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Semi-stochastic and excited-state approaches in FCIQMC

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FCIQMC is an approach introduced by Booth, Thom and Alavi in 20091 to stochastically sample the solution of the Schrödinger equation, and has since seen rapid algorithmic developments and many applications. In this talk we present two separate developments. Firstly, we build on the semi-stochastic adaptation to FCIQMC introduced by Umrigar and co-workers2. In this, the most important part of the projection is performed exactly, rather than stochastically, thus resulting in reduced noise. We demonstrate the dramatic improvements that can occur with this approach for a variety of systems, both chemical and model in nature. Secondly, we consider the calculation excited-state properties. This is initially done by analogy with the Lanczos algorithm, subsequently allowing spectral and finite-temperature properties to be calculated. Finding that this approach has some stability issues, we consider a separate approach to sample individual excited states, and apply it to obtain highly accurate results for the carbon dimer.

[1] – G. H. Booth, A. J. W. Thom, and A. Alavi, J. Chem. Phys. 131, 054106 (2009) [2] – F. R. Petruzielo, A. A. Holmes, H. J. Changlani, M. P. Nightingale, and C. J. Umrigar, Phys. Rev. Lett. 109, 230201 (2012)

This talk is part of the Theoretical Chemistry Informal Seminars series.

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