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Markus Reiher

Publications and source records attributed to Markus Reiher.

At least 127 records · Page 7Linked to original sources
arXiv2016

A nonorthogonal state-interaction approach for matrix product state wave functions

We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate for example transition and spin-orbit coupling matrix elements between arbitrary electronic states provided that they share the same one-electron basis functions and active orbital space, respectively. The key element is the transformation of the MPS wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation exploiting a sequence of non-unitary transformations following a proposal by Malmqvist (Int. J. Quantum Chem. 30, 479 (1986)). This is well-known for traditional wave-function parametrizations but has not yet been exploited for MPS wave functions.

physics.chem-ph↗
arXiv2016

The Polarizable Embedding Density Matrix Renormalization Group Method

The polarizable embedding (PE) approach is a flexible embedding model where a pre-selected region out of a larger system is described quantum mechanically while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.

physics.chem-ph↗
arXiv2016

Molecular propensity as a driver for explorative reactivity studies

Quantum chemical studies of reactivity involve calculations on a large number of molecular structures and comparison of their energies. Already the set-up of these calculations limits the scope of the results that one will obtain, because several system-specific variables such as the charge and spin need to be set prior to the calculation. For a reliable exploration of reaction mechanisms, a considerable number of calculations with varying global parameters must be taken into account, or important facts about the reactivity of the system under consideration can go undetected. For example, one could miss crossings of potential energy surfaces for different spin states or might not note that a molecule is prone to oxidation. Here, we introduce the concept of molecular propensity to account for the predisposition of a molecular system to react across different electronic states in certain nuclear configurations. Within our real-time quantum chemistry framework, we developed an algorithm that allows us to be alerted to such a propensity of a system under consideration.

physics.comp-ph↗
arXiv2016

Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group

We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess in a study of a heme model the accuracy of the strongly- and partially-contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.

physics.chem-ph↗
arXiv2016

Elucidating Reaction Mechanisms on Quantum Computers

We show how a quantum computer can be employed to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical-computer simulations for such problems, to significantly increase their accuracy and enable hitherto intractable simulations. Detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. This demonstrates that quantum computers will realistically be able to tackle important problems in chemistry that are both scientifically and economically significant.

quant-ph↗
arXiv2016

The Delicate Balance of Static and Dynamic Electron Correlation

Multi-configurational approaches yield universal wave function parameterizations that can qualitatively well describe electronic structures along reaction pathways. For quantitative results, multi-reference perturbation theory is required to capture dynamic electron correlation from the otherwise neglected virtual orbitals. Still, the overall accuracy suffers from the finite size and choice of the active orbital space and peculiarities of the perturbation theory. Fortunately, the electronic wave functions at equilibrium structures of reactants and products can often be well described by single-reference methods and hence are accessible to accurate coupled cluster calculations. Here, we calculate the heterolytic double dissociation energy of four 3d-metallocenes with the complete active space self-consistent field method and compare to highly accurate coupled cluster data. Our coupled cluster data are well within the experimental error bars. This accuracy can also be approached by complete active space calculations with an orbital selection based on information entropy measures. The entropy based active space selection is discussed in detail. We find a very subtle balance between static and dynamic electron correlation effects that emphasizes the need for algorithmic active space selection and that differs significantly from restricted active space results for identical active spaces reported in the literature.

physics.chem-ph↗
arXiv2016

Tensor Network States with Three-Site Correlators

We present a detailed analysis of various tensor network parameterizations within the Complete Graph Tensor Network States (CGTNS) approach. We extend our 2-site CGTNS scheme by introducing 3-site correlators. For this we devise three different strategies. The first relies solely on 3-site correlators and the second on 3-site correlators added on top of the 2-site correlator ansatz. To avoid an inflation of the variational space introduced by higher-order correlators, we limit the number of higher-order correlators to the most significant ones in the third strategy. Approaches for the selection of these most significant correlators are discussed. The sextet and doublet spin states of the spin-crossover complex manganocene serve as a numerical test case. In general, the CGTNS scheme achieves a remarkable accuracy for a significantly reduced size of the variational space. The advantages, drawbacks, and limitations of all CGTNS parameterizations investigated are rigorously discussed.

quant-ph↗
arXiv2016

New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation

Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our newcomputational toolbo x which implements the quantum chemical density matrix renormalization group in a second-generation algorithm. We present an overview of the different components of this toolbox.

physics.chem-ph↗
arXiv2016

Systematic Error Estimation for Chemical Reaction Energies

For the theoretical understanding of the reactivity of complex chemical systems accurate relative energies between intermediates and transition states are required. Despite its popularity, density functional theory (DFT) often fails to provide sufficiently accurate data, especially for molecules containing transition metals. Due to the huge number of intermediates that need to be studied for all but the simplest chemical processes, DFT is to date the only method that is computationally feasible. Here, we present a Bayesian framework for DFT that allows for error estimation of calculated properties. Since the optimal choice of parameters in present-day density functionals is strongly system dependent, we advocate for a system-focused re-parameterization. While, at first sight, this approach conflicts with the first-principles character of DFT that should make it in principle system independent, we deliberately introduce system dependence because we can then assign a stochastically meaningful error to the system-dependent parametrization that makes it non-arbitrary. By re-parameterizing a functional that was derived on a sound physical basis to a chemical system of interest we obtain a functional that yields reliable confidence intervals for reaction energies. We demonstrate our approach at the example of catalytic nitrogen fixation.

physics.chem-ph↗
arXiv2016

Spin-adapted Matrix Product States and Operators

Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in MPSs and MPOs by virtue of the Wigner--Eckart theorem at the example of the spin-adapted quantum chemical Hamiltonian operator.

physics.chem-ph↗
arXiv2016

Automated Selection of Active Orbital Spaces

One of the key challenges of quantum-chemical multi-configuration methods is the necessity to manually select orbitals for the active space. This selection requires both expertise and experience and can therefore impose severe limitations on the applicability of this most general class of ab initio methods. A poor choice of the active orbital space may yield even qualitatively wrong results. This is obviously a severe problem, especially for wave function methods that are designed to be systematically improvable. Here, we show how the iterative nature of the density matrix renormalization group combined with its capability to include up to about one hundred orbitals in the active space can be exploited for a systematic assessment and selection of active orbitals. These benefits allow us to implement an automated approach for active orbital space selection, which can turn multi-configuration models into black box approaches.

physics.chem-ph↗
arXiv2015

Accelerating Wave Function Convergence in Interactive Quantum Chemical Reactivity Studies

The inherently high computational cost of iterative self-consistent-field (SCF) methods proves to be a critical issue delaying visual and haptic feedback in real-time quantum chemistry. In this work, we introduce two schemes for SCF acceleration. They provide a guess for the initial density matrix of the SCF procedure generated by extrapolation techniques. SCF optimizations then converge in fewer iterations, which decreases the execution time of the SCF optimization procedure. To benchmark the proposed propagation schemes, we developed a test bed for performing quantum chemical calculations on sequences of molecular structures mimicking real-time quantum chemical explorations. Explorations of a set of six model reactions employing the semi-empirical methods PM6 and DFTB3 in this testing environment showed that the proposed propagation schemes achieved speedups of up to thirty percent as a consequence of a reduced number of SCF iterations.

physics.chem-ph↗
arXiv2015

Heuristics-Guided Exploration of Reaction Mechanisms

For the investigation of chemical reaction networks, the efficient and accurate determination of all relevant intermediates and elementary reactions is mandatory. The complexity of such a network may grow rapidly, in particular if reactive species are involved that might cause a myriad of side reactions. Without automation, a complete investigation of complex reaction mechanisms is tedious and possibly unfeasible. Therefore, only the expected dominant reaction paths of a chemical reaction network (e.g., a catalytic cycle or an enzymatic cascade) are usually explored in practice. Here, we present a computational protocol that constructs such networks in a parallelized and automated manner. Molecular structures of reactive complexes are generated based on heuristic rules derived from conceptual electronic-structure theory and subsequently optimized by quantum chemical methods to produce stable intermediates of an emerging reaction network. Pairs of intermediates in this network that might be related by an elementary reaction according to some structural similarity measure are then automatically detected and subjected to an automated search for the connecting transition state. The results are visualized as an automatically generated network graph, from which a comprehensive picture of the mechanism of a complex chemical process can be obtained that greatly facilitates the analysis of the whole network. We apply our protocol to the Schrock dinitrogen-fixation catalyst to study alternative pathways of catalytic ammonia production.

physics.chem-ph↗
arXiv2015

Real-time feedback from iterative electronic structure calculations

Real-time feedback from iterative electronic structure calculations requires to mediate between the inherently unpredictable execution times of the iterative algorithm employed and the necessity to provide data in fixed and short time intervals for real-time rendering. We introduce the concept of a mediator as a component able to deal with infrequent and unpredictable reference data to generate reliable feedback. In the context of real-time quantum chemistry, the mediator takes the form of a surrogate potential that has the same local shape as the first-principles potential and can be evaluated efficiently to deliver atomic forces as real-time feedback. The surrogate potential is updated continuously by electronic structure calculations and guarantees to provide a reliable response to the operator for any molecular structure. To demonstrate the application of iterative electronic structure methods in real-time reactivity exploration, we implement self-consistent semi-empirical methods as the data source and apply the surrogate-potential mediator to deliver reliable real-time feedback.

physics.comp-ph↗
arXiv2015

An Efficient Matrix Product Operator Representation of the Quantum-Chemical Hamiltonian

We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications in a purely matrix product based framework. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from a viewpoint of Hilbert space decimation and attained a higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states (MPS), where operators are correspondingly represented as matrix product operators (MPO). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach; for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries - abelian and non-abelian - and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.

physics.comp-ph↗
arXiv2015

Relativistic Kinetic-Balance Condition for Explicitly Correlated Basis Functions

This paper presents the derivation of a kinetic-balance condition for explicitly correlated basis functions employed in semi-classical relativistic calculations. Such a condition is important to ensure variational stability in algorithms based on the first-quantized Dirac theory of 1/2-fermions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation for the $4^N$ components of the spinor of an $N$-fermion system to the non-relativistic limit, which is in accordance with recent developments in the field of exact decoupling in relativistic orbital-based many-electron theory.

physics.chem-ph↗