S. Wouters

T3NS: Three-Legged Tree Tensor Network States

K. Gunst, F. Verstraete, S. Wouters, Ö. Legeza, D. Van Neck
Journal of Chemical Theory and Computation
14 (4), pp 2026–2033
2018
A1

Abstract 

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two virtual indices, as in the matrix product state (MPS) ansatz of the density matrix renormalization group (DMRG). Branching tensors have no physical index, but up to three virtual indices. In this way, advantages of DMRG, in particular a low computational cost and a simple implementation of symmetries, are combined with advantages of TTNS, namely incorporating more entanglement. Our code is capable of simulating quantum chemical Hamiltonians, and we present several proof-of-principle calculations on LiF, N$_2$, and the bis(μ-oxo) and μ–η$^2$:η$^2$ peroxo isomers of [Cu$_2$O$_2$]$^{2+}$.

Block product density matrix embedding theory for strongly correlated spin systems

K. Gunst, S. Wouters, S. De Baerdemacker, D. Van Neck
Physical Review B
95, 195127
2017
A1

Abstract 

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic J1−J2 model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.

Open Access version available at UGent repository
Green Open Access

Cumulant Approximated Second-Order Perturbation Theory Based on Density Matrix Renormalization Group for Transition Metal Complexes: A Benchmark Study

Q. M. Phung, S. Wouters, K. Pierloot
Journal of Chemical Theory and Computation
12 (9), 4352–4361
2016
A1

Abstract 

The complete active space second-order perturbation theory (CASPT2) can be extended to larger active spaces by using the density matrix renormalization group (DMRG) as solver. Two variants are commonly used: the costly DMRG-CASPT2 with exact 4-particle reduced density matrix (4-RDM) and the cheaper DMRG-cu(4)-CASPT2 in which the 4-cumulant is discarded. To assess the accuracy and limitations of the latter variant DMRG-cu(4)-CASPT2 we study the spin state energetics of iron porphyrin Fe(P) and its model compound FeL2, a model for the active center of NiFe hydrogenase, and manganese-oxo porphyrin MnO(P)+; a series of excited states of chromium hexacarbonyl Cr(CO)6; and the interconversion of two Cu2O22+ isomers. Our results clearly show that PT2 on top of DMRG is essential in order to obtain quantitative results for transition metal complexes. Good results were obtained with DMRG-cu(4)-CASPT2 as compared to full CASPT2 and DMRG-CASPT2 in calculations with small and medium-sized active spaces. In calculations with large-sized active spaces (~ 30 active orbitals), the performance of DMRG-cu(4)-CASPT2 is less impressive due to the errors originating from both the finite number of renormalized states m and the 4-RDM approximation.

DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes

S. Wouters, V. Van Speybroeck, D. Van Neck
Journal of Chemical Physics
145 (5), 054120
2016
A1

Abstract 

We have implemented internally contracted complete active space second order perturbation theory (CASPT2) with the density matrix renormalization group (DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. Internally contracted CASPT2 requires to contract the generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of the reference wavefunction. The required 4-RDM elements can be obtained from 3-particle reduced density matrices (3-RDM) of different wavefunctions, formed by symmetry-conserving single-particle excitations op top of the reference wavefunction. In our spin-adapted DMRG code chemps2 [https://github.com/sebwouters/chemps2], we decompose these excited wavefunctions as spin-adapted matrix product states, and calculate their 3-RDM in order to obtain the required contraction of the generalized Fock matrix with the 4-RDM of the reference wavefunction. In this work, we study the longitudinal static second hyperpolarizability of all-trans polyenes C_{2n}H_{2n+2} [n = 4 - 12] in the cc-pVDZ basis set. DMRG-SCF and DMRG-CASPT2 yield substantially lower values and scaling with system size compared to RHF and MP2, respectively.

A practical guide to density matrix embedding theory in quantum chemistry

S. Wouters, C. A. Jiménez-Hoyos, Q. Sun, G. K.-L. Chan
Journal of Chemical Theory and Computation
Publication Date (Web): May 09, 2016
2016
A1
Published while none of the authors were employed at the CMM

Abstract 

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction. The source code for the calculations in this work can be obtained from https://github.com/sebwouters/qc-dmet.

A practical guide to density matrix embedding theory in quantum chemistry

S. Wouters, C.A. Jiménez-Hoyos, Q. Sun, G. K.-L. Chan, A. Bruder
Journal of Chemical Theory and Computation
2016
A1
Published while none of the authors were employed at the CMM

Abstract 

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction. The source code for the calculations in this work can be obtained from https://github.com/sebwouters/qc-dmet

The enantioselectivity of the manganese-salen complex in the epoxidation of unfunctionalized olefins and the influence of grafting

T. Bogaerts, S. Wouters, P. Van der Voort, V. Van Speybroeck
Journal of Molecular Catalysis A: Chemical
Vol. 406, 106-113
2015
A1

Abstract 

Jacobsen’s complexes are famous for their usability for enantioselective epoxidations. However, the applicability of this catalytic system has been severely limited by several practical problems such as deactivation and separation after reaction. Grafting of Jacobsen-type complexes on solid supports is an attractive way to overcome these problems but led to a decrease in selectivity. A combined theoretical and experimental approach is presented to unravel the factors governing enantioselectivity. The importance of different substituents was determined by analyzing the transition state for the oxygen transfer using the full system as a model. An analysis of the asymmetric complex has shown an inherent tendency for a decreased selectivity due to the lack of specific bulky groups. Experimentally an immobilized Jacobsen catalyst on a metal organic framework (MIL-101) was synthesized which confirms the computational tendencies but the decrease in selectivity is limited, indicating that the MIL-101(Cr) is a suitable carrier for this complex.

Open Access version available at UGent repository

DOI 

10.1016/j.molcata.2015.05.020

Mechanistic investigation on the oxygen transfer with the manganese-salen complex

T. Bogaerts, S. Wouters, P. Van der Voort, V. Van Speybroeck
ChemCatChem
7 (17), 2711–2719
2015
A1

Abstract 

The most well-known application of salen complexes is the use of a chiral ligand loaded with manganese to form the Jacobsen complex. This organometallic catalyst is used in the epoxidation of unfunctionalized olefins and can achieve very high selectivities. Although this application was proposed many years ago, the mechanism of oxygen transfer remains a question until now. In this paper, the epoxidation mechanism is investigated by an ab initio kinetic modeling study. First of all a proper DFT functional is selected which yields the correct ordering of the various spin states. Our results show that the epoxidation proceeds via a radical intermediate. Starting from the radical intermediate, these results can explain the experiments with radical probes. The subtle influences in the transition state using the full Jacobsen catalyst explain the experimentally observed product distribution.

PPV Polymerization via the Gilch Route: Diradical Character of Monomers

J.D. Nikolic, S. Wouters, J. Romanova, A. Shimizu, B. Champagne, T. Junkers, D. Vanderzande, D. Van Neck, M. Waroquier, V. Van Speybroeck, S. Catak
Chemistry - A European Journal
21, 19176-19185
2015
A1

Abstract 

Despite various studies on the polymerization of poly(p-phenylene vinylene) (PPV) through different precursor routes, detailed mechanistic knowledge on the individual reaction steps and intermediates is still incomplete. The present study aims to gain more insight into the radical polymerization of PPV through the Gilch route. The initial steps of the polymerization involve the formation of a p-quinodimethane intermediate, which spontaneously self-initiates through a dimerization process leading to the formation of diradical species; chain propagation ensues on both sides of the diradical or chain termination occurs by the formation of side products, such as [2.2]paracyclophanes. Furthermore, different p-quinodimethane systems were assessed with respect to the size of their aromatic core as well as the presence of heteroatoms in/on the conjugated system. The nature of the aromatic core and the specific substituents alter the electronic structure of the p-quinodimethane monomers, affecting the mechanism of polymerization. The diradical character of the monomers has been investigated with several advanced methodologies, such as spin-projected UHF, CASSCF, CASPT2, and DMRG calculations. It was shown that larger aromatic cores led to a higher diradical character in the monomers, which in turn is proposed to cause rapid initiation.

CheMPS2: Improved DMRG-SCF routine and correlation functions

S. Wouters, W. Poelmans, S. De Baerdemacker, P.W. Ayers, D. Van Neck
Computer Physics Communications
191, 235-237
2015
A1

Abstract 

CheMPS2, our spin-adapted implementation of the density matrix renormalization group (DMRG) for ab initio quantum chemistry (Wouters et al., 2014), has several new features. A speed-up of the augmented Hessian Newton–Raphson DMRG self-consistent field (DMRG-SCF) routine is achieved with the direct inversion of the iterative subspace (DIIS). For extended molecules, the active space orbitals can be localized by maximizing the Edmiston–Ruedenberg cost function. These localized orbitals can be ordered according to the topology of the molecule by approximately minimizing the bandwidth of the exchange matrix with the Fiedler vector. The electronic structure can be analyzed by means of the two-orbital mutual information, spin, spin-flip, density, and singlet diradical correlation functions.

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