Matt Welborn in Tom Miller’s group in Caltech recently published a paper on improved subsystem selection in projector-based WF-in-DFT embedding. Congratulations Matt!

# Category Archives: Research

# How Markovian is exciton dynamics in purple bacteria?

Felix’s work on Markovianity in photosynthetic energy transport has been published: Felix Vaughan, N Linden and F R Manby, J. Chem. Phys. **146**, 124113 (2017); http://dx.doi.org/10.1063/1.4978568.

Modelling the interaction between excitons and the surrounding environment is a non-trivial problem. Many interesting insights about excitonic energy transfer have made use of a Markovian or “memoryless” approximation to this interaction. In this paper we assess the applicability of this approximation by employing a new metric of non-Markovianity.

We find that for smooth spectral densities the Markovian approximation works well provided that a precise change to the system Hamiltonian is made, which for the dimer system studied corresponds to an increase in the coupling strength between chromophores. We also find that discrete vibrational modes resonant with the eigenstates of the Hamiltonian induce the greatest degree of non-markovianity. Ultimately we conclude that to model exciton dynamics coupled to realistic spectral densities a Markovian approximation is not suitable.

# Delocalization errors in WF-in-DFT embedding are large, but fixable

Delocalization error in approximate DFT clearly manifests itself in homodimer cation systems (like H_{2}^{+} or (H_{2}O)_{2}^{+}), with GGA functionals typically leading to large energy errors and qualitatively incorrect structures. It also causes problems in a variety of other chemically important contexts.

We have found that the delocalization error in densities can cause major errors in WF-in-DFT embedding – these errors are not particular to the projector-based scheme we use,but simple expose a limitation of partitioning systems based on the electron density when that electron density is qualitatively flawed.

Following work from Kieron Burke, we have found the simple expedient of using Hartree-Fock densities in WF-in-DFT calculations really improves reliability in cases where there is a serious delocalization error, and doesn’t cause major problems (in the examples we have studied) when there is not a big delocalization error.

You can read about this work in a paper that has just appeared online: Pennifold *et al.*, ‘Correcting density-driven errors in projection-based embedding’, *J. Chem. Phys. ***146**, 084113 (2017);** **DOI: 10.1063/1.4974929.

# Pump-probe experiments on photosynthetic light-harvesting complexes are not easy to interpret

Clem’s paper on the interpretation of pump-probe experiments on the purple-bacteria light-harvesting complex LHII is now in print in J Phys Chem B.

Through careful and extensive calculations involving molecular dynamics, time-dependent density functional theory, and quantum dynamics we have shown that the interpretation of anisotropy decay rates in terms of strength of coupling to a dissipative bath is not so easily justified. The reason is that static (or inhomogeneous) disorder itself produces anisotropy decay at about the experimentally observed rate.

The paper also contains an epic, paper-length appendix on how to compute such quantities for the circularly degenerate oscillator model.

Congratulations Clem!

C. Stross, M. W. Van der Kamp, T. A. A. Oliver, J. N. Harvey, N. Linden and F. R. Manby, “How Static Disorder Mimics Decoherence in Anisotropy Pump–Probe Experiments on Purple-Bacteria Light Harvesting Complexes”, J. Phys. Chem. B, **120**, 11449-11463 (2016), DOI: 10.1021/acs.jpcb.6b09916

# Quantum Drude oscillators without the dipole approximation

Interactions between Drude oscillators (two opposite charges, one fixed, one mobile, interacting by a spring) are almost always modelled in the dipole approximation. This is because the Hamiltonian for describing Drude oscillators in this way is quadratic in the creation/annihilation operators (or equivalently, is quadratic in position and momentum) and can therefore be diagonalized exactly through a normal-mode transformation.

Second-order perturbation theory for the interaction of two such oscillators produces the expected –*C*_{6} *R*^{–6} dispersion interaction. At short distances this diverges, and the exact interaction energy ceases to be defined at all.

Therefore people use screening functions to fix up the short range. How much are the screening functions fixing up the divergence, and how much are they just compensating for the use of the dipole interaction Hamiltonian? Now we can find out, because Mainak has calculated the (almost) exact binding energy between Drude oscillators with the full Coulomb interaction.

Quantum mechanics of Drude oscillators with full Coulomb interaction

M. Sadhukhan and F. R. Manby, Phys. Rev. B **94**, 115106 (2016) 10.1103/PhysRevB.94.115106

# CCSD(T)-in-DFT for enzymology

Our paper *A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase *has appeared online in JCTC, and was one of the most highly downloaded papers soon after publication.

The great thing about this is that by tuning in CCSD(T) for just a handful of reacting atoms, almost all of the dependence on the approximate exchange-correlation functional is eliminated.

# Molpro 2015

The latest release of Molpro provides a range of new functionality, including methods developed in the Manby group

## Wavefunction-in-DFT embedding

A key new addition is wavefunction-in-DFT embedding through the projector method with basis-set truncation. This enables straightforward embedding of practically any electronic structure method implemented in Molpro in a chemical environment modelled by DFT. Unlike many embedding methods of this kind

there are no issues with partitioning across covalent bonds.

We have performed many calculations using the combination CCSD(T)-in-DFT, with the expensive coupled-cluster calculation only on a few, chemically active atoms. *The exciting opportunity here is that the method all but eliminates dependence on choice of exchange-correlation functional*.

The research behind this functionality was carried out by Martina Stella, Simon Bennie and Rob Pennifold in the Manby group; and by Jason Goodpaster and Taylor Barnes in Tom Miller’s group at Caltech.

## Distinguishable cluster theory

Distinguishable cluster theory with singles and doubles (DCSD) is a simple modification of CCSD, but with remarkable properties, including the ability to dissociate molecules correctly even with a closed-shell reference state.

The method was developed by Daniel Kats while he was a DFG-funded postdoc in the Manby group. There is much discussion about what exactly this approximation means (but see Daniel’s interesting paper about a screened Coulomb derivation). Whatever it turns out to mean, DCSD is already a useful tool and a powerful addition to the set of available methods. Now in Molpro running it is as simple as replacing `ccsd` with `dcsd` in the input (and the computational cost is the same as CCSD). Gradients as well as F12, orbital-optimized and Brueckner variants are available.