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Path integral algorithm

As it was derived in the previous Section 4.6.5 the Mulliken density functional electronegativity requires the knowledge of the electronic density under the external potential influence. Being exposed all the ingredients for the analytical expression for the partition function with only the external potential dependence, the electronic density computed through out of Feymnan-Kleinert path integral algorithm takes the form, see also Eq. (2.11) ... [Pg.250]

Tuckerman M, Berne B J, Martyna G J and Klein M L 1993 Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals J. Chem. Phys. 99 2796-808... [Pg.2289]

Cao, J., Martyna, G.J. Adiabatic path integral molecular dynamics methods. II. Algorithms. J. Chem. Phys. 104 (1996) 2028-2035. [Pg.35]

The most simple procedure can be carried out in the case of path integral for the equilibrium density matrix, i.e., with it = j6. Specifically, the Metropolis algorithm [Metropolis et al., 1953] applies to n-dimension-al integrals of the general form... [Pg.59]

M. E. Tuckerman, B. J. Berne, G. J. Martyna, and M. L. Klein, /. Chem. Phys., 99, 2796 (1993). Efficient Molecular Dynamics and Hybrid Monte Carlo Algorithms for Path Integrals. [Pg.393]

The first numerical results from a strictly quantum mechanical calculation were given a few years ago [89]. In particular, P. Kornilovitch formulated a path integral representation of a three-dimensional JT polaron. Applying a QMC algorithm, he calculated the energy of the ground state, the DOS and the effective mass of a single... [Pg.826]

M. E. Tuckerman, D. Marx, M. L. Klein, and M. ParrineUo (1996) Efficient and general algorithms for path integral Car-Parrinello molecular dynamics. J. Chem. Phys. 104, p. 5579... [Pg.191]

G. J. Martyna, A. Hughes, and M. E. Tuckerman (1999) Molecular dynamics algorithms for path integrals at constant pressure. J. Chem,. Phys. 110, p. 3275... [Pg.191]

The path-integral formulation of a quantum systems goes back to [37], and forms the basis of most QMC algorithms. Instead of following the historical route and discussing the Trotter-Suzuki (checkerboard) decomposition [38,39] for path integrals with discrete time steps At we will directly describe the continuous-time formulation used in modern codes. [Pg.615]

All extensions affect the integration algorithm as well as the derivation of forward, backward, and correspondence analysis rules. For instance, the existence of paths can be checked, but not all paths can be created in a deterministic way. Thus, the constructs either have to be restricted, or generated forward, backward, and correspondence analysis rules have to be manually post-processed. [Pg.706]

Variations on this surface hopping method that utilize Pechukas [106] formulation of mixed quantum-classical dynamics have been proposed [107,108]. Surface hopping algorithms [109-111] for non-adiabatic dynamics based on the quantum-classical Liouville equation [109,111-113] have been formulated. In these schemes the dynamics is fully prescribed by the quantum-classical Liouville operator and no additional assumptions about the nature of the classical evolution or the quantum transition probabilities are made. Quantum dynamics of condensed phase systems has also been carried out using techniques that are not based on surface hopping algorithms, in particular, centroid path integral dynamics [114] and influence functional methods [115]. [Pg.435]


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