A mathematical simulation and a numerical investigation of dynamics of intramolecular tautomerny transformation without considering processes of a proton relaxation. Part I. A description of a mathematical model
There is a quantum statistical model of prototropic tautomeic transformation caused by vertical transition between different adiabatic potentials with two minima divided by potential barrier offered. Formula for the probability function defining time of tautomer transformation without regard to vibronic relaxation is received.
1. Квитко Г. В., Кузин Э. Л., Шоть Д....
Numerical solution of the Schrödinger equations with polynomial potentials (Part I)
The fundamental solution of a Cauchy problem and the spectral task for a one-dimensional Schrodinger equations with potential in the form of polynomials m P (x) (m 6) is solved. Numerical calculations are applied to modelling adiabatic potentials with two minima characteristic for a proton in compounds with intramolecular hydrogen bonds.
Арсеньев А. А.
Оценка функции Грина оператора Шрёдингера // Теоретическая и математическая ...
Numerical solution of the Schrödinger equations with polynomial potentials (Part II)
... Российского государственного университета им. И. Канта. 2009. Вып. 10. С. 104—111.
Kvitko G., Kuzin E., Shott D.
Schrodinger equations, proton, Cauchy problem, Green's function,
specter, Ritz method, adiabatic potential, fundamental solution.
Mathematical Model of Intramolecular Tautomeric Transformation and the Processes of a Relaxation of the Proton
A quantum statistical model of intramolecular tautomeric transformation is offered, accounts for the vibration of a proton as a result of its interaction with the surrounding medium simulated by the quantized field of radiation. Effective adiabatic potentials of the proton are approximated by the parabolas of various curvatures. The estimation for the vibrational relaxation time and the formula for the constant of tautomeric equilibrium.
Грибов Л. А., Дементьев В. А.,...