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# QCMaquis - a DMRG Program

# Main content

The QCMaquis software suite allows for an efficient optimization of a matrix product state (MPS) wave function based on a second-generation density matrix renormalization group (DMRG) algorithm [1]. The quantum-chemical operators are represented as matrix product operators (MPOs) which provides the necessary flexibility to accommodate abelian and non-abelian symmetries as well as the implementation of non relativistic and relativistic quantum chemical Hamiltonians [2], respectively, in a unified framework. We have implemented the special unitary group of degree 2 (SU(2)) in the MPO representation of the non-relativistic Hamiltonian to ensure spin conservation [3].

## Features

The ** current** release version 1.0 of QCMaquis includes:

- Optimization of spin-adapted SU(2) MPS wave functions with the DMRG algorithm
- Non-relativistic and scalar-relativistic quantum-chemical Hamiltonians
- Calculation of excited states
- A python tool set to analyze the MPS wave function and its quantum entanglement
- DMRG-CI and DMRG-SCF interface to the Molcas program package for:
- DMRG-SCF calculations w/wo reaction field (e.g. PCM)
- State-specific and state-averaged DMRG-SCF calculations
- Analytic gradients for state-specific DMRG-SCF calculations

**Soon available:**

- GUI for an automated CAS selection [4]
- Three- and four-particle density matrices
- One-, two- and three-particle transition density matrices between two states
- Second-order optimization algorithm for DMRG-SCF [5]

- DMRG-CI and DMRG-SCF interface to the Molcas program package for:
- Analytic (excited state) gradients for state-averaged DMRG-SCF wave functions
- DMRG-NEVPT2 interface to Molcas [6]
- State-interaction calculations for spin-orbit coupling, electronic and magnetic properties [7]

- Interface to the Dalton program package for:
- Polarizable-embedding DMRG [8]
- Short-range DFT-long-range DMRG for open- and/or closed-shell molecules
- Ensemble-DFT-DMRG [9]

- Interfaces to the Bagel and Dirac program packages for:
- Relativistic four- and two-component DMRG-SCF/CI calculations [2]
- Electronic and magnetic properties [2]

## Obtaining QCMaquis

The QCMaquis software suite is free of charge. In order to obtain it, please send a request with your affiliation and preferred user name to .

## Documentation

A detailed installation guide and manual for QCMaquis can be found **here.**

## Citations

We kindly request that, for reproducibility reasons, any use of the QCMaquis software suite for DMRG calculations in MOLCAS that results in published material should cite the set-up steered by settings and warm-up procedures described in:

**Check for a preprint on arXiv.org (to appear soon).**

Y. Ma, S. Keller, C. Stein, S. Knecht, R. Lindh, M. Reiher, in preparation .

The DMRG calculations are then conducted with the software QCMaquis that requires a citation. It is described in the following paper:

**Check the journal article**

S. Keller, M. Dolfi, M. Troyer, M. Reiher, J. Chem. Phys. 2015, 143, 244118.

**References**

[1] S. Keller, M. Dolfi, M. Troyer, M. Reiher, J. Chem. Phys. 2015, 143, 244118.

[2] S. Battaglia, A. Muolo, S. Keller, S. Knecht, M. Reiher, in preparation.

[3] S. Keller and M. Reiher,* *J. Chem. Phys. 2016, 144, 134101.

[4] C. J. Stein, M. Reiher, J. Chem. Theory Comput. 2016, 12, 1760.

[5] Y. Ma, S. Knecht, S. Keller, M. Reiher, arXiv:1611.05972.

[6] L. Freitag, S. Knecht, C. Angeli, M. Reiher, J. Chem. Theory Comput. 2017, asap.

[7] S. Knecht, S. Keller, J. Autschbach, M. Reiher, J. Chem. Theory Comput. 2016, 12, 5881.

[8] E. D. Hedegård, M. Reiher, J. Chem. Theory Comput. 2016, 12, 4242.

[9] E. D. Hedegård, S. Knecht, J. S. Kielberg, H. J. A. Jensen, M. Reiher, J. Chem. Phys. 2015, 142, 224108.

[10] Y. Ma, S. Keller, C. Stein, S. Knecht, R. Lindh, M. Reiher, in preparation.

[11] www.molcas.org

## Further Reading

QCMaquis builds upon the ALPS MPS project. The ALPS MPS codes implement the DMRG algorithm for variational ground and low-lying excited state search as well as time evolution of arbitrary one- and two-dimensional models in a matrix-product-state representation. They have been developed at ETH Zurich by Michele Dolfi and Bela Bauer in the group of Matthias Troyer with contributions from Sebastian Keller and Alexandr Kosenkov and at the University of Geneva by Timothée Ewart and Adrian Kantian in the group of Thierry Giamarchi.

**For further information on the ALPS project, please visit **alps.comp-phys.org .

**Refer to the original ALPS MPS paper:**

M. Dolfi, B. Bauer, S. Keller, A. Kosenkov, T. Ewart, A. Kantian, T. Giamarchi, M. Troyer, *Comp. Phys. Commun. ***2014***, 12, *3430*. *doi:10.1016/j.cpc.2014.08.019

ALPS is a general open-source framework for the description of strongly correlated many-particle systems.

B. Bauer, et al. (ALPS Collaboration), The ALPS project release 2.0: open source software for strongly correlated systems, *J. Stat. Mech.* **2011** P05001. http://dx.doi.org/10.1088/1742-5468/2011/05/P05001.