On the Choice of Method for Solution of the Vibrational Schrödinger Equation in Hybrid Statistical Physics - Quantum Mechanical Modeling of Molecular Solvation

  • Bojana KoteskaEmail author
  • Dragan Sahpaski
  • Anastas Mishev
  • Ljupčo Pejov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 231)


Several numerical methods for solution of vibrational Schrödinger equation in the course of hybrid statistical physics – quantum mechanical modeling of molecular solvation phenomena were applied, tested, and compared. The mentioned numerical methods were applied to compute the anharmonic OH stretching vibrational frequencies of the free and solvated hydroxide anion in diluted water solutions on the basis of one-dimensional vibrational potential energies computed at various levels of theory, including density functional theory based methodologies, as well as methods based on many-body perturbation theory. The tested methods included: i) simple Hamiltonian matrix diagonalization technique, based on representation of the vibrational potential in Simons-Parr-Finlan (SPF) coordinates, ii) Numerov algorithm and iii) Fourier grid Hamiltonian method (FGH). Considering the Numerov algorithm as a reference method, the diagonalization technique performs remarkably well in a very wide range of frequencies and frequency shifts. FGH method, on the other hand, though showing a very good performance as well, exhibits more significant (and non-uniform) discrepancies with the Numerov algorithm, even for rather modest frequency shifts. Particular aspects related to HPC-implementation of the numerical algorithms for the applied methodologies were addressed.


Fourier grid Hamiltonian method Numerov algorithm diagonalization of Hamiltonian matrix solvation intermolecular interactions anharmonic O-H vibrational frequency shifts Monte-Carlo simulation 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bojana Koteska
    • 1
    Email author
  • Dragan Sahpaski
    • 1
  • Anastas Mishev
    • 1
  • Ljupčo Pejov
    • 2
  1. 1.Faculty of Computer Science and EngineeringUniversity Sts Cyril and MethodiusSkopjeMacedonia
  2. 2.Faculty of Natural Sciences &, Mathematics Institute of ChemistryUniversity Sts Cyril and MethodiusSkopjeMacedonia

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