Hamiltonian approach

Fehrensen B, Luckhaus D and Quack M 1999 Inversion tunneling in aniline from high resolution infrared spectroscopy and an adiabatic reaction path Hamiltonian approach Z. Phys. Chem., NF 209 1-19... 

There have been attempts to develop methods where the BSSE is excluded explicitly in the computational expressions, an example of this is the Chemical Hamiltonian Approach (CHA)," but such methods are not yet commonly used. 

M. Menon and R. E. AUen, New technique for molecular-dynamics computer simulations Hellmann- Feynman theorem and subspace Hamiltonian approach , Phys. Rev. B33 7099 (1986) Simulations of atomic processes at semiconductor surfaces General method and chemisorption on GaAs(llO) , ibid B38 6196 (1988). 

Calculating the exact response of a semiconductor heterostructure to an ultrafast laser pulse poses a daunting challenge. Fortunately, several approximate methods have been developed that encompass most of the dominant physical effects. In this work a model Hamiltonian approach is adopted to make contact with previous advances in quantum control theory. This method can be systematically improved to obtain agreement with existing experimental results. One of the main goals of this research is to evaluate the validity of the model, and to discover the conditions under which it can be reliably applied. 

Orbitally degenerate grormd states, in general, cannot be treated in the spin-Hamiltonian approach. In this case, SOC has to be evaluated explicitly on an extended basis of spin-orbit functions. However, in coordination chemistry and bioinorganic chemistry, this is only of marginal importance, because the metal centers of... 

The authors [33] have elucidated the linear dependence of Ao0 (z-dep) on E for the polyanions by a quantum chemical consideration. A model Hamiltonian approach to the charge transfer (CT) interaction between a polyanion and solvents has been made on the basis of the Mulliken s CT complex theory [34]. 

The third term, Uqt, in Eq. (27) is due to the partial electron transfer between an ion and solvents in its immediate vicinity. The model Hamiltonian approach [33], described in Section V, has shown that Uqt (= AW in Ref. 33) per primary solvent molecule, for an ion such as the polyanion, can also be expressed as a function of E, approximately a quadratic equation ... 

The GED approach is a general procedure based on the exact solutions to the n-electron system. Only one Hamiltonian is required at variance with the infinite Hamiltonian approach (defined on the parametric -space) characteristic of the BO scheme. All the base functions are expanded from a unique origin of the I-frame. The characteristics of the n-electrons diabatic base functions are independent from the positions taken by the sources of the external potential. 

To estimate the consequences of such a bridge modification in a quantitative fashion one needs to treat an extended system where donor and acceptor sites are separated by intervening WCPs. We used the effective Hamiltonian approach described in Sect. 2.7 to clarify the distance dependence of the electronic coupling in DNA and the effect of bridge modifications [50]. 

We applied the effective Hamiltonian approach to DNA fragments of standard geometry with d=a=GGG, determined the effective couphng from Eq. 18, and analyzed the coupling following Eq. 24. Now, we will discuss the results for various bridge compositions (Table 7) [51]. 

In the perturbative "transfer Hamiltonian approach developed by Bardeen 58), the tip and sample are treated as two non-interacting subsystems. Instead of trying to solve the problem of the combined system, each separate component is described by its wave function, i tip and i/zj, respectively. The tunneling current is then calculated by considering the overlap of these in the tunnel junction. This approach has the advantage that the solutions can be found, for many practical systems, at least approximately, by solution of the stationary Schrodinger equation. 

To sense the effect one cluster would have on the other let us consider the effective hamiltonian approach. There, one cluster is subjected to the field ofthe other. With obvious notations one can define an effective parametric electronuc-lear problem for each partner via the functional ... 

S. Bonella and D. F. Coker. Semiclassical implementation of the mapping Hamiltonian approach for nonadiabatic dynamics using focused initial distribution sampling. J. Chem. Phys., 118(10) 4370-4385, Mar 2003. 

The origin of the LR-SS difference was imputed to the incapability of the nonlinear effective solute Hamiltonian used in these solvation models to correctly describe energy expectation values of mixed solute states, i.e., states that are not stationary. Since in a perturbation approach such as the LR treatment the perturbed state can be seen as a linear combination of zeroth-order states, the inability of the effective Hamiltonian approach to treat mixed states causes an incorrect redistribution of the solvent terms among the various perturbation orders [32],... 

In the coherent (Hamiltonian) approach to the four-state spin system, the state populations are just the diagonal elements of the corresponding density matrix p(r, f), which obeys the Bloch or Redfield equation [211] ... 

A similar result was expected in Ref. 221 for cps(c>) = 1 — cp(cr), but the obtained difference between the recombination rates in the opposite limits was half as much kc for the slowest conversion and kj2 for the fastest one. This is because the isotropic Ag mechanism determining the spin conversion in Ref. 221 mixes the singlet with the 7b) sublevel only. In the rate approximation one can easily get the same, assuming that the spin transitions between the singlet and triplet RIPs occurs with equal rates in the forward and backward directions as in Eq. (3.585b). However, the transition from the slow to the fast conversion limit resulting from the rate approximation differs somehow from that obtained with the Hamiltonian approach in Ref. 221. 

The increase of second-order hyperpolarizabilities upon backbone elongation has also been evaluated by quantum chemical means by the Bredas group [74]. With a valence effective Hamiltonian approach (VEH/SOS) the parameters in the sum-over-states expression are evaluated leading to the second-order hyperpolarizabilities yof the molecules. With the VEH/SOS approach the description of larger molecules is feasible, which means in the case of PTA molecules longer than the tetramer. 

The expressions in equations (7.139) to (7.143) are exact to second order in perturbation theory. There are also higher-order terms of the same operator form as given in (7.137) but such contributions are much smaller as long as the interaction terms are small compared with the separation of the n and states this is usually the case. It is important to appreciate that the form of the yl-doubling operator is the same even when these higher order effects are included. This is a real advantage of the effective Hamiltonian approach. The correct form of the Hamiltonian can be established by a limited perturbation treatment. Thus, no approximation is made in fitting the parameters of this Hamiltonian to experimental data. The limitations, such as they are, arise only when the parameters so determined are compared with theoretical expectations. 

---