# SMMP - Stochastic Methods for Molecular Properties

Possible titles:

1. Stochastic Methods for Molecular Properties (SMMP)
2. Stochastic Methods for Chiroptical Properties (SMCP or ChiroStoch)

3. Deterministic methods need large Hilbert spaces for effective expansions of the many-electron wave function This is however largely redundant (Ivanic 2001)

4. Stochastic algorithms are highly parallelizable in the number of walkers. I will develop my skills in parallel programming techniques by developing this project.

Research questions:

• Understanding chiroptical properties for large chemical systems

Objectives of the project:

• The calculation of molecular properties with high accuracy and for systems of relevant size

1. High accuracy means coupled cluster (CC) wave functions
2. Systems for which CC is an option are limited by its polynomial scaling
3. It is possible to reduce the scaling, e.g. by means of local approaches to the electron correlation problem, but this has been proven to not be as effective for molecular properties as for energies
• Devise the appropriate stochastic approach to the solution of response equations

1. We want the stochastic approach because it's (supposedly) embarassingly parallel. This can enable the study of the response properties for larger systems and provide benchmark results for lower level calculations.
2. Low scaling (or better parallelization options) + (perhaps?) controllable error of stochastic methods are the key advantages. Find relevant literature on both! (Booth 2014), (Coccia 2012)
• The creation of the appropriate software toolbox with good scalability.

1. The toolbox will be freely available under the appropriate open source license (GPL most likely!)

General background on quantum chemistry:

State of the art:

• The fermion sign problem. How do FCIQMC and CCMC avoid it? The sign problem is NP-hard (Troyer 2005) thus not solvable in polynomial time

TODO:

• Size of the systems investigated by stochastic methods in Fock space?
• Properties by stochastic methods? VMC/DMC/FCIQMC?
• Local correlation approaches for molecular properties?
• L. Guidoni might have published some FCIQMC calculations on large molecular systems.

### References

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2. George H. Booth, Simon D. Smart, Ali Alavi. Linear-scaling and parallelisable algorithms for stochastic quantum chemistry. Molecular Physics 112, 1855–1869 Informa UK Limited, 2014. Link

3. Emanuele Coccia, Olga Chernomor, Matteo Barborini, Sandro Sorella, Leonardo Guidoni. Molecular Electrical Properties from Quantum Monte Carlo Calculations: Application to Ethyne. J. Chem. Theory Comput. 8, 1952–1962 American Chemical Society (ACS), 2012. Link

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32. Roland A