Multireference Nature of Chemistry: The Coupled-Cluster View

Lyakh, Dmitry I.; Musiał, Monika; Lotrich, Victor F.; Bartlett, Rodney J.

doi:10.1021/cr2001417

Cited by 516 publications

(504 citation statements)

References 465 publications

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“…To perform a frozen-core calculation in ECISD and ECEPA, we employed the constrained optimization in SUHF to obtain the HF core orbitals. 16 This can be achieved by averaging the corevirtual (CV) block (and VC block) of the SUHF Fock matrix as 8 for both σ = α, β. At SCF convergence, it is guaranteed that the α and β orbitals share the same core space, 61,62,69 while the SUHF energy is minimized under such a constraint.…”

Section: Computational Detailsmentioning

confidence: 99%

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Tsuchimochi

Ten‐no

2017

J. Chem. Theory Comput.

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We propose a size-consistent generalization of the recently developed spin-extended configuration interaction with singles and doubles (ECISD), where a CI wave function is explicitly spin-projected. The size-consistent effect is effectively incorporated by treating quadruples within the formulation of coupled electron pair approximation. As in coupled-cluster theory, quadruple excitations are approximated by a disconnected product of double excitations. Despite its conceptual similarity to the standard single-and multireference analogues, such a generalization requires careful derivation, as the spin-projected CI space is non-orthogonal and overcomplete. Although our methods generally yield better results than ECISD, size-consistency is only approximately retained because the action of a symmetry-projection operator is size-inconsistent. In this work, we focus on simple models where exclusion-principle-violating terms, which eliminate undesired contributions to the correlation effects, are either completely neglected or averaged. These models possess an orbital-invariant energy functional that is to be minimized by diagonalizing an energy-shifted effective Hamiltonian within the singles and doubles manifold. This allows for a straightforward generalization of the ECISD analytical gradients needed to determine molecular properties and geometric optimization. Given the multireference nature of the spin-projected Hartree-Fock method, the proposed approaches are expected to handle static correlation, unlike single-reference analogues. We critically assess the performance of our methods using dissociation curves of molecules, singlet-triplet splitting gaps, hyperfine coupling constants, and the chromium dimer. The size-consistency and size-extensivity of the methods are also discussed.

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Section: Computational Detailsmentioning

confidence: 99%

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Tsuchimochi

Ten‐no

2017

J. Chem. Theory Comput.

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“…We here focus on DMRG, 20,21 a variational method which minimizes the energy of a wavefunction parametrized as a matrix product state (MPS). 22,23 DMRG can handle active spaces of around [30][31][32][33][34][35][36][37][38][39][40] orbitals, and in some cases even up to 100 [24][25][26][27][28][29][30][31][32][33][34] . However, by themselves the mentioned methods are not efficient for obtaining quantitative accuracy and for this dynamic correlation must also be calculated.…”

Section: Introductionmentioning

confidence: 99%

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Sharma

Knizia

Guo

et al. 2017

J. Chem. Theory Comput.

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We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration reference wave functions-including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multi-reference linearized coupled cluster method (MRLCC) [S. Sharma, A. Alavi, J. Chem. Phys. 143, 102815 (2015)], and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first-order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr2, pentacene and oxo-Mn(Salen), we shown that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation -calculating second order instead of third order energy corrections, use of internal contraction and approximations made in the reference wavefunction due to DMRG.

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“…To this end, new methods and approaches are continuously being developed and applied to problems related to heterogeneous catalysis by oxide surfaces [3,4]. While theoretical chemists have developed over the past 50 years a wide set of computational approaches to study with extremely high accuracy molecular reactions (from configuration interaction [5] to coupled cluster [6] methods and quantum Monte Carlo [7] ), when one deals with reactions occurring at solid surfaces the method of choice becomes density functional theory (DFT). In the past three decades there has been a formidable advance in the computational description of adsorption and reaction at metal, semiconductor, and insulator surfaces with these methods [8,9].…”

Section: Introductionmentioning

confidence: 99%

First Principles Calculations on Oxide-Based Heterogeneous Catalysts and Photocatalysts: Problems and Advances

Pacchioni

2014

Catal Lett

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Density functional theory (DFT) has become an essential complement of experiments to interpret, rationalize, and understand structures, spectroscopic data, microscopy analyses, etc. of relevance in heterogeneous catalysis and photocatalysis. However, one of the major goals of theory in catalysis remains the prediction of reaction enthalpies and entropies, of transition state structures, and the identification of reaction mechanisms. While accurate theoretical methods are currently available to study the thermochemistry of molecular systems, this is much less so when reactions involve solid surfaces and in particular oxide materials. The problem stems from the approximate nature of the exchange-correlation functionals used in all DFT approaches. Attempts to improve the accuracy of reaction energies is at the core of the efforts made in the past 30 years to generate new functionals. In this review we will discuss some recent advances in the theoretical description of oxides and their surfaces in heterogeneous catalysis and photocatalysis. In particular, we will focus on two problems: (1) the determination of an oxide band gap and the proper alignment of the occupied and unoccupied levels with respect to the vacuum level, an aspect relevant for the red-ox properties of the material, and (2) the calculation of reaction energies at oxide surfaces. To this end, we will discuss and comment on the performance of current implementations of exchange-correlation functionals (standard GGA, GGA?U, hybrid functionals, meta-GGA, etc.) or alternative approaches (like the quasiparticle GW method), in predicting band alignment and chemical reactivity at oxide surfaces. The role of dispersion forces will be also briefly discussed.

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Multireference Nature of Chemistry: The Coupled-Cluster View

Cited by 516 publications

References 465 publications

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

First Principles Calculations on Oxide-Based Heterogeneous Catalysts and Photocatalysts: Problems and Advances

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