• This record comes from PubMed

DMRG-Tailored Coupled Cluster Method in the 4c-Relativistic Domain: General Implementation and Application to the NUHFI and NUF3 Molecules

. 2024 Oct 22 ; 20 (20) : 8862-8875. [epub] 20241009

Status PubMed-not-MEDLINE Language English Country United States Media print-electronic

Document type Journal Article

Heavy atom compounds represent a challenge for computational chemistry due to the need for simultaneous treatment of relativistic and correlation effects. Often such systems also exhibit strong correlation, which hampers the application of perturbation theory or single-reference coupled cluster (CC) methods. As a viable alternative, we have proposed externally correcting the CC method using the density matrix renormalization group (DMRG) wave functions, yielding the DMRG-tailored CC method. In a previous paper [J. Chem. Phys. 2020, 152, 174107], we reported a first implementation of this method in the relativistic context, which was restricted to molecules with real double group symmetry. In this work, we present a fully general implementation of the method, covering complex and quaternion double groups as well. The 4c-TCC method thus becomes applicable to polyatomic molecules, including heavy atoms. For the assessment of the method, we performed calculations of the chiral uranium compound NUHFI, which was previously studied in the context of the enhancement of parity violation effects. In particular, we performed calculations of a cut of the potential energy surface of this molecule along the stretching of the N-U bond, where the system exhibits strong multireference character. Since there are no experimental data for NUHFI, we have performed also an analogous study of the (more symmetric) NUF3 molecule, where the vibrational frequency of the N-U bond can be compared with spectroscopic data.

See more in PubMed

White S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 1992, 69, 2863–2866. 10.1103/PhysRevLett.69.2863. PubMed DOI

White S. R.; Martin R. L. Ab initio quantum chemistry using the density matrix renormalization group. J. Chem. Phys. 1999, 110, 4127–4130. 10.1063/1.478295. DOI

Chan G. K.-L.; Head-Gordon M. Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group. J. Chem. Phys. 2002, 116, 4462–4476. 10.1063/1.1449459. DOI

Legeza Ö.; Röder J.; Hess B. A. Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach. Phys. Rev. B 2003, 67, 125114.10.1103/PhysRevB.67.125114. DOI

Schollwöck U. The density-matrix renormalization group in the age of matrix product states. Annals of Physics 2011, 326, 96–192. 10.1016/j.aop.2010.09.012. DOI

Olivares-Amaya R.; Hu W.; Nakatani N.; Sharma S.; Yang J.; Chan G. K.-L. The ab-initio density matrix renormalization group in practice. J. Chem. Phys. 2015, 142, 034102.10.1063/1.4905329. PubMed DOI

Kurashige Y.; Yanai T. Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: Theory and application to the study of chromium dimer. J. Chem. Phys. 2011, 135, 094104.10.1063/1.3629454. PubMed DOI

Saitow M.; Kurashige Y.; Yanai T. Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function. J. Chem. Phys. 2013, 139, 044118.10.1063/1.4816627. PubMed DOI

Wouters S.; Nakatani N.; Van Neck D.; Chan G. K.-L. Thouless theorem for matrix product states and subsequent post density matrix renormalization group methods. Phys. Rev. B 2013, 88, 075122.10.1103/PhysRevB.88.075122. DOI

Yanai T.; Chan G. K.-L. Canonical transformation theory for multireference problems. J. Chem. Phys. 2006, 124, 194106.10.1063/1.2196410. PubMed DOI

Ren J.; Yi Y.; Shuai Z. Inner Space Perturbation Theory in Matrix Product States: Replacing Expensive Iterative Diagonalization. J. Chem. Theory Comput. 2016, 12, 4871–4878. 10.1021/acs.jctc.6b00696. PubMed DOI

Beran P.; Matoušek M.; Hapka M.; Pernal K.; Veis L. Density matrix renormalization group with dynamical correlation via adiabatic connection. J. Chem. Theory Comput. 2021, 17, 7575.10.1021/acs.jctc.1c00896. PubMed DOI

Barcza G.; Werner M. A.; Zaránd G.; Pershin A.; Benedek Z.; Legeza Ö.; Szilvási T. Toward Large-Scale Restricted Active Space Calculations Inspired by the Schmidt Decomposition. J. Phys. Chem. A 2022, 126, 9709–9718. 10.1021/acs.jpca.2c05952. PubMed DOI

Friesecke G.; Barcza G.; Legeza O. Predicting the FCI energy of large systems to chemical accuracy from restricted active space density matrix renormalization group calculations. J. Chem. Theory Comput. 2024, 20, 87–102. 10.1021/acs.jctc.3c01001. PubMed DOI

Veis L.; Antalík A.; Brabec J.; Neese F.; Legeza Ö.; Pittner J. Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions. J. Phys. Chem. Lett. 2016, 7, 4072–4078. 10.1021/acs.jpclett.6b01908. PubMed DOI

Kinoshita T.; Hino O.; Bartlett R. J. Coupled-cluster method tailored by configuration interaction. J. Chem. Phys. 2005, 123, 074106.10.1063/1.2000251. PubMed DOI

Hino O.; Kinoshita T.; Chan G. K.-L.; Bartlett R. J. Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone. J. Chem. Phys. 2006, 124, 114311.10.1063/1.2180775. PubMed DOI

Veis L.; Antalík A.; Brabec J.; Neese F.; Legeza Ö.; Pittner J. J. Phys. Chem. Lett. 2017, 8, 291.10.1021/acs.jpclett.6b02912. PubMed DOI

Faulstich F. M.; Laestadius A.; Legeza Ö.; Schneider R.; Kvaal S. Analysis of the Tailored Coupled-Cluster Method in Quantum Chemistry. SIAM Journal on Numerical Analysis 2019, 57, 2579–2607. 10.1137/18M1171436. DOI

Faulstich F. M.; Máté M.; Laestadius A.; Csirik M. A.; Veis L.; Antalik A.; Brabec J.; Schneider R.; Pittner J.; Kvaal S.; Legeza Ö. Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer. J. Chem. Theory Comput. 2019, 15, 2206–2220. 10.1021/acs.jctc.8b00960. PubMed DOI PMC

Leszczyk A.; Máté M.; Legeza Ö.; Boguslawski K. Assessing the accuracy of tailored coupled cluster methods corrected by electronic wave functions of polynomial cost. J. Chem. Theory Comp. 2022, 18, 96.10.1021/acs.jctc.1c00284. PubMed DOI

Neese F. The ORCA program system. WIREs Computational Molecular Science 2012, 2, 73–78. 10.1002/wcms.81. DOI

Antalik A.; Veis L.; Brabec J.; Demel O.; Legeza O.; Pittner J. Toward the efficient local tailored coupled cluster approximation and the peculiar case of oxo-Mn(Salen). J. Chem. Phys. 2019, 151, 084112.10.1063/1.5110477. PubMed DOI

Lang J.; Antalik A.; Veis L.; Brandejs J.; Brabec J.; Legeza O.; Pittner J. Near-linear Scaling in DMRG-based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T). J. Chem. Theor. Comput. 2020, 16, 3028.10.1021/acs.jctc.0c00065. PubMed DOI

Antalik A.; Nachtigallova D.; Lo R.; Matousek M.; LAng J.; Legeza O.; Pittner J.; Hobza P.; Veis L. Ground state of the Fe(II)-porphyrin model system corresponds to the quintet state: DFT, DMRG-TCCSD and DMRG-TCCSD(T) computations. Phys. Chem. Chem. Phys. 2020, 22, 17033.10.1039/D0CP03086D. PubMed DOI

Brandejs J.; Višňák J.; Veis L.; Maté M.; Legeza O.; Pittner J. Toward DMRG-tailored coupled cluster method in the 4c-relativistic domain. J. Chem. Phys. 2020, 152, 174107.10.1063/1.5144974. PubMed DOI

Wormit M.; Olejniczak M.łg.; Deppenmeier A.-L.; Borschevsky A.; Saue T.; Schwerdtfeger P. Strong enhancement of parity violation effects in chiral uranium compounds. Phys. Chem. Chem. Phys. 2014, 16, 17043–17051. 10.1039/C4CP01904K. PubMed DOI

Jiang W.; Wilson A. K. Multireference composite approaches for the accurate study of ground and excited electronic states: C2, N2, and O2. J. Chem. Phys. 2011, 134, 034101.10.1063/1.3514031. PubMed DOI

Mintz B.; Williams T. G.; Howard L.; Wilson A. K. Computation of potential energy surfaces with the multireference correlation consistent composite approach. J. Chem. Phys. 2009, 130, 234104.10.1063/1.3149387. PubMed DOI

Chan G. K.-L.; Kállay M.; Gauss J. State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. J. Chem. Phys. 2004, 121, 6110–6116. 10.1063/1.1783212. PubMed DOI

Máté M.; Petrov K.; Szalay S.; Legeza Ö. Compressing multireference character of wave functions via fermionic mode optimization. J. Math. Chem. 2023, 61, 362–375. 10.1007/s10910-022-01379-y. DOI

Boguslawski K.; Tecmer P. Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry. J. Chem. Theory Comput. 2017, 13, 5966–5983. 10.1021/acs.jctc.6b01134. PubMed DOI

Nowak A.; Legeza O.; Boguslawski K. Orbital entanglement and correlation from pCCD-tailored coupled cluster wave functions. J. Chem. Phys. 2021, 154, 084111.10.1063/5.0038205. PubMed DOI

Leszczyk A.; Máté M.; Legeza O.; Boguslawski K. Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost. J. Chem. Theory Comput. 2022, 18, 96–117. 10.1021/acs.jctc.1c00284. PubMed DOI

Nowak A.; Boguslawski K. A configuration interaction correction on top of pair coupled cluster doubles. Phys. Chem. Chem. Phys. 2023, 25, 7289–7301. 10.1039/D2CP05171K. PubMed DOI

Li X.; Paldus J. Dissociation of N2 triple bond: a reduced multireference CCSD study. Chem. Phys. Lett. 1998, 286, 145–154. 10.1016/S0009-2614(97)01132-9. DOI

Leszczyk A.; Dome T.; Tecmer P.; Kedziera D.; Boguslawski K. Resolving the π-assisted U–N σf-bond formation using quantum information theory. Phys. Chem. Chem. Phys. 2022, 24, 21296–21307. 10.1039/D2CP03377A. PubMed DOI

Kramers H. A. Théorie générale de la rotation paramagnétique dans les cristaux. Proceedings of the Royal Netherlands Academy of Arts and Sciences 1930, 33 (6-10), 959–972.

Fleig T.; Olsen J.; Marian C. M. The generalized active space concept for the relativistic treatment of electron correlation. I. Kramers-restricted two-component configuration interaction. J. Chem. Phys. 2001, 114, 4775–4790. 10.1063/1.1349076. PubMed DOI

Saue T. DIRAC, a relativistic ab initio electronic structure program, 2018. http://www.diracprogram.org.

Visscher L.et al.DIRAC24, 2024. https://zenodo.org/doi/10.5281/zenodo.10680560.

Saue T.; Jensen H. J. A. Quaternion symmetry in relativistic molecular calculations: The Dirac–Hartree–Fock method. J. Chem. Phys. 1999, 111, 6211–6222. 10.1063/1.479958. DOI

Dyall K. G.; Fægri K. Jr.. Introduction to Relativistic Quantum Chemistry; Oxford University Press, 2007.

Visscher L. On the construction of double group molecular symmetry functions. Chem. Phys. Lett. 1996, 253, 20–26. 10.1016/0009-2614(96)00234-5. DOI

Visscher L. The Dirac equation in quantum chemistry: Strategies to overcome the current computational problems. J. Comput. Chem. 2002, 23, 759–766. 10.1002/jcc.10036. PubMed DOI

Thyssen J.Development and Applications of Methods for Correlated Relativistic Calculations of Molecular Properties. Ph.D. thesis, University of Southern Denmark, 2001.

Li X.; Paldus J. Reduced multireference CCSD method: An effective approach to quasidegenerate states. J. Chem. Phys. 1997, 107, 6257.10.1063/1.474289. DOI

Lyakh D. I.; Lotrich V. F.; Bartlett R. J. The tailored CCSD(T) description of the automerization of cyclobutadiene. Chem. Phys. Lett. 2011, 501, 166–171. 10.1016/j.cplett.2010.11.058. DOI

Melnichuk A.; Bartlett R. J. Relaxed active space: Fixing tailored-CC with high order coupled cluster. I. J. Chem. Phys. 2012, 137, 214103.10.1063/1.4767900. PubMed DOI

Melnichuk A.; Bartlett R. J. Relaxed active space: Fixing tailored-CC with high order coupled cluster. II. J. Chem. Phys. 2014, 140, 064113.10.1063/1.4862676. PubMed DOI

Piecuch P.; Oliphant N.; Adamowicz L. A state-selective multireference coupled-cluster theory employing the single-reference formalism. J. Chem. Phys. 1993, 99, 1875–1900. 10.1063/1.466179. DOI

Piecuch P.; Adamowicz L. State-selective multireference coupled-cluster theory employing the single-reference formalism: Implementation and application to the H8 model system. J. Chem. Phys. 1994, 100, 5792–5809. 10.1063/1.467143. DOI

Legeza Ö.; Sólyom J. Optimizing the density-matrix renormalization group method using quantum information entropy. Phys. Rev. B 2003, 68, 195116.10.1103/PhysRevB.68.195116. DOI

Battaglia S.; Keller S.; Knecht S. Efficient Relativistic Density-Matrix Renormalization Group Implementation in a Matrix-Product Formulation. J. Chem. Theory Comput. 2018, 14, 2353–2369. 10.1021/acs.jctc.7b01065. PubMed DOI

Szalay S.; Pfeffer M.; Murg V.; Barcza G.; Verstraete F.; Schneider R.; Legeza Ö. Tensor product methods and entanglement optimization forab initioquantum chemistry. Int. J. Quantum Chem. 2015, 115, 1342–1391. 10.1002/qua.24898. DOI

Menczer A.; Legeza Ö.. Massively Parallel Tensor Network State Algorithms on Hybrid CPU-GPU Based Architectures. arXiv 2023, arXiv:2305.05581v1.10.48550/arXiv.2305.05581. DOI

Menczer A.; Legeza Ö.. Boosting the effective performance of massively parallel tensor network state algorithms on hybrid CPU-GPU based architectures via non-Abelian symmetries, 2023. https://arxiv.org/abs/2309.16724.

Menczer A.; Kapás K.; Werner M. A.; Legeza O. Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method. Phys. Rev. B 2024, 109, 195148.10.1103/PhysRevB.109.195148. DOI

Menczer A.; van Damme M.; Rask A.; Huntington L.; Hammond J.; Xantheas S. S.; Ganahl M.; Legeza Ö. Parallel implementation of the Density Matrix Renormalization Group method achieving a quarter petaFLOPS performance on a single DGX-H100 GPU node. J. Chem. Theory Comput. 2024, 20, 8397–8404. 10.1021/acs.jctc.4c00903. PubMed DOI PMC

Brandejs J.; Pototschnig J.; Saue T.. Generating coupled cluster code for modern distributed memory tensor software, 2024. https://arxiv.org/abs/2409.06759.

Atkinson B. E.; Hu H.-S.; Kaltsoyannis N. Post Hartree–Fock calculations of pnictogen–uranium bonding in EUF3 (E = N–Bi). Chem. Commun. 2018, 54, 11100–11103. 10.1039/C8CC05581E. PubMed DOI

TURBOMOLE, v7.52020, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH,1989–2007. https://www.turbomole.org.

Dyall K. G. Core correlating basis functions for elements 31–118. Theor. Chem. Acc. 2012, 131, 1217.10.1007/s00214-012-1217-8. DOI

Dunning T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007.10.1063/1.456153. DOI

Dunning T. H., Jr.ANL vibration–rotation analysis program for diatomic molecules, 1979.

Visscher L. Approximate molecular Dirac-Coulomb calculations using a simple Coulombic correction. Theor. Chem. Acc. 1997, 98, 68.10.1007/s002140050280. DOI

Andrews L.; Wang X.; Lindh R.; Roos B.; Marsden C. Simple NUF3 and PUF3Molecules with Triple Bonds to Uranium. Angew. Chem., Int. Ed. 2008, 47, 5366–5370. 10.1002/anie.200801120. PubMed DOI

Van Gundy R. A.Electronic Structure of Metal-Containing Diatomic Ions. Ph.D. thesis, Faculty of the James T. Laney School of Graduate Studies of Emory University, 2018.

King D. M.; Liddle S. T. Progress in molecular uranium-nitride chemistry. Coord. Chem. Rev. 2014, 266–267, 2–15. 10.1016/j.ccr.2013.06.013. DOI

Balasubramanian S. G.; et al. TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations. J. Chem. Phys. 2020, 152, 184107.10.1063/5.0004635. PubMed DOI PMC

Furness J. W.; Kaplan A. D.; Ning J.; Perdew J. P.; Sun J. Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation. J. Phys. Chem. Lett. 2020, 11, 8208–8215. 10.1021/acs.jpclett.0c02405. PubMed DOI

Holzer C.; Franzke Y. J.; Kehry M. Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties. J. Chem. Theory Comput. 2021, 17, 2928–2947. 10.1021/acs.jctc.1c00203. PubMed DOI

Perdew J. P.; Staroverov V. N.; Tao J.; Scuseria G. E. Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction. Phys. Rev. A 2008, 78, 052513.10.1103/PhysRevA.78.052513. DOI

Find record

Citation metrics

Loading data ...

Archiving options

Loading data ...