Project Ideas

Initiated by AJWT and uncurated. Contact to discuss, or do edit or add discussion and links.

General Projects

P: FED/resHF extended to excitation rank L: FED-CI(L)/resHF-CI(L)

Aim: Determine whether FED-CI(L)/resHF-CI(L) is useful for determining good references in post-NOCI methods, e.g. NOCI-QMC or NOCI-PT2.

Next: Figure out how to determine the energy improvement cheaply.

P: Pivotal FRI preconditioning for FCIQMC

Aim: Implement preconditioned FCIQMC in HANDE, and replace the usual stochastic rounding with pivotal FRI compression.

Next: Compare conventional and pivotal-compressed preconditioned FCIQMC against NECI and test whether pivotal compression reduces variance at fixed cost.

Refs: Blunt, Thom, Scott, JCTC 15 3537 '19. Greene, Webber, Weare, Berkelbach, JCTC 15 4834 '19.

September 2026 — [Electronic Structure Conference (MES 2026)]

P: Non-orthogonal analogue of MPS-MRCI for DMRG

October 2024 — [Triennial Congress of the International Society for Theoretical Chemical Physics (ISTCP 2024)]

P: Local orbitals with fixed sparsity for CCMC

Aim: Use local orbitals developed for MP2 with a fixed sparsity pattern for CCMC.

Some thresholding, but generally very good and local.

Talk: 14/10/24, Martin Head-Gordon, "MP2 Made Better and Faster? Recent Developments in Regularization and Local Correlation".

Refs: JCP 158 064105 '23

P: Size consistency of CCMC

Aim: Check size consistency of CCMC on Ne, $\mathrm {Ne} _{2}$, etc.

P: Use SCF diabatic-like states for MASH

Aim: Use SCF diabatic-like states for MASH.

MASH is a deterministic version of surface hopping which couples a fictitious degree of freedom to decide which of two surfaces to hop on.

Talk: 14/10/24, Jeremy Richardson, "Breaking down the Barrier between the Quantum and Classical Worlds".

Refs: Nat Commun. 15 4335 '24. JCP 158 104111 '23.

P: Bootstrap embedding for He in clusters

Aim: Use bootstrap embedding to look at He in clusters.

Talk: 14/10/24, Troy van Voorhis, "Bootstrap Embedding".

QuEmb software available on GitHub.

TODO: Advertise HANDE hackathons on website

P: Understanding the nodal surface (post ByteDance)

Aim: Evaluate FermiNet's nodal surface for quality somehow.

P: Resolution of the Identity / density fitting for HANDE two-electron integrals (post ByteDance)

P: Enforce spin symmetry using $S_{+}|\Psi \rangle =0$ (post ByteDance)

Aim: Investigate whether the $S_{+}|\Psi \rangle =0$ requirement can be used to enforce spin symmetry ($S^{2}$).

TODO: Read Pfau Science 2024

Q: How exactly are internally and externally contracted defined?

Refs: Siegbahn 1980, 1983

L: Quantum Course — Schmidt decomposition and properties of the Density Matrix

L: Quantum Course — Adiabatic connection used in DFT and ADC — how?

TODO: Interact more with Yi Sun on this Bootstrap embedding

Q: Do complex nuclear coordinates lead to plane-wave boundary conditions?

P: Do DMC on fullerenes

P: High-order CCMC on benzene

Aim: Do CCMCSDTQ5/pVDZ and CCSDTQ/pVTZ on benzene at Eriksen's geometries with Chebyshev.

He has cc-pVTZ benzene results.

Talk: 15/10/24, Janus Juul Eriksen, "Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set".

P: Biradicals

Refs: JCP 147 164120 '20

Q: What happens when two $\Delta$SCF states cross, i.e. switch $n_{s}$ value?

$\Delta$SCF is justified by the correspondence between exact $(n,w(\mathbf {r} ))$ and $(n_{s},w_{s}(\mathbf {r} ))$. The functional is not of the density but of $n,w$ or the 1PDM. The numbering of states between $n_{s}$ and $n$ may differ.

Talk: 15/10/24, Weitao Yang, "ΔSCF Excited-State Approach: Theoretical Foundation, Linear Conditions for Fractional Charges, and Physical Meaning of Orbital Energies".

Refs: 2403.04604

Q: Why do forward and backward barriers differ in the adiabatic connection?

A quantity ${\mathcal {R}}_{\lambda }$ was defined which corresponds to the difference in the adiabatic connection's $W_{\lambda }$ for a barrier. Shapes of this for forward and backward barriers of $\mathrm {H} +\mathrm {N} _{2}\rightarrow \mathrm {HN} _{2}$ were very different. Changing the amount of HF exchange just shifts energies up and down (i.e. you get any result you want).

Talk: 15/10/24, Andrew Teale, "DFT Reaction Barriers: An Adiabatic-Connection Perspective".

P: What barriers are bad in DFT and why?

P: Separating Static and Dynamic Correlation: MCPDFT and others (Gagliardi, Pernal)

Q: What is a restricted Boltzmann machine useful for?

P: Understanding UCC

Aim: Understand how different ansätze differ and what effects they have.

P: Simulate decoherence in quantum computing by coupling to a bath?

P: Apply Multistate DFT to hDFT/hNOCI

Aim: Apply this approach directly to the hDFT code or hNOCI code in RevQCMagic.

Talk: 17/10/24, Jiali Gao, "Multistate Density Functional Theory and Applications".

Refs: JPCL 13 7762 '22, JCTC 18 7403 '23. JCTC 20 8474 '24. JCTC 18 6407 '22

Q: Is MS-DFT for the HF functional just NOCI?

Q: Where are the $\mathrm {F} ^{+}\cdots \mathrm {F} ^{-}$ states in hHF/hDFT? How do they compare to the VB states?

Talk: 17/10/24, Wei Wu, "Multireference Density Functional Theory with Valence Bond Methods".

Refs: Acc. Chem. Res. 54 3895 '21. KCP 157 084106 '22. JCTC 8 1608 '12.

TODO: Review of Multireference DFT

Q: Can we do complex scaling or tracking by changing $\hbar$? Do NOCI with solutions with different $\hbar$ values?

$\hbar \rightarrow 0$ is like strong correlation.

Talk: 17/10/24, Chen Li, "Improving Density Functional Approximations through Exact Constraints and Exact Wave Function".

Refs: cf Gori Giorgi PRA 75 042511 '07.

Q: Can we interact fragments' HF solutions by e-e-scaling the electrons? Is this just the same as bringing them in from infinity?

Q: How can we DAMP CCMC so it doesn't explode into the whole of CC space, so not needing an explicit truncation?

Is it because we are not in spin eigenfunctions so we always spawn heavily into higher levels?

P: Cancellation in the true CC solution and stochastic symmetry breaking

Aim: Determine whether there is a lot of cancellation in the true CC solution which might not be visible in a spin-symmetry-broken stochastic snapshot, i.e. whether fluctuation-induced symmetry breaking causes lots of particles which do not cancel.

Q: How do the CC(P;Q) moment corrections actually work?

Talk: 17/10/24, Piotr Piecuch, "Converging High-Level Coupled-Cluster Energetics with Semi-Stochastic, CIPSI-Driven, and Adaptive CC(P; Q) Methods".

Refs: JCP 159 084108 '23. JCP 154 124103 '21.

CCpy code available on GitHub.

Q: For Ne@C70, what level of CC(P;Q) would be needed to get $<1\ \mathrm {cm} ^{-1}$ accuracy?

TODO: Buy "Interacting Electrons"

P: Calculate the diabaticity of different SCF states

Aim: Calculate $\langle \Psi _{\mu }|\nabla |\Psi _{\nu }\rangle$ for different SCF states.

Q: Can the concept of diabaticity be applied to DFT? Can we calculate these adiabatic couplings in terms of densities?

September 2024 — [Conference on Molecular Electronic Structure (MES 2024)]

P: Finite-Temperature holomorphic Hartree--Fock and DFT

Aim: Investigate whether this may alleviate some of the challenges of solutions coalescing.

P: A Language for Electron Correlation

Aim: In order to use a generative AI language model to help tackle electron correlation, develop a language which is mostly transferable between different molecules (and certainly within the same molecule).

It should probably be based on localised orbitals in some way, but what is the best way of doing this? Can it be a simple type of decorator saying: correlate these orbitals? This might be a good fast starting guess for something at least.

L: Gradient Enhanced Kriging

Talk: Roland Lindh, "Variations on the use of subspace Gradient Enhance Kriging for SCF/DFT orbital optimization".

JCPA for orbital version.

L: Multistate DFT

Talk: Jiali Gao, "Multistate Density Functional Theory and Applications".

Some H matrix of densities.

Theophilou Subspace Theorem (1979).

Refs: JPCL 2022, 13, 7762. JCTC 2022 18 6407. JPCL 12 7409 '21. JCTC 4c00545. JCPL 4838 8 2017.

P: On-top Pair Density Functional for WF Theories

Aim: Apply to hNOCI.

Talk: Kasia Pernal, "On-top pair density functionals for wavefunction theories".

P: Automated construction of hHF states from dissociated atoms

P: Tetracene NOCI calculations

P: NOCI in a larger context — water clusters

P: PySurf for dynamics — with NOCI?

Talk: Shirin Faraji, "Databased accelerated on-the-fly hybrid quantum/classical dynamics".

P: NOCI + Piris Global Natural Orbital Functional

Talk: Mario Piris, "Recent Advances in Natural Orbital Functional Theory: Insights into Molecular Dynamics and Beyond".

P: CCMC + F12

Next: Generate the 3-e integrals from Libint? Use form like Ten-NO pTC2.

TODO: Code AFQMC