arXiv subjects

Mahir E. Ocak

Publications and source records attributed to Mahir E. Ocak.

3 recordsLinked to original sources

arXiv2012

Monomer Basis Representation Method For Calculating The Spectra Of Molecular Clusters I. The Method And Qualitative Models

Firstly, a sequential symmetry adaptation procedure is derived for semidirect product groups. Then, this sequential symmetry adaptation procedure is used in the development of new method named Monomer Basis Representation (MBR) for calculating the vibration-rotation-tunneling (VRT) spectra of molecular clusters. The method is based on generation of optimized bases for each monomer in the cluster as a linear combination of some primitive basis functions and then using the sequential symmetry adaptation procedure for generating a small symmetry adapted basis for the solution of the full problem. It is seen that given an optimized basis for each monomer the application of the sequential symmetry adaptation procedure leads to a generalized eigenvalue problem instead of a standard eigenvalue problem if the procedure is used as it is. In this paper, MBR method will be developed as a solution of that problem such that it leads to generation of an orthogonal optimized basis for the cluster being studied regardless of the nature of the primitive bases that are used in the generation of optimized bases of the monomers.

physics.chem-ph↗

arXiv2012

Monomer Basis Representation Method For Calculating The Spectra Of Molecular Clusters II. Application To Water Dimer

The Monomer Basis Representation (MBR) method developed in the first paper is applied to water dimer in order to illustrate its application and to show its validity. The calculations are done by using the SAPT-5st potential surface. Monomers are treated as rigid bodies. Radial coordinate is separated from the angular coordinates adiabatically. MBR method is used for solving the five dimensional angular problem. Then, the results of the angular calculations are fit to a Morse function to find the potential surface for the radial motion. The results show that the method works efficiently and accurately.

physics.chem-ph↗

arXiv2012

Quantum Mechanical Results Of The Matrix Elements Of The Boltzmann Operator Obtained From Series Representations

Recently developed series representations of the Boltzmann operator are used to obtain Quantum Mechanical results for the matrix elements, , of the imaginary time propagator. The calculations are done for two different potential surfaces: one of them is an Eckart Barrier and the other one is a double well potential surface. Numerical convergence of the series are investigated. Although the zeroth order term is sufficient at high temperatures, it does not lead to the correct saddle point structure at low temperatures where the tunneling is important. Nevertheless the series converges rapidly even at low temperatures. Some of the double well calculations are also done with the bare potential (without Gaussian averaging). Some equations of motion related with bare potentials are also derived. The use of the bare potential results in faster integrations of equations of motion. Although, it causes lower accuracy in the zeroth order approximation, the series show similar convergence properties both for Gaussian averaged calculations and the bare potential calculations. However, the series may not converge for bare potential calculations at low temperatures because of the low accuracy of zeroth order approximation. Interestingly, it is found that the number of saddle points of increases as the temperature is lowered. An explanation of observed structures at low temperatures remains as a challenge. Besides, it has implications for the quantum instanton theory of reaction rates at very low temperatures.

physics.chem-ph↗