CONTENTS
to
"Monte Carlo Methods in Ab Initio Quantum Chemistry"
Brian L. Hammond, William A. Lester, Jr.
and Peter J. Reynolds

1 ...... Introduction to Monte Carlo Methods
1.1 ...... Random Numbers and Statistical Analysis
1.1.1 ...... Probability density and distribution functions
1.1.2 ...... Characterization of probability density functions
1.1.3 ...... Functions of random variates and the central limit theorem
1.2 ...... Generation of Pseudorandom Numbers
1.2.1 ...... Generation of uniform variates
1.2.2 ...... Generation of non-uniform random variates
1.3 ...... Random Walks and Metropolis Sampling
1.3.1 ...... Markov chains
1.3.2 ...... Random walks in state space
1.3.3 ...... The Metropolis method
1.3.4 ...... The generalized Metropolis method
1.4 ...... Monte Carlo Integration
1.4.1 ...... Uniform sampling
1.4.2 ...... Importance sampling
1.4.3 ...... Expected values using importance sampling

2 ...... Variational Methods
2.1 ...... Review of the Variational Method
2.2 ...... Monte Carlo Evaluation of Expectation Values
2.2.1 ...... Simple Metropolis sampling
2.2.2 ...... Importance sampling: Fokker-Planck formalism
2.2.3 ...... Importance sampling: Metropolis formalism
2.2.4 ...... Electronic properties
2.2.5 ...... Evaluation of the variance
2.3 ...... Other Sampling Methods
2.3.1 ...... Guiding functions
2.3.2 ...... Correlated sampling
2.4 ...... Monte Carlo Optimization
2.4.1 ...... Optimization criteria
2.4.2 ...... Energy optimization
2.4.3 ...... Variance optimization

3 ...... Green's Function Methods
3.1.1 ...... Green's function formalism
3.1.2 ...... Time-dependent Green's functions
3.2 ...... Diffusion Monte Carlo
3.2.1 ...... Short time approximation
3.2.2 ...... Importance sampling
3.2.3 ...... Estimating the ground state energy
3.2.4 ...... ``Pure'' diffusion Monte Carlo
3.3 ...... Exact Green's Function Methods
3.3.1 ...... Green's function Monte Carlo for a bounded potential
3.3.2 ...... Domain Green's function Monte Carlo
3.3.3 ...... Coulomb Green's function Monte Carlo
3.3.4 ...... Feynman-Kac Coulomb correction
3.3.5 ...... Explicit sampling of the Coulomb singularity
3.4 ...... Comparison of QMC Methods

4 ...... Treating Fermions
4.1 ...... Nodal Methods
4.1.1 ...... Fixed-node approximation
4.1.2 ...... Understanding the nodes
4.1.3 ...... Releasing the nodes
4.1.4 ...... Adaptive nodes
4.2 ...... Interacting Walker Methods
4.2.1 ...... Pairing methods
4.2.2 ...... Fully interacting ensembles

5 ...... Variational Trial Functions
5.1 ...... Properties of the Exact Wave Function
5.2 ...... General Trial Function Forms
5.3 ...... Hartree-Fock and Beyond
5.3.1 ...... Hartree-Fock and correlation energies
5.3.2 ...... Linear combination of atomic orbitals and the self-consistent field equations
5.3.3 ...... Cusp conditions
5.3.4 ...... Some Hartree-Fock trial function properties
5.3.5 ...... Post Hartree-Fock methods
5.4 ...... Correlated Molecular Orbital Functions

6 ...... Excited States
6.1 ...... Transforming Energy Decay Curves
6.2 ...... Explicit Orthogonalization
6.3 ...... Fixed-Node Method
6.4 ...... Concurrent Evaluation of Many States

7 ...... Electronic Properties
7.1 ...... VMC Properties
7.2 ...... Approximate Phi_0^2 Estimators
7.3 ...... Rigorous Sampling of Phi_0^2
7.3.1 ...... Future walking
7.3.2 ...... Time correlation methods
7.3.3 ...... Discussion of Phi_0^2 methods
7.4 ...... Excited State Properties
7.5 ...... Static and Dynamic QMC Polarizabilities

8 ...... Derivatives and Finite Differences
8.1 ...... Finite Differences and Correlated Sampling
8.2 ...... Virial and Hellmann-Feynman Theorems
8.2.1 ...... The virial theorem
8.2.2 ...... The Hellmann-Feynman theorem
8.3 ...... Analytic Energy Derivatives
8.3.1 ...... Analytic energy gradients
8.3.2 ...... Higher derivatives and derivative properties

9 ...... Heavy Atoms
9.1 ...... Valence Only Methods
9.1.1 ...... Effective core potentials
9.1.2 ...... Model potentials
9.1.3 ...... Pseudo Hamiltonians
9.2 ...... Approximate All-Electron Methods
9.2.1 ...... All-electron damped-core QMC
9.2.2 ...... Effective two-electron potentials
9.3 ...... Acceleration Methods
9.3.1 ...... Metropolis acceleration
9.3.2 ...... Langevin-based acceleration

A ...... Atomic Units
B ...... Evaluating the Trial Function
B.1 ...... Efficient Evaluation of the Trial Function
B.2 ...... Computing the Inverse Slater Matrix
B.3 ...... Molecular Orbitals and Correlation Functions
C ...... Sample Diffusion Monte Carlo Program
D ...... Bibliography 


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