Breaking the carbon dimer: The challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods

Booth, George H.; Cleland, Deidre; Thom, Alex J. W.; Alavi, Ali

doi:doi:10.1063/1.3624383

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How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations ab...

An approximate density-functional method using the Harris-Foulkes functional

We present a method which uses the results of a molecular Kohn-Sham calculation at a reference geometry to approximate the energy at many different geometries. The Kohn-Sham electron density of the reference geometry is decomposed into atomic fragments, which move with the nuclei to approximate the density at a new geometry and the energy is evaluated with the Harris-Foulkes functional. Preliminary results for a biological quantum-mechanics/molecular-mechanics trajectory are promising: the error...

The full configuration interaction quantum Monte Carlo (FCIQMC) method, as well as its “initiator” extension (i-FCIQMC), is used to tackle the complex electronic structure of the carbon dimer across the entire dissociation reaction coordinate, as a prototypical example of a strongly correlated molecular system. Various basis sets of increasing size up to the large cc-pVQZ are used, spanning a fully accessible N-electron basis of over 10¹² Slater determinants, and the accuracy of the method is demonstrated in each basis set. Convergence to the FCI limit is achieved in the largest basis with only O[10⁷] walkers within random errorbars of a few tenths of a millihartree across the binding curve, and extensive comparisons to FCI, CCSD(T), MRCI, and CEEIS results are made where possible. A detailed exposition of the convergence properties of the FCIQMC methods is provided, considering convergence with elapsed imaginary time, number of walkers and size of the basis. Various symmetries which can be incorporated into the stochastic dynamic, beyond the standard abelian point group symmetry and spin polarisation are also described. These can have significant benefit to the computational effort of the calculations, as well as the ability to converge to various excited states. The results presented demonstrate a new benchmark accuracy in basis-set energies for systems of this size, significantly improving on previous state of the art estimates.

Article Outline

INTRODUCTION
FCIQMC METHOD
1. i -FCIQMC extension
SYMMETRY CONSIDERATIONS
RESULTS AND ANALYSIS OF THE METHOD
1. Comparison to exact results
2. A cc-pVDZ basis
3. Further enlargement of the one-electron basis
4. Excited states
5. Scaling
CONCLUSIONS

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KEYWORDS and PACS

Keywords

bonds (chemical), carbon, configuration interactions, dissociation, excited states, molecular electronic states, Monte Carlo methods, quantum theory

PACS

31.15.vn

Electron correlation calculations for diatomic molecules
33.15.Fm

Bond strengths, dissociation energies

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.3624383

PUBLICATION DATA

ISSN

0021-9606 (print)

1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef

American Institute of Physics

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