arXiv subjects

Christopher J. Stein

Publications and source records attributed to Christopher J. Stein.

24 records · Page 2Linked to original sources

arXiv2017

Vibrational Density Matrix Renormalization Group

Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. However, the unfavorable scaling and the resulting high computational cost of standard variational approaches limit their application to small molecules with only few vibrational modes. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG.

physics.chem-ph↗

arXiv2017

Automated Identification of Relevant Frontier Orbitals for Chemical Compounds and Processes

Quantum-chemical multi-configurational methods are required for a proper description of static electron correlation, a phenomenon inherent to the electronic structure of molecules with multiple (near-)degenerate frontier orbitals. Here, we review how a property of these frontier orbitals, namely the entanglement entropy is related to static electron correlation. A subset of orbitals, the so-called active orbital space, is an essential ingredient for all multi-configurational methods. We proposed an automated selection of this active orbital space, that would otherwise be a tedious and error prone manual procedure, based on entanglement measures. Here, we extend this scheme to demonstrate its capability for the selection of consistent active spaces for several excited states and along reaction coordinates.

physics.chem-ph↗

arXiv2016

Measuring Multi-Configurational Character by Orbital Entanglement

One of the most critical tasks at the very beginning of a quantum chemical investigation is the choice of either a multi- or single-configurational method. Naturally, many proposals exist to define a suitable diagnostic of the multi-configurational character for various types of wave functions in order to assist this crucial decision. Here, we present a new orbital-entanglement based multi-configurational diagnostic termed $Z_{s(1)}$. The correspondence of orbital entanglement and static (or nondynamic) electron correlation permits the definition of such a diagnostic. We chose our diagnostic to meet important requirements such as well-defined limits for pure single-configurational and multi-configurational wave functions. The $Z_{s(1)}$ diagnostic can be evaluated from a partially converged, but qualitatively correct, and therefore inexpensive density matrix renormalization group wave function as in our recently presented automated active orbital selection protocol. Its robustness and the fact that it can be evaluated at low cost make this diagnostic a practical tool for routine applications.

physics.chem-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

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

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↗