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Table of contents
1 General introduction
2 Weak interactions
2.1 Introduction
2.2 Dispersion interactions
3 Electronic Structure Methodology
3.1 Time-independent Schrödinger Equation
3.1.1 Born-Oppenheimer Approximation
3.1.2 Electronic Schrödinger Equation
3.1.3 Nuclear Schrödinger Equation
3.2 The Variational Principle
3.3 Solving the Electronic Schrödinger Equation
3.3.1 Slater Determinant
3.3.2 Hartree-Fock Equations
3.3.3 Restricted Closed-Shell Hartree-Fock
3.3.4 Roothaan-Hall Equations
3.3.5 Self-consistent Field
3.4 Configuration Interaction (CI)
3.5 Perturbational theories
3.5.1 Møller-Plesset Perturbation Theory
3.6 Coupled Cluster Theory
3.7 Basis Sets
3.8 Basis Set Superposition Error
3.9 Complete Basis Set Extrapolation
3.9.1 Binding energy definition
3.9.2 Hartree-Fock energy
3.9.3 The correlation energy
4 The CaHe X1+ state
4.1 Introduction
4.2 Computational details
4.2.1 Influence of basis sets size
4.2.2 Bond-functions role
4.3 Comparison of methods
4.4 Determination of dispersion coefficients
4.5 Comparison with literature
4.6 Vibrational levels of the CaHe 1+ state
4.7 Conclusion
5 The MgHe 1+ state
5.1 Introduction
5.2 Computational details
5.3 Results and discussions
5.3.1 Basis set
5.3.2 Influence of core correlation effect
5.3.3 Influence of bond functions
5.3.4 PES characteristics : r0 and ǫ
5.3.5 Difference between basis and C-basis set
5.3.6 Basis set superposition error (BSSE)
5.4 Fit quality
5.5 Conventional CBS approximation
5.5.1 Fitting of the HF energies
5.5.2 Fitting of the correlation energies
5.6 Non conventional CBS approximation
5.7 Vibrational level of MgHe ground state
5.8 Conclusion
6 Introduction to quantum Monte Carlo methods
6.1 Variational Quantum Monte Carlo
6.1.1 Energy point calculation
6.1.2 VMC wave functions
6.2 Metropolis algorithm
6.3 Diffusion Monte Carlo
6.3.1 Why diffusion?
6.3.2 DMC method
6.3.3 Time evolution and Green’s function
6.3.4 Move acceptance
6.3.5 DMC wave function
6.3.6 DMC Energy Evaluation
6.4 Error analysis
6.4.1 Correlated samples
6.4.2 Correlation analysis
6.4.3 The DMC case
6.4.4 Statistical errors
6.4.5 Systematic errors
6.5 Calculation of main properties
6.5.1 Radial distribution
6.5.2 Pair correlation function
6.5.3 Two-dimensional histograms
6.6 Pseudo-codes
6.6.1 VMC
6.6.2 DMC
6.7 Conclusion
7 Doped helium nanodroplets
7.1 Introduction
7.2 4He nanodroplet properties
7.2.1 Superfluidity
7.2.2 Temperature of the droplets
7.3 Experimental aspects
7.3.1 Production of helium nanodroplets
7.3.2 Doping of droplets
7.4 Applications of helium nanodroplets
7.4.1 Helium Nanodroplet Isolation Spectroscopy
7.4.2 Other applications
8 DMC computational details
8.1 Introduction
8.2 Influence of the number of walkers
8.3 Influence of the time step
8.4 Influence of the duration of the simulation
8.5 Influence of the number of blocks
8.6 Influence of the random number seed
8.7 Trial wavefunction and parameters
8.8 Conclusion
9 DMC results for MgHen and CaHen clusters
9.1 Introduction
9.2 Ancilotto’s model
9.2.1 Principle
9.2.2 Limits of the model
9.2.3 The alkaline earth case
9.3 Pair potential of the He2, MgHe and CaHe
9.4 Energy calculation
9.4.1 Binding energy model
9.5 Comparison with literature
9.6 Ca and Mg positions on the droplets
9.6.1 Radial probability densities
9.6.2 Helium densities in cylinder coordinates
9.6.3 Structural relaxation of the MgHeN cluster
9.7 Pair density distributions
9.8 Adiabatic model for Mg solvation
9.8.1 Energy profile with a geometrical constraint
9.8.2 Evolution of the helium density
9.8.3 Rovibrational calculation in the constrained potential
9.9 Conclusion
10 Dynamics of Mg doped Helium Clusters
10.1 Introduction
10.2 Potential energy curves
10.2.1 Mg2 (X1+ g ) .
10.2.2 MgHe (X1+)
10.2.3 Effective He2 potential
10.3 Dynamic results
10.3.1 MgHe1998
10.3.2 Mg2He1997
10.4 Conclusion
11 General conclusions
A Electronic energies
B Position of Mg for several MgHe potentials
