Eliminating spin contamination in auxiliary-field quantum Monte Carlo: Realistic potential energy curve of F2
J. Chem. Phys. 128, 114309 (2008); doi:10.1063/1.2838983
Published 19 March 2008
You are not logged in to this journal. Log in
The use of an approximate reference state wave function |
r
in electronic many-body methods can break the spin symmetry of Born–Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated |
r
. The method is applied to the difficult F2 molecule, which is unbound within unrestricted Hartree–Fock (UHF). With a UHF |
r
, spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF |
r
. Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.
©2008 American Institute of Physics
r
in electronic many-body methods can break the spin symmetry of Born–Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated |
r
. The method is applied to the difficult F2 molecule, which is unbound within unrestricted Hartree–Fock (UHF). With a UHF |
r
, spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF |
r
. Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.
©2008 American Institute of Physics
| History: | Received 10 December 2007; accepted 8 January 2008; published 19 March 2008 |
| Permalink: |
http://link.aip.org/link/?JCPSA6/128/114309/1 |
KEYWORDS and PACS
RELATED DATABASES
PUBLICATION DATA
0021-9606 (print)
1089-7690 (online)
REFERENCES (42)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- R. J. Bartlett and M. Musia
, Rev. Mod. Phys. 79, 291 (2007). - D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980).
- P. J. Reynolds, D. M. Ceperley, B. J. Alder, and W. A. Lester, J. Chem. Phys. 77, 5593 (1982).
- W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001), and references therein.
- S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003).
- D. M. Ceperley and B. J. Alder, J. Chem. Phys. 81, 5833 (1984).
- S. Zhang and M. H. Kalos, Phys. Rev. Lett. 67, 3074 (1991).
- S. Zhang, in Quantum Monte Carlo Methods in Physics and Chemistry, edited by M. P. Nightingale and C. J. Umrigar (Kluwer Academic, Dordrecht, 1999);
- W. A. Al-Saidi, H. Krakauer, and S. Zhang, Phys. Rev. B 73, 075103 (2006).
- W. A. Al-Saidi, S. Zhang, and H. Krakauer, J. Chem. Phys. 124, 224101 (2006).
- M. Suewattana, W. Purwanto, S. Zhang, H. Krakauer, and E. J. Walter, Phys. Rev. B 75, 245123 (2007).
- W. A. Al-Saidi, H. Krakauer, and S. Zhang, J. Chem. Phys. 125, 154110 (2006).
- W. A. Al-Saidi, H. Krakauer, and S. Zhang, J. Chem. Phys. 126, 194105 (2007).
- W. A. Al-Saidi, S. Zhang, and H. Krakauer, J. Chem. Phys. 127, 144101 (2007).
- E. R. Davidson and W. T. Borden,
J. Phys. Chem.87, 4783 (1983) , http://pubs3.acs.org/acs/journals/doilookup?in_doi=10.1021/j150642a005. - C.-J. Huang, C. Filippi, and C. J. Umrigar, J. Chem. Phys. 108, 8838 (1998).
- J. S. Sears, C. D. Sherrill, and A. I. Krylov, J. Chem. Phys. 118, 9084 (2003).
- R. C. Lochan and M. Head-Gordon, J. Chem. Phys. 126, 164101 (2007).
- K. Hijikata, J. Chem. Phys. 34, 221 (1961).
- M. S. Gordon and D. G. Truhlar,
Theor. Chim. Acta 71, 1 (1987) . - J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
- A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
- P. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch,
J. Phys. Chem. 98, 11623 (1994) . - M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 98, Revision A.11.4, Gaussian, Inc., Pittsburgh, PA, 2002.
- T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989).
- K. L. Schuchardt, B. T. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, and T. L. Windus,
J. Chem. Inf. Model. 47, 1045 (2007) . - E. Aprà, T. Windus, T. Straatsma, E. Bylaska, W. de Jong, S. Hirata, M. Valiev, M. Hackler, L. Pollack, K. Kowalski et al., NWCHEM, a computational chemistry package for parallel computers, Version 4.6, Pacific Northwest National Laboratory, Richland, Washington 99352-0999, USA, 2004.
- F. W. Bobrowicz and W. A. Goddard III, in Methods of Electronic Structure Theory, edited by H. F. Schaefer, III (Plenum, New York, 1977), pp. 79–127.
- M. W. Schmidt and M. S. Gordon,
Annu. Rev. Phys. Chem. 49, 233 (1998) . - D. C. Cartwright and P. J. Hay, J. Chem. Phys. 70, 3191 (1979).
- A spin (as opposed to charge) decomposition (ni,
−ni,
), which breaks spin symmetry, is found to be more efficient and is used in most lattice model constrained path Monte Carlo calculations (see, e.g., Ref. 33). This case will require further investigation. - S. Zhang, J. Carlson, and J. E. Gubernatis, Phys. Rev. B 55, 7464 (1997).
- M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. J. Su et al.,
J. Comput. Chem. 14, 1347 (1993) . - A. S. Coolidge, H. M. James, and E. L. Vernon, Phys. Rev. 54, 726 (1938).
- D. Feller and K. A. Peterson, J. Chem. Phys. 108, 154 (1998).
- L. Bytautas and K. Ruedenberg, J. Chem. Phys. 122, 154110 (2005).
- C. Filippi and C. J. Umrigar, J. Chem. Phys. 105, 213 (1996).
- M. O. Sinnokrot and C. D. Sherrill, J. Chem. Phys. 115, 2439 (2001).
- M. Musia
and R. J. Bartlett, J. Chem. Phys. 122, 224102 (2005). - H. Edwards, E. Good, and D. Long,
J. Chem. Soc., Faraday Trans. 2 72, 984 (1976) . - K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).








