Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting

Wu, Xing‐De; Lindsey, Michael; Zhou, Tiangang; Tong, Yu; Lin, Lin

doi:10.1103/physrevb.102.085123

Cited by 22 publications

(57 citation statements)

References 45 publications

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“…( 8) in Ref. 36 ). This corresponds to an additional constraint on the approximate density matrix D, namely…”

Section: Brief Review Of Density Matrix Embedding Theorymentioning

confidence: 96%

“…Because of the mean-field form of Φ, it can be characterized entirely by its 1-RDM D, and the bath orbitals are defined via a singular value decomposition of a sub-block of D (for a complete discussion see Refs. 5,36 , and for additional work, including some that goes beyond assuming a mean-field Φ, see Refs. 3,[24][25][26][27]29,[45][46][47][48][49] ).…”

Section: Brief Review Of Density Matrix Embedding Theorymentioning

confidence: 99%

“…In the context of SCF-DMET, the procedure for correlation potential fitting is a crucial step for numerical robustness and different approaches have been proposed 3,5,19,27,28,35,36,48,49 . One place where numerical issues can arise is when the global low-level Hamiltonian becomes gapless, in which case the least-squares cost function becomes non-differentiable.…”

Section: Brief Review Of Density Matrix Embedding Theorymentioning

confidence: 99%

“…Global information, in particular the one-electron reduced density matrix (1-RDM), is made consistent between all the impurities with the help of a low-level Hartree-Fock (HF) type of theory. In the self-consistent-field DMET (SCF-DMET) 1 , this global information is then used to update the impurity problems in the next self-consistent iteration, until a certain consistency condition of the 1-RDM is satisfied between the high-level and low-level theories [1][2][3][4]35,36 .…”

Section: Introductionmentioning

confidence: 99%

“…Problem (1) can be solved by reformulating the correlation potential fitting as a semidefinite programming (SDP) problem 36 , which is a convex optimization and is typically a robust procedure. The gapless problem (2), however, is an intrinsic problem in DMET.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the pure state $v$-representability of density matrix embedding theory

Faulstich¹,

Kim²,

Cui³

et al. 2021

Preprint

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“…( 8) in Ref. 36 ). This corresponds to an additional constraint on the approximate density matrix D, namely…”

Section: Brief Review Of Density Matrix Embedding Theorymentioning

confidence: 96%

Section: Brief Review Of Density Matrix Embedding Theorymentioning

confidence: 99%

Section: Brief Review Of Density Matrix Embedding Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the pure state $v$-representability of density matrix embedding theory

Faulstich¹,

Kim²,

Cui³

et al. 2021

Preprint

Self Cite

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Pure State v-Representability of Density Matrix Embedding Theory

Faulstich

Kim

Cui

et al. 2022

J. Chem. Theory Comput.

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Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are noninteracting pure-state v-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. To relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for the 2D Hubbard and hydrogen model systems indicate that, in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.

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Second-Order Active-Space Embedding Theory

Evangelista

2022

J. Chem. Theory Comput.

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Quantum embedding schemes are a promising way to extend multireference computations to large molecules with strong correlation effects localized on a small number of atoms. This work introduces a second-order active-space embedding theory [ASET(2)] which improves upon mean-field frozen embedding by treating fragment−environment interactions via an approximate canonical transformation. The canonical transformation employed in ASET(2) is formulated using the driven similarity renormalization group. The ASET(2) scheme is benchmarked on the NN bond dissociation in pentyldiazene, the S 0 to S 1 excitation in 1-octene, and the interaction energy of the O 2 −benzene complex. The ASET(2) explicit treatment of fragment−environment interactions beyond the mean-field level generally improves the accuracy of embedded computations, and it becomes necessary to achieve an accurate description of excitation energies of 1-octene and the singlet−triplet gap of the O 2 − benzene complex.

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Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting

Cited by 22 publications

References 45 publications

On the pure state $v$-representability of density matrix embedding theory

On the pure state $v$-representability of density matrix embedding theory

Pure State v-Representability of Density Matrix Embedding Theory

Second-Order Active-Space Embedding Theory

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