Adiabatic energy maps

Very few calculations of adiabatic energy maps for disaccharides coupled with molecular dynamics simulations have been undertaken, partially as a result of the great expense and labor involved in such studies. One molecule which has been studied by both of these t3npes of molecular mechanics calculations is sucrose. 

Figure 2. The calculated adiabatic energy map for sucrose. Contours are indicated at 2, 4, 6, and 8 kcal/mol above the global SI minimum. The stars refer to the various minima calculated with the present potential energy function.

Preparation of the adiabatic energy map for sucrose revealed that while only one conformation is allowed for this molecule if it is kept rigid, when flexibility is taken into account, several... 

Figure 10. Relaxed (adiabatic) conformational energy map for p-maltose as computed by Brady and coworkers.i3 Contours are drawn at 2,4,6, 8, and 10 kcal/mol above the minimum near < ), y = -60°, -40°. The p-maltose structure may be derived from that of p-cellobiose in Fig. 1 by inversion of the stereochemical configuration at Cl.

An adiabatic potential energy map for sucrose and molecular dynamics simulations applied to the minimum energy conformations indicated by this map have been reported. An anafysis of sucrose, maltose, and lactose by n.m.r. spectroscopy, differential scanning calorimetry (DSC), and x-ray diffraction was aimed at an understanding of molecular behaviour in the ciystals. ... 

From the above discussion, we can see that the purpose of this paper is to present a microscopic model that can analyze the absorption spectra, describe internal conversion, photoinduced ET, and energy transfer in the ps and sub-ps range, and construct the fs time-resolved profiles or spectra, as well as other fs time-resolved experiments. We shall show that in the sub-ps range, the system is best described by the Hamiltonian with various electronic interactions, because when the timescale is ultrashort, all the rate constants lose their meaning. Needless to say, the microscopic approach presented in this paper can be used for other ultrafast phenomena of complicated systems. In particular, we will show how one can prepare a vibronic model based on the adiabatic approximation and show how the spectroscopic properties are mapped onto the resulting model Hamiltonian. We will also show how the resulting model Hamiltonian can be used, with time-resolved spectroscopic data, to obtain internal... 

Figure 24. Diabatic (left) and adiabatic (right) population probabilities of the C (full line), B (dotted line), and X (dashed line) electronic states as obtained for Model II, which represents a three-state five-mode model of the benzene cation. Shown are (A) exact quantum calculations of Ref. 180 mean-field trajectory results [panels (B),(E)] and quasi-classical mapping results including the full [panels (C),(F)] and 60% [panels (D),(G)] of the electronic zero-point energy, respectively.

Finally, we discuss applications of the ZPE-corrected mapping formalism to nonadiabatic dynamics induced by avoided crossings of potential energy surfaces. Figure 27 shows the diabatic and adiabatic electronic population for Model IVb, describing ultrafast intramolecular electron transfer. As for the models discussed above, it is seen that the MFT result (y = 0) underestimates the relaxation of the electronic population while the full mapping result (y = 1) predicts a too-small population at longer times. In contrast to the models... 

Figure 27. Diabatic (a) and adiabatic (b) population probabilities for Model IVb. Shown are exact quantum results (thick full lines), mean-field-trajectory results (upper thin full line), quasi-classical mapping results including the full zero-point energy (i.e. y = 1, lower thin full line), as well as ZPE-corrected mapping results corresponding to y = 0.6 (dashed line) and y = 0.8 (dotted line), respectively.

Our protocol and the adiabatic mapping procedure described by Ha et al (8) have two features in common. They are both based on molecular mechanics approach, and they both start with several structures scattered at regular intervals over the (( ), j ) space. But the objectives of the approaches are fundamentally different. Whereas the adiabatic mapping procedure is intended to fully characterize the conformational energy surface of disaccharides, our... 

One approach is adiabatic mapping whereby one or two coordinates are identified as dominant within the true reaction coordinate. This might be a single bond that is made or broken in the reaction, or perhaps two such bonds. One then systematically increases or decreases the value of this coordinate(s), while optimizing the energy of the remainder of the system keeping this coordinate frozen. 

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