PROPOSALS

Introduction

The detailed knowledge of the electronic structure of atoms, molecules, clusters and solids is the basis of any understanding of matter. The capability to calculate the electronic structure without help of empirical data, i.e., using first-principles approaches, and to predict physical and chemical properties of matter resulting from this structure, opens manifold possibilities to explain the outcome of experiments, to supplement experimental data as well as to direct chemical or physical processes. The modern first-principles approaches of quantum chemistry and solid state physics nowadays allow the quantitative investigation of systems with substantial size and complexity. Two basic approaches are widely used today, namely wavefunction-based methods and density functional approaches. Despite the progress made during the last decades, a large number of unsolved problems of fundamental as well as technical type still exist. Examples are the often inefficient scaling of the computational effort of wavefunction-based approaches with the system size or the construction of more reliable density functionals. These topics are in the focus of the new DFG programme Modern and universal first-principles methods for many-electron systems in chemistry and physics.

The main goal of the new programme is the development of more efficient first-principles methods for electronic structure calculations of realistic systems. It is intended to achieve this by bringing together various groups of scientists from different fields, i.e., theoretical chemistry (quantum chemistry), theoretical physics (atomic, molecular and solid state physics) as well as applied mathematics. It is hoped that an interdisciplinary programme can be established, resulting both in a creation of innovative approaches as well as a fixing of weaknesses of the existing methods. The first-principles character of the developed methods is an indispensable requirement to achieve systematic improvements and universal applicability. It is hoped that the development of more reliable and more efficient methods for electronic structure calculations and their future implementation as standard approaches in computer codes will open new fields of application not only in chemistry and physics but also in biology and materials sciences.

Scope

The interdisciplinary programme comprises the fields of theoretical chemistry (quantum chemistry), theoretical physics (atomic, molecular and solid state physics) as well as applied mathematics. The focus is on the development, implementation and calibration of new as well as the systematic improvement of existing methods for first-principles calculations of the electronic structure of realistic systems, i.e., atoms, molecules, clusters and solids.

Semiempirical approaches of quantum chemistry as well as model Hamiltonian techniques of solid state physics are part of the programme. The same applies to routine investigations of physical or chemical systems with standard computer codes, e.g., computational chemistry.

Scientific Programme

In the following some central fields of research in the planned programme are briefly outlined.

Wavefunction methods

• Improvement and extension of local correlation ab initio methods for large molecules, i.e., linear scaling techniques. Extension of the existing schemes to open shell cases as well as implementation of property evaluations. Combination of local correlation techniques with the resolution of identity approximation for the integral evaluation in the local basis.

• Formulation and development of multi-reference extensions of the coupled- cluster approach. Formulation and implementation of spin-adapted

coupled-cluster approaches for open shell systems, especially for low spin cases. Efficient implementation including analytical derivatives and property evaluation.

• Extensions of the coupled-cluster singles and doubles approach towards an efficient treatment of higher excitations, i.e., triples and quadruples. Highly accurate total energy evaluations and predicition of molecular properties. Development of analytical derivatives as well as response techniques.

• Combination of local correlation techniques for large molecules with density functional and/or semiempirical schemes and/or classical force field approaches.

• Implementation of correlation approaches with wavefunctions explicitly depending on the interelectronic distance.

• Development of ab initio techniques for the accurate calculation of electronic states with a large number of unpaired electrons, e.g., evaluation of magnetic coupling in compounds with several d- or f-elements.

• Extension of wavefunction correlation methods to periodic systems, i.e., polymers and solids. Extension of the incremental scheme to metals, e.g., by the use of non-orthogonal orbitals. Calculation of correlation corrections to properties.

• Development of first-principles approaches for amorphous or partially amorphous solids. Calculation of local structural and energetic properties.

Density functional methods

• Extension of the optimized potential method concept. Derivation of a universal and efficient correlation energy functional.

• Development of a consistent description of magnetic solids, i.e., investigation of spin and especially orbital magnetism. Construction of improved exchange and correlation energy functionals, e.g., construction of a current density functional on the basis of the Airy gas. Study of the relationship between macroscopic magnetisation and microscopic current density.

• Density functional theory for multi-reference cases, e.g., coupling of multi-configuration self-consistent field or configuration interaction approaches with density functional theory.

• Density functional approach for Luttinger liquids. Investigation of the possible existence of metallic chain compounds with Luttinger liquid behaviour.

• Development of density functionals leading to improved band structures.

Density matrix methods

• Extension of the density matrix renormalization group (DMRG) to ab initio electronic structure calculations. Treatment of near-degeneracies in realistic systems with large numbers of electrons (> 18) in a large number of active orbitals (> 18), e.g., transition metal of lanthanide/actinide complexes. Investigation of convergence properties, achievable accuracy and computational efficiency of the DMRG with respect to the system parameters.

• Formulation and implementation of cumulant expansions.

Numerical techniques

• Application of methods from multi-scale analysis within ab initio quantum chemistry. Aiming towards an improved description of the characteristic length and energy scales of physical processes underlying various types of electron correlations.

• Development of wavelet-based nonlinear approximation schemes for correlated wavefunctions.

• Combination of wavelet representations of Jastrow-type wavefunctions with the auxiliary field Monte Carlo method. Application of the Hubbard— Stratonovitch transformation to the wavefunction provides an accurate guiding function for the Monte Carlo algorithm.

• Efficient techniques for the evaluation of matrix functions within the framework of nonstandard wavelet representations of operators.

• Applications to strongly correlated systems where Jastrow-type correlation factors are not sufficient any more.