Variational optimization and multi-determinants (60' lecture)

Cyrus Umrigar

Link to Presentation slides (in PPT or PDF) format:

Topics

• Introduction
  • Importance of optimizing wave functions
  • Energy versus variance minimization
• Forms of wave functions
• Efficient energy minimization methods
  • Newton method
  • Linear method for nonlinear parameters
  • Perturbation theory / perturbative effective fluctuation method
• Mixed energy and variance optimization
• Stabilization of optimization methods
• Examples
  • Si_2 and C_2 as examples of weak and strong correlation
  • First-row dimers
  • Solids
• Direct optimization of DMC energy

References

• • M. P. Nightingale and Melik-Alaverdian, Phys. Rev. Lett., 87, 043401 (2001).
  • C. Filippi and S. Fahy, J. Chem. Phys., 112, 3523 (2000);
  • D. Prendergast, D. Bevan and S. Fahy, Phys. Rev. B, 66, 155104 (2002);
  • A. Scemama and C. Filippi, PRB, (2006).
  • Casula and Sorella, J. Chem. Phys., 119, 6500 (2003).
  • Sorella, PRB 71, 241103 (2005).
  • C. J. Umrigar, Filippi, PRL 94, 150201 (2005)
  • C. J. Umrigar, Toulouse, Filippi, Sorella, Hennig, PRL 98, 110201 (2007).
  • J. Toulouse, C. J. Umrigar, J. Chem. Phys., 126, 084102 (2007).