Bond, bridge coordinate

It must be understood that there are as many eigenvalue equations for this Hamiltonian as there are values of Q for the H-bond bridge coordinate. Thus, the meaning of the notation fl> (Q) in the ket t(Q)), is that this ket is parametrically dependent on the coordinate Q. Of course, when the H-bond bridge is at equilibrium, that is, Q = 0, the Hamiltonian involved in Eq. (28) reduces to the Hamiltonian (21). This leads us to write the following equivalence between the ket notations met, respectively, in Eqs. (24) and (28) ... 

Now, to go further, we will pass to the Boson representation given in Table V. Within this representation, the IP H-bond bridge coordinate appearing in Eq. (63) takes the form ... 

Finally, the time-dependent thermal averages of the H-bond bridge coordinate, in both quantum representations II and ///, evolve according to... 

Besides, the notation Q(f) for the time-dependent H-bond bridge coordinate interacting with the thermal bath may be viewed as the coordinate of a Brownian oscillator Q(f), which is a time-dependent stochastic variable ... 

Note that Eq. (160) must be incorporated because the ACF (158) is involving the integral over time of the H-bond bridge coordinate. That is the reason for the presence of the new variable S(t) besides the usual ones Q(f) and v(f). Note that following Lax [63], the integral S(t) of the time-dependent random variable Q(f) is itself a time random variable. 

Here, P is the Dyson time-ordering operator [57], Q (t)IP is the coordinate in the interaction picture with respect to the thermal bath and to the diagonal part of the Hamiltonian of the H-bond bridge, and the notation (( )e)siow has the meaning of a partial trace on the thermal bath and on the H-bond bridge coordinates. 

Here, Q is the H-bond bridge coordinate, whereas Hpast is the Hamiltonian of the high frequency mode ... 

Of course, the kinetic operator of the fast mode commutes with the partial derivative of the H-bond bridge coordinate, that is,... 

Here, Q(f)IP is the H-bond bridge coordinate in the interaction picture that is given by... 

Dimensionless between the H-bond bridge coordinate and the /th oscillator of the thermal bath. 

Bosons corresponding to the g and u symmetrized H-bond bridge coordinates with = l and [au,at] = ]... 

Trifluorophosphane can behave as a /x3 donor towards a triangular palladium core.559,360 The symmetrically bridging / -coordination mode has little precedent for tertiary ligands based on Group 15 atoms. The synthesis of a Pd1 dimer featuring a strongly bonded symmetrically bridging /i2-phosphole unit, which is the first example of this coordination mode for a tertiary phosphane, has been reported.561... 

It is conceivable that analogous changes also take place here but probably more efficiently, because the ligand dissociation step involved only weakly bonded bridging Cl- rather than a relatively strongly coordinated phosphite ligand ... 

The crystal structure of the eNOS—SEITU complex is shown in Fig. 11. As expected, the ureido group H-bonds with Glu363 similar to the way L-Arg interacts with Glu363. Two water molecules form H-bonding bridges between the inhibitor and heme propionates. The inhibitor sulfur is A from the heme iron but appears not to coordinate with iron,... 

Fig. 19. The asymmetric unit in NaBr (XV) 2HaO showing A, a complex cation Na (XV) 2HaO and B, a complexed ion pair NaBr, (XV), HaO. The fourth water molecule forms a hydrogen bonded bridge between a coordinated water molecule and the coordinated bromide ion...

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