Interaction, quantum-classical

Finally, the parametrization of the van der Waals part of the QM-MM interaction must be considered. This applies to all QM-MM implementations irrespective of the quantum method being employed. From Eq. (9) it can be seen that each quantum atom needs to have two Lennard-Jones parameters associated with it in order to have a van der Walls interaction with classical atoms. Generally, there are two approaches to this problem. The first is to derive a set of parameters, e, and G, for each common atom type and then to use this standard set for any study that requires a QM-MM study. This is the most common aproach, and the derived Lennard-Jones parameters for the quantum atoms are simply the parameters found in the MM force field for the analogous atom types. For example, a study that employed a QM-MM method implemented in the program CHARMM [48] would use the appropriate Lennard-Jones parameters of the CHARMM force field [52] for the atoms in the quantum region. 

The second term on the right hand-side of Eq. (1-3) accounts for the electrostatic interaction between classical and quantum zones, and will depend on the specifics of the QM implementation. 

H2O, where N/2 molecules have N OH stretch chromophores. In this case we need to label the transition dipoles and frequencies by an index i that runs from 1 to N. In addition, in general these chromophores interact, with couplings (in frequency units) coy. In this case the above mixed quantum/classical formula can be generalized to [95 98]... 

The concept of coherent control, which we have developed with isolated molecules in the gas phase, is universal and should apply to condensed matter as well. We anticipate that the coherent control of wave functions delocalized over many particles in solids or liquids will be a useful tool to track the temporal evolution of the delocalized wave function modulated by many-body interactions with other particles surrounding itself. We may find a clue to better understand the quantum-classical boundary by observing such dynamical evolution of wave functions of condensed matter. In the condensed phase, however, the coherence lifetime is in principle much shorter than in the gas phase, and the coherent control is more difficult accordingly. In this section, we show our recent efforts to develop the coherent control of condensed matter. 

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

The mixed quantum classical description of EET can be achieved in using Eq. (49) together with the electronic ground-state classical path version of Eq. (50). As already indicated this approach is valid for any ratio between the excitonic coupling and the exciton vibrational interaction. If an ensemble average has been taken appropriately we may also expect the manifestation of electronic excitation energy dissipation and coherence decay, however, always in the limit of an infinite temperature approach. 

I. Horenko, B. Schmidt, and C. Schutte. A theoretical model for molecules interacting with intense laser pulses The floquet-based quantum-classical Liouville equation. The Journal of Chemical Physics, 115(13) 5733-5743, 2001. 

Following, we determine the effects of the interactions between the quantum and classical subsystems on the optimization procedures of the MCSCF electronic wavefunction by evaluating the contributions of the quantum-classical interactions to the gradient and Hessian terms in the above equation. 

In order to avoid awkward explanation of the precise nature of this, so-called dispersion interaction, many authors label it a quantum interaction without classical analogue, content that it should remain a mystery. The similarity between van der Waals, metallic and ionic interactions in the solid state, argues against this dictum. 

We perform numerical modeling of atomic processes in various real plasmas including LHD fuel-pellet ablation and short-pulse laser interaction plasmas [21], We are developing a mixed quantum-classical code to study excited hydrogen atom formation in neutrals of back scattered protons at wall surfaces. 

Throughout this chapter we have been concerned with statistical approaches applied to isolated molecules. Since most (unimolecular) reactions occur in an environment comprised of other molecules, it is important to examine the effects of molecule-molecule interaction on the kinetics and dynamics of unimolecular reactions. Take the difference between quantum and classical transport as an example. Based on recent studies of quantum-classical... 

The simplest way to keep the electronic structure of the quantum subsystem as close as possible to what it would be in the entire macromolecule consists of saturating the dangling bonds with monovalent atoms called link atoms. Typically, hydrogen atoms are used. The computation now consists of a model molecule of the reactive part interacting with classical surroundings, similar to the case of solutions. This approach has been introduced by Singh and Kollman [8] and has been put in a operational form by Field et al. [9],... 

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