10419approximation with two-body correlations has so far been tested only for the propagation of wave functions in model system-bath Hamiltonian~.~ These models used realistic potentials with barriers very similar to those encountered in H-exchange reactions, and the test calculations showed the mean field approximation with explicit system-bath correlation to be extremely accurate over times long enough for the wave packet to move away from the saddle point region. Nevertheless, numerical calculations of rate constants for problems with three or more degrees of freedom must be carried out to verify the applicability of the approach presented here to more challenging problems. Some such applications are in progress. Acknowledgment. This work has been supported by a JuniorFellowship from the Society of Fellows, Harvard University. The calculations reported were performed on a S U N 4/65 SPARC 1 station, funded by the Milton Fund Award of the Harvard Medical School.Ab initio electronic structure calculations using analytical energy derivative methods and automated potential energy surface walking techniques have been carried out on the tautomerization reaction path connecting formamide (F) H2N-CH0, through a transition state (TS), to formamidic acid (FA) HN-CHOH. The zero-point corrected F -FA, and F -TS energy differences are predicted to be 12.1 and 48.9 kcal/mol, respectively, when configuration interaction methods are used to treat electron correlation. An imaginary frequency of 23911' cm-' is obtained along the reaction coordinate at the TS. Isotopic substitution of F to generate H,N-CDO and subsequent calculation of the harmonic vibrational frequencies and eigenvectors allowed ambiguities in the assignment of the infrared spectrum of F to be resolved. The geometry of the F tautomer is found to be slightly nonplanar, but to have zero-point energy that permits the planar geometry to be dynamically accessed. Extensions to situations in which tautomerization is assisted by neighboring solvent molecule(s) are considered. In particular, the intimate involvement of a single H 2 0 solvent molecule reduces the zero-point-corrected F -FA and F -TS energy differences to 10.6 and 22.6 kcal/mol, respectively. Intimate solvent participation is thus found to much more strongly affect the activation energy than the overall thermodynamics in this case. The imaginary frequency corresponding to the reaction coordinate at the transition state changes to 20011' cm-I when a single H 2 0 is intimately involved.
Marginal lands have received wide attention for their potential to improve food security and support bioenergy production. However, environmental issues, ecosystem services, and sustainability have been widely raised over the use of marginal land. Knowledge of the extent, location, and quality of marginal lands as well as their assessment and management are limited and diverse. There are many perceptions about what constitutes marginal lands and so clear definitions are needed. This paper provides a review of the historical development of marginal concept, its application and assessment. Challenges and priority research needs of marginal land assessment and management were also discussed.
An algorithm for locating stationary points corresponding to local minima and transition states on potential energy surfaces is developed and analyzed. This method, which represents a substantial extension of an earlier algorithm, utilizes local gradient and Hessian (i.e., first and second energy derivative) information to generate a series of ‘‘steps’’ that are followed to the desired stationary point. By designing the step sequence to move energetically downhill in all coordinates, local minima can be found. By stepping uphill along one local eigenmode of the Hessian while minimizing the energy along all other modes, one locates transition states. A key element of this development is a more efficient parametrization of the step vector in terms of quantities that permit the direction (i.e., uphill or downhill) and length of the step to be carefully controlled. This, in turn, allows ‘‘walks’’ that trace streambeds connecting local minima to transition states and to neighboring local minima more closely than has been found using the earlier methods. Such streambed walks provide information that can be used in subsequent reaction-path dynamics simulations.
The structures and binding energies of several cation:ether complexes (K+:dimethyl ether, K+:dimethoxyethane, K+:12-crown-4 and K+:18-crown-6) were determined with second and fourth order perturbation theory using correlation consistent basis sets. Several of these are the largest correlated calculations yet attempted on crown ethers. The observed systematic convergence to the complete basis set limit provides a standard by which the accuracy of previous studies can be measured and facilitates the calibration of density functional methods. Recent Fouier transform ion cyclotron resonance experiments predicted K+:18-crown-6 binding energies which were significantly smaller than ab initio calculations. None of the potential sources of error examined in the present study were large enough to explain this difference. Although the 6-31+G* basis set used in an earlier theoretical study was smaller than the smallest of the correlation consistent basis sets, with suitable correction for basis set superposition error, it appears capable of yielding binding energies within several kcal/mol of the basis set limit. Perturbation theory calculations exploiting the ‘‘resolution of the identity’’ approximation were found to faithfully reproduce binding energies and conformational differences. Although the cation–ether interaction is dominated by classical electrostatics, the accuracy of density functional techniques was found to be quite sensitive to the choice of functionals. The local density SVWN procedure performed well for binding energies and conformational differences, while underestimating K+O distances by up to 0.08 Å. The gradient-corrected Becke–Lee–Yang–Parr functional underestimated the K+:12c4 binding energy by 4–7 kcal/mol or 15%.
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