Reinhart Ahlrichs

ELECTRONIC STRUCTURE CALCULATIONS ON WORKSTATION COMPUTERS: THE PROGRAM SYSTEM TURBOMOLE

The basic structure of the program system TURBOMOLE for SCF - including first and second analytical derivatives with respect to nuclear coordinates - and MP2 calculations is briefly described. The program takes full advantage of all discrete point group symmetries and has only modest - and (partially) adjustable - I/O and background storage requirements. The performance of TURBOMOLE is documented for demonstrative applications.

Fully optimized contracted Gaussian basis sets for atoms Li to Kr

Various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self‐consistent field ground state energies with respect to all basis set parameters, i.e., orbital exponents and contraction coefficients.

TREATMENT OF ELECTRONIC EXCITATIONS WITHIN THE ADIABATIC APPROXIMATION OF TIME DEPENDENT DENSITY FUNCTIONAL THEORY

Time dependent density functional methods are applied in the adiabatic approximation to compute low-lying electronic excitations of N2, ethylene, formaldehyde, pyridine and porphin. Out of various local, gradient-corrected and hybrid (including exact exchange) functionals, the best results are obtained for the three-parameter Lee-Yang-Parr (B3LYP) functional proposed by Becke. B3LYP yields excitation energies about 0.4 eV too low but typically gives the correct ordering of states and constitutes a considerable improvement over HF-based approaches requiring comparable numerical work.

Auxiliary basis sets to approximate Coulomb potentials

We demonstrate accuracy and computational efficiency resulting from an approximate treatment of Coulomb operators which is based on the expansion of molecular electron densities in atom-centered auxiliary basis sets. This is of special importance in density functional methods which separate the treatment of Coulomb and exchange-correlation terms. Auxiliary basis sets are optimized as much as possible for isolated atoms and then augmented for use in molecular electronic structure calculations. For molecules involving atoms up to Br this typically affects energies by only 10−4 au per atom, and computed structure constants by less than 0.1 pm in bond distances and 0.1° in bond angles.

Efficient molecular numerical integration schemes

New grids for three‐dimensional numerical integration are introduced. They include a new mapping for radial integration of the Gauss–Chebyshev type which seems to surpass in accuracy the existing integration schemes as proposed by Becke [J. Chem. Phys. 88, 2547 (1988)], Murray et al. [Mol. Phys. 78, 997 (1993)], or Gill et al. [Chem. Phys. Lett. 209, 506 (1993)]. Lebedev grids are employed for spherical integration. Open ended quadrature schemes are presented using the efficient Lobatto formula for the θ integration. These grids are employed for self‐consistent density functional calculations using local approximation and nonlocal corrections and are implemented into the program package turbomole. The results of grid tests and demonstrative applications of energy and especially analytical gradient calculations are given.

RI-MP2 : OPTIMIZED AUXILIARY BASIS SETS AND DEMONSTRATION OF EFFICIENCY

Abstract Applications of the RI-MP2 method require high-quality auxiliary basis sets employed to approximate charge distributions. A variational procedure is proposed and applied to optimize auxiliary bases for main group and transition metal atoms which are tested for more than 350 molecules. The RI approximation affects molecular MP2 energies by less than 60 μ E h per atom and equilibrium distances by less than 0.2 pm. We further comment on the extension from RHF to UHF and the exploitation of molecular symmetry. Applications to (Cu 2 S) n clusters and hydrocarbons C n H 2 n +2 document a significant reduction of computation times which allows for calculations with up to 1000 basis functions in C 1 symmetry.

Adiabatic time-dependent density functional methods for excited state properties

This work presents theory, implementation, and validation of excited state properties obtained from time-dependent density functional theory (TDDFT). Based on a fully variational expression for the excited state energy, a compact derivation of first order properties is given. We report an implementation of analytic excited state gradients and charge moments for local, gradient corrected, and hybrid functionals, as well as for the configuration interaction singles (CIS) and time-dependent Hartree–Fock (TDHF) methods. By exploiting analogies to ground state energy and gradient calculations, efficient techniques can be transferred to excited state methods. Benchmark results demonstrate that, for low-lying excited states, geometry optimizations are not substantially more expensive than for the ground state, independent of the molecular size. We assess the quality of calculated adiabatic excitation energies, structures, dipole moments, and vibrational frequencies by comparison with accurate experimental data f...

The averaged coupled-pair functional (ACPF): A size-extensive modification of MR CI(SD)

Abstract To account for unlinked-cluster effects at the multireference level, we propose a generalization (MR ACPF) of the “coupled-pair functional” (CPF). Comparison with full CI results for BeH 2 , H 2 O, CH 2 , O 2 and the five lowest-lying 2 A 1 states of CH 2 + , shows the superiority of MR ACPF over MR CI(SD) and MR LCCM. Large-scale calculations for F 2 (up to a [7s5p3d2flg] CGTO basis set and 6 references) show better convergence to the experimental D e values on basis set and reference space extension than does MR CI(SD).

Fast evaluation of the Coulomb potential for electron densities using multipole accelerated resolution of identity approximation

A new computational approach is presented that allows for an accurate and efficient treatment of the electronic Coulomb term in density functional methods. This multipole accelerated resolution of identity for J (MARI-J) method partitions the Coulomb interactions into the near- and far-field parts. The calculation of the far-field part is performed by a straightforward application of the multipole expansions and the near-field part is evaluated employing expansion of molecular electron densities in atom-centered auxiliary basis sets (RI-J approximation). Compared to full RI-J calculations, up to 6.5-fold CPU time savings are reported for systems with about 1000 atoms without any significant loss of accuracy. Other multipole-based methods are compared with regard to reduction of the CPU times versus the conventional treatment of the Coulomb term. The MARI-J approach compares favorably and offers speedups approaching two orders of magnitude for molecules with about 400 atoms and more than 5000 basis functio...

Gaussian basis sets of quadruple zeta valence quality for atoms H-Kr

We present Gaussian basis sets of quadruple zeta valence quality with a segmented contraction scheme for atoms H to Kr. This extends earlier work on segmented contracted split valence (SV) and triple zeta valence (TZV) basis sets. Contraction coefficients and orbital exponents are fully optimized in atomic Hartree–Fock (HF) calculations. As opposed to other quadruple zeta basis sets, the basis set errors in atomic ground-state HF energies are less than 1 mEh and increase smoothly across the Periodic Table, while the number of primitives is comparably small. Polarization functions are taken partly from previous work, partly optimized in atomic MP2 calculations, and for a few cases determined at the HF level for excited atomic states nearly degenerate with the ground state. This leads to basis sets denoted QZVP for HF and density functional theory (DFT) calculations, and for some atoms to a larger basis recommended for correlated treatments, QZVPP. We assess the performance of the basis sets in molecular HF...