Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale

Mikael Scott, Gabriel L. S. Rodrigues, Xin Li, and Mickael G. Delcey (2024)
Highlighted by Jan Jensen

As I've said before, one of the big problems in quantum chemistry is that we still can't routinely predict the reactivity of TM-containing compounds with the same degree of accuracy as we can for organic molecules. This paper might offer a solution by combining CASSCF with DFT in a variational way.

While such a combination has been done before, that implementation basically compute the DFT energy based on the CASSCF density. If you haven't heard of this approach, it's probably because it didn't work very well. 

This paper presents a variational implementation, where you minimise the energy if a CASSCF wavefunction subject to an exchange-correlation density functional, an the results are significantly better - in some cases approaching chemical accuracy! This is pretty impressive given that they used off-the-shelf GGA functionals (BLYP and PBE) so further improvements in accuracy with bespoke functionals is quite likely.

Oh, and one of the applications presented in the paper is multiconfigurational calculation on an entire metallo-protein!

This work is licensed under a Creative Commons Attribution 4.0 International License.

Ultrafast X-ray Auger probing of photoexcited molecular dynamics

McFarland, B. K.; Farrell, J. P.; Miyabe, S.; Tarantelli, F.; Aguilar, A.; Berrah, N.; Bostedt, C.; Bozek, J. D.; Bucksbaum, P. H.; Castagna, J. C.; Coffee, R. N.; Cryan, J. P.; Fang, L.; Feifel, R.; Gaffney, K. J.; Glownia, J. M.; Martinez, T. J.; Mucke, M.; Murphy, B.; Natan, A.; Osipov, T.; Petrović, V. S.; Schorb, S.; Schultz, T.; Spector, L. S.; Swiggers, M.; Tenney, I.; Wang, S.; White, J. L.; White, W.; Gühr, M. Nat Commun 2014, 5, doi:10.1038/ncomms5235.
Highlighted by Mario Barbatti

The deconvolution of nuclear and electronic ultrafast motions poses a great challenge for spectroscopic approaches and nonadiabatic dynamics simulations has been a valuable tool to help with this task.

But are dynamics simulations providing reliable information?

Take, for instance, thymine. The ultrafast dynamics of this molecule has been under debate for a decade. 

Thymine has the longest excited-state lifetime among the five canonical nucleobases in the gas phase. According to Ref. (1), after 267-nm excitation, thymine shows a double-exponential deactivation with 105-fs and 5.12-ps time constants. 

The long time constant, which has been assigned to the excited-state lifetime of thymine, was attributed at first to a trapping of the population in the S₁ (nπ*) state after a quick relaxation from the initially excited S₂ (ππ*) state (2) (see Fig. 1). 

As a second possibility, an independent study proposed that the deactivation occurred solely on the ππ* state, without any major influence of the nπ* state (3). In this case, the trapping site would be located at another region of the S₁ surface at a minimum with ππ* character. 

Either way, from one of those S₁ minima, thymine would take a few picoseconds to find the seam of conical intersections to the ground state, explaining its longer lifetime. 

Fig. 1 - After photoexcitation, how does thymine returns to the ground state?

This interpretation has been disputed since different sets of dynamics simulations at CASSCF level predicted that the S₂ (ππ*) → S₁ (nπ*) relaxation time itself occurs on a few picoseconds (4,5). Hence both, elongated S₂ (ππ*) → S₁ (nπ*) relaxation and then S₁ (nπ*) trapping, would contribute to the long time constant.

This entangled story has gained another chapter with a curious twist (6): based on ultrafast X-ray Auger probe spectroscopy and simulations (ADC(2), CK-CIS), McFarland and co-authors found strong evidences that thymine excitation at 266 nm should populate the S₁ (nπ*) state within only 200 fs, just like in the first proposal.

It makes possible that the S₂ (ππ*) trapping was, after all, an artifact of dynamics simulations limited to CASSCF surfaces.

References

(1) Canuel, C.; Mons, M.; Piuzzi, F.; Tardivel, B.; Dimicoli, I.; Elhanine, M. J. Chem. Phys. 2005, 122, 074316-074316. doi:10.1063/1.1850469
(2) Perun, S.; Sobolewski, A. L.; Domcke, W. J. Phys. Chem. A 2006, 110, 13238-13244. doi:10.1021/jp0633897
(3) Merchán, M.; González-Luque, R.; Climent, T.; Serrano-Andrés, L.; Rodriuguez, E.; Reguero, M.; Pelaez, D. J. Phys. Chem. B 2006, 110, 26471-26476. doi:10.1021/jp066874a
(4) Hudock, H. R.; Levine, B. G.; Thompson, A. L.; Satzger, H.; Townsend, D.; Gador, N.; Ullrich, S.; Stolow, A.; Martínez, T. J. J. Phys. Chem. A 2007, 111, 8500-8508. doi:10.1021/jp0723665
(5) Szymczak, J. J.; Barbatti, M.; Soo Hoo, J. T.; Adkins, J. A.; Windus, T. L.; Nachtigallová, D.; Lischka, H. J. Phys. Chem. A 2009, 113, 12686-12693.doi:10.1021/jp905085x
(6) McFarland, B. K.; Farrell, J. P.; Miyabe, S.; Tarantelli, F.; Aguilar, A.; Berrah, N.; Bostedt, C.; Bozek, J. D.; Bucksbaum, P. H.; Castagna, J. C.; Coffee, R. N.; Cryan, J. P.; Fang, L.; Feifel, R.; Gaffney, K. J.; Glownia, J. M.; Martinez, T. J.; Mucke, M.; Murphy, B.; Natan, A.; Osipov, T.; Petrović, V. S.; Schorb, S.; Schultz, T.; Spector, L. S.; Swiggers, M.; Tenney, I.; Wang, S.; White, J. L.; White, W.; Gühr, M. Nat Commun 2014, 5, doi:10.1038/ncomms5235.

Tunneling in the Bergman Cyclization

Greer, E. M.; Cosgriff, C. V.; Doubleday, C. J. Am. Chem. Soc. DOI: 10.1021/ja402445a

Contributed by Dean Tantillo

Edyta Greer and Christopher Cosgriff, in collaboration with Chuck Doubleday, have reported a quantum chemical study of the Bergman reaction of cyclodec-3-en-1,5-diyne (below). Using DFT and CASSCF calculations, they found evidence for a large contribution from heavy atom tunneling to the rate of this reaction even above room temperature.  

The performance of several levels of theory was examined, including a modified BLYP functional (mBLYP) and CCSD(T) on CASSCF geometries; the mBLYP/CASSCF method performed best.  Multidimensional tunneling effects were treated using the small curvature tunneling (SCT) approach in POLYRATE.  

It was predicted that at 200K, 60% of the rate is due to tunneling.  Moreover, the bulk of the tunneling was predicted to originate from energy levels within 2.3 kcal/mol of the transition state.  At temperatures between 310-350K a smaller energy range is predicted (~1.5 kcal/mol), which corresponds to only small changes in the length of the forming C-C bond (<0.2 Å) from its value at the transition state (this energy range is also smaller for wider barriers).  At these temperatures, rate enhancements of >30% due to tunneling were predicted.  

Experimentally testable predictions of the 12-C/13-C kinetic isotope effect at various temperatures were also made. This work not only puts some meat on the bones of various concepts associated with heavy atom tunneling, it also issues a challenge to experimentalists.

Accurate ab Initio Spin Densities

Katharina Boguslawski, Konrad H. Marti, Örs Legeza and Markus Reiher Journal of Chemical Theory and Computation 2012, 8, 1970 (Paywall)

The spin density problem
Obtaining accurate spin density distributions and predicting the correct ground state from a number of close lying states of different spin is a challenging problem in quantum chemistry, particularly when transition metal systems are considered. This paper highlights how density-matrix renomarlization group¹ (DMRG) based methods can be used to calculate spin density distributions for molecules that are too large to be treated by complete-active-space self-consistent-field (CASSCF) methods. What I found particularly exciting is the prospect of using DMRG results in the benchmarking and development of new density functionals.

Benchmarking DMRG
The electronic structure of a simple model system of iron nitrosyl is manipulated by surrounding it with point-charges (simulating ligands), adjusting the position of these charges means the system becomes either single- or multi-reference. The results convincingly show how DMRG can converge to a CASSCF(7,7) reference spin density by controlling the number of reference active-system states in the DMRG. The DMRG calculations were carried out using the Reiher group's Qc-Dmrg-ETH code.

Spin densities for large active spaces and comparison to DFT
A problem arrises in CASSCF when the number of active electrons and orbitals required to correctly describe the system becomes too large (this article suggests 18 electrons in 18 orbitals as a practical limit). The paper goes on to show that much larger active spaces are possible with DMRG and, more importantly, that the spin density converges very quickly both with respect to active space and the number of active-system states. The resulting spin densities are then compared to a number of common density functionals, none of which accurately reproduces the DMRG result. Whilst DMRG calculations are not yet commonplace in the computational chemistry community, this paper convinces me that they will have an important role to play in solving the spin density problem.

References
(1) For an introduction to DMRG see: Chan, G. K.-L.; Dorando, J. J.; Ghosh, D.; Hachmann. J.; Neuscamman, E.; Wang, H.;Yanai, T. An Introduction to the Density Matrix Renormalization Group Ansatz in Quantum Chemistry. In Frontiers in Quantum Systems in Chemistry and Physics, 1st ed.; Wilson, S., Grout, P. J.; Maruani, J., Delgado-Barrio, G., Piecuch, P., Eds.; Springer: Dordrecht, The Netherlands, 2008; Vol. 18, pp 49-65. arXiv:0711.1398v1.