Fully Quantum Embedding with Density Functional Theory for Full Configuration Interaction Quantum Monte Carlo

Petras, Hayley R.; Graham, Daniel S.; Ramadugu, Sai Kumar; Goodpaster, Jason D.; Shepherd, James J.

doi:10.1021/acs.jctc.9b00571

Cited by 20 publications

(20 citation statements)

References 98 publications

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“…We used EOM-CCSD as the excited-state wave function method throughout this paper; however, we see no limitations in applying this absolutely localization embedding strategy to other excited-state wave function methods as well, like the complete active space with second-order perturbation theory (CASPT2). , We are currently exploring such embedding strategies. We anticipate success since we have shown that our embedding method is robust with respect to the wave function method, at least in the ground state, by utilizing i -FCIQMC in absolutely localized projection-based quantum embedding …”

Section: Discussionmentioning

confidence: 99%

Absolutely Localized Projection-Based Embedding for Excited States

Wen

Graham

Chulhai

et al. 2019

J. Chem. Theory Comput.

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119

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We present a quantum embedding method that allows for the calculation of local excited states embedded in a Kohn-Sham density functional theory (DFT) environment. Projection-based quantum embedding methodologies provide a rigorous framework for performing DFT-in-DFT and wave function in DFT (WF-in-DFT) calculations. The use of absolute localization, where the density of each subsystem is expanded in only the basis functions associated with the atoms of that subsystem, provide improved computationally efficiency for WF-in-DFT calculations by reducing the number of orbitals in the WF calculation. In this work, we extend absolutely localized projection-based quantum embedding to study localized excited states using EOM-CCSD-in-DFT and TDDFT-in-DFT. The embedding results are highly accurate compared to the corresponding canonical EOM-CCSD and TDDFT results on the full system, with TDDFT-in-DFT frequently more accurate than canonical TDDFT. The 1 arXiv:1909.12423v1 [physics.chem-ph] 26 Sep 2019 absolute localization method is shown to eliminate the spurious low-lying excitation energies for charge transfer states and prevent over delocalization of excited states.Additionally, we attempt to recover the environment response caused by the electronic excitations in the high-level subsystem using different schemes and compare their accuracy. Finally, we apply this method to the calculation of the excited state energy of green fluorescent protein and show that we systematically converge to the full system results. Here we demonstrate how this method can be useful in understanding excited states, specifically which chemical moieties polarize to the excitation. This work shows absolutely localized projection-based quantum embedding can treat local electronic excitations accurately, and make computationally expensive WF methods applicable to systems beyond current computational limits. many systems. 16 However, the computational cost of EOM-CCSD (scaling as O(N 6 )) restricts its usage to about 50 or fewer atoms in a moderate basis. Methods that extend the applicability of EOM-CCSD to larger systems include the use of local orbitals, [17][18][19][20][21] restricted virtual spaces, 22,23 and multiscale approaches. [24][25][26][27] Multiscale approaches treat different regions of the molecule with methods of varying cost and accuracy to reflect their importance. 28,29 For example, one may use EOM-CCSD to describe the important region of the molecule while using molecular mechanics (MM), in EOM-CCSD-in-MM methods, [30][31][32] or DFT, in EOM-CCSD-in-DFT methods, 33 to describe the remainder of the molecule. Such approaches take advantage of the high accuracy of EOM-CCSD and the low scaling of MM or DFT to go beyond the size/accuracy limits of any one method alone.Density functional theory embedding provides a formally exact framework for performing multiscale calculations. This approach has been shown to be accurate for combining density functional theory with wave function theory. The key choice in density function theory embedd...

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Section: Discussionmentioning

confidence: 99%

Absolutely Localized Projection-Based Embedding for Excited States

Wen

Graham

Chulhai

et al. 2019

J. Chem. Theory Comput.

Self Cite

119

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“…There have been attempts to fix the sign problem by leveraging this understanding directly, using a fixed-node or trial wave function approach. , The initiator approach in FCIQMC removes the annihilation plateau at the cost of introducing a small error in the energy (which can be removed by increasing the number of walkers in the simulation) . The motivation for and derivation of this approximation were ultimately related to the alleviation of the sign problem, allowing FCIQMC to be used to study a much broader scope of applications than it originally could in its canonical form. ,, The development of the initiator approximation in DMQMC achieved a similar outcome, allowing us to apply it in our previous work on the uniform electron gas and simple ab initio molecular systems. , Sign problem aside, there has recently been a slate of other improvements to FCIQMC (or FCIQMC-like) methods that are beyond the scope of this work to review in detail. − Additionally, large-scale implementations of FCIQMC and related methods have also been recently developed; several recent papers that review current challenges and developments are provided for the interested reader. , …”

Section: Introductionmentioning

confidence: 99%

The Sign Problem in Density Matrix Quantum Monte Carlo

Petras

Benschoten

Ramadugu

et al. 2021

J. Chem. Theory Comput.

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Density matrix quantum Monte Carlo (DMQMC) is a recently developed method for stochastically sampling the N-particle thermal density matrix to obtain exact-on-average energies for model and ab initio systems. We report a systematic numerical study of the sign problem in DMQMC based on simulations of atomic and molecular systems. In DMQMC, the density matrix is written in an outer product basis of Slater determinants. In principle, this means that DMQMC needs to sample a space that scales in the system size, N, as O[(exp(N))2]. In practice, removing the sign problem requires a total walker population that exceeds a system-dependent critical walker population (N c), imposing limitations on both storage and compute time. We establish that N c for DMQMC is the square of N c for FCIQMC. By contrast, the minimum N c in the interaction picture modification of DMQMC (IP-DMQMC) is only linearly related to the N c for FCIQMC. We find that this difference originates from the difference in propagation of IP-DMQMC versus canonical DMQMC: the former is asymmetric, whereas the latter is symmetric. When an asymmetric mode of propagation is used in DMQMC, there is a much greater stochastic error and is thus prohibitively expensive for DMQMC without the interaction picture adaptation. Finally, we find that the equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger systems with large basis sets. This suggests that IP-DMQMC offers a way to ameliorate the cost of moving between a Slater determinant space and an outer product basis.

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“…1,34 Subsequently, there were also a wide variety of FCIQMC or FCIQMC-like methods developments which are beyond the scope of this work to review in detail. [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] Large scale implementations of the FCIQMC method and related methods have also been developed and these papers review current challenges and developments for the interested reader. 51,52 Here, we conduct a systematic investigation of the sign problem in density matrix quantum Monte Carlo (DMQMC).…”

Section: Introductionmentioning

confidence: 99%