Theory of complex molecular interactions: computer graphics, distance geometry, molecular mechanics, and quantum mechanics

Abstract

Complex molecules such as proteins and nucleic acids have fascinated chemists because of their essential role in the functioning of biological systems. The chemist would like to know the structure and energies of the conformations of these molecules. To a first approximation, the situation looks hopeless. Although modern quantum mechanics can give powerful insights into the structure and potential energy surface of small molecules,1,2 macromolecular systems may be composed of 500 atoms or more with uncountable local energy minima.

Protein Design and the Development of New Therapeutics and Vaccines

“…However, it is completely impractical to use quantum mechanical methods to calculate the energy and analytical derivatives of the energy for all of the coordinates of a system as large as a protein. Fortunately, it has been demonstrated that empirical energy equations and classical mechanical methods are surprisingly accurate at representing the conformations and noncovalent interactions for chemical systems in which the chemical bonding does not change during the process of interest (Kollman, 1985). Thus, in cases in which chemical bonding is changing (e.g., enzyme catalysis) one can use hybrid approaches, analyzing the part of the system in which the reaction occurs with quantum mechanics and the remainder of the system with (classical) molecular mechanics.…”

Water Pollution

“…One promising method for determining rate constant data for catalytic processes is to calculate the ground state energy of the chemical-substrate complex with molecular mechanics (Allinger, 1976;Boyd and Lipkowitz, 1982;Kollman, 1985). The ground state energy can be used to calculate the free energy of activation and the rate constant from transition-state theory (Laidler, 1965).…”

Ab initioapproach for many-electron systems without invoking orbitals: An integral formulation of density-functional theory

“…It distinguishes the present formulation from any other ab initio theory of electronic structure and offers the possibility to perform ab initio calculations for molecules with very many electrons. (2) The parameter q represents the accuracy of the solution. On the one hand, it resembles K, the number of basis functions used in the solution of the KS equations (5), in that the limits for K-• °° and q-> °° are the same, the exact KS density; on the other hand, q need only be a positive integer whereas K has a minimum requirement of K> jN.…”

“…For macromolecules of biological interest, calculations of structure are out of the reach of current methods, and have to depend on empirical models. 2 In contrast, the Hohenberg-Kohn-Sham densityfunctional theory (DFT) 3 establishes the validity of the use of the electron density as the basic variable for ground states, though at the cost of having not exactly known kinetic energy and exchange-correlation energy functionals. For the approximation of the exchangecorrelation functional, the local-density approximation 33 and others beyond the local-density approximation 4 have been widely applied to atoms, molecules, and solids.…”

“…The minimum principle of E[p'] subject to JV(rW=TV (2) leads to the Euler equation for the ground state p(r),…”