Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in Molecules

Quantum Information Orbitals (QIO): Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality

The simultaneous treatment of static and dynamic correlations in strongly correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the representational complexity of the many-body wave function is a formidable and longstanding problem. As a contribution toward its solution, we show that the total orbital correlation actually reveals and quantifies the intrinsic complexity of the wave function, once it is minimized via orbital rotations. To demonstrate the power of this concept in practice, an iterative scheme is proposed to optimize the orbitals by minimizing the total orbital correlation calculated by the tailored coupled cluster singles and doubles (TCCSD) ansatz. The optimized orbitals enable the limited TCCSD ansatz to capture more nontrivial information on the many-body wave function, indicated by the improved wave function and energy. An initial application of this scheme shows great improvement of TCCSD in predicting the singlet ground state potential energy curves of the strongly correlated C2 and Cr2 molecule.

Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method

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 connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, 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 two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term

We present a linear scaling atomic orbital based algorithm for the computation of the most expensive exchange-type RI-MP2-F12 term by employing numerical quadrature in combination with CABS-RI to avoid six-center-three-electron integrals. Furthermore, a robust distance-dependent integral screening scheme, based on integral partition bounds [Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101], is used to drastically reduce the number of the required three-center-one-electron integrals substantially. The accuracy of our numerical quadrature/CABS-RI approach and the corresponding integral screening is thoroughly assessed for interaction and isomerization energies across a variety of numerical integration grids. Our method outperforms the standard density fitting/CABS-RI approach with errors below 1 μEh even for small grid sizes and moderate screening thresholds. The choice of the grid size and screening threshold allows us to tailor our ansatz to a desired accuracy and computational efficiency. We showcase the approach's effectiveness for the chemically relevant system valinomycin, employing a triple-ζ F12 basis set combination (C54H90N6O18, 5757 AO basis functions, 10,266 CABS basis functions, 735,783 grid points). In this context, our ansatz achieves higher accuracy combined with a 135× speedup compared to the classical density fitting based variant, requiring notably less computation time than the corresponding RI-MP2 calculation. Additionally, we demonstrate near-linear scaling through calculations on linear alkanes. We achieved an 817-fold acceleration for C80H162 and an extrapolated 28,765-fold acceleration for C200H402, resulting in a substantially reduced computational time for the latter─from 229 days to just 11.5 min. Our ansatz may also be adapted to the remaining MP2-F12 terms, which will be the subject of future work.

Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond

block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.

Nonunitary projective transcorrelation theory inspired by the F12 ansatz

An alternative nonunitary transcorrelation, inspired by the F12 ansatz, is investigated. In contrast to the Jastrow transcorrelation of Boys-Handy, the effective Hamiltonian of this projective transcorrelation features: 1. a series terminating formally at four-body interactions. 2. no spin-contamination within the non-relativistic framework. 3. simultaneous satisfaction of the singlet and triplet first-order cusp conditions. 4. arbitrary choices of pairs for correlation including frozen-core approximations. We discuss the connection between the projective transcorrelation and F12 theory with applications to small molecules, to show that the cusp conditions play an important role to reduce the uncertainty arising from the nonunitary transformation.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

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.

Transcorrelated selected configuration interaction in a bi-orthonormal basis and with a cheap three-body correlation factor

In this work, we develop a mathematical framework for a selected configuration interaction (SCI) algorithm within a bi-orthogonal basis for transcorrelated (TC) calculations. The bi-orthogonal basis used here serves as the equivalent of the standard Hartree-Fock (HF) orbitals. However, within the context of TC, it leads to distinct orbitals for the left and right vectors. Our findings indicate that the use of such a bi-orthogonal basis allows for a proper definition of the frozen core approximation. In contrast, the use of HF orbitals results in bad error cancellations for ionization potentials and atomization energies (AE). Compared to HF orbitals, the optimized bi-orthogonal basis significantly reduces the positive part of the second-order energy (PT2), thereby facilitating the use of standard extrapolation techniques of hermitian SCI. While we did not observe a significant improvement in the convergence of the SCI algorithm, this is largely due to the use in this work of a simple three-body correlation factor introduced in a recent study. This correlation factor, which depends only on atomic parameters, eliminates the need for re-optimization of the correlation factor for molecular systems, making its use straightforward and user-friendly. Despite the simplicity of this correlation factor, we were able to achieve accurate results on the AE of a series of 14 molecules on a triple-zeta basis. We also successfully broke a double bond until the full dissociation limit while maintaining the size consistency property. This work thus demonstrates the potential of the BiO-TC-SCI approach in handling complex molecular systems.

Optimizing Jastrow factors for the transcorrelated method

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.