Skip to main content

The New Resonating Valence Bond Method for Ab-Initio Electronic Simulations

  • Chapter
  • First Online:
Many-Electron Approaches in Physics, Chemistry and Mathematics

Part of the book series: Mathematical Physics Studies ((MPST))

Abstract

The Resonating Valence Bond theory of the chemical bond was introduced soon after the discovery of quantum mechanics and has contributed to explain the role of electron correlation within a particularly simple and intuitive approach where the chemical bond between two nearby atoms is described by one or more singlet electron pairs. In this chapter Pauling’s resonating valence bond theory of the chemical bond is revisited within a new formulation, introduced by P. W. Anderson after the discovery of High-T\(_\text {c}\) superconductivity. It is shown that this intuitive picture of electron correlation becomes now practical and efficient, since it allows us to faithfully exploit the locality of the electron correlation, and to describe several new phases of matter, such as Mott insulators, High-T\(_\text {c}\) superconductors, and spin liquid phases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Google TurboRVB web page for further informations.

References

  1. Anderson, P.W.: The resonating valence bond state in La\(_2\)CuO\(_4\) and superconductivity. Science 235, 1196 (1987)

    Google Scholar 

  2. Attaccalite, C., Sorella, S.: Stable liquid hydrogen at high pressure by a novel ab initio molecular-dynamics calculation. Phys. Rev. Lett. 100(11), 114501 (2008)

    Article  ADS  Google Scholar 

  3. Benedict, W.S., Gailar, N., Plyler, E.K.: Rotation-vibration spectra of deuterated water vapor. J. Chem. Phys. 24(6), 1139–1165 (1956)

    Article  ADS  Google Scholar 

  4. Burkatzki, M., Filippi, C., Dolg, M.: Energy-consistent pseudopotentials for quantum monte carlo calculations. J. Chem. Phys. 126(23), 234105 (2007)

    Article  ADS  Google Scholar 

  5. Chakravorty, S.J., Gwaltney, S.R., Davidson, E.R., Parpia, F.A., p Fischer, C. F.: Ground-state correlation energies for atomic ions with 3 to 18 electrons. Phys. Rev. A 47(5), 3649–3670 (1993)

    Google Scholar 

  6. Clough, S.A., Beers, Y., Klein, G.P., Rothman, L.S.: Dipole moment of water from Stark measurements of H\(_2\)O, HDO, and D\(_2\)O. J. Chem. Phys. 59(5), 2254 (1973)

    Article  ADS  Google Scholar 

  7. Feller, D., Boyle, C.M., Davidson, E.R.: One-electron properties of several small molecules using near Hartree–Fock limit basis sets. J. Chem. Phys. 86(6), 3424 (1987)

    Google Scholar 

  8. Foulkes, W.M.C., Mitas, L., Needs, R.J., Rajagopal, G.: Quantum Monte Carlo simulations of solids. Rev. Mod. Phys. 73(1), 33–83 (2001)

    Article  ADS  Google Scholar 

  9. Gdanitz, R.J.: Accurately solving the electronic schrödinger equation of atoms and molecules using explicitly correlated (\(r_{12}\))-/MR-CI. the ground state of beryllium dimer Be\(_2\). Chem. Phys. Lett. 312, 578 (1999)

    Article  ADS  Google Scholar 

  10. Merritt, J.M., Bondybey, V.E., Heaven, M.C.: Beryllium dimer—caught in the act of bonding. Science 324(5934), 1548 (2009)

    Google Scholar 

  11. Marchi, M., Azadi, S., Casula, M., Sorella, S.: Resonating valence bond wave function with molecular orbitals: application to first-row molecules. J. Chem. Phys. 131(15), 154116 (2009)

    Article  ADS  Google Scholar 

  12. Neuscamman, E.: Size consistency error in the antisymmetric geminal power wave function can be completely removed. Phys. Rev. Lett. 109(20), 203001 (2012)

    Article  ADS  Google Scholar 

  13. Nguyen, H.V., Galli, G.: A first-principles study of weakly bound molecules using exact exchange and the random phase approximation. J. Chem. Phys. 132, 044109 (2010)

    Article  ADS  Google Scholar 

  14. Petruzielo, F.R., Toulouse, J., Umrigar, C.J.: Basis set construction for molecular electronic structure theory: Natural orbital and Gauss-Slater basis for smooth pseudopotentials. J. Chem. Phys. 134(6), 064104 (2011)

    Article  ADS  Google Scholar 

  15. Røeggen, I., Veseth, L.: Interatomic potential for the \(X^1 \Sigma ^+_g\) state of Be\(_2\), revisited. Int. J. Quantum Chem. 101, 201 (2005)

    Google Scholar 

  16. Sorella, S.: Wave function optimization in the variational Monte Carlo method. Phys. Rev. B 71(24), 241103 (2005)

    Article  ADS  Google Scholar 

  17. Sorella, S., Capriotti, L.: Algorithmic differentiation and the calculation of forces by quantum Monte Carlo. J. Chem. Phys. 133(23), 234111 (2010)

    Article  ADS  Google Scholar 

  18. Sorella, S., Casula, M., Rocca, D.: Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods. J. Chem. Phys. 127(1), 014105 (2007)

    Article  ADS  Google Scholar 

  19. Umrigar, C.J., Toulouse, J., Filippi, C., Sorella, S., Hennig, R.G.: Alleviation of the fermion-sign problem by optimization of many-body wave functions. Phys. Rev. Lett. 98(11), 110201 (2007)

    Article  ADS  Google Scholar 

  20. Verhoeven, J., Dymanus, A.: Magnetic properties and molecular quadrupole tensor of the water molecule by beam-maser Zeeman spectroscopy. J. Chem. Phys. 52(6), 3222 (1970)

    Article  ADS  Google Scholar 

  21. Zen, A., Luo, Y., Sorella, S., Guidoni, L.: Molecular properties by Quantum Monte Carlo: an investigation on the role of the wave function ansatz and the basis set in the water molecule. J. Chem. Theory Comput. 9(10), 4332–4350 (2013)

    Google Scholar 

Download references

Acknowledgments

We acknowledge Mariapia Marchi for sending us unpublished data about the beryllium dimer.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sandro Sorella .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Sorella, S., Zen, A. (2014). The New Resonating Valence Bond Method for Ab-Initio Electronic Simulations. In: Bach, V., Delle Site, L. (eds) Many-Electron Approaches in Physics, Chemistry and Mathematics. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-06379-9_21

Download citation

Publish with us

Policies and ethics