Propagator methods

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

LInderberg J and Ohrn Y 1973 Propagator Methods in Quantum Chemistry (New York Academic)... 

Cederbaum L S and Domcke W 1977 Theoretical aspects of ionization potentials and photoelectron spectroscopy a Green s function approach Adv. Chem. Phys. 36 205-344 Oddershede J 1987 Propagator methods Adv. Chem. Phys. 69 201-39... 

The center of the wavepacket thus evolves along the trajectory defined by classical mechanics. This is in fact a general result for wavepackets in a hannonic potential, and follows from the Ehrenfest theorem [147] [see Eqs. (154,155) in Appendix C]. The equations of motion are straightforward to integrate, with the exception of the width matrix, Eq. (44). This equation is numerically unstable, and has been found to cause problems in practical applications using Morse potentials [148]. As a result, Heller inboduced the P-Z method as an alternative propagation method [24]. In this, the matrix A, is rewritten as a product of matrices... 

There are three main methods for calculating the effect of a perturbation derivative techniques, perturbation theory and propagator methods. The former two are closely related while propagator methods are somewhat different, and will be discussed separately. 

Choosing a non-zero value for uj corresponds to a time-dependent field with a frequency u, i.e. the ((r r)) propagator determines the frequency-dependent polarizability corresponding to an electric field described by the perturbation operator QW = r cos (cut). Propagator methods are therefore well suited for calculating dynamical properties, and by suitable choices for the P and Q operators, a whole variety of properties may be calculated. " ... 

So far everything is exact. A complete manifold of excitation operators, however, means that all excited states are considered, i.e. a full Cl approach. Approximate versions of propagator methods may be generated by restricting the excitation level, i.e. tmncating h. A complete specification furthermore requires a selection of the reference, normally taken as either an HF or MCSCF wave function. 

More recently Equation Of Motion (EOM) methods have been used in connection with other types of wave functions, most notably coupled cluster.Such EOM methods are closely related to propagator methods, and give working equations which are similar to those encountered in propagator theory. 

These data are ideal tests for renormalized ab initio methods. Perturbative propagator methods have yielded poor agreement with experiment for F and OH [40]. For example, OVGF predictions for F and OH with a polarized, triple C basis augmented with diffuse functions are 5.00 and 2.86 eV, respectively. 

Applications of electron propagator methods with a single-determinant reference state seldom have been attempted for biradicals such as ozone, for operator space partitionings and perturbative corrections therein assume the dominance of a lone configuration in the reference state. Assignments of the three lowest cationic states were inferred from asymmetry parameters measured with Ne I, He I and He II radiation sources [43]. 

This e qnession for the propagators is still exact, as long as, the principal sub-manifold h and its complement sub-manifold h arc complete, and the characteristics of the propagator is reflected in the construction of these submanifolds (47,48). It should be noted that a different (asymmetric) metric for the superoperator space, Eq. (2.5), could be invoked so that another decoupling of the equations of motion is obtained (62,63,82-84). Such a metric will not be explored here, but it just shows the versatility of the propagator methods. 

Section II discusses the real wave packet propagation method we have found useful for the description of several three- and four-atom problems. As with many other wave packet or time-dependent quantum mechanical methods, as well as iterative diagonalization procedures for time-independent problems, repeated actions of a Hamiltonian matrix on a vector represent the major computational bottleneck of the method. Section III discusses relevant issues concerning the efficient numerical representation of the wave packet and the action of the Hamiltonian matrix on a vector in four-atom dynamics problems. Similar considerations apply to problems with fewer or more atoms. Problems involving four or more atoms can be computationally very taxing. Modern (parallel) computer architectures can be exploited to reduce the physical time to solution and Section IV discusses some parallel algorithms we have developed. Section V presents our concluding remarks. 

B. Semiclassical Herman-Kluk-Type Frozen Gaussian Wavepacket Propagation Method... 

For the collision dynamics, a semi-classical method is quite accurate for intermediate energies about 50 keV. Note the use of a more recent collision program using the propagation method for the N " (ls2s) + He metastable system. 

In many chemical and even biological systems the use of an ab initio quantum dynamics method is either advantageous or mandatory. In particular, photochemical reactions may be most amenable to these methods because the dynamics of interest is often completed on a short (subpicosecond) timescale. The AIMS method has been developed to enable a realistic modeling of photochemical reactions, and in this review we have tried to provide a concise description of the method. We have highlighted (a) the obstacles that should be overcome whenever an ab initio quantum chemistry method is coupled to a quantum propagation method, (b) the wavefunction ansatz and fundamental... 

Sun, H. Dalton, L. Chen, A., Systematic design and simulation of polymer microring resonators with the combination of beam propagation method and matrix model, In Digest of the IEEE LEOS Summer Topical Meetings, 2007, 217 218... 

Newtonian Propagation Methods Applied to the Photodissociation Dynamics of Ij. 

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