A new semiempirical potential function for hydrogen bonds and its possible use in studying the DNA molecule

Abstract

Abstract A semiempirical potential function V ( r,R ) is proposed for describing the protons in hydrogen bonds. It consists of: the Morse potential V A ( r ), which describes the covalent bond AH in the R 1 AH⋯BR 2 system; a Coulombic term E e.s. , which contains the Coulombic point interaction of each atom of the R 1 AH group with the BR 2 molecule and the interaction of the hydrogen atom with the R 1 A group having non-equilibrium lengths R  R 0 ; the potential V R ( R ), which describes the exponential repulsion of atoms A and B owing to the partial overlap of their shells; another Morse potential V B ( R—r ), which accounts for all other effects such as the redistribution of charge density by the approach of the hydrogen and boron atoms, their mutual polarization, and partly also Van der Waals forces. The parameters of the proton potential were found for the (H 2 O) 2 dimer and for three hydrogen bonds of a guanine—cytosine (GC) pair for weak and medium strong hydrogen bonds without high proton excitation levels. Using the dependence on R of the bond energy ϵ( R ) (for the water dimer) and the V ( r,R ) values at R = R 0 (for the GC pair), we extrapolated the V ( r,R ) functions to non-equilibrium r = R 0 and R = R 0 values. A simple method of solving a one-dimensional Schrodinger equation is proposed for such a potential function. Wavefunctions and the corresponding energy levels were obtained. These data make it possible to study the influence of hydrogen bonds in the ground and excited states on the character of the atomic vibrations in the GC pair and the processes in poly-GC with one adenine-thymine pair by absorption of excess energy and also the influence of dielectric surroundings (in particular, water) on the properties of the hydrogen bonds in (H 2 O) 2 .