Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group

We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess in a study of a heme model the accuracy of the strongly- and partially-contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.Comment: 9 pages, 4 figures, 2 table

Assessing weak hydrogen binding on Ca+ centers: An accurate many-body study with large basis sets

Weak H2 physisorption energies present a significant challenge to even the best correlated theoretical many-body methods. We use the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to accurately predict the binding energy of Ca+ - 4H2. Attention has recently focused on this model chemistry to test the reliability of electronic structure methods for H2 binding on dispersed alkaline earth metal centers. A modified Cholesky decomposition is implemented to realize the Hubbard-Stratonovich transformation efficiently with large Gaussian basis sets. We employ the largest correlation-consistent Gaussian type basis sets available, up to cc-pCV5Z for Ca, to accurately extrapolate to the complete basis limit. The calculated potential energy curve exhibits binding with a double-well structure.Comment: 10 pages, 7 figures. Submitted to JC

Orbital optimization in the perfect pairing hierarchy. Applications to full-valence calculations on linear polyacenes

We describe the implementation of orbital optimization for the models in the perfect pairing hierarchy [Lehtola et al, J. Chem. Phys. 145, 134110 (2016)]. Orbital optimization, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the {\pi} space. While local minima and {\sigma}-{\pi} symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the {\pi} subspace, as well as in the full {\sigma}{\pi} valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimized orbitals are used. PH is found to yield good agreement with previously published density matrix renormalization group (DMRG) data in the {\pi} space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger bases or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.Comment: 19 pages, 4 figure

Energy-Based Molecular Orbital Localization in a Specific Spatial Region

We present a novel energy-based localization procedure able to localize molecular orbitals into specific spatial regions. The method is applied to several cases including both conjugated and non-conjugated systems. The obtained localized molecular orbitals are used in a multiscale framework based on the multilevel Hartree-Fock approach. An almost perfect agreement with reference values is achieved for both ground state properties, such as dipole moments, and local excitation energies calculated at the coupled cluster level. The proposed approach is useful to extend the application range of high level electron correlation methods. In fact, the reduced number of molecular orbitals can lead to a large reduction in the computational cost of correlated calculations.Comment: 29 pages and 7 figure

A Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals

In this contribution, we present the implementation of a second-order CASSCF algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called Norm-Extended Optimization, guarantees convergence of the optimization, but it involves the full Hessian of the wavefunction and is therefore computationally expensive. Coupling the second-order procedure with the Cholesky decomposition leads to a significant reduction in the computational cost, reduced memory requirements, and an improved parallel performance. As a result, CASSCF calculations of larger molecular systems become possible as a routine task. The performance of the new implementation is illustrated by means of benchmark calculations on molecules of increasing size, with up to about 3000 basis functions and 14 active orbitals

Development of efficient electronic-structure methods based on the adiabatic-connection fluctuation-dissipation theorem and Møller–Plesset perturbation theory

One of the major goals of quantum chemistry is to develop electronic-structure methods, which are not only highly accurate in the evaluation of electronic ground-state properties, but also computationally tractable and versatile in their application. A theory with great potential in this respect, however, without being free from shortcomings is the random phase approximation (RPA). In this work, developments are presented, which address the most important of these shortcomings subject to the constraint to obtain low- and linear-scaling electronic-structure methods. A scheme combining an elegant way to introduce local orbitals and multi-node parallelism is put forward, which not only allows to evaluate the RPA correlation energy in a fraction of the time of former theories, but also enables a scalable decrease of the high memory requirements. Furthermore, a quadratic-scaling self-consistent minimization of the total RPA energy with respect to the one-particle density matrix in the atomic-orbital space is introduced, making the RPA energy variationally stable and independent of the quality of the reference calculation. To address the slow convergence with respect to the size of the basis set and the self-correlation inherent in the RPA functional, range-separation of the electron-electron interaction is exploited for atomic-orbital RPA, yielding a linear-scaling range-separated RPA method with consistent performance over a broad range of chemical problems. As a natural extension, the concepts including local orbitals, self-consistency, and range-separation are further combined in a RPA-based generalized Kohn–Sham method, which not only shows a balanced performance in general main group thermochemistry, kinetics, and noncovalent interactions, but also yields accurate ionization potentials and fundamental gaps. The origin of the self-correlation error within RPA lies in the neglect of exchange-effects in the calculation of the interacting density-density response functions. While range-separation is a reasonable approach to counteract this shortcoming — since self-correlation is pronounced at short interelectronic distances — a more rigorous but computationally sophisticated approach is to introduce the missing exchange-effects, at least to some extent. To make RPA with exchange methods applicable to systems containing hundreds of atoms and hence a suitable choice for practical applications, a framework is developed, which allows to devise highly efficient low- and linear-scaling RPA with exchange methods. The developments presented in this work, however, are not only limited to RPA and beyond-RPA methods. The connection between RPA and many-body perturbation theory is further used to present a second-order Møller–Plesset perturbation theory method, which combines the tools to obtain low- and linear-scaling RPA and beyond-RPA methods with efficient linear-algebra routines, making it highly efficient and applicable to large molecular systems comprising several thousand of basis functions

Modern quantum chemistry with [Open]Molcas

Artículo escrito por un elevado número de autores, sólo se referencian el que aparece en primer lugar, los autores pertenecientes a la UAM y el nombre del grupo de colaboración, si lo hubiereThe following article appeared in The Journal of Chemical Physics 152.21 (2020): 214117 and may be found at https://doi.org/10.1063/5.0004835MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree–Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functionsF.A. acknowledges financial support from the EU-H2020 research and innovation programme under Grant Agreement No. 654360 within the framework of the NFFA-Europe Transnational Access Activity. Part of this work was performed, thanks to computer resources provided by CINECA, under Project No. HPC-EUROPA3 (Grant No. INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action of the H2020 Programme. D.-C.S. and J.A. acknowledge support from the U.S. Department of Energy, Office of Basic Energy Sciences, Heavy Element Chemistry program, under Grant No. DE-SC0001136. S.B. acknowledges support from the Swiss National Science Foundation (Grant No. P2SKP2_184034). A.B. is grateful for support from ETH Zurich (ETH Fellowship No. FEL-49 18-1). M.R. acknowledges support from the Swiss National Science Foundation (Project No. 200021_182400). L.D.V., L.P.-G., and M.Ol. acknowledge a MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca) grant “Dipartimento di Eccellenza 2018-2022.” M.Ol. acknowledges NSF Grant No. CHE-CLP-1710191. M.D. and M.L. acknowledges support from the Olle Engkvist Foundation. E.D.L. and V.V. acknowledge computational resources provided by SNIC through LUNARC and NSC. T.B.P. acknowledges support from the Research Council of Norway through its Centres of Excellence scheme, Project No. 262695, and through Research Grant No. 240698. K.P. acknowledges financial support from KU Leuven through Grant No. C14/15/052. L.S. acknowledges financial support from Ministerio de Economía y Competitividad, Spain (Dirección General de Investigación y Gestión del Plan Nacional de I+D+i, Grant No. MAT2017-83553- P). J.S.-M. acknowledges support from the EU-H2020 Marie Curie Actions (AttoDNA, FP8-MSCA-IF, Grant No. 747662). I.S. gratefully acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 678169 PhotoMutant). L.U. and X.G. gratefully acknowledge scientific Grant Nos. R-143-000-A80- 114 and R-143-000-A65-133 from the National University of Singapore. Computational resources of the NSCC (ASPIRE-1, Grant No. 11001278) were used for this study

Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method

The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schroedinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of non-orthogonal Slater determinants, the method resembles an ensemble of density-functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low-power of system size, similar to the corresponding independent-electron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high-performance computing platforms and numerical libraries. In this review, we provide a self-contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure in molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed.Comment: 22 pages, 11 figure