arXiv subjects

Markus Reiher

Publications and source records attributed to Markus Reiher.

At least 145 records · Page 8Linked to original sources

arXiv2014

Mode-Tracking Based Stationary-Point Optimization

In this work, we present a transition-state optimization protocol based on the Mode-Tracking algorithm [J. Chem. Phys. 118 (2003) 1634]. By calculating only the eigenvector of interest instead of diagonalizing the full Hessian matrix and performing an eigenvector following search based on the selectively calculated vector, we can efficiently optimize transition-state structures. The initial guess structures and eigenvectors are either chosen from a linear interpolation between the reactant and product structures, from a nudged-elastic band search, from a constrained-optimization scan, or from the minimum-energy structures. Alternatively, initial guess vectors based on chemical intuition may be defined. We then iteratively refine the selected vectors by the Davidson subspace iteration technique. This procedure accelerates finding transition states for large molecules of a few hundred atoms. It is also beneficial in cases where the starting structure is very different from the transition-state structure or where the desired vector to follow is not the one with lowest eigenvalue. Explorative studies of reaction pathways are feasible by following manually constructed molecular distortions.

physics.comp-ph↗

arXiv2014

Self-Consistent Embedding of Density-Matrix Renormalization Group Wavefunctions in a Density Functional Environment

We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.

physics.chem-ph↗

arXiv2014

Electric Transition Dipole Moment in pre-Born-Oppenheimer Molecular Structure Theory

This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed with explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The complete derivation and the calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated via translationally invariant integral expressions. As a numerical example the electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X ^1Sigma^+_g and B ^1Sigma^+_u electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.

physics.chem-ph↗

arXiv2014

Hydrogen-Activation Mechanism of [Fe] Hydrogenase Revealed by Multi-Scale Modeling

When investigating the mode of hydrogen activation by [Fe] hydrogenases, not only the chemical reactivity at the active site is of importance but also the large-scale conformational change between the so-called open and closed conformations, which leads to a special spatial arrangement of substrate and iron cofactor. To study H2 activation, a complete model of the solvated and cofactor-bound enzyme in complex with the substrate methenyl-H4MPT+ was constructed. Both the closed and open conformations were simulated with classical molecular dynamics on the 100 ns time scale. Quantum-mechanics/molecular-mechanics calculations on snapshots then revealed the features of the active site that enable the facile H2 cleavage. The hydroxyl group of the pyridinol ligand can easily be deprotonated. With the deprotonated hydroxyl group and the structural arrangement in the closed conformation, H2 coordinated to the Fe center is subject to an ionic and orbital push-pull effect and can be rapidly cleaved with a concerted hydride transfer to methenyl-H4MPT+. An intermediary hydride species is not formed.

physics.bio-ph↗

arXiv2014

Gradient-Driven Molecule Construction: An Inverse Approach Applied to the Design of Small-Molecule Fixating Catalysts

Rational design of molecules and materials usually requires extensive screening of molecular structures for the desired property. The inverse approach to deduce a structure for a predefined property would be highly desirable, but is, unfortunately, not well-defined. However, feasible strategies for such an inverse design process may be successfully developed for specific purposes. We discuss options for calculating 'jacket' potentials that fulfill a predefined target requirement - a concept that we recently introduced [T. Weymuth, M. Reiher, MRS Proceediungs, 2013, 1524, DOI:10.1557/opl.2012.1764]. We consider the case of small-molecule activating transition metal catalysts. As a target requirement we choose the vanishing geometry gradients on all atoms of a subsystem consisting of a metal center binding the small molecule to be activated. The jacket potential can be represented within a full quantum model or by a sequence of approximations of which a field of electrostatic point charges is the simplest. In a second step, the jacket potential needs to be replaced by a chemically viable chelate-ligand structure for which the geometry gradients on all of its atoms are also required to vanish. In order to analyze the feasibility of this approach, we dissect a known dinitrogen-fixating catalyst to study possible design strategies that must eventually produce the known catalyst.

physics.chem-ph↗

arXiv2014

Inverse Quantum Chemistry: Concepts and Strategies for Rational Compound Design

The rational design of molecules and materials is becoming more and more important. With the advent of powerful computer systems and sophisticated algorithms, quantum chemistry plays an important role in rational design. While traditional quantum chemical approaches predict the properties of a predefined molecular structure, the goal of inverse quantum chemistry is to find a structure featuring one or more desired properties. Herein, we review inverse quantum chemical approaches proposed so far and discuss their advantages as well as their weaknesses.

physics.chem-ph↗

arXiv2014

Interactive Chemical Reactivity Exploration

Elucidating chemical reactivity in complex molecular assemblies of a few hundred atoms is, despite the remarkable progress in quantum chemistry, still a major challenge. Black-box search methods to find intermediates and transition-state structures might fail in such situations because of the high-dimensionality of the potential energy surface. Here, we propose the concept of interactive chemical reactivity exploration to effectively introduce the chemist's intuition into the search process. We employ a haptic pointer device with force-feedback to allow the operator the direct manipulation of structures in three dimensions along with simultaneous perception of the quantum mechanical response upon structure modification as forces. We elaborate on the details of how such an interactive exploration should proceed and which technical difficulties need to be overcome. All reactivity-exploration concepts developed for this purpose have been implemented in the Samson programming environment.

physics.chem-ph↗

arXiv2014

New Benchmark Set of Transition-Metal Coordination Reactions for the Assessment of Density Functionals

We present the WCCR10 data set of ten ligand dissociation energies of large cationic transition metal complexes for the assessment of approximate exchange--correlation functionals. We analyze nine popular functionals, namely BP86, BP86-D3, B3LYP, B3LYP-D3, B97-D-D2, PBE, TPSS, PBE0, and TPSSh by mutual comparison and by comparison to experimental gas-phase data measured with well-known precision. The comparison of all calculated data reveals a large, system-dependent scattering of results with nonnegligible consequences for computational chemistry studies on transition metal compounds. Considering further the comparison with experiment, the non-empirical functionals PBE and TPSS turn out to be among the best functionals for our reference data set. The deviation can be lowered further by including Hartree--Fock exchange. Accordingly, PBE0 and TPSSh are the two most accurate functionals for our test set, but also these functionals exhibit deviations from experiment by up to 50 kJ/mol for individual reactions. As an important result we found no functional to be reliable for all reactions. Furthermore, for some of the ligand dissociation energies studied in this work, dispersion corrections yield results which increase the deviation from experiment. This deviation increases further if structure optimization including dispersion corrections is performed. Finally, we compare our results to other benchmark studies and highlight that the performance assessed for different density functionals depends significantly on the reference molecule set chosen.

physics.chem-ph↗

arXiv2014

Determining Factors for the Accuracy of DMRG in Chemistry

The Density Matrix Renormalization Group (DMRG) algorithm has been a rising star for the accurate ab initio exploration of Born-Oppenheimer potential energy surfaces in theoretical chemistry. However, owing to its iterative numerical nature, pit falls, that can affect the accuracy of DMRG energies, need to be circumvented. Here, after a brief introduction into this quantum chemical method, we discuss criteria that determine the accuracy of DMRG calculations.

physics.chem-ph↗

arXiv2014

Quantum Entanglement in Carbon-Carbon, Carbon-Phosphorus and Silicon-Silicon Bonds

The chemical bond is an important local concept to understand chemical compounds and processes. Unfortunately, like most local concepts, the chemical bond and the bond order do not correspond to any physical observable and thus cannot be determined as an expectation value of a quantum chemical operator. We recently demonstrated [Boguslawski et al., J. Chem. Theory Comput., 2013, 9, 2959--2973] that one- and two-orbital-based entanglement measures can be applied to interpret electronic wave functions in terms of orbital correlation. Orbital entanglement emerged to be a powerful tool to provide a qualitative understanding of bond-forming and bond-breaking processes, and allowed for an estimation of bond orders of simple diatomic molecules beyond the classical bonding models. In this article we demonstrate that the orbital entanglement analysis can be extended to polyatomic molecules to understand chemical bonding.

cond-mat.str-el↗

arXiv2013

Four-Component Density Matrix Renormalization Group

We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin-orbit coupling. Numerical results based on the four-component Dirac-Coulomb Hamiltonian are presented for the standard reference molecule for correlated relativistic benchmarks: thallium hydride.

physics.chem-ph↗

arXiv2013

Unravelling the quantum-entanglement effect of noble gas coordination on the spin ground state of CUO

The accurate description of the complexation of the CUO molecule by Ne and Ar noble gas matrices represents a challenging task for present-day quantum chemistry. Especially, the accurate prediction of the spin ground state of different CUO--noble-gas complexes remains elusive. In this work, the interaction of the CUO unit with the surrounding noble gas matrices is investigated in terms of complexation energies and dissected into its molecular orbital quantum entanglement patterns. Our analysis elucidates the anticipated singlet--triplet ground-state reversal of the CUO molecule diluted in different noble gas matrices and demonstrates that the strongest uranium-noble gas interaction is found for CUOAr4 in its triplet configuration.

physics.chem-ph↗

arXiv2013

Orbital entanglement in bond-formation processes

The accurate calculation of the (differential) correlation energy is central to the quantum chemical description of bond-formation and bond-dissociation processes. In order to estimate the quality of single- and multi-reference approaches for this purpose, various diagnostic tools have been developed. In this work, we elaborate on our previous observation [J. Phys. Chem. Lett. 3, 3129 (2012)] that one- and two-orbital-based entanglement measures provide quantitative means for the assessment and classification of electron correlation effects among molecular orbitals. The dissociation behavior of some prototypical diatomic molecules features all types of correlation effects relevant for chemical bonding. We demonstrate that our entanglement analysis is convenient to dissect these electron correlation effects and to provide a conceptual understanding of bond-forming and bond-breaking processes from the point of view of quantum information theory.

physics.chem-ph↗

arXiv2013

An efficient implementation of two-component relativistic exact-decoupling methods for large molecules

We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the relativistic decoupling transformation has to be evaluated with primitive functions, the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules. For the established exact-decoupling protocols, a minimal matrix operation count is established and discussed in detail. Furthermore, we apply our recently developed local DLU scheme [J. Chem. Phys. 136 (2012) 244108] to accelerate this step. With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and (Abelian as well as non-Abelian) point group symmetry to accelerate both the exact-decoupling and the two-electron part. The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms, for which the cohesive energy is calculated and extrapolated to the bulk.

physics.chem-ph↗

arXiv2012

Elimination of the Translational Kinetic Energy Contamination in pre-Born-Oppenheimer Calculations

In this paper we present a simple strategy for the elimination of the translational kinetic energy contamination of the total energy in pre-Born--Oppenheimer calculations carried out in laboratory-fixed Cartesian coordinates (LFCCs). The simple expressions for the coordinates and the operators are thus preserved throughout the calculations, while the mathematical form and the parametrisation of the basis functions are chosen so that the translational and rotational invariances are respected. The basis functions are constructed using explicitly correlated Gaussian functions (ECGs) and the global vector representation. First, we observe that it is not possible to parametrise the ECGs so that the system is at rest in LFCCs and at the same time the basis functions are square-integrable with a non-vanishing norm. Then, we work out a practical strategy to circumvent this problem by making use of the properties of the linear transformation between the LFCCs and translationally invariant and center-of-mass Cartesian coordinates as well as the transformation properties of the corresponding basis function parameter matrices. By exploiting these formal mathematical relationships we can identify and separate the translational contamination terms in the matrix representation of the kinetic energy operator in the LFCC formalism. We present numerical examples for the translational contamination and its elimination for the two lowest rotational energy levels of the singlet hydrogen molecule, corresponding to para- and ortho-H2, respectively, treated as four-particle quantum systems.

physics.chem-ph↗

arXiv2012

Optimized Unrestricted Kohn-Sham Potentials from Ab Initio Spin Densities

The reconstruction of the exchange-correlation potential from accurate ab initio electron densities can provide insights into the limitations of the currently available approximate functionals and provide guidance for devising improved approximations for density-functional theory (DFT). For open-shell systems, the spin density is introduced as an additional fundamental variable in Spin-DFT. Here, we consider the reconstruction of the corresponding unrestricted Kohn-Sham potentials from accurate ab initio spin densities. In particular, we investigate whether it is possible to reconstruct the spin exchange-correlation potential, which determines the spin density in spin-unrestricted Kohn-Sham-DFT, despite the numerical difficulties inherent to the optimization of potentials with finite orbital basis sets. We find that the recently developed scheme for unambiguously singling out an optimal optimized potential [J. Chem. Phys. 135, 244102 (2011)] can provide such spin potentials accurately. This is demonstrated for two test cases, the lithium atom and the dioxygen molecule, and target (spin) densities from Full-CI and CASSCF calculations, respectively.

cond-mat.str-el↗

arXiv2012

Spin in Density-Functional Theory

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. While density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn-Sham DFT schemes for open-shell systems, which imply different definitions of the exchange-correlation energy functional and lead to different exact conditions on this functional. Finally, we suggest some possible directions for future developments.

physics.chem-ph↗

arXiv2012

Entanglement Measures for Single- and Multi-Reference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multi-reference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.

quant-ph↗