Dr. Köster M. Andreas

University of Hannover, 1992

University of Montreal, 1993/94

Tel: 5747-3910
Fax: 57 47 33 89

Research at a Glance

  • Understanding chemical and biological reactions from their molecular foundation complements the practice of modern technology. In answering the most basic questions about chemical reactions, theoretical chemists import methods and concepts from the physical and mathematical science. This approach develops an understanding of chemistry and biology from the principles of physics. During the past decade the application range of theoretical chemistry has been dramatically increased. The main reason for the phenomenal growth of this research area are the development of new algorithms and the increased availability of computational power.
  • The research group of Andreas M. Köster focus on the development of density functional theory (DFT) methods and their applications to problems in molecular science and material research. Closed collaboration with experimental chemists and physicists ensure the continuous exchange of experimental and theoretical observations. The current research activities are in the fields of cluster research, nanotechnology and catalysis.

deMon (density of Montréal) is a software package for density functional theory (DFT) [1-3] calculations. It uses the linear combination of Gaussian-type orbital (LCGTO) approach for the self-consistent solution of the Kohn-Sham (KS) DFT equations. The calculation of the four-center electron repulsion integrals is avoided by introducing an auxiliary function basis for the variational fitting of the Coulomb potential [4-6]. Some of the features of the deMon package are:

  • Variational fitting of the Coulomb potential
  • Geometry optimization and transition state search
  • Molecular dynamic simulations (MD)
  • Time-dependent DFT (TD-DFT)
  • Calculation of properties like polarizabilities, hyperpolarizabilities, NMR, IR and Raman spectra and intensities, thermodynamic data
  • Parallelized code (MPI)
  • Interfaces for visualization software (Molden, Molekel, Vu)
  • Portability to various computer platforms and operating systems

For further details concerning theory, implementation and program features click here

Prof. Dr. Andreas M. Köster

(Group Leader)

Dr. Florian Janetzko

(Research Associate)

Q. Roberto Flores Moreno

(Ph.D. Student)

Q. Jorge Martin del Campo Ramirez

(Ph.D. Student)

Q. Bernardo Antonio Zuniga Gutierrez

(Ph.D. Student)

Gabriel Ulises Gamboa

(Ph.D. Student)

Rodrigo José Álvarez Montero Méndez

(Lic. Student)

  • P. Calaminici, A.M. Köster, Structures and Vibrations of V3O and V3O-: A Density Functional Study, Int. J. Quantum Chem. 91, 317 (2003)

  • A.M. Köster, A. Goursot, D.R. Salahub, deMon in Comprehensive Coordination Chemistry II: From Biology to Nanotechnology, Vol. 1, Chapter 2.57, pp 681, Editors: J. McCleverty , T.J. Meyer, B. Lever, Elsevier (2003)

  • P. Calaminici, A.M. Köster, D.R. Salahub, Negative Ion Photoelectron Spectra Simulation of V3O from a Density Functional Study, J. Chem. Phys. 118, 4913 (2003)

  • A.M. Köster, Hermite Gaussian Auxiliary Function for the Variational Fitting of the Coulomb Potential in Density Functional Methods, J. Chem. Phys. 118, 9943 (2003)

  • C. Quintanar, R. Caballero, A.M. Köster, Effect of Long-Rang Interactions in Embedded Ionic Cluster Calculations, Int. J. Quantum Chem. 96, 483 (2004)

  • J.U. Reveles, A.M. Köster, Geometry Optimization in Density Functional Methods, J. Comput. Chem. 25, 1109 (2004)

  • A.M. Köster, R. Flores-Moreno, J.U. Reveles, Efficient and Reliable Numerical Integration of Exchange.- Correlation Energies and Potentials, J. Chem. Phys. 121, 681 (2004)

  • A.M. Köster, J.U. Reveles, J.M. del Campo, Calculation of the Exchange-Correlation Potential with Auxiliary Function Densities, J. Chem Phys. 121, 3417 (2004)

  • P. Calaminici, R. Flores-Moreno, A.M. Köster, Structures and Vibrations of Nb3O- and NS30: A Density Functional Study , J. Chem. Phys. 121, 3558 (2004)

  • D.R. Salahub, J. Weber, A. Goursot, A.M. Köster, A. Vela, Applied Density Functional Theory and the deMon Code, 1964 — 2004, in Theory and Applications of the Computational Chemistry: The First 40 Years, Editors: C. E. Dykstra, G. Frenkling, K.S. Kim, G. Scuseria, (2005)

  • A.M. Köster, G. Geudtner, Z. Gómez, P. Calaminici, First Principle and Energy Separation, J. Phys. Chem. 103, 1257(2005)

  • P. Calaminici, V.D. Domínguez-Soria, G. Geudtner, E. Hernández-Marín, A.M. Köster, Parallelization of the Variational Fitting of the Coulomb Potential, Revista Superficies y Vacío, 18 (2005)

Development of Density Functional Theory (DFT) Methods

Over the last decade density functional theory methods have emerged to a powerful tool for theoretical and computational chemistry. These methods combine the reliable description of the electronic structure with a moderate scaling behavior. Therefore, they are well suited for the accurate description of large systems with several hundred atoms. The research group of Andreas M. Köster is actively involved in the development of the density functional theory program deMon2k[1]. This program is based on the linear combination of Gaussian-type orbitals (LCGTO) and the use of auxiliary functions to represent an approximated density [2]. In combination with pseudo-potentials all elements up to Lawrencium can be treated with deMon2k. Efficient algorithms for the calculation of three-center Coulomb integrals [3,4] and the numerical integration of the exchange-correlation potential [5,6] have been developed by our research group. As a result, the Kohn-Sham matrix construction in deMon2k scales nearly linear [7]. The parallel Version of deMon2k is efficient without using expensive intercommunication and, therefore, well suited for the accurate calculation of systems with several hundred atoms on economic architectures, like clusters.

Based on the molecular deMon2k version the cyclic cluster approximation is currently imple­mented (CONACYT Project 40379-F). With this approach surface and bulk structures can be studied with the same methodology (basis set, functional etc.) as molecules. The CCA is particularly well suited for the description of local defects that lift ideal periodicity. Therefore, this method has a bright perspective in solid-state chemistry. It will close the gap between reliable periodic and molecular cluster DFT methods.

Besides the development and implementation of new density functional theory approaches our research group is also involved in the implementation of several molecular properties in deMon.

Current research is focused on geometry optimization [8] and transition state search algorithms for systems with several hundred atoms, efficient algorithms for the calculation of effective and model core potential integrals and their derivatives as well as linear scaling self-consistent field acceleration methods. The group is also involved in several joint implementation projects within the deMon developer community. To obtain more information about deMon2k please contact Prof. Dr. Patrizia Calaminici (pcalaminmail.cinvestav.mx).


  1. A.M. Köster, P. Calaminici, M.E. Casida, R. Flores-Moreno, G. Geudtner, A. Goursot, T. Heine, A. Ipatov, F. Janetzko, S. Patchkovskii, J.U. Reveles, A. Vela, D.R. Salahub, deMon2k, The deMon Developers (2005)
  2. A.M. Köster, J.U. Reveles, J.M. del Campo, J. Chem. Phys. 121,3417 (2004)
  3. A.M. Köster, J. Chem. Phys. 104, 4114 (1996)
  4. A.M. Köster, J. Chem. Phys. 118, 9943 (2003)
  5. M. Krack, A.M. Köster, J. Chem. Phys. 108, 3226 (1998)
  6. A.M. Köster, R. Flores-Moreno, J.U. Reveles, J. Chem. Phys. 121, 681 (2004)
  7. A.M. Köster, A. Goursot, D.R. Salahub in "Comprehensive Coordination Chemistry-II: From Biology to Nanotechnology", Vol. 1, Chapter 2.57, pp. 681, Editors: J. McCleverty, T.J. Meyer, B. Lever, Elsevier (2003)
  8. J.U. Reveles, A.M. Köster, J. Comput. Chem. 25, 1109 (2004)

Theoretical Chemistry I

This course gives an introduction to Theoretical Chemistry based on wave-function methods. For density functional methodology the course Theoretical Chemistry II is offered in CINVESTAV. In the first part of the course Theoretical Chemistry I the Hartree-Fock method is derived within the molecular orbital theory. For the inclusion of correlation the configuration ­interaction (CI) approach is discussed. In a next step symmetry adapted and localized molecular orbitals are introduced. The aim of this first section of the course is to make the students familiar with the standard mathematical techniques in molecular orbital theory. The second part of the course focuses on approximations and their practical implementation. The aim of this part of the course is to provide the theoretical background for the integral approximations used in modern electronic structure codes, like deMon2k.

Table of Contents:

  • Born-Oppenheimer Approximation
  • Atomic Units
  • The Antisymmetry Principle
  • The MO-LCAO Approximation
  • Molecular Hartree-Fock Calculations
  • Molecular Configuration-Interaction
  • Symmetry of Molecular Orbitals
  • Localized Molecular Orbitals
  • Semi-empirical Methods
  • Dunlap Approximation
  • Calculation of Molecular Integrals

Suggested Literature:

  • F.L. Pilar, Elementary Quantum Chemistry, 2nd Edition (McGraw-Hill, New York, 1990)
  • A. Szabo, N .S. Ostlund, Modern Quantum Chemistry (Dover Publications, New York, 1996)
  • T. Helgaker, P. Jorgensen, J. Olsen, Molecular Electronic Structure Theory (Wiley, New York, 2000)