- Stochastic Methods for Molecular Properties (SMMP)
Stochastic Methods for Chiroptical Properties (SMCP or ChiroStoch)
Deterministic methods need large Hilbert spaces for effective expansions of the many-electron wave function
This is however largely redundant (Ivanic 2001)
Stochastic algorithms are highly parallelizable in the number of walkers.
I will develop my skills in parallel programming techniques by developing this project.
- 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
- High accuracy means coupled cluster (CC) wave functions
- Systems for which CC is an option are limited by its polynomial scaling
- 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
- 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.
- Low scaling (or better parallelization options) + (perhaps?) controllable error of stochastic methods
are the key advantages. Find relevant literature on both!
The creation of the appropriate software toolbox with good scalability.
- The toolbox will be freely available under the appropriate open source license (GPL most likely!)
General background on quantum chemistry:
- "Frontiers in electronic structure theory" (Sherrill 2010)
- Quantum chemistry as an effective complement to experiment citePlaceholder5, citePlaceholder6, citePlaceholder7, citePlaceholder8, (Goddard 1985)
State of the art:
- Recent reviews on QMC approaches: citePlaceholder10, citePlaceholder11, citePlaceholder12, citePlaceholder13, citePlaceholder14, citePlaceholder15 and (Foulkes 2001)
- DMC (Wick rotation of the Schrodinger equation (Wick 1954) and isomorphism with a classical diffusion problem)
- Self-Healing QMC
- Auxiliary Field QMC
- Fermion QMC
- Stochastic Coupled Cluster: Thom introduces the FCIQMC-like stochastic algorithm for solving the CC equations (Thom 2010)
The methods leverages the stochastic sampling strategies of the FCI wave function in a discrete Fock space first proposed by Alavi et al.(Booth 2009)
- Linked Coupled Cluster Monte Carlo: the stochastic algorithm for the solution of the CC equations in the linked (term-by-term size-extensive) form (Franklin 2016)
- Initiator approximation: the same group proposes the initiator approximation for the CCMC algorithm (Spencer 2016)
- Stochastic Møller-Plesset (Thom 2007)
- Local approaches to QMC citePlaceholder23, citePlaceholder24
Properties by QMC
- Dynamic polarizabilities citePlaceholder25, citePlaceholder26
- Large systems citePlaceholder27, citePlaceholder28
- Forces: correlated sampling (Filippi 2000) and space warp coordinate transformation (Umrigar 2009)
Work by Assaraf and Caffarel on improved estimators (Assaraf 2000) and (Assaraf 2003)
- Static electric properties (dipole and quadrupole moments, static polarizabilities): polarizabilities by finite differences for ethyne (Coccia 2012)
polarizability of the hydrogen atom by modified sampling (Li 2007)
- Most recent review on wave function-based response theory (Helgaker 2012)
- Foundational work citePlaceholder96, citePlaceholder97, citePlaceholder98, citePlaceholder99
- CC response theory
- Local approaches to CC (really a lot of literature...)
- Local approaches to CC response theory citePlaceholder100, citePlaceholder101, (McAlexander 2016)
Problems to address:
- 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
- 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.