Reaction path calculations

In Gaussian, a reaction path calculation is requested with the IRC keyword in the route section. Before you can run one, however, certain requirements must be met. An IRC calculation begins at a transition structure and steps along the reaction path a fixed number of times (the default is 6) in each direction, toward the two minima that it connects. However, in most cases, it will not step all the way to the minimum on either side of the path. 

All the reaction paths calculated with the CD method were determined by stepping forward (from reactant to intermediate state) and backward (from intermediate... 

For both reaction path calculations, it only took two modified NEB cycles to optimize the new images to the MEP. The reason for this very fast convergence is that the initial approximation for the extra images on the path is not too far from the MEP. 

Reactions for common minerals fall in both categories, but many important cases tend, except under acidic conditions, to be surface controlled (e.g., Aagaard and Helgeson, 1982 Stumm and Wollast, 1990). For this reason and because of their relative simplicity, we will consider in this chapter rate laws for surface-controlled reactions. The problem of integrating rate laws for transport-controlled reactions into reaction path calculations, nonetheless, is complex and interesting (Steefel and Lasaga, 1994), and warrants further attention. 

Integrating isotope fractionation into the reaction path calculation is a matter of applying the mass balance equations while tracing over the course of the reaction path the system s total isotopic composition. Much of the effort in programming an isotope model consists of devising a careful accounting of the mass of each isotope. 

Fig. 31.2. Masses of species produced by reacting pyrite with a hypothetical groundwater that is held in equilibrium with atmospheric oxygen, according to the reaction path calculation shown in Figure 31.1.

The process of mutation by tautomerization is similar to the excited-state process described here. If a misprint induced by a tautomer takes place during replication, then an error is recorded. Because reaction path calculations of DNA base pairs show similar potential-energy characteristics to those discussed here, we anticipate being able to explore the relevance of tautomerization dynamics to mutagenesis. In this area, we are currently examining these and other systems, also in solutions. 

Figure 7.43. Predicted reaction path for the meteoric diagenetic system of the Floridan aquifer. These reaction path calculations agree reasonably well with observations, as shown by variousl symbols. Reaction path calculations of this nature can be applied to other modern meteoric diagenetic systems, and perhaps, with modifications to ancient systems now removed from original meteoric water. (After Plummer et al., 1983.)...

For a qualitative characterization of the PE surface relevant for the hydrogen transfer reaction, a simplified version of the MEP approach can be adopted. In this so-called coordinate-driven MEP approach one defines one of the 3N— 6 intramolecular degrees of freedom as the reaction coordinate, while the remaining (3N — 7) coordinates are optimized at each step of the reaction path calculation. There are no strict rules for choosing the reaction coordinate. In principle, it can be any of the 3N — 6 degrees of freedom. In practice, it should be the coordinate which changes the most when the reaction proceeds. 

A superior method for the calculation of excited-state PE surfaces is CC2, which is a simplified and computationally efficient variant of coupled-cluster theory with single and double excitations [22], CC2 can be considered as the equivalent of MP2 for excited electronic states. Efficient implementations of CC2 with density fitting [23] and analytic gradients [24] allow reaction path calculations for rather large systems. Being a singlereference method, CC2 fails in the vicinity of conical intersections of excited states with the electronic ground state. 

Nondynamical electron correlation effects are generally important for reaction path calculations, when chemical bonds are broken and new bonds are formed. The multiconfiguration self-consistent field (MCSCF) method provides the appropriate description of these effects [25], In the last decade, the complete active space self-consistent field (CASSCF) method [26] has become the most widely employed MCSCF method. In the CASSCF method, a full configuration interaction (Cl) calculation is performed within a limited orbital space, the so-called active space. Thus all near degeneracy (nondynamical electron correlation) effects and orbital relaxation effects within the active space are treated at the variational level. A full-valence active space CASSCF calculation is expected to yield a qualitatively reliable description of excited-state PE surfaces. For larger systems, however, a full-valence active space CASSCF calculation quickly becomes intractable. 

Example 4. Evaporation and homogeneous redox reactions Example 5.—Irreversible reactions Example 6.--Reaction-path calculations Example 7.--Gas-phase calculations Example 8. Surface complexation... 

Reaction-path calculation. A sequence of mass transfer calculations that follows defined phase (or reaction) boundaries during incremental steps of reaction progress. 

A set of five programs known as The Geochemist s Workbench or GWB was developed by Bethke (1994) with a wide range of capabilities similar to EQ3/6 and PHREEQC v. 2. GWB performs speciation, mass transfer, reaction-path calculations, isotopic calculations, temperamre dependence for 0-300 °C, independent redox calculations, and sorption calculations. Several electrolyte databases are available including ion association with Debye-Huckel activity coefficients, the Pitzer formulation, the Harvie-M0ller-Weare formulation, and a... 

Chemical reaction path calculations (Alpers and Nordstrom, 1999 Bethke, 1996) have only seen limited use as applied to fluid-mineral interactions in the human body (e.g., Davis et al., 1992). The potential further applications in this realm are intriguing, both for understanding chemical reactions between body fluids and earth materials, and in understanding potential changes in body fluid chemistry in response to physiological processes and therapeutic treatments such as toxic metal chelation therapy. 

Using the concept of partial equilibria Thorstenson (1970) has predicted in a reaction path calculation the compositional changes in the aqueous phase as a function of the amount of organic matter decomposed. Figure 15.11 gives the distribution of predominant dissolved species at hypothetical equilibrium as a function of increments of organic matter decomposed, represented in this example by C3H7O2N (= alanine). 

Examples for Saddle-Point and Reaction-Path Calculations... 

J. C. M. Uitdehaag, B. A. van der Veen, L. Dijkhuizen, R. Elber, and B. W. Dijkstra (2001) Enzymatic circularization of a malto-octaose linear chain studied by stochastic reaction path calculations on cyclodextrin glycosyltransferase. Proteins Structure Function and Genetics 43, pp. 327-335... 

Reaction (9) is well-known to occur under mild conditions even in aqueous solutions of alkali hydroxides (ref. 33). The details of this reaction have recently been investigated by reaction path calculations (refs. 34, 35) with the result that a facile nucleophilic attack of CO... 

The dynamics of the so-called biological water molecules in the immediate vicinity of a protein have been studied using dielectric relaxation [18], proton and O NMR relaxation [19], reaction path calculation [20], and analytical statistical mechanical models [21]. While the dielectric relaxation time of ordinary water molecules is 10 ps [16], both the dielectric [18] and nuclear magnetic resonance (NMR) relaxation studies [19], indicate that near the protein surface the relaxation dynamics are bimodal with two components in the 10-ns and 10-ps time scale, respectively. The 10-ns relaxation time cannot be due to the motion of the peptide chains, which occurs in the 100-ns time scale. From the study of NMR relaxation times of " O at the protein surface, Halle et al. [19c,d] suggested dynamic exchange between the slowly rotating internal and the fast external water molecules. 

The 0 K IR spectrum in the range 3600-3800 cm i is shown in Fig. 3.12 and is presented with no energy shift. As seen, the spectrum is fairly complex but does show intensities in qualitative accord with experiment, shown in Fig. 3.6. Our analysis indicates that the relatively intense lines at 3620 cm are the monomer OF -symmetric stretch and those at 3710 cm i are the asymmetric stretch. We stress that these are preliminary results and likely not well converged. More accurate DMC and Multimode-reaction path calculations for the four monomer stretches indicate that the single reference energies are 40-100 cm high [28]. 

Most applications in the regulatory environment have used speciation-solubility models. A few used surface complexation models. Applications of surface complexa-tion models mostly used the model and data from Dzombak and Morel (1990). Reaction path calculations are mostly limited to the titration and mixing calculations of two fluids. 

Reaction-path calculations Reactive transport calculations... 

In the case of reaction path and inverse mass balance calculations, the involvement of the modeler in producing a geochemical model is crucial. Calculations may indicate that dozens or hundreds of minerals are supersaturated in a system. To perform reaction path calculations, the modeler has to use geochemical, geological, and mineralogical knowledge to decide which are the most likely phases to exist in the particular geologic environment of interest. 

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