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

Abstract

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 10(12) 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[10(7)] 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.

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

“…In the large walker number limit, the i-FCIQMC tends to the FCIQMC algorithm, which itself converges rigorously to the FCI energy. In previous work, simulations with different walker numbers were performed to explicitly demonstrate convergence towards this limit by finding correlation energies over an increasing range of walker numbers 13 . In the present work we will show that this limit can be rigorously found from a single calculation.…”

“…However, in order to alleviate this scaling problem, an adaptation of this method has been developed, called initiator-FCIQMC (i-FCIQMC) 12,13,15 . The determinant space is instantaneously divided into those determinants exceeding a population of n add walkers, termed initiator determinants, and those that do not.…”

“…FCI Quantum Monte Carlo and its 'initiator' adaptation (i-FCIQMC) are novel methods developed in a series of recent papers [11][12][13][14][15][16] in which the FCI equations are simulated by representing the determinant coefficients as a set of walkers evolving over discretized imaginary time. This allows much larger Hilbert spaces to be studied, with the largest space accurately sampled to date being 10 108 , in a previous study of the 54-electron gas 16 .…”

Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

“…We hope that the findings of the present work will translate both to alternative UEG models [86,87], ab initio systems, and to other explicitly correlated methods in the solid state such as CCSD-F12 [32,33,[88][89][90] or FCIQMC-F12 [2,61,[91][92][93][94], where the additional computational cost for calculating the F12 contribution becomes negligible in comparison to these more expensive parent methods. The application of the methods outlined in this work to real, ab initio solid state systems is expected to significantly expand the scope of the whole range of quantum chemical wave function based methods.…”

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

“…[52] Recently, Alavi et al have developed the FCIQMC method which allows very efficient evaluation of the FCI wavefunction. [53][54][55][56][57] In the present calculation, the FCI eigenvector was obtained by performing the Nesbet update scheme and was selected because of its ease of implementation. [58] In the Nesbet method, a expansion coefficient c µ is updated by ∆c µ…”