Ab Initio Calculations on Porphyrins in the Condensed Phase
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The geometry optimization of a cluster of molecules, such as a porphyrin molecule surrounded by many solvent molecules, is difficult due to the many minima on the associated potential energy surface. Several methods for finding the global minimum, such as simulated annealing(SA) and genetic algorithms, 8 have been previously utilized on molecules with many degrees of freedom. However, because these methods require the evaluation of the energy at a large number of geometries, only MM potentials have been used, as ab initio or even semiempirical energies have been considered too computationally demanding for these methods. The implementation of the all-fragment option in GAMESS has made it possible to carry out these types of calculations at the EFP level of theory. In this study, the use of SA is demonstrated in the optimization of formamide with 3 water molecules and of glutamic acid (both the neutral and zwitterionic forms) with 10 water molecules. Technical difficulties have prevented us from producing an EFP for a molecule the size of a porphyrin, so that global optimization methods have not yet been utilized on solvated porphyrins. Previously, we reported 9 geometry optimizations on isolated zinc and free-base octobromotetraphenyl porphyrin (OBrTPP), octobromo porphyrin (OBrP), and tetraphenyl porphyrin (TPP), as well as on the ZnOBrTPP surrounded by 10 (EFP) water molecules. For this study we have found the minimum energy geometry for the water-soluble octobromo-tetrapyridinal porphyrin(+4) cation (OBrTPyP4), and compare it to the structures reported in Ref. 9. Such calculations will be used as a reference when we carry out the SA on the solvated porphyrins. METHODS The GAMESS program has been modified to carry out the SA calculations. The method implemented is similar to that suggested by Parks.'° In SA, a series of Monte Carlo simulations are carried out, starting at a high temperature, and then decreasing the temperature in small increments. In a Monte Carlo simulation, a trial step is generated by incrementing each variable by the product of the current maximum for that variable and a random number between 0 and 1. If the energy at the new geometry is lower than the energy at the current geometry, the step is accepted. If the energy at the new geometry is higher than the energy at the current geometry, the step is accepted only if, exp((Eold - Enew)/kT) >r
(1)
where EoId and E,,w are the current energy and the trial energy, respectively, T is the temperature, k is Boltzmann's constant, and r is another random number between 0 and 1. Otherwise, the step is rejected and a new trial step is generated. Thus, at the high initial temperature, the probability of accepting a step is high, allowing the system to sample a large volume of the variable space. This should prevent the system from getting trapped in a relatively high energy local minimum, and increases the probability that the more selective low-temperature steps will locate the global minimum. A two-step method has been used in this work to optimize s
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