Accurate ab Initio Spin Densities.

We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and ß electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].

Generation of potential energy surfaces in high dimensions and their haptic exploration.

A method is proposed for the automated generation of potential energy surfaces in high dimensions. It combines the existing algorithm for the definition of new energy data points, based on the interpolating moving least-squares algorithm with a simulated annealing procedure. This method is then studied in a haptic quantum chemistry environment that requires a fast evaluation of gradients on a potential energy surface with automatic improvement of its accuracy. As an example we investigate the nitrogen binding pathway in the Schrock dinitrogen fixation complex with this set-up.

Construction of CASCI-type wave functions for very large active spaces.

We present a procedure to construct a configuration-interaction expansion containing arbitrary excitations from an underlying full-configuration-interaction-type wave function defined for a very large active space. Our procedure is based on the density-matrix renormalization group (DMRG) algorithm that provides the necessary information in terms of the eigenstates of the reduced density matrices to calculate the coefficient of any basis state in the many-particle Hilbert space. Since the dimension of the Hilbert space scales binomially with the size of the active space, a sophisticated Monte Carlo sampling routine is employed. This sampling algorithm can also construct such configuration-interaction-type wave functions from any other type of tensor network states. The configuration-interaction information obtained serves several purposes. It yields a qualitatively correct description of the molecule's electronic structure, it allows us to analyze DMRG wave functions converged for the same molecular system but with different parameter sets (e.g., different numbers of active-system (block) states), and it can be considered a balanced reference for the application of a subsequent standard multi-reference configuration-interaction method.

New electron correlation theories for transition metal chemistry.

Electronic structure theory faces many computational challenges in transition metal chemistry. Usually, density functional theory is the method of choice for theoretical studies on transition metal complexes and clusters mostly because it is the only feasible one, although its results are not systematically improvable. By contrast, multireference ab initio methods could provide a correct description of the electronic structure, but are limited to small molecules because of the tremendous computational resources required. In recent years, conceptually new ab initio methods emerged that turned out to be promising for theoretical coordination chemistry. We review and discuss two efficient parametrization schemes for the electronic wave function, the matrix product states and the complete-graph tensor network states. Their advantages are demonstrated at example transition metal complexes. Especially, tensor network states might provide the key to accurately describe strongly correlated and magnetic molecular systems in transition metal chemistry.

Haptic quantum chemistry.

We present an implementation designed to physically experience quantum mechanical forces between reactants in chemical reactions. This allows one to screen the profile of potential energy surfaces for the study of reaction mechanisms. For this, we have developed a interface between the user and a virtual laboratory by means of a force-feedback haptic device. Potential energy surfaces of chemical reactions can be explored efficiently by rendering in the haptic device the gradients calculated with first-principles methods. The underlying potential energy surface is accurately fitted on the fly by the interpolating moving least-squares (IMLS) scheme to a grid of quantum chemical electronic energies (and geometric gradients). In addition, we introduce a new IMLS-based method to locate minimum-energy paths between two points on a potential energy surface.

Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters.

The accurate first-principles calculation of relative energies of transition metal complexes and clusters is still one of the great challenges for quantum chemistry. Dense lying electronic states and near degeneracies make accurate predictions difficult, and multireference methods with large active spaces are required. Often density functional theory calculations are employed for feasibility reasons, but their actual accuracy for a given system is usually difficult to assess (also because accurate ab initio reference data are lacking). In this work we study the performance of the density matrix renormalization group algorithm for the prediction of relative energies of transition metal complexes and clusters of different spin and molecular structure. In particular, the focus is on the relative energetical order of electronic states of different spin for mononuclear complexes and on the relative energy of different isomers of dinuclear oxo-bridged copper clusters.