A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

Roemelt, Michael; Guo, S.Y.; Chan, Garnet Kin‐Lic

doi:10.1063/1.4950757

Cited by 62 publications

(57 citation statements)

References 74 publications

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“…Polynuclear copper complexes can serve as functional and structural models of multicopper enzymes 16,102,103 . Dinuclear copper complexes constitute important building blocks for materials such as metal-organic frameworks [104][105][106] , and an important test case for electronic structure methods 16,[27][28][29]107 .…”

Section: Gaussian Process Regression (Gpr)mentioning

confidence: 99%

Exchange Spin Coupling from Gaussian Process Regression

et al. 2020

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Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates ("error bars") along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science. File list (4) download file view on ChemRxiv supp.pdf (2.07 MiB) download file view on ChemRxiv ms.pdf (5.17 MiB) download file view on ChemRxiv Cu2-dataset.zip (22.06 MiB) download file view on ChemRxiv py_regression.zip (17.79 MiB)

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Section: Gaussian Process Regression (Gpr)mentioning

confidence: 99%

Exchange Spin Coupling from Gaussian Process Regression

et al. 2020

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“…[i] µ wavefunctions using the same renormalized basis (similar to performing a state-averaged DMRG optimization, and related to the algorithm used in Ref. 44). An advantage of our current t-MPS-NEVPT2 implementation, however, is that it is easily parallelized by separating the correlation energy contributions into O(N 2 act ) components:…”

Section: Propagate Wavefunctions |φmentioning

confidence: 99%

Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes

Sokolov

Guo

Ronca

et al. 2017

The Journal of Chemical Physics

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In earlier work [J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N -electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally-contracted perturbation formulation, and (ii) yielded the fully uncontracted NEVPT2 energy. Here, we present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group (td-DMRG) algorithm. In addition, we report a low-scaling MPS-based implementation of strongly-contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in all-trans polyenes (C 4 H 6 to C 24 H 26 ), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals.

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“…Calculation and storage of such high order RDMs is limited to an active space of around 25 orbitals beyond which it become prohibitively expensive [54][55][56][57] . To circumvent this difficulty, some researches have resorted to approximating the higher body RDM by reconstructing its disconnected part by antisymmetric multiplication of lower body RDM and ignoring the density cumulant which is the connected part 53,[58][59][60][61][62] .…”

Section: Parameterizing Dynamic Correlation: Problems and Solutionsmentioning

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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A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

Cited by 62 publications

References 74 publications

Exchange Spin Coupling from Gaussian Process Regression

Exchange Spin Coupling from Gaussian Process Regression

Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes

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

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