relativistic correction to the helium-helium interaction energy has been calculated for the first time, using two independent methods based on expansions in explicitly correlated Gaussian functions. At the equilibrium interatomic distance of 5.6 bohr, this correction amounts to +15.4 +/- 0.6 mK. As a by-product, a new upper bound of -10.9985 K for the nonrelativistic Born-Oppenheimer interaction energy has been obtained.

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Exponentially correlated Gaussian functions in variational calculations. Momentum space properties of the ground state helium dimer

Cited by 20 publications

References 74 publications

Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Single Photon Double Ionization of the Helium Dimer

Relativistic Correction to the Helium Dimer Interaction Energy

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