Quantum molecular dynamic

Kosloff R 1994 Propagation methods for quantum molecular-dynamics Annu. Rev. Phys. Chem. 45 145-78... 

Quack M 1992 Time dependent intramolecular quantum dynamics from high resolution spectroscopy and laser chemistry Time Dependent Quantum Molecular Dynamics Experiment and Theory. Proc. NATO ARW 019/92 (NATO ASI Ser. Vol 299) ed J Broeckhove and L Lathouwers (New York Plenum) pp 293-310... 

The study of quautum effects associated with nuclear motion is a distinct field of chemistry, known as quantum molecular dynamics. This section gives an overview of the methodology of the field for fiirtlier reading, consult [1, 2, 3, 4 and 5,]. 

In its most fiindamental fonn, quantum molecular dynamics is associated with solving the Sclirodinger equation for molecular motion, whether using a single electronic surface (as in the Bom-Oppenlieimer approximation— section B3.4.2 or with the inclusion of multiple electronic states, which is important when discussing non-adiabatic effects, in which tire electronic state is changed [15,16, YL, 18 and 19]. 

Finally, Sections B3.4.10. touches on the application of quantum molecular dynamics to a very exciting field laser interactions with molecules. This field presents, in principle, the opportunity to influence chemistry by lasers rather than to simply observe it. 

The scope of this section restricts the discussion. One omitted topic is the collision and interaction of molecules with surfaces (see [20, 21] and section A3.9). This topic coimects quantum molecular dynamics in gas and condensed phases. Depending on the time scales of the interaction of a molecule witli a surface, the... 

As in any field, it is usefiil to clarify tenninology. Tliroughout this section an atom more specifically refers to its nuclear centre. Also, for most of the section the /)= 1 convention is used. Finally, it should be noted that in the literature the label quantum molecular dynamics is also sometimes used for a purely classical description of atomic motion under the potential created by tlie electronic distribution. 

A comer-stone of a large portion of quantum molecular dynamics is the use of a single electronic surface. Since electrons are much lighter than nuclei, they typically adjust their wavefiinction to follow the nuclei [26]. Specifically, if a collision is started in which the electrons are in their ground state, they typically remain in the ground state. An exception is non-adiabatic processes, which are discussed later in this section. 

Zhang J Z H 1999 Theory and Application of Quantum Molecular Dynamics (River Edge, NJ World Scientific)... 

Y. Ohm et al, in Tlme-Dependeni Quantum Molecular Dynamics, J. Broeckhove and... 

J, C. Light, in Time-Dependent Quantum Molecular Dynamics J. Broeckhove and L. Lathouwers, eds., E lenum, New York, 1992, pp. 185-199. 

New Methods in Quantum Molecular Dynamics of Large Polyatomic Systems... 

Ronnie Kosloff Quantum molecular dynamics on grids. In R. E. Wyatt and J. Z. Zhang, editors. Dynamics of Molecules and Chemical Reactions, pages 185-230. Marcel Dekker, New York (1996)... 

In this paper we present a number of time integrators for various problems ranging from classical to quantum molecular dynamics. These integrators share some common features they are new, they are second-order accurate and time-reversible, they improve substantially over standard schemes in well-defined model situations — and none of them has been tested on real applications at the time of this writing. This last feature will hopefully change in the near future [20]. 

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

The Car-Parrinello quantum molecular dynamics technique, introduced by Car and Parrinello in 1985 [1], has been applied to a variety of problems, mainly in physics. The apparent efficiency of the technique, and the fact that it combines a description at the quantum mechanical level with explicit molecular dynamics, suggests that this technique might be ideally suited to study chemical reactions. The bond breaking and formation phenomena characteristic of chemical reactions require a quantum mechanical description, and these phenomena inherently involve molecular dynamics. In 1994 it was shown for the first time that this technique may indeed be applied efficiently to the study of, in that particular application catalytic, chemical reactions [2]. We will discuss the results from this and related studies we have performed. 

Finally, from the dynamics simulations it was found that the Cp rings are very flexible, and during the simulation they are not very closely attached to the metal centre as often anticipated. For further details regarding the metallocene and mono-cyclopentadienyl based olefin polymerisation studied by quantum molecular dynamics simulation we refer to [2] and [8-10]. 

If the inverse in Eq. (2.8) does not exist then the metric is singular, in which case the parameterization of the manifold of states is redundant. That is, the parameters are not independent, or splitting of the manifold occurs, as in potential curve crossing in quantum molecular dynamics. In both cases, the causes of the singularity must be studied and revisions made to the coordinate charts on the manifold (i.e. the way the operators are parameterized) in order to proceed with calculations. 

A formulation of electronic rearrangement in quantum molecular dynamics has been based on the Liouville-von Neumann equation for the density matrix. Introducing an eikonal representation, it naturally leads to a general treatment where Hamiltonian equations for nuclear motions are coupled to the electronic density matrix equations, in a formally exact theory. Expectation values of molecular operators can be obtained from integrations over initial conditions. 

The development of an ab initio quantum molecular dynamics method is guided by the need to overcome two main obstacles. First, one needs to develop an efficient, yet accurate, method for solving the electronic Schrodinger equation for both ground and excited electronic states. Second, the quantum mechanical character of the nuclear dynamics must be addressed. (This is necessary for the description of photochemical and tunneling processes.) This section provides a detailed discussion of the approaches we have taken to solve these two problems. 

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