Potential surface-solution

In the full quantum mechanical picture, the evolving wavepackets are delocalized functions, representing the probability of finding the nuclei at a particular point in space. This representation is unsuitable for direct dynamics as it is necessary to know the potential surface over a region of space at each point in time. Fortunately, there are approximate formulations based on trajectories in phase space, which will be discussed below. These local representations, so-called as only a portion of the FES is examined at each point in time, have a classical flavor. The delocalized and nonlocal nature of the full solution of the Schtddinger equation should, however, be kept in mind. 

A chemical reaction takes place on a potential surface that is determined by the solution of the electronic Schrddinger equation. In Section, we defined an anchor by the spin-pairing scheme of the electrons in the system. In the discussion of conical intersections, the only important reactions are those that are accompanied by a change in the spin pairing, that is, interanchor reactions. We limit the following discussion to these class of reactions. 

The metal-ion complexmg properties of crown ethers are clearly evident m their effects on the solubility and reactivity of ionic compounds m nonpolar media Potassium fluoride (KF) is ionic and practically insoluble m benzene alone but dissolves m it when 18 crown 6 is present This happens because of the electron distribution of 18 crown 6 as shown m Figure 16 2a The electrostatic potential surface consists of essentially two regions an electron rich interior associated with the oxygens and a hydrocarbon like exterior associated with the CH2 groups When KF is added to a solution of 18 crown 6 m benzene potassium ion (K ) interacts with the oxygens of the crown ether to form a Lewis acid Lewis base complex As can be seen m the space filling model of this... 

Since P depends on the solution of the secular equation, which in turn depends on P, it is clear that we must solve iteratively for the molecular orbitals. In general, we will consider only the first few iterations and start the first iteration with = ZM, where is the effective charge of the nuclear core of the pth orbital (for more than one orbital per atom we have ZA = EM(y4) Zfi). The potential surface of the system is then approximated by... 

VB POTENTIAL SURFACES FOR REACTIONS IN SOLUTIONS 2.2 1. General Considerations... 

VB Potential Surface for Proton Transfer Reactions in Solutions... 

FIGURE 2.6. An EVB-LD potential surface for proton transfer between an acid R"COO/t H and an ROsR molecule in solution. The independent coordinates r1 and r3 are the distances between the proton and Oa and Os, respectively. Regions of the potential surface that have more than 50% ionic character are dotted (see Ref. 6 for more details). 

In the previous chapter we considered a rather simple solvent model, treating each solvent molecule as a Langevin-type dipole. Although this model represents the key solvent effects, it is important to examine more realistic models that include explicitly all the solvent atoms. In principle, we should adopt a model where both the solvent and the solute atoms are treated quantum mechanically. Such a model, however, is entirely impractical for studying large molecules in solution. Furthermore, we are interested here in the effect of the solvent on the solute potential surface and not in quantum mechanical effects of the pure solvent. Fortunately, the contributions to the Born-Oppenheimer potential surface that describe the solvent-solvent and solute-solvent interactions can be approximated by some type of analytical potential functions (rather than by the actual solution of the Schrodinger equation for the entire solute-solvent system). For example, the simplest way to describe the potential surface of a collection of water molecules is to represent it as a sum of two-body interactions (the interac-... 

With a realistic solvent model, we can explore the properties of solvated molecules. As before, we take a classical approach by adding the solute-solvent interaction term (USs) to the potential surface of the system and write... 

The term Uss is the solvent-solvent interaction term [the Unb and Uqq terms of eq. (3.1)] and t/ind is the induced dipoles three-body term which includes now the field both from the solute and the solvent. With a potential surface for a solvated solute we can address the important issue of evaluating solvation energies. In principle, one can try to evaluate the average poten-... 

Now knowing how to evaluate solvation-free energies, we are ready to explore the effect of the solvent on the potential surface of the reacting solute atoms. Adapting the EVB approach we can describe the reaction by including the solute-solvent interaction in the diagonal elements of the solute Hamiltonian, using... 

With the gas-phase potential surface we can obtain the solution Hamiltonians by eq. (3.23), adding the solvent-solute interaction to the classical part of the diagonal EVB matrix elements. That is, we use... 

POTENTIAL SURFACES FOR AMIDE HYDROLYSIS IN SOLUTION AND IN SERINE PROTEASES... 

The above results give the asymptotic points of the potential surface in solution. Furthermore, with the use of the calculated solvation energies of the different fragments we can obtain from eq. (2.34) the asymptotic points for the gas-phase potential surface. This is done in Table 7.2. 

Exercise 7.3. The discussion above gave you all the relevant information about the solution potential surface. Summarize this information in an energy diagram. 

FIGURE 7.6. Comparing the potential surfaces for the catalytic reaction of trypsin (upper figure) to the corresponding reaction in solution (lower figure). The different configurations that define the corners of the potential surface are drawn on the upper left portion of the figure. 

FIGURE 9.1. The potential surface for proton transfer reaction and the effect of constrainir the tiA B distance. The figure demonstrates that the barrier for proton transfer increasi drastically if the A — B distance is kept at a distance larger than 3.5 A. However, in solutic and good enzymes the transfer occurs through pathway a where the A - B distance is arour 2.7 A. 

FIGURE 9.5. The potential surface for the 0"C = 0— 0-C-0" step in amide hydrolysis in solution, where the surface is given in terms of the angle 0 and the distance b. The heavy contour lines are spaced by fi (at room temperature) and can be used conveniently in estimating entropic effects. The figure also shows the regions (cross hatched) where the potential is less than for the corresponding reaction in the active site of subtilisin. 

After learning to estimate AG7" and AS, we might ask how AASf is affected by the steric restriction of the protein environment. As is clear from eq. (9.7), we need the differences between the entropic contributions to A G rather than the individual AS. This requires the examination of the difference between the potential surfaces of the protein and solution reaction. Here we exploit the fact that the electrostatic potential changes rather slowly and use the approximation... 

Barium, effectiveness as cofactor for, see also Enzyme cofactors phospholipase, 204 SNase, 200-204 Bond-breaking processes, 12 potential surfaces for, 13-14, 18-20 in solutions, 22,46-54... 

See also Enzyme cofactors downhill trajectories for, 196,197 mechanism of catalytic reaction, 190-192 metal substitution, 200-204 potential surfaces for, 192-195,197 rate-limiting step of, 190 reference solution reaction for, 192-195,... 

Potential Surfaces for Amide Hydrolysis in Solution and in Serine Proteases, 173... 

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