Kleber C. Mundim   Professor Instituto de Química Universidade de Brasília

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He is developing new quantum mechanical methods to study electronic properties in molecules to be used for computer new materials and drug design. He also works on Chemical Optimization Processes  usingGSAmethod, as well as ond-Algebra to describe non-Linear Arrhenius reaction rate processes. 

Research Interests :

• Classical Molecular Dynamics (Program THOR ): Development of computational code based on Classical Force Field methods for calculating Biomolecules and Solids molecular strucutre. See the publications : 53, 61

• Phenomenological Approach to Deviations from Arrhenius Law: Although chemical reaction processes and transport phenomena are usually dealt with in the Arrhenius theory, which predicts that the logarithm of the transport rate or chemical reaction rate is a linear function of the inverse of the temperature and the activation energy is constant, many experimental researchers have recently reported non-Arrhenius temperature dependency in these kind of problems. In such materials the logarithm of diffusivity or reaction rate, plotted against the reciprocal of the absolute temperature, exhibits a negative deviation from linearity. It is also important to highlight that many experiments across a range of fields present non-Arrhenius behavior, such as diffusion, electrical conductivity, rate reaction in chemistry and biology processes, super conductivity, nonlinear resistors and various transport phenomena in materials science. In the light of existing problems in this subject, our main objective, is to propose an alternative approach to describe non-Arrhenius diffusivity, chemical reaction processes, as well as a new temperature-dependence for the diffusion activation energy. Furthermore, the present study provides new insights into the deviations from linearity in many non-Arrhenius phenomena, such as VTF and non-exponential processes. See the publications : 82, 84

• The origin of life: In order to discuss some prebiotic stages, we developed a computer simulations assuming an autocatalytic polymerization of RNA-like chains from a random collection of oligomers in two dimensions through an equilibrium process. In the study we consider the effect of the possible cross-links (non-specific weak bindings among or within the polymers), that may actually contribute to the folded shape of some real polymers, and we show that cross-linking favors the appearance of larger polymers. Furthermore, we discuss the obtained scenario with regard to some experimental results, which compare well with our numerical ones. See the publications : 23

• TOF-MS-GSA procedure: A  new  statistical  and  stochastical  method  for  the  determination  of dynamical features of the molecular dication dissociation processes, following the single photon double ionization has been developed. The method is based on an extension of the Generalized Simulated Annealing statistical methodology, previously applied in other fields. The results are consistent with previous determination of the metastable lifetime of the dication, but the analysis also provides additional information about the dynamics of the reaction. 83, 86.

• Hamiltonian Dynamics of Ferroelectric Liquid Crystals: We present ferroelectric liquid crystals as a simple non-integrable Hamiltonian system. The disordered-helicoidal phase transition undergoes a Hopf bifurcation. The Poincaré sections of the solutions in the helicoidal phase, shows the existence of spatial chaotic behavior of the molecular structure depending on temperature and external magnetic field. The ordered - helicoidal phase transition is also studied as second order derivative Hamiltonian theory.

• Stochastic Molecular Dynamics (Hartree-Fock-GSA ): Development a stochastic algorithm to investigate the real restrict- and unrestricted Hartree–Fock problem. The approach is based on a global optimization method, the Generalized Simulated Annealing. The main characteristic of this method is that it enables the mapping of the electronic hyper-surface in such a way as to guarantee that the absolute minimum of the functional in focus will be achieved.

• Global Optimization Process through GSA: Due to the increasing pressure for reducing costs and inventories, in order to remain competitive in the global marketplace, the global optimization methodology has become the “holy grail” in process industries. The most common 21st century goals are maximizing through put, minimizing cost, and/or efficiency. This is one of the major quantitative tools in the economy and industrial decision making. Optimization procedure is one of the major quantitative tools in the machinery of decision-making. In this project, we examine the basic characteristic of optimization problems and their solution techniques and we  also propose an alternative global optimization process using the "Generalized Simulated Annealing" procedure. We have applied it to simulated problems in chemistry, physics, biology and others industry subjects. This early result shows that the application of simulated annealing to computation of optimization process is encouraging and it deserves further research.

• Potential Surface Energy through GSA procedure: We developped a stochastic optimization technique, based on generalized simulated annealing (GSA), as a new option to fit potential energy surfaces (PES) for reactive scattering dynamics. This procedure can reproduced the PES of reaction utilizing the ab initio calculation. 

• Stochastic molecular dynamics in simulations of metalloid impurities in metals:  A hybrid approach is described, which combines stochastic classical molecular dynamics and first-principles density functional theory to model the atomic structure and properties of large solid-state systems. The stochastic molecular dynamics using generalized simulated annealing (GSA) is based on nonextensive statistical mechanics and thermodynamics. Examples of applications are given on metalloid.

• Stochastic molecular dynamics in simulations of  protein: We propose a stochastic optimization technique based on the generalized simulated annealing (GSA) method for mapping minima points of molecular conformational energy surfaces. The energy maps are obtained by coupling a classical molecular force field THOR package with a GSA procedure. Unlike the usual molecular dynamics MD method, the method proposed in this study is force independent; that is, we obtain the optimized conformation without calculating the force, and only potential energy is involved. Therefore, we do not need to know the conformational energy gradient to arrive at equilibrium conformations.

• Multifractality, Levinthal paradox, and energy hypersurface: Multifractal properties in the potential energy hypersurface of polypeptides and proteins are investigated. Characteristic multifractal behavior for different molecular systems is obtained from the f ( a) spectra. The analysis shows that the dimension of the phase space of the problem influences the accessibility to different parts of the potential energy hypersurface. Also, we show that it is necessary to take into account the H-bond formation between amino acids in the conformational-folding search. The present findings indicate that the f (a) function describes some structural properties of a protein. The behavior of the f ( a) spectra gives an alternative explanation about the Levinthal paradox. Furthermore, the anomalous temperature dependence of the Raman spin-lattice relaxation rates can be related to the perturbations in the secondary structures.

• New Stochastic Strategy to Analyze Helix Folding in Protein: We propose an alternative stochastic strategy to search secondary structures based on the generalized simulated annealing (GSA) algorithm, by using conformational preferences based on the Ramachandran map. We optimize the search for polypeptide conformational space and apply to peptides considered to be good
  -helix promoters above a critical number of residues. Our strategy to obtain conformational energies consist in coupling a classical force field (THOR package) with the GSA procedure, biasing the
  backbone angles (f,y) to the allowed regions in the Ramachandran map. For polyalanines we obtained stable
  -helix structures when the number of residues were equal or exceeded 13 amino acids residues. We also observed that the energy gap between the global minimum and the first local minimum tends to increase with the polypeptide size.  When compared with molecular dynamics or Monte Carlo methods, GSA can be considered the fastest.

•  q-Integral: Development of an alternative strategy to reduce the CPU time to evaluate the bi-electronic integrals in ab initio quantum mechanics calculations. An analytical procedure to evaluate the energy of a molecule as well as two-electron integrals is proposed. This approach is based on the generalized exponential function (d-exponential) and is particularly advantageous because it reduces substantially the CPU time in quantum mechanical calculations. It is important to point out that the new methodology is applicable to any kind of molecular system including relatively large molecular systems in the context of the Hartree–Fock (HF) and density functional theories (DFT). 

•  Diesel-like fuel obtained by pyrolysis of vegetable oils: The pyrolysis reactions of soybean, palm tree, and castor oils were studied, showing the formation of olefins, paraffins, carboxylic acids, and aldehydes. The adequate choice of distillation temperature (DT) ranges made it possible to isolate fuels with physical–chemical properties comparable to those specified for petroleum based fuels. The catalytic upgrading of the soybean pyrolytic fuel over HZSM-5 zeolite at 400 Celsius was also studied and has shown a partial deoxygenation of the pyrolytic products.