Publications
Publications in reversed chronological order. All papers can be found on either the arXiv or ChemRxiv
2023
- Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of ChemistryPhalgun Lolur, Mårten Skogh, Werner Dobrautz, Christopher Warren, Janka Biznárová, and 5 more authorsJournal of Chemical Theory and Computation, Jan 2023
Decoherence and gate errors severely limit the capabilities of state-of-the-art quantum computers. This work introduces a strategy for reference-state error mitigation (REM) of quantum chemistry that can be straightforwardly implemented on current and near-term devices. REM can be applied alongside existing mitigation procedures, while requiring minimal postprocessing and only one or no additional measurements. The approach is agnostic to the underlying quantum mechanical ansatz and is designed for the variational quantum eigensolver. Up to two orders-of-magnitude improvement in the computational accuracy of ground state energies of small molecules (H2, HeH+, and LiH) is demonstrated on superconducting quantum hardware. Simulations of noisy circuits with a depth exceeding 1000 two-qubit gates are used to demonstrate the scalability of the method.
@article{Lolur2023, doi = {10.1021/acs.jctc.2c00807}, url = {https://doi.org/10.1021/acs.jctc.2c00807}, year = {2023}, month = jan, publisher = {American Chemical Society ({ACS})}, volume = {19}, number = {3}, pages = {783--789}, author = {Lolur, Phalgun and Skogh, M{\aa}rten and Dobrautz, Werner and Warren, Christopher and Bizn{\'{a}}rov{\'{a}}, Janka and Osman, Amr and Tancredi, Giovanna and Wendin, G\"{o}ran and Bylander, Jonas and Rahm, Martin}, title = {Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry}, journal = {Journal of Chemical Theory and Computation}, dimensions = {true}, project_quantum = {true}, project_mitigation = {true} } - Ferromagnetic domains in the large-U Hubbard model with a few holes: A full configuration interaction quantum Monte Carlo studySujun Yun, Werner Dobrautz, Hongjun Luo, Vamshi Katukuri, Niklas Liebermann, and 1 more authorPhys. Rev. B, Feb 2023
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of U in the large-U limit. In the so-called Nagaoka limit (one-hole system at infinite U), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing U. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or 12, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.
@article{PhysRevB.107.064405, title = {Ferromagnetic domains in the large-$U$ Hubbard model with a few holes: A full configuration interaction quantum Monte Carlo study}, author = {Yun, Sujun and Dobrautz, Werner and Luo, Hongjun and Katukuri, Vamshi and Liebermann, Niklas and Alavi, Ali}, journal = {Phys. Rev. B}, volume = {107}, issue = {6}, pages = {064405}, numpages = {9}, year = {2023}, month = feb, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.107.064405}, url = {https://link.aps.org/doi/10.1103/PhysRevB.107.064405}, dimensions = {true}, project_guga = {true}, project_hubbard = {true} } - The OpenMolcas Web: A Community-Driven Approach to Advancing Computational ChemistryGiovanni Li Manni, Ignacio Fdez. Galván, Ali Alavi, Flavia Aleotti, Francesco Aquilante, and 103 more authorsJournal of Chemical Theory and Computation, May 2023
The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.
@article{LiManni2023, doi = {10.1021/acs.jctc.3c00182}, url = {https://doi.org/10.1021/acs.jctc.3c00182}, year = {2023}, month = may, publisher = {American Chemical Society ({ACS})}, author = {Manni, Giovanni Li and Galv{\'{a}}n, Ignacio Fdez. and Alavi, Ali and Aleotti, Flavia and Aquilante, Francesco and Autschbach, Jochen and Avagliano, Davide and Baiardi, Alberto and Bao, Jie J. and Battaglia, Stefano and Birnoschi, Letitia and Blanco-Gonz{\'{a}}lez, Alejandro and Bokarev, Sergey I. and Broer, Ria and Cacciari, Roberto and Calio, Paul B. and Carlson, Rebecca K. and Couto, Rafael Carvalho and Cerd{\'{a}}n, Luis and Chibotaru, Liviu F. and Chilton, Nicholas F. and Church, Jonathan Richard and Conti, Irene and Coriani, Sonia and Cu{\'{e}}llar-Zuquin, Juliana and Daoud, Razan E. and Dattani, Nike and Decleva, Piero and de Graaf, Coen and Delcey, Mickaël G. and Vico, Luca De and Dobrautz, Werner and Dong, Sijia S. and Feng, Rulin and Ferr{\'{e}}, Nicolas and Filatov(Gulak), Michael and Gagliardi, Laura and Garavelli, Marco and Gonz{\'{a}}lez, Leticia and Guan, Yafu and Guo, Meiyuan and Hennefarth, Matthew R. and Hermes, Matthew R. and Hoyer, Chad E. and Huix-Rotllant, Miquel and Jaiswal, Vishal Kumar and Kaiser, Andy and Kaliakin, Danil S. and Khamesian, Marjan and King, Daniel S. and Kochetov, Vladislav and Kro{\'{s}}nicki, Marek and Kumaar, Arpit Arun and Larsson, Ernst D. and Lehtola, Susi and Lepetit, Marie-Bernadette and Lischka, Hans and R{\'{\i}}os, Pablo L{\'{o}}pez and Lundberg, Marcus and Ma, Dongxia and Mai, Sebastian and Marquetand, Philipp and Merritt, Isabella C. D. and Montorsi, Francesco and M\"{o}rchen, Maximilian and Nenov, Artur and Nguyen, Vu Ha Anh and Nishimoto, Yoshio and Oakley, Meagan S. and Olivucci, Massimo and Oppel, Markus and Padula, Daniele and Pandharkar, Riddhish and Phung, Quan Manh and Plasser, Felix and Raggi, Gerardo and Rebolini, Elisa and Reiher, Markus and Rivalta, Ivan and Roca-Sanju{\'{a}}n, Daniel and Romig, Thies and Safari, Arta Anushirwan and S{\'{a}}nchez-Mansilla, Aitor and Sand, Andrew M. and Schapiro, Igor and Scott, Thais R. and Segarra-Mart{\'{\i}}, Javier and Segatta, Francesco and Sergentu, Dumitru-Claudiu and Sharma, Prachi and Shepard, Ron and Shu, Yinan and Staab, Jakob K. and Straatsma, Tjerk P. and S{\o}rensen, Lasse Kragh and Tenorio, Bruno Nunes Cabral and Truhlar, Donald G. and Ungur, Liviu and Vacher, Morgane and Veryazov, Valera and Vo{\ss}, Torben Arne and Weser, Oskar and Wu, Dihua and Yang, Xuchun and Yarkony, David and Zhou, Chen and Zobel, J. Patrick and Lindh, Roland}, title = {The {OpenMolcas} Web: A Community-Driven Approach to Advancing Computational Chemistry}, journal = {Journal of Chemical Theory and Computation}, dimensions = {true}, project_devel = {true}, chemrxiv = {https://chemrxiv.org/engage/chemrxiv/article-details/63cab14daadd95af647a2d9e} } - Optimizing Jastrow factors for the transcorrelated methodJ. Philip Haupt, Seyed Mohammadreza Hosseini, Pablo López Rı́os, Werner Dobrautz, Aron Cohen, and 1 more authorThe Journal of Chemical Physics, Jun 2023
We investigate the optimization of flexible tailored real-space Jastrow factors for use in the transcorrelated (TC) method in combination with highly accurate quantum chemistry methods, such as initiator full configuration interaction quantum Monte Carlo (FCIQMC). Jastrow factors obtained by minimizing the variance of the TC reference energy are found to yield better, more consistent results than those obtained by minimizing the variational energy. We compute all-electron atomization energies for the challenging first-row molecules C2, CN, N2, and O2 and find that the TC method yields chemically accurate results using only the cc-pVTZ basis set, roughly matching the accuracy of non-TC calculations with the much larger cc-pV5Z basis set. We also investigate an approximation in which pure three-body excitations are neglected from the TC-FCIQMC dynamics, saving storage and computational costs, and show that it affects relative energies negligibly. Our results demonstrate that the combination of tailored real-space Jastrow factors with the multi-configurational TC-FCIQMC method provides a route to obtaining chemical accuracy using modest basis sets, obviating the need for basis-set extrapolation and composite techniques.
@article{Haupt2023, doi = {10.1063/5.0147877}, url = {https://doi.org/10.1063/5.0147877}, year = {2023}, month = jun, publisher = {{AIP} Publishing}, volume = {158}, number = {22}, author = {Haupt, J. Philip and Hosseini, Seyed Mohammadreza and R{\'{\i}}os, Pablo L{\'{o}}pez and Dobrautz, Werner and Cohen, Aron and Alavi, Ali}, title = {Optimizing Jastrow factors for the transcorrelated method}, journal = {The Journal of Chemical Physics}, dimensions = {true}, project_tc = {true} } - Orders of magnitude increased accuracy for quantum many-body problems on quantum computers via an exact transcorrelated methodIgor O. Sokolov, Werner Dobrautz, Hongjun Luo, Ali Alavi, and Ivano TavernelliPhys. Rev. Res., Jun 2023
Transcorrelated methods provide an efficient way of partially transferring the description of electronic correlations from the ground-state wave function directly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys. Rev. B 99, 075119 (2019)] have demonstrated that the use of momentum-space representation, combined with a nonunitary similarity transformation, results in a Hubbard Hamiltonian that possesses a significantly more “compact” ground-state wave function, dominated by a single Slater determinant. This compactness/single-reference character greatly facilitates electronic structure calculations. As a consequence, however, the Hamiltonian becomes non-Hermitian, posing problems for quantum algorithms based on the variational principle. We overcome these limitations with the Ansatz-based quantum imaginary-time evolution algorithm and apply the transcorrelated method in the context of digital quantum computing. We demonstrate that this approach enables up to four orders of magnitude more accurate and compact solutions in various instances of the Hubbard model at intermediate interaction strength (U/t=4), enabling the use of shallower quantum circuits for wave-function Ansätzes. In addition, we propose a more efficient implementation of the quantum imaginary-time evolution algorithm in quantum circuits that is tailored to non-Hermitian problems. To validate our approach, we perform hardware experiments on the ibmq_lima quantum computer. Our work paves the way for the use of exact transcorrelated methods for the simulations of ab initio systems on quantum computers.
@article{PhysRevResearch.5.023174, title = {Orders of magnitude increased accuracy for quantum many-body problems on quantum computers via an exact transcorrelated method}, author = {Sokolov, Igor O. and Dobrautz, Werner and Luo, Hongjun and Alavi, Ali and Tavernelli, Ivano}, journal = {Phys. Rev. Res.}, volume = {5}, issue = {2}, pages = {023174}, numpages = {19}, year = {2023}, month = jun, publisher = {American Physical Society}, doi = {10.1103/PhysRevResearch.5.023174}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.5.023174}, dimensions = {true}, project_quantum = {true}, project_tc = {true}, project_hubbard = {true} } - Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Tackle Flat Energy LandscapesDavid Fitzek, Robert S. Jonsson, Werner Dobrautz, and Christian SchäferarXiv, Jun 2023
Variational quantum algorithms (VQAs) represent a promising approach to utilizing current quantum computing infrastructures. VQAs are based on a parameterized quantum circuit optimized in a closed loop via a classical algorithm. This hybrid approach reduces the quantum processing unit load but comes at the cost of a classical optimization that can feature a flat energy landscape. Existing optimization techniques, including either imaginary time-propagation, natural gradient, or momentum-based approaches, are promising candidates but place either a significant burden on the quantum device or suffer frequently from slow convergence. In this work, we propose the quantum Broyden adaptive natural gradient (qBang) approach, a novel optimizer that aims to distill the best aspects of existing approaches. By employing the Broyden approach to approximate updates in the Fisher information matrix and combining it with a momentum-based algorithm, qBang reduces quantum-resource requirements while performing better than more resource-demanding alternatives. Benchmarks for the barren plateau, quantum chemistry, and the max-cut problem demonstrate an overall stable performance with a clear improvement over existing techniques in the case of flat optimization landscapes. qBang introduces a new development strategy for gradient-based VQAs with a plethora of possible improvements.
@article{2304.13882, author = {Fitzek, David and Jonsson, Robert S. and Dobrautz, Werner and Schäfer, Christian}, title = {Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Tackle Flat Energy Landscapes}, year = {2023}, eprint = {arXiv:2304.13882}, journal = {arXiv}, project_devel = {true}, project_quantum = {true} } - Ab Initio Transcorrelated Method enabling accurate Quantum Chemistry on near-term Quantum HardwareWerner Dobrautz, Igor O. Sokolov, Ke Liao, Pablo López Ríos, Martin Rahm, and 2 more authorsarXiv, Jun 2023
Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields, including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and limited connectivity) hamper the straightforward implementation of most quantum algorithms and call for more noise-resilient solutions. In quantum chemistry, the limited number of available qubits and gate operations is particularly restrictive since, for each molecular orbital, one needs, in general, two qubits. In this study, we propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach, which transfers – without any approximation – correlation from the wavefunction directly into the Hamiltonian, thus reducing the number of resources needed to achieve accurate results with noisy, near-term quantum devices. In particular, we show that the exact transcorrelated approach not only allows for more shallow circuits but also improves the convergence towards the so-called basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, therefore, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using just 4 and 6 qubits, respectively. Conventional methods require at least ten times more qubits for the same accuracy.
@article{2303.02007, author = {Dobrautz, Werner and Sokolov, Igor O. and Liao, Ke and Ríos, Pablo López and Rahm, Martin and Alavi, Ali and Tavernelli, Ivano}, title = {Ab Initio Transcorrelated Method enabling accurate Quantum Chemistry on near-term Quantum Hardware}, year = {2023}, eprint = {arXiv:2303.02007}, journal = {arXiv}, project_tc = {true}, project_quantum = {true} }
2022
- Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systemsWerner Dobrautz, Vamshi M. Katukuri, Nikolay A. Bogdanov, Daniel Kats, Giovanni Li Manni, and 1 more authorPhys. Rev. B, May 2022
A novel combined unitary and symmetric group approach is used to study the spin-12 Heisenberg model and related Fermionic systems in a total spin-adapted representation, using a linearly-parameterised Ansatz for the many-body wave function. We show that a more compact ground-state wave function representation—indicated by a larger leading ground-state coefficient—is obtained when combining the symmetric group Sn, in the form of permutations of the underlying lattice site ordering, with the cumulative spin coupling based on the unitary group U(n). In one-dimensional systems the observed compression of the wave function is reminiscent of block-spin renormalization group approaches, and allows us to study larger lattices (here taken up to 80 sites) with the spin-adapted full configuration interaction quantum Monte Carlo method, which benefits from the sparsity of the Hamiltonian matrix and the corresponding sampled eigenstates that emerge from the reordering. We find that in an optimal lattice ordering the configuration state function with highest weight already captures with high accuracy the spin-spin correlation function of the exact ground-state wave function. This feature is found for more general lattice models, such as the Hubbard model, and ab initio quantum chemical models, exemplified by one-dimensional hydrogen chains. We also provide numerical evidence that the optimal lattice ordering for the unitary group approach is not generally equivalent to the optimal ordering obtained for methods based on matrix-product states, such as the density-matrix renormalization group approach.
@article{PhysRevB.105.195123, title = {Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems}, author = {Dobrautz, Werner and Katukuri, Vamshi M. and Bogdanov, Nikolay A. and Kats, Daniel and Li Manni, Giovanni and Alavi, Ali}, journal = {Phys. Rev. B}, volume = {105}, issue = {19}, pages = {195123}, numpages = {17}, year = {2022}, month = may, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.105.195123}, url = {https://link.aps.org/doi/10.1103/PhysRevB.105.195123}, dimensions = {true}, project_guga = {true} } - Performance of a one-parameter correlation factor for transcorrelation: Study on a series of second row atomic and molecular systemsWerner Dobrautz, Aron J. Cohen, Ali Alavi, and Emmanuel GinerThe Journal of Chemical Physics, Jun 2022
In this work, we investigate the performance of a recently proposed transcorrelated (TC) approach based on a single-parameter correlation factor [E. Giner, J. Chem. Phys. 154, 084119 (2021)] for systems involving more than two electrons. The benefit of such an approach relies on its simplicity as efficient numerical–analytical schemes can be set up to compute the two- and three-body integrals occurring in the effective TC Hamiltonian. To obtain accurate ground state energies within a given basis set, the present TC scheme is coupled to the recently proposed TC–full configuration interaction quantum Monte Carlo method [Cohen et al., J. Chem. Phys. 151, 061101 (2019)]. We report ground state total energies on the Li–Ne series, together with their first cations, computed with increasingly large basis sets and compare to more elaborate correlation factors involving electron–electron–nucleus coordinates. Numerical results on the Li–Ne ionization potentials show that the use of the single-parameter correlation factor brings on average only a slightly lower accuracy (1.2 mH) in a triple-zeta quality basis set with respect to a more sophisticated correlation factor. However, already using a quadruple-zeta quality basis set yields results within chemical accuracy to complete basis set limit results when using this novel single-parameter correlation factor. Calculations on the H2O, CH2, and FH molecules show that a similar precision can be obtained within a triple-zeta quality basis set for the atomization energies of molecular systems.
@article{Dobrautz2022, doi = {10.1063/5.0088981}, url = {https://doi.org/10.1063/5.0088981}, year = {2022}, month = jun, publisher = {{AIP} Publishing}, volume = {156}, number = {23}, pages = {234108}, author = {Dobrautz, Werner and Cohen, Aron J. and Alavi, Ali and Giner, Emmanuel}, title = {Performance of a one-parameter correlation factor for transcorrelation: Study on a series of second row atomic and molecular systems}, journal = {The Journal of Chemical Physics}, dimensions = {true}, project_tc = {true} }
2021
- Benchmark study of Nagaoka ferromagnetism by spin-adapted full configuration interaction quantum Monte CarloSujun Yun, Werner Dobrautz, Hongjun Luo, and Ali AlaviPhys. Rev. B, Dec 2021
We investigate Nagaoka ferromagnetism in the two-dimensional Hubbard model with one hole using the spin-adapted [SU(2) conserving] full configuration interaction quantum Monte Carlo method. This methodology gives us access to the ground-state energies of all possible spin states S of finite Hubbard lattices, here obtained for lattices up to 26 sites for various interaction strengths (U). The critical interaction strength, Uc, at which the Nagaoka transition occurs is determined for each lattice and is found to be proportional to the lattice size for the larger lattices. Below Uc, the overall ground states are found to favour the minimal total spin (S=12), and no intermediate spin state is found to be the overall ground state on lattices larger than 16 sites. However, at Uc, the energies of all the spin states are found to be nearly degenerate, implying that large fluctuations in total spin can be expected in the vicinity of the Nagaoka transition.
@article{PhysRevB.104.235102, title = {Benchmark study of Nagaoka ferromagnetism by spin-adapted full configuration interaction quantum Monte Carlo}, author = {Yun, Sujun and Dobrautz, Werner and Luo, Hongjun and Alavi, Ali}, journal = {Phys. Rev. B}, volume = {104}, issue = {23}, pages = {235102}, numpages = {6}, year = {2021}, month = dec, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.104.235102}, url = {https://link.aps.org/doi/10.1103/PhysRevB.104.235102}, dimensions = {true}, project_guga = {true}, project_hubbard = {true} } - Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)_4S_4] CubanesGiovanni Li Manni, Werner Dobrautz, Nikolay A. Bogdanov, Kai Guther, and Ali AlaviThe Journal of Physical Chemistry A, May 2021
Polynuclear transition-metal (PNTM) clusters owe their catalytic activity to numerous energetically low-lying spin states and stable oxidation states. The characterization of their electronic structure represents one of the greatest challenges of modern chemistry. We propose a theoretical framework that enables the resolution of targeted electronic states with ease and apply it to two [Fe(III)4S4] cubanes. Through direct access to their many-body wave functions, we identify important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters, which are core properties in understanding their catalytic activity. The simulated magnetic coupling constants predicted by our strategy allow us to make qualitative connections between spin interactions and geometrical distortions, demonstrating its predictive power. Moreover, despite its simplicity, the strategy provides magnetic coupling constants in good agreement with the available experimental ones. The complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures together with the geometrical distortions represent two possible ways to release spin frustration (spin-driven Jahn–Teller distortion). Our paradigm provides a simple, yet rigorous, route to uncover the electronic structure of PNTM clusters and may be applied to a wide variety of such clusters.
@article{LiManni2022, doi = {10.1021/acs.jpca.1c00397}, url = {https://doi.org/10.1021/acs.jpca.1c00397}, year = {2021}, month = may, publisher = {American Chemical Society ({ACS})}, volume = {125}, number = {22}, pages = {4727--4740}, author = {Manni, Giovanni Li and Dobrautz, Werner and Bogdanov, Nikolay A. and Guther, Kai and Alavi, Ali}, title = {Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe({III})$_4$S$_4$] Cubanes}, journal = {The Journal of Physical Chemistry A}, dimensions = {true}, project_guga = {true}, project_tm = {true}, chemrxiv = {https://chemrxiv.org/engage/chemrxiv/article-details/60c75153bb8c1a47713dbc97} } - Spin-Pure Stochastic-CASSCF via GUGA-FCIQMC Applied to Iron–Sulfur ClustersWerner Dobrautz, Oskar Weser, Nikolay A. Bogdanov, Ali Alavi, and Giovanni Li ManniJournal of Chemical Theory and Computation, Sep 2021
In this work, we demonstrate how to efficiently compute the one- and two-body reduced density matrices within the spin-adapted full configuration interaction quantum Monte Carlo (FCIQMC) method, which is based on the graphical unitary group approach (GUGA). This allows us to use GUGA-FCIQMC as a spin-pure configuration interaction (CI) eigensolver within the complete active space self-consistent field (CASSCF) procedure and hence to stochastically treat active spaces far larger than conventional CI solvers while variationally relaxing orbitals for specific spin-pure states. We apply the method to investigate the spin ladder in iron–sulfur dimer and tetramer model systems. We demonstrate the importance of the orbital relaxation by comparing the Heisenberg model magnetic coupling parameters from the CASSCF procedure to those from a CI-only (CASCI) procedure based on restricted open-shell Hartree–Fock orbitals. We show that the orbital relaxation differentially stabilizes the lower-spin states, thus enlarging the coupling parameters with respect to the values predicted by ignoring orbital relaxation effects. Moreover, we find that, while CASCI results are well fit by a simple bilinear Heisenberg Hamiltonian, the CASSCF eigenvalues exhibit deviations that necessitate the inclusion of biquadratic terms in the model Hamiltonian.
@article{Dobrautz2021, doi = {10.1021/acs.jctc.1c00589}, url = {https://doi.org/10.1021/acs.jctc.1c00589}, year = {2021}, month = sep, publisher = {American Chemical Society ({ACS})}, volume = {17}, number = {9}, pages = {5684--5703}, author = {Dobrautz, Werner and Weser, Oskar and Bogdanov, Nikolay A. and Alavi, Ali and Manni, Giovanni Li}, title = {Spin-Pure Stochastic-{CASSCF} via {GUGA}-{FCIQMC} Applied to Iron{\textendash}Sulfur Clusters}, journal = {Journal of Chemical Theory and Computation}, dimensions = {true}, project_guga = {true}, project_devel = {true}, project_tm = {true}, project_fciqmc = {true} }
2020
- Compression of Spin-Adapted Multiconfigurational Wave Functions in Exchange-Coupled Polynuclear Spin SystemsGiovanni Li Manni, Werner Dobrautz, and Ali AlaviJournal of Chemical Theory and Computation, Feb 2020
We present a protocol based on unitary transformations of molecular orbitals to reduce the number of nonvanishing coefficients of spin-adapted configuration interaction expansions. Methods that exploit the sparsity of the Hamiltonian matrix and compactness of its eigensolutions, such as the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm in its spin-adapted implementation, are well suited to this protocol. The wave function compression resulting from this approach is particularly attractive for antiferromagnetically coupled polynuclear spin systems, such as transition-metal cubanes in biocatalysis, and Mott and charge-transfer insulators in solid-state physics. Active space configuration interaction calculations on N2 and CN– at various bond lengths, the stretched square N4 compounds, the chromium dimer, and a [Fe2S2]2– model system are presented as a proof-of-concept. For the Cr2 case, large and intermediate bond distances are discussed, showing that the approach is effective in cases where static and dynamic correlations are equally important. The [Fe2S2]2– case shows the general applicability of the method.
@article{LiManni2020, doi = {10.1021/acs.jctc.9b01013}, url = {https://doi.org/10.1021/acs.jctc.9b01013}, year = {2020}, month = feb, publisher = {American Chemical Society ({ACS})}, volume = {16}, number = {4}, pages = {2202--2215}, author = {Manni, Giovanni Li and Dobrautz, Werner and Alavi, Ali}, title = {Compression of Spin-Adapted Multiconfigurational Wave Functions in Exchange-Coupled Polynuclear Spin Systems}, journal = {Journal of Chemical Theory and Computation}, dimensions = {true}, project_guga = {true}, project_tm = {true}, chemrxiv = {https://chemrxiv.org/engage/chemrxiv/article-details/60c7451abb8c1a16363da600} } - NECI: N-Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methodsKai Guther, Robert J. Anderson, Nick S. Blunt, Nikolay A. Bogdanov, Deidre Cleland, and 20 more authorsThe Journal of Chemical Physics, Jul 2020
We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green’s functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.
@article{Guther2020, doi = {10.1063/5.0005754}, url = {https://doi.org/10.1063/5.0005754}, year = {2020}, month = jul, publisher = {{AIP} Publishing}, volume = {153}, number = {3}, pages = {034107}, author = {Guther, Kai and Anderson, Robert J. and Blunt, Nick S. and Bogdanov, Nikolay A. and Cleland, Deidre and Dattani, Nike and Dobrautz, Werner and Ghanem, Khaldoon and Jeszenszki, Peter and Liebermann, Niklas and Manni, Giovanni Li and Lozovoi, Alexander Y. and Luo, Hongjun and Ma, Dongxia and Merz, Florian and Overy, Catherine and Rampp, Markus and Samanta, Pradipta Kumar and Schwarz, Lauretta R. and Shepherd, James J. and Smart, Simon D. and Vitale, Eugenio and Weser, Oskar and Booth, George H. and Alavi, Ali}, title = {{NECI}: N-Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methods}, journal = {The Journal of Chemical Physics}, dimensions = {true}, project_guga = {true}, project_devel = {true}, project_fciqmc = {true} } - Foundation of Multi-Configurational Quantum ChemistryGiovanni Li Manni, Kai Guther, Dongxia Ma, and Werner DobrautzNov 2020
After introducing the fundamental goals—solving the Schrödinger equation—and the associated problems of quantum chemistry, we describe the basics of multiconfigurational approaches to solve the latter. As an exact—or full configuration interaction (FCI)—solution, even in a finite basis set, comes with an exponential scaling cost, the importance of an efficient representation in either a Slater determinant or configuration state function basis is discussed. With the help of such an efficient representation it is possible to apply iterative techniques, like the Davidson method, to obtain the exact solution of the most important low-lying eigenstates of the Hamiltonian, describing a quantum chemical system. As the exponential scaling still restricts these direct approaches to rather modest system sizes, we discuss in depth the multi-configurational extension of the self-consistent field method (MCSCF), which captures the static correlation of a problem and serves as a starting point for many more elaborate techniques. In addition, we present the complete active space approach—and the generalized and restricted extensions thereof—, which allows an intuitive construction of the chemically important reference space and enables a much more compact description of the important degrees of freedom of a problem at hand. We explain the state-specific and state-averaged approaches to obtain excited states within the MCSCF method and conclude this chapter by presenting stochastic Monte-Carlo approaches to solve the FCI problem for unprecedented active space sizes.
@misc{LiManni2021, doi = {10.1002/9781119417774.ch6}, url = {https://doi.org/10.1002/9781119417774.ch6}, year = {2020}, month = nov, publisher = {Wiley}, pages = {133--203}, author = {Manni, Giovanni Li and Guther, Kai and Ma, Dongxia and Dobrautz, Werner}, title = {Foundation of Multi-Configurational Quantum Chemistry}, dimensions = {true}, project_guga = {true} }
2019
- PhD ThesisDevelopment of Full Configuration Interaction Quantum Monte Carlo Methods for Strongly Correlated Electron SystemsWerner DobrautzUniversity of Stuttgart, Mar 2019
Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a prominent method to calculate the exact solution of the Schrödinger equation in a finite antisymmetric basis and gives access to physical observables through an efficient stochastic sampling of the wavefunction that describes a quantum mechanical system. Although system-agnostic (black-box-like) and numerically exact, its effectiveness depends crucially on the compactness of the wavefunction: a property that gradually decreases as correlation effects become stronger. In this work, we present two -conceptually distinct- approaches to extend the applicability of FCIQMC towards larger and more strongly correlated systems. In the first part, we investigate a spin-adapted formulation of the FCIQMC algorithm, based on the Unitary Group Approach. Exploiting the inherent symmetries of the nonrelativistic molecular Hamiltonian results in a dramatic reduction of the effective Hilbert space size of the problem. The use of a spin-pure basis explicitly resolves the different spin-sectors, even when degenerate, and the absence of spin-contamination ensures the sampled wavefunction is an eigenfunction of the total spin operator. Moreover, targeting specific many-body states with conserved total spin allows an accurate description of chemical processes governed by the intricate interplay of them. We apply the above methodology to obtain results, not otherwise attainable with conventional approaches, for the spin-gap of the high-spin cobalt atom ground- and low-spin excited state and the electron affinity of scandium within chemical accuracy to experiment. Furthermore we establish the ordering of the scandium anion bound states, which has until now not been experimentally determined. In the second part, we investigate a methodology to explicitly incorporate electron correlation into the initial Ansatz of the ground state wavefunction. Such an Ansatz induces a compact description of the wavefunction, which ameliorates the sampling of the configuration space of a system with FCIQMC. Within this approach, we investigate the two-dimensional Hubbard model near half-filling in the intermediate interaction regime, where such an Ansatz can be exactly incorporated by a nonunitary similarity transformation of the Hamiltonian based on a Gutzwiller correlator. This transformation generates novel three-body interactions, tractable due to the stochastic nature of FCIQMC, and leads to a non-Hermitian effective Hamiltonian with extremely compact right eigenvectors. The latter fact allows application of FCIQMC to larger lattice sizes, well beyond the reach of the method applied to the original Hubbard Hamiltonian.
@phdthesis{dobrautz-phd, title = {Development of Full Configuration Interaction Quantum Monte Carlo Methods for Strongly Correlated Electron Systems}, author = {Dobrautz, Werner}, school = {University of Stuttgart}, year = {2019}, month = mar, url = {http://dx.doi.org/10.18419/opus-10593}, doi = {10.18419/opus-10593}, project_devel = {true}, project_fciqmc = {true}, project_guga = {true}, project_tc = {true}, project_thesis = {true}, owner = {dobrautz}, timestamp = {2019.04.16} } - Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformationsWerner Dobrautz, Hongjun Luo, and Ali AlaviPhys. Rev. B, Feb 2019
Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller correlator leads to a non-Hermitian effective Hamiltonian, which can be expressed exactly in momentum-space representation and contains three-body interactions. We apply this methodology to study the two-dimensional Hubbard model with repulsive interactions near half filling in the intermediate interaction strength regime (U/t=4). We show that at optimal or near optimal strength of the Gutzwiller correlator, the similarity-transformed Hamiltonian has extremely compact right eigenvectors, which can be sampled to high accuracy using the full configuration interaction quantum Monte Carlo (FCIQMC) method and its initiator approximation. Near-optimal correlators can be obtained using a simple projective equation, thus obviating the need for a numerical optimization of the correlator. The FCIQMC method, as a projective technique, is well suited for such non-Hermitian problems, and its stochastic nature can handle the three-body interactions exactly without undue increase in computational cost. The highly compact nature of the right eigenvectors means that the initiator approximation in FCIQMC is not severe and that large lattices can be simulated, well beyond the reach of the method applied to the original Hubbard Hamiltonian. Results are provided in lattice sizes up to 50 sites and compared to auxiliary-field QMC. New benchmark results are provided in the off-half-filling regime, with no severe sign problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy.
@article{PhysRevB.99.075119, title = {Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformations}, author = {Dobrautz, Werner and Luo, Hongjun and Alavi, Ali}, journal = {Phys. Rev. B}, volume = {99}, issue = {7}, pages = {075119}, numpages = {20}, year = {2019}, month = feb, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.99.075119}, url = {https://link.aps.org/doi/10.1103/PhysRevB.99.075119}, dimensions = {true}, project_tc = {true}, project_hubbard = {true} } - Efficient formulation of full configuration interaction quantum Monte Carlo in a spin eigenbasis via the graphical unitary group approachWerner Dobrautz, Simon D. Smart, and Ali AlaviThe Journal of Chemical Physics, Sep 2019
We provide a spin-adapted formulation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, based on the Graphical Unitary Group Approach (GUGA), which enables the exploitation of SU(2) symmetry within this stochastic framework. Random excitation generation and matrix element calculation on the Shavitt graph of GUGA can be efficiently implemented via a biasing procedure on the branching diagram. The use of a spin-pure basis explicitly resolves the different spin-sectors and ensures that the stochastically sampled wavefunction is an eigenfunction of the total spin operator Ŝ 2. The method allows for the calculation of states with low or intermediate spin in systems dominated by Hund’s first rule, which are otherwise generally inaccessible. Furthermore, in systems with small spin gaps, the new methodology enables much more rapid convergence with respect to walker number and simulation time. Some illustrative applications of the GUGA-FCIQMC method are provided: computation of the 2F − 4F spin gap of the cobalt atom in large basis sets, achieving chemical accuracy to experiment, and the Σg+1, Σg+3, Σg+5, and Σg+7 spin-gaps of the stretched N2 molecule, an archetypal strongly correlated system.
@article{Dobrautz2019, doi = {10.1063/1.5108908}, url = {https://doi.org/10.1063/1.5108908}, year = {2019}, month = sep, publisher = {{AIP} Publishing}, volume = {151}, number = {9}, author = {Dobrautz, Werner and Smart, Simon D. and Alavi, Ali}, title = {Efficient formulation of full configuration interaction quantum Monte Carlo in a spin eigenbasis via the graphical unitary group approach}, journal = {The Journal of Chemical Physics}, dimensions = {true}, project_guga = {true}, project_devel = {true}, project_fciqmc = {true} } - Similarity transformation of the electronic Schrödinger equation via Jastrow factorizationAron J. Cohen, Hongjun Luo, Kai Guther, Werner Dobrautz, David P. Tew, and 1 more authorThe Journal of Chemical Physics, Aug 2019
By expressing the electronic wavefunction in an explicitly correlated (Jastrow-factorized) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits the use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionization potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort.
@article{Cohen2019, doi = {10.1063/1.5116024}, url = {https://doi.org/10.1063/1.5116024}, year = {2019}, month = aug, publisher = {{AIP} Publishing}, volume = {151}, number = {6}, author = {Cohen, Aron J. and Luo, Hongjun and Guther, Kai and Dobrautz, Werner and Tew, David P. and Alavi, Ali}, title = {Similarity transformation of the electronic Schr\"{o}dinger equation via Jastrow factorization}, journal = {The Journal of Chemical Physics}, dimensions = {true}, project_tc = {true} }
2018
- Time Propagation and Spectroscopy of Fermionic Systems Using a Stochastic TechniqueKai Guther, Werner Dobrautz, Olle Gunnarsson, and Ali AlaviPhys. Rev. Lett., Aug 2018
We present a stochastic method for solving the time-dependent Schrödinger equation, generalizing a ground state full configuration interaction quantum Monte Carlo method. By performing the time integration in the complex plane close to the real-time axis, the numerical effort is kept manageable and the analytic continuation to real frequencies is efficient. This allows us to perform ab initio calculation of electron spectra for strongly correlated systems. The method can be used as a cluster solver for embedding schemes.
@article{PhysRevLett.121.056401, title = {Time Propagation and Spectroscopy of Fermionic Systems Using a Stochastic Technique}, author = {Guther, Kai and Dobrautz, Werner and Gunnarsson, Olle and Alavi, Ali}, journal = {Phys. Rev. Lett.}, volume = {121}, issue = {5}, pages = {056401}, numpages = {5}, year = {2018}, month = aug, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.121.056401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.056401}, dimensions = {true}, project_devel = {true}, project_fciqmc = {true} }