Biomedical subjects

Christian Kollmar

Publications and source records attributed to Christian Kollmar.

4 recordsLinked to original sources

PubMed2006

A size extensive energy functional derived from a double configuration interaction approach: the role of N representability conditions.

Starting from a configuration interaction (CI) approach including only doubly excited configurations, the corresponding energy functional is modified by introduction of a topological factor in the normalization condition of the CI coefficients in such a way that it gets inherently size extensive. Constraints imposed by N representability conditions on the modified functional are discussed and lead to a specific choice of the topological factor. The basic variable in the modified energy functional is the second-order reduced density matrix parametrized in terms of CI-like coefficients. Test calculations for a variety of small molecules show that the numerical results obtained with the new functional are in very good agreement with those obtained from coupled cluster singles doubles calculations.

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PubMed2005

Optimization of auxiliary basis sets for the LEDO expansion and a projection technique for LEDO-DFT.

We present a systematic procedure for the optimization of the expansion basis for the limited expansion of diatomic overlap density functional theory (LEDO-DFT) and report on optimized auxiliary orbitals for the Ahlrichs split valence plus polarization basis set (SVP) for the elements H, Li--F, and Na--Cl. A new method to deal with near-linear dependences in the LEDO expansion basis is introduced, which greatly reduces the computational effort of LEDO-DFT calculations. Numerical results for a test set of small molecules demonstrate the accuracy of electronic energies, structural parameters, dipole moments, and harmonic frequencies. For larger molecular systems the numerical errors introduced by the LEDO approximation can lead to an uncontrollable behavior of the self-consistent field (SCF) process. A projection technique suggested by Löwdin is presented in the framework of LEDO-DFT, which guarantees for SCF convergence. Numerical results on some critical test molecules suggest the general applicability of the auxiliary orbitals presented in combination with this projection technique. Timing results indicate that LEDO-DFT is competitive with conventional density fitting methods.

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PubMed2004

The "JK-only" approximation in density matrix functional and wave function theory.

Various energy functionals applying the "JK-only" approximation which leads to two-index two-electron integrals instead of four-index two-electron integrals in the electron-electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration self-consistent field calculations for the best possible "JK-only" wave function are compared to those obtained from the pair excitation multiconfiguration self-consistent (PEMCSCF) method and two versions of density matrix functional theory. One of these is derived making explicit use of some necessary conditions for N representability of the second-order density matrix. It is shown that this method models the energy functional based on the best possible "JK-only" wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlation energy is incorporated by "JK-only" approaches for larger molecules.

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PubMed2004

The structure of the second-order reduced density matrix in density matrix functional theory and its construction from formal criteria.

Some formal requirements for the second-order reduced density matrix are discussed in the context of density matrix functional theory. They serve as a basis for the ad hoc construction of the second-order reduced density matrix in terms of the first-order reduced density matrix and lead to implicit functionals where the occupation numbers of the natural orbitals are obtained as diagonal elements of an idempotent matrix the elements of which represent the variational parameters to be optimized. The numerical results obtained from a first realization of such an implicit density matrix functional give excellent agreement with the results of full configuration interaction calculations for four-electron systems like LiH and Be. Results for H2O taken as an example for a somewhat larger molecule are numerically less satisfactory but still give reasonable occupation numbers of the natural orbitals and indicate the capability of density matrix functional theory to cope with static electron correlation.

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