CHAMP is a quantum Monte Carlo suite of programs for electronic structure calculations on a variety of systems (atoms, molecules, clusters, solids and nanostructures) principally written by Cyrus Umrigar and Claudia Filippi with major contributions by Julien Toulouse and Devrim Guclu, postdocs at Cornell and smaller contributions by others.

In each case, the very best quantum Monte carlo algorithms have been used. A great deal of attention has been paid to the implementation of highly efficient algorithms, a variety of sophisticated wave functions, and tools to optimize them, with particular emphasis on all-electron and pseudopotential finite systems. For such systems, the code can also compute forces on the nuclei, a necessary precursor of molecular dynamics calculations. There are both serial and parallel (MPI) versions of the codes.

Particularly noteworthy features of CHAMP are:

• Efficient wave function optimization by linear combination of energy and variance minimization
• A variety of sophisticated forms of the Jastrow factor
• An accelerated Metropolis method
• Efficient diffusion Monte Carlo algorithms
• Numerical forces on nuclei for finite systems

The wave function parameters can be optimized by variance minimization, but we rarely use this method now. For finite systems, it is possible to optimize not only the Jastrow part but also the determinantal part of the wave function (CI coefficients, orbital coefficients and exponents).

• Optimized trial wave functions for quantum Monte Carlo calculations,
  C.J. Umrigar, K.G. Wilson and J.W. Wilkins, Phys. Rev. Lett.,60, 1719 (1988).
• A method for determining many-body wave functions,
  C.J. Umrigar, K.G. Wilson and J.W. Wilkins,
  in Computer simulation studies in condensed matter physics: recent developments,
  ed. by D.P. Landau, K.K. Mon and H.B. Schuttler (Springer-Verlag 1988).
• Two Aspects of Quantum Monte Carlo: Determination of Accurate Wavefunctions and Determination of Potential Energy Surfaces of Molecules,
  C.J. Umrigar, Int. J. Quant. Chem. Symp., 23, 217 (1989).

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Although naive energy minimization is far less efficient than variance minimization, in recent years we have developed three energy minimization schemes that are very efficient and that allow one to systematically extrapolate away the fixed-node error for many systems.

• Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions,
  C. J. Umrigar, J. Toulouse, C. Filippi, S. Sorella and R. G. Hennig,
  Phys. Rev. Lett. 98, 110201 (2007). [pdf]


• Optimization of quantum Monte Carlo wave functions by energy minimization,
  J. Toulouse, C. J. Umrigar,
  J. Chem. Phys.Phys. 126, 084102 (2007). [pdf]


• Energy and Variance Optimization of Many-Body Wave Functions
  C. J. Umrigar and Claudia Filippi,
  Phys. Rev. Lett. 94, 150201 (2005). [pdf]

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The "effective fluctutation potential" method is an approach originally proposed by S. Fahy to optimize the wave function by energy minimization. It was further developed and implemented in the code by C. Filippi, F. Schautz and A. Scemama to optimize orbital and CI coefficients.

• Variational Monte Carlo in Solids,
  S. Fahy, in Quantum Monte Carlo Methods in Physics and Chemistry,
  ed. by M.P. Nightingale and C.J. Umrigar. NATO ASI Series, Vol. C-525 (Kluwer Academic Publishers, Boston, 1999).
• Optimal orbitals from energy fluctuations in correlated wave functions,
  C. Filippi and S. Fahy, J. Chem. Phys. 112, 3523 (2000).
• Optimization of CI coefficients in multi-determinant Jastrow-Slater wave functions
  F. Schautz and S. Fahy, J. Chem. Phys. 116, 3533 (2002).

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These include forms that are systematically improvable (within the constraint of not using more than e-e-n correlations) and obey all three types of cusp conditions exactly. For large systems the option exists to use Jastrow functions that go exactly to a constant beyond some distance, thereby improving the scaling of the computer time with system size. The earlier forms of the Jastrow factor are described in the first three references above in:

• Multiconfiguration wave functions for Quantum Monte Carlo calculations of first-row diatomic molecules
  Claudia Filippi and C.J. Umrigar, J. Chem. Phys. 105, 213 (1996).

The most recent form has not been published but notes can be obtained from Cyrus Umrigar.

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It allows one to make very large moves and still have a high acceptance, resulting in very short autocorrelation times. The gain, compared to other Metropolis methods is particularly large when pseudopotentials are not used.

• Accelerated Metropolis Method,
  C.J. Umrigar, Phys. Rev. Lett. 71, 408 (1993).
• Variational Monte Carlo Basics and Applications to Atoms and Molecules,
  C.J. Umrigar, in Quantum Monte Carlo Methods in Physics and Chemistry, ed. by M.P. Nightingale and C.J. Umrigar. NATO ASI Series, Series C, Mathematical and Physical Sciences, Vol. C-525, (Kluwer Academic Publishers, Boston, 1999).

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It takes into account the singularities in the local energy and velocity at nodes of the wave function and at particle coincidences.

• A Diffusion Monte Carlo Algorithm with Very Small Time-Step Errors,
  C.J. Umrigar, M.P. Nightingale and K.J. Runge, J. Chem. Phys., 99, 2865 (1993).

The algorithm has since then been extended to use pseudopotentials and employ single-electron moves.

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It employs correlated sampling along with a space-warp coordinate transformation that improves the efficiency.

• Two Aspects of Quantum Monte Carlo: Determination of Accurate Wavefunctions and Potential Energy Surfaces of Molecules,
  C.J. Umrigar, Int. J. Quant. Chem. Symp., 23, 217 (1989).
• Correlated sampling in quantum Monte Carlo: A route to forces,
  C. Filippi and C. J. Umrigar, Phys. Rev. B., 61, R16291, (2000).
• Interatomic forces and correlated sampling in quantum Monte Carlo,
  C. Filippi and C. J. Umrigar, in Recent Advances in Quantum Monte Carlo Methods, Part II, pgs. 12-29, edited by W.A.Lester, Jr., S.M. Rothstein, and S. Tanaka (World Scientific, Singapore, 2002).

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