Quantum many-body dynamics method

Thus far we have examined the determination of a field that will control the quantum many-body dynamics of a system when all that is specified is the initial and final states of the system and the constraints imposed by the equations of motion and physical limitations on the field. When posed in this fashion, the calculation of the control field is an inverse problem that has similarities to the determination of the interaction potential from scattering data. Despite the similarities, the mathematical methods used are very different. Because only the end points of the initial-to-final state transforma-... 

Two lines of inquiry will be important in future work in photochemistry. First, both the traditional and the new methods for studying photochemical processes will continue to be used to obtain information about the subtle ways in which the character of the excited state and the molecular dynamics defines the course of a reaction. Second, there will be extension and elaboration of recent work that has provided a first stage in the development of methods to control, at the level of the molecular dynamics, the ratio of products formed in a branching chemical reaction. These control methods are based on exploitation of quantum interference effects. One scheme achieves control over the ratio of products by manipulating the phase difference between two excitation pathways between the same initial and final states. Another scheme achieves control over the ratio of products by manipulating the time interval between two pulses that connect various states of the molecule. These schemes are special cases of a general methodology that determines the pulse duration and spectral content that maximizes the yield of a desired product. Experimental verifications of the first two schemes mentioned have been reported. Consequently, it is appropriate to state that control of quantum many-body dynamics is both in principle possible and is... 

The potential energy surface is the central quantity in the discussion and analysis of the dynamics of a reaction. Its determination requires the solution of the many-body electronic Schrodinger equation. While in the early days of theoretical surface science quantum chemical methods had a significant impact, nowadays electronic structure calculations using density functional theory (DFT) [20, 21] are predominantly used. DFT is based on the fact that the exact ground state density and energy can be determined by the minimisation of the energy functional E[n ... 

The computation of the equilibrium properties of quantum systems is a challenging problem. The simulation of dynamical properties, such as transport coefficients, presents additional problems since the solution of the quantum equations of motion for many-body systems is even more difficult. This fact has prompted the development of approximate methods for dealing with such problems. 

Twenty years ago Car and Parrinello introduced an efficient method to perform Molecular Dynamics simulation for classical nuclei with forces computed on the fly by a Density Functional Theory (DFT) based electronic calculation [1], Because the method allowed study of the statistical mechanics of classical nuclei with many-body electronic interactions, it opened the way for the use of simulation methods for realistic systems with an accuracy well beyond the limits of available effective force fields. In the last twenty years, the number of applications of the Car-Parrinello ab-initio molecular d3mam-ics has ranged from simple covalent bonded solids, to high pressure physics, material science and biological systems. There have also been extensions of the original algorithm to simulate systems at constant temperature and constant pressure [2], finite temperature effects for the electrons [3], and quantum nuclei [4]. 

In this review, I have interpreted the term Car-Parrinello methods in the broad sense to mean those which combine first-principles quantum mechanical methods with molecular dynamics methods. I use this term synonymously with uh initio molecular dynamics, first-principles molecular dynamics, and ab initio simulations. Thus, ways of solving the many-body electronic problem, such as Hartree-Fock and correlation methods, are included, in addition to the projector-augmented plane-wave method. In the original Car-Parrinello method, molecular motion is treated classically via... 

In this subsection the more accurate CMD method [4-6,8] is described and analyzed in some detail. The method holds great promise for the study of quantum dynamics in condensed matter because systems having nonquadratic many-body potentials can be simulated for relatively long times. The numerical effort in this approach scales with system size as does a classical MD simulation, although the total overall computational cost will always be larger. Here the CMD method is first motivated by further analysis of the effective harmonic theory. This discussion is an abbreviated form of the historical line of development contained in Paper... 

The quantum mechanical many-body nature of the interatomic forces is taken into account naturally through the Hellmann-Feynman theorem. Since the scheme usually uses a minimal basis set for the electronic structure calculation and the Hamiltonian matrix elements are parametrized, large numbers of atoms can be tackled within the present computer capabilities. One of the distinctive features of this scheme in comparison with other empirical schemes is that all the parameters in the model can be obtained theoretically. It is therefore very useful for studying novel materials where experimental data are not readily available. The scheme has been demonstrated to be a powerful method for studying various structural, dynamical, and electronic properties of covalent systems. 

Increases in computer power and improvements in algorithms have greatly extended the range of applicability of classical molecular simulation methods. In addition, the recent development of Internal Coordinate Quantum Monte Carlo (ICQMC) has allowed the direct comparison of classical simulations and quantum mechanical results for some systems. In particular, it has provided new insights into the zero point energy problem in many body systems. Classical studies of non-linear dynamics and chaos will be compared to ICQMC results for several systems of interest to nanotechnology applications. The ramifications of these studies for nanotechnology applications will be discussed. 

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