Arne Lüchow

Quantum Monte Carlo methods

Simulations of complex systems have seen rapid progress over the last decade not only due to the continuous acceleration of computer resources but also due to improvements of methods and algorithms. Simulations complement experiments and model calculations in the effort to get insight into complex systems such as materials, complex liquids, or complicated molecules. As such, computer simulations are a strongly interdisciplinary field where chemistry meets physics, biology, and material science. Most simulations are based on classical physics because the interaction between atoms or even larger entities can be modeled accurately with classical mechanics for most problems as long as no chemical reactions are involved. If the interaction between atoms in a molecule or between molecules is to be calculated, for instance, to obtain parameters for modeling the interactions in classical simulations, classical physics has to be abandoned because these interactions involve the electron distributions which require a quantum mechanical description.

Structural Versatility of Anion-π Interactions in Halide Salts with Pentafluorophenyl Substituted Cations

A series of pentafluorophenyl substituted ammonium, iminium, amidinium, and phosphonium halides are presented which show extensive anion-pi interactions. Hereby, the well-known anion-donor-pi-acceptor as well as eta6 anion-pi-complex type interactions are observed. The latter is supported by fixation of the anion on top of the aromatic system through hydrogen bonding. This arrangement was investigated by theoretical methods showing a highly attractive anion-pi interaction. In addition an eta2-type coordination of the anions to only two C-atoms of the electron-deficient ring system is described.

On the accuracy of the fixed-node diffusion quantum Monte Carlo method

The accuracy of the fixed-node diffusion quantum Monte Carlo (FN-DQMC) method is compared to the coupled cluster method CCSD(T). For a test set of 20 small molecules and 17 reactions the electronic contribution to the reaction enthalpy is calculated with the FN-DQMC method using the nodes of a Slater determinant calculated at the HF/cc-pVTZ level. By comparison with reference reaction enthalpies the FN-DQMC method is shown to be more accurate than the CCSD(T)/cc-pVDZ method and almost as accurate as CCSD(T)/cc-pVTZ. The deviation from the reference data is comparable to the CCSD(T)/cc-pVTZ deviation, but, with only two exceptions, of opposite sign.

Linear scaling for the local energy in quantum Monte Carlo

The scaling of the diffusion quantum Monte Carlo method can be greatly improved when localized orbitals and short-range correlation functions are employed as recently suggested by the authors. The local diffusion quantum Monte Carlo method is described in detail with a careful analysis of errors. The new method achieves near linear scaling in the calculation of the local energy. Results demonstrating the improved performance are presented.

Performance of diffusion Monte Carlo for the first dissociation energies of transition metal carbonyls.

Fixed node diffusion Monte Carlo (FNDMC) calculations are carried out for the first ligand dissociation energies of the prototype transition metal carbonyls Cr(CO)6, Fe(CO)5, Ni(CO)4, and Fe(CO)4N2. Since Hartree-Fock theory performs particularly badly for these type of compounds they are difficult to treat with conventional ab initio methods. We find that a Kohn-Sham determinant from a standard density functional provides a balanced description of the fermionic nodal hyper surfaces of all compounds involved in the dissociation reaction. With one exception, the experimental dissociation enthalpies are reproduced by FNDMC within the statistical accuracy of the method.

Single electron densities: a new tool to analyze molecular wavefunctions.

A new partitioning scheme for the electron density of a many‐electron wavefunction into single electron densities is proposed. These densities are based on the most probable arrangement of the electrons in an atom or molecule. Therefore, they contain information about the electron‐electron interaction and, most notably, the Fermi hole due to the antisymmetry of the many‐electron wavefunction. The single electron densities overlap and can be combined to electron pair distributions close to the qualitative electron pairs that represent, for instance, the basis of the valence shell electron pair repulsion model. Single electron analyses are presented for the water, ethane, and ethene molecules. The effect of electron correlation on the single electron and pair densities is investigated for the water molecule.

Direct optimization of nodal hypersurfaces in approximate wave functions

The fixed-node variant of the diffusion quantum Monte Carlo method (FN-DMC) is capable of obtaining the exact eigenvalues (albeit numerically with statistical error) of a many-electron Hamilton operator, provided that the nodal hypersurface of the exact wave function is given. The use of nodes of a trial wave function leads to the node location error. The authors have developed local criteria to assess the accuracy of the nodes based on the distances of the nodal hypersurfaces of PsiT, TPsiT, and HPsiT which coincide for the exact wave function. These criteria are used to develop direct optimization methods for the nodal hypersurface. The optimization of the nodes is demonstrated for simple wave functions of the Be atom and the C2 molecule and verified with FN-DMC calculations.

The effects of methyl internal rotation and 14N quadrupole coupling in the microwave spectra of two conformers of N,N-diethylacetamide

The gas phase structures and internal dynamics of N,N-diethylacetamide were determined with very high accuracy using a combination of molecular beam Fourier-transform microwave spectroscopy and quantum chemical calculations at high levels. Conformational studies yielded five stable conformers with C1 symmetry. The two most energetically favorable conformers, conformer I and II, could be found in the experimental spectrum. For both conformers, quadrupole hyperfine splittings of the (14)N nucleus and torsional fine splittings due to the internal rotation of the acetyl methyl group occurred in the same order of magnitude and were fully assigned. The rotational constants, centrifugal distortion constants as well as the quadrupole coupling constants of the (14)N nucleus were determined and fitted to experimental accuracy. The V3 potentials were found to be 517.04(13) cm(-1) and 619.48(91) cm(-1) for conformer I and II, respectively, and compared to the V3 potentials found in other acetamides. Highly accurate CCSD(T) and DMC calculations were carried out for calculating the barriers to internal rotation in comparison with the experimentally deduced V3 values.

Structure and energetics of phenol(H2O)n, n⩽7: Quantum Monte Carlo calculations and double resonance experiments

Using a variety of methods phenol water clusters phenol(H2O)n, n⩽7, are investigated with a focus on phenol(H2O)5,6. n A comprehensive search for low-energy isomers is conducted on a polarizable intermolecular potential energy surface. Zero-point energy contributions are calculated rigorously with the rigid-body n quantum Monte Carlo method. The OH stretch vibrational spectra of the isomers are calculated using n a local-mode model and compared with experimental isomer-selective IR–UV spectral hole burning (SHB) spectra. The topology of n the clusters phenol(H2O)5,6 n is shown in deviate from the corresponding pure water clusters.

Maxima of |Ψ|2: a connection between quantum mechanics and Lewis structures.

The maxima of squared electronic wave functions |Ψ|2 are analyzed for a number of small molecules. They are in principle observables and show considerable chemical insight from first principles. The maxima contain substantial information about the relative electron positions in a molecule, such as the pairing of opposite spin electrons and the Pauli repulsion which are lost in the electron density. Single bond and double bond as well as polar bond pairs and lone pairs are obtained from the maximum analysis. In many cases, we find a correspondence to the electron arrangements in molecules as assumed by Lewis in 1916.