Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states

Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry

doi:10.1063/1.3077920

Cited by 75 publications

(118 citation statements)

References 42 publications

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“…23 An additional study used the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to also examine the X 1 Σ g + C 2 ground state PES (0.9−3.0 Å). 49 The FCIQMC-F12 method used the cc-pVDZ basis set, while AFQMC used The C 2 vibrational energy levels are obtained from solutions to the nuclear Schrodinger equation. These solutions are found by a discrete variable representation procedure 50 in which the potential energy curves are fitted to even-tempered Gaussians.…”

Section: Journal Of Chemical Theory and Computationmentioning

confidence: 99%

Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure

Roskop

Kong

Valeev

et al. 2013

J. Chem. Theory Comput.

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The performance of the [2]S and [2]R12 universal perturbative corrections that account for one-and manybody basis set errors of single-and multiconfiguration electronic structure methods is assessed. A new formulation of the [2]R12 methods is used in which only strongly occupied orbitals are correlated, making the approach more amenable for larger computations. Three model problems are considered using the aug-ccpVXZ (X = D,T,Q) basis sets: the electron affinity of fluorine atom, a conformational analysis of two Si2H4structures, and a description of the potential energy surfaces of the X 1Σg+, a 3Πu, b 3Σg-, and A1Πu states of C2. In general, the [2]R12 and [2]S corrections enhance energy convergence for conventional multireference configuration interaction (MRCI) and multireference perturbation theory (MRMP2) calculations compared to their complete basis set limits. For the electron affinity of the F atom, [2]R12 electron affinities are within 0.001 eV of the experimental value. The [2]R12 conformer relative energy error for Si2H4 is less than 0.1 kcal/mol compared to the complete basis set limit. The C2 potential energy surfaces show nonparallelity errors that are within 0.7 kcal/mol compared to the complete basis set limit. The perturbative nature of the [2]R12 and [2]S methods facilitates the development of a straightforward textbased data exchange standard that connects an electronic structure code that can produce a two-particle density matrix with a code that computes the corrections. This data exchange standard was used to implement the interface between the GAMESS MRCI and MRMP2 codes and the MPQC methods is used in which only strongly occupied orbitals are correlated, making the approach more amenable for larger computations. Three model problems are considered using the aug-cc-pVXZ (X = D,T,Q) basis sets: the electron affinity of fluorine atom, a conformational analysis of two Si 2 H 4 structures, and a description of the potential energy surfaces of the X 1 Σ g + , a 3 Π u , b 3 Σ g -, and A 1 Π u states of C 2 . In general, the [2] R12 and [2] S corrections enhance energy convergence for conventional multireference configuration interaction (MRCI) and multireference perturbation theory (MRMP2) calculations compared to their complete basis set limits. For the electron affinity of the F atom, [2] R12 electron affinities are within 0.001 eV of the experimental value. The [2] R12 conformer relative energy error for Si 2 H 4 is less than 0.1 kcal/mol compared to the complete basis set limit. The C 2 potential energy surfaces show nonparallelity errors that are within 0.7 kcal/mol compared to the complete basis set limit. The perturbative nature of the [2] R12 and [2] S methods facilitates the development of a straightforward text-based data exchange standard that connects an electronic structure code that can produce a two-particle density matrix with a code that computes the corrections. This data exchange standard was used to implement the interface between the GAMESS MRCI and MRMP2 codes and t...

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Section: Journal Of Chemical Theory and Computationmentioning

confidence: 99%

Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure

Roskop

Kong

Valeev

et al. 2013

J. Chem. Theory Comput.

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“…In AFQMC, first conceived by G. Sugiyama and S. E. Koonin [20], later perfected and extended by S. Zhang [21,22,25] and F.Assaad [23] and successfully applied to the investigation of molecular systems [26][27][28], the association between (4) and a stochastic process in D(N ) is made possible by a discretization:…”

Section: The Phaseless Afqmcmentioning

confidence: 99%

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

Motta

Galli

Moroni

et al. 2014

The Journal of Chemical Physics

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The phaseless Auxiliary Field Quantum Monte Carlo method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we apply the method to the calculation of imaginary time correlation functions. We give a detailed description of the technique and we test the quality of the results for static and dynamic properties against exact values for small systems.

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“…The coefficients of |δχ V n and |δχ V n are sampled at the end of each subblock using Eqs. (27) and (35). Statistical data is collected for M b subblocks for each parallel diffusion before an update of the small basis.…”

Section: Algorithmmentioning

confidence: 99%

“…We use condition λ n n = 0 [See Eq (27)] to determine the value of E S n . In practice, we adjust the reference energy of the guiding functions every iteration as e −βE X,ℓ+1 n = e −βE X,ℓ n (δ n,m + λ m n ).…”

Section: E Calculation Of the Partition Functionmentioning

confidence: 99%

“…10,27,28 One could potentially extend these methods to finite temperature, limiting the projector e −βĤ to finite β. Thermodynamical averages can be later obtained from derivatives of the Helmholtz free energy F (β) = −1/β ln[tr(e −βĤ )], wherê H is the many-body Hamiltonian operator and tr(X) the trace of X over the complete many-body Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

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Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Reboredo

Kim

2014

The Journal of Chemical Physics

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(1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to have maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates.Possible applications of this method to calculate the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can be also used to accelerate the calculation of the ground or excited states with Quantum Monte Carlo.

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Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states

Cited by 75 publications

References 42 publications

Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure

Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

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