## Wednesday, August 27, 2014

### Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?

McKee, W. C.; Agarwal, J.; Schaefer, H. F.; Schleyer, P. v. R. Angew. Chem. Int. Ed. 2014, 53, 7875-7878
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Trying to get carbon to bond in unnatural ways seems to be a passion for many organic chemists! Schleyer has been interested in unusual carbon structures for decades and he and Schaefer now report a molecule with a pentacoordinate carbon bound to five other carbon atoms. Their proposed target is pentamethylmethane cation C(CH3)5+ 1.1 The optimized geometry of 1, which has C3h symmetry, at MP2/cc-pVTZ is shown in Figure 1. The bonds from the central carbon to the equatorial carbon are a rather long 1.612 Å, but the bonds to the axial carbon are even longer, namely 1.736 Å. Bader analysis shows five bond critical points, each connecting the central carbon to one of the methyl carbons. Wiberg bond index and MO analysis suggests that the central carbon is tetravalent, with a 2-electron-3-center bond involving the central and axial carbons.
 1 TS1 TS2
Figure 1. MP2/cc-pVTZ optimized geometries of 1 and dissociation transition states.

So while 1 is a local energy minimum, it sits in a very shallow well. One computed dissociation path, which passes through TS1 (Figure 1) on its way to 2-methyl-butyl cation and methane has a barrier of only 1.65 kcal mol-1 (CCSD(T)/CBS + ZPE). A second dissociation pathway goes through TS2 to t-butyl cation and ethane with a barrier of only 1.34 kcal mol-1. Worse still is that the free energy estimates suggest “spontaneous dissociation … through both pathways”.

Undoubtedly, this will not be the last word on trying to torture a poor carbon atom.

### References

(1) McKee, W. C.; Agarwal, J.; Schaefer, H. F.; Schleyer, P. v. R. "Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?," Angew. Chem. Int. Ed. 201453, 7875-7878, DOI: 10.1002/anie.201403314.

### InChIs

1: InChI=1S/C6H15/c1-6(2,3,4)5/h1-5H3/q+1
InChIKey=GGCBGJZCTGZYFV-UHFFFAOYSA-N

## Tuesday, August 12, 2014

### Torquoselective Ring Opening of Fused Cyclobutenamides: Evidence for a Cis,Trans-Cyclooctadienone Intermediate

Wang, X.-N.; Krenske, E. H.; Johnston, R. C.; Houk, K. N.; Hsung, R. P.  J. Am. Chem. Soc. 2014, 136, 9802-9805
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Houk’s theory of torquoselectivity is a great achievement of computational chemistry, as told in Chapter 4.6 of the second edition of my book. Houk, in a collaboration with Krenske and Hsung, now report on an application of torquoselectivity in the formation of a cis-trans-cyclooctadienone intermediate.1

The proposed reaction is shown in Scheme 1, where the bicyclic compound undergoes a conrotatory ring opening in just one orientation to form the E,E-cyclooctadienone, which can then ring close to product.

Scheme 1.

Houk ran M06-2x//6-311+G(d,p)//B3LYP/6-31G(d) computations on the model system 1, passing over the two torquodistinctive transition states TSEE and TSZZ, and on to produce the two cyclooctadienones2EE and 2ZZ, respectively. As seen in Figure 1, the barrier through TSEE is favored by 9.8 kcal mol-1, and leads to the much more favorable cycloocatadienone 2EE.
 10.0 TSEE32.3 2EE9.4 TSZZ42.1 2ZZ21.0 TS247.5
Figure 1. B3LYP/6-31G(d) optimized structures and relative free energies (kcal mol-1) at M06-2x//6-311+G(d,p)//B3LYP/6-31G(d).

Ring closure taking TSEE to product goes through TS2 (Figure 1), with a very high barrier, 47.5 kcal mol-1above reactant, suggesting that this path is not likely to occur. Instead, they propose that 2EE is first protonated (2EEH+) and then cyclizes through TS2H(Figure 2). This barrier is only 6.2 kcal mol-1, some 44 kcal mol-1 lower than the neutral process through TS2.
 2EEH+ TS2H+
Figure 2. B3LYP/6-31G(d) optimized structures

### References

(1) Wang, X.-N.; Krenske, E. H.; Johnston, R. C.; Houk, K. N.; Hsung, R. P. "Torquoselective Ring Opening of Fused Cyclobutenamides: Evidence for a Cis,Trans-Cyclooctadienone Intermediate," J. Am. Chem. Soc.2014136, 9802-9805, DOI: 10.1021/ja502252t.

## Sunday, August 10, 2014

### Ionic materials and van der Waals

Bučko, Tomáš, Sébastien Lebègue, Jürgen Hafner, and János G. Ángyán. "Improved density dependent correction for the description of London dispersion forces." Journal of Chemical Theory and Computation 9, (2013): 4293-4299.

Bučko, Tomáš, Sébastien Lebègue, János G. Ángyán, and Jürgen Hafner. "Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning." The Journal of Chemical Physics 141, (2014): 034114.

Contributed by David Bowler
Reposted from Atomistic Computer Simulations with permission

One of the areas which has grown explosively in DFT in recent years is modelling van der Waals interactions (I’ve written about this before). The semi-empirical approach originated by Tkatchenko and Scheffler[1] (normally known as TS) uses the calculated DFT charge density, which is divided between the atoms in the system to give an effective volume occupied by each atom; the ratio of this volume to a free atom volume is then used to rescale the C6 coefficients and polarisabilities found for free atoms. This brings us to an ever-present problem with ab initio methods: how to divide a continuous charge density or wavefunction between the atoms in the system.

TS use Hirshfeld partitioning[2], which creates a distance-dependent weight for each atom according to the ratio between the free atom charge density for the atom and the sum of free atom charge densities for the whole system. This can be used to give a volume and hence the relevant vdW quantities (see Eq. 7-9 in [1] for more detail). But this is not the only way to divide space (and hence charge density) between atoms: Voronoi polyhedra, Bader’s atoms-in-molecules[3], and Becke’s integral partitioning[4] are only some of the methods in common use, along with Mulliken charges as a way of assigning charge to atoms. We discuss these methods in Section 17.2 of the book, and show an example of how different methods and basis sets can change the charge by more than half an electron.

The papers I want to discuss in this blog[5,6] address another problem with the Hirshfeld approach: as it uses free, neutral atoms as the references to divide the charge density, it performs poorly for ionic materials. Instead, they use an update of Hirshfeld partitioning which iterates the charge density decomposition, and interpolates between reference densities of the free atoms in different charge states. It is a relatively small change to make to the process, but has a very strong effect on ionic materials, improving agreement with experiment and high-level theory markedly[5].

Whenever a change is made to an approach, it is important to characterise the effect on the existing performance; in an extensive follow-up paper, the authors do this[6], looking at an large collection of test systems. The main criticism that can be made of the new, iterative approach is that it worsens the modelling of molecular interactions (particularly those which have an obvious van der Waals component). However, the improvement of other systems, particularly ionic solids and molecules interacting with charges on surfaces, is sufficiently strong that this would be well worth using in most circumstances. The authors make the parameters they have used clear (k point meshes, plane wave cutoffs), and the approach is available in VASP (though I would have preferred to have seen it made freely available!).

[1] Phys. Rev. Lett. 102, 073005 (2009) DOI:10.1103/PhysRevLett.102.073005
[2] Theor. Chim. Acta 44, 129 (1977) DOI:10.1007/BF00549096
[3] R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press (1990).
[4] J. Chem. Phys., 88, 2547 (1988) DOI:10.1063/1.454033
[5] J. Chem. Theory Comput. 9, 4293 (2013) DOI:10.1021/ct400694h
[6] J. Chem. Phys. 141, 034114 (2014) DOI:10.1063/1.4890003

## Tuesday, August 5, 2014

### 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.

### A two-coordinate boron cation featuring C–B+–C bonding

Shoji, Y.; Tanaka, N.; Mikami, K.; Uchiyama, M.; Fukushima, T.  Nat. Chem. 2014, 6, 498-503
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

This paper is a bit afield from the usual material I cover but this is an interesting reaction. Shoji and coworkers have prepared the two-coordinate boron species 1,1 and confirmed its geometry by an x-ray crystal structure. What I find interesting is its reaction with CO2, which gives 2 and organoboranes that are not identified, though presumably derived from 3.

M06-2x/6-311+G(d,p) computations support a hypothetical mechanism whereby first a complex between1 and CO2 is formed (CP1), that is 4.4 kcal mol-1 above isolated reactants. Then passing through TS1, which is 4.2 kcal mol-1 above CP1, an intermediate is formed (INT), which is almost 6 kcal mol-1 below starting materials. A second transition state is then traversed (about 1 kcal mol-1 below starting materials), to form an exit complex between 2 and 3, which can then separate to the final products with an overall exothermicity of 10.6 kcal mol-1. The structures of these critical points are shown in Figure 1.
 1(0.0) CP1(4.4) TS1(8.6) INT(-5.7) TS2(-1.1) CP2(-9.0)
Figure 1. M06-2x/6-311+G(d,p) optimized structures. Relative energy in kcal mol-1.

### References

(1) Shoji, Y.; Tanaka, N.; Mikami, K.; Uchiyama, M.; Fukushima, T. "A two-coordinate boron cation featuring C–B+–C bonding," Nat. Chem. 20146, 498-503, DOI: 10.1038/nchem.1948.

### InChIs

1: InChI=1S/C18H22B/c1-11-7-13(3)17(14(4)8-11)19-18-15(5)9-12(2)10-16(18)6/h7-10H,1-6H3/q+1
InChIKey=WLUJABFTLHAEMI-UHFFFAOYSA-N
2: InChI=1S/C10H11O/c1-7-4-8(2)10(6-11)9(3)5-7/h4-5H,1-3H3/q+1
InChIKey=CUJVTHUIQVMVHD-UHFFFAOYSA-N
3: InChI=1S/C9H11BO/c1-6-4-7(2)9(10-11)8(3)5-6/h4-5H,1-3H3
InChIKey=ZJKBFARYTPYYGV-UHFFFAOYSA-N

## Tuesday, July 29, 2014

### Protein structure prediction from sequence variation

Debora S. Marks, Thomas A. Hopf and Chris Sander Nature Biotechnology 2012, 30, 1072
Contributed by +Jan Jensen

This perspective paper gives a great overview of a very new and very promising sub-field of computational protein structure determination that started with this 2011 paper (see also this interesting blogpost).  The method predicts distance restraints between two amino acids by looking for correlated changes in the protein sequence. These distance restraints are then used to determine 3D protein structures using the same software package used to compute NMR structures using NOE constraints.

The method has been tested on globular and membrane proteins up to 258 and 483 amino acids, respectively. About 0.5 to 0.75 predicted constraints per residue is needed and ca 5$L$ (where $L$ is the number of amino acids) diverse sequences are needed to produce reasonable protein structures with $C_\alpha$ RMSDs < 5 Å relative to the corresponding x-ray structures.

A $C_\alpha$ RMSD of 5 Å may sounds like a lot but active site geometries may be significantly more accurate due to "strong evolutionary constraints".  For example while the structure of trypsin was predicted with a $C_\alpha$ RMSD of 4.3 Å, the relative orientation of the catalytic triad was predicted with a $C_\alpha$ RMSD of only 0.6 Å (1.3 Å all atom-RMSD).

Furthermore, x-ray structures are often refined using, for example, MD simulations before they are used in computational studies. I would be very interesting to compare computational predictions (e.g. activation energies, pKa values of active site residues, or docking scores) based on x-ray structures and evolutionary constraints, i.e. to compare their chemical accuracy.

The number of available sequences is growing very quickly, so I believe the main general issue that must be addressed with this method is the efficient prediction of structures of globular proteins larger than ca 400 amino acids using distance restraints. This is still quite a demanding task.

The authors provide a very nice web-service for the prediction of contacts and structures, which I have used in my own research.

In conclusion, this method provides a very nice complement to homology modeling for cases where no close structural homologs, but many sequence homologues, are available. Given the pace with which new sequences are determined it won't be too many years before a reasonable protein structure can be predicted for the vast majority of cases.

## Friday, July 25, 2014

### Local hyperdynamics

Soo Young Kim, Danny Perez and Arthur F. Voter J. Chem. Phys. 139, 144110 (2013)
Contributed by David Bowler
Reposted from Atomistic Computer Simulations with permission

One of the key desires in atomistic simulations of all kinds, whether chemistry, biology, physics, materials science or earth sciences, is to be able to model accurately the long-time evolution of large systems. There have been good advances in recent years in linear scaling approaches to DFT and quantum chemistry[1], and significant progress in time acceleration (e.g. metadynamics[2] and hyperdynamics[3]).

The paper I will discuss here[4] points to a way to combine these two efforts, so that significant time acceleration can be applied to large systems. In combination with linear scaling electronic structure methods, this will allow us to achieve linear scaling in both size and time. The method, local hyperdynamics (LHD), is a development of the original hyperdynamics (HD) method, which is designed to increase the rate at which a system escapes from energy valleys. The idea behind HD is fairly simple, though elegant: a boost potential is added to the energy surface of the system being modelled so as to raise the bottom of the valleys in the system. This boost potential must go to zero if the system approaches a transition state; this requirement ensures that the rates of escape are not changed relative to each other, but leads to poor scaling with system size. As a larger system is modelled, it is more likely that a transition state will be found in some part of the system, and the boost becomes zero more and more of the time. The boosted time or hypertime can be evaluated during the simulation and related to the true system dynamics.

LHD defines local regions (centred normally on bonds) within which a local boost is applied. This allows the dynamics of the entire system to be boosted, and as the regions are independent, when one region goes through a transition, the other regions will not be affected. As the boost is only local, the dynamics are no longer conservative, though the authors make good arguments to suggest that, on average, using a Langevin thermostat, dynamics which are very close to conservative are followed.

The regions need to be large enough to encompass the characteristic length-scale of interactions and transitions being modelled, otherwise there will may be incorrect boosts from neighbouring domains. Once the system size is larger than the region size, the authors demonstrate that the boost factor achieved is constant with system size.

As each region has its own boost factor, some care has to be applied to ensure that boosting is uniform throughout the system. Given a target boost factor, the local boosting can be monitored and adjusted to ensure that it matches the target on average. The authors suggest that this time-evolving correction to the boost should be called a boostostat. There are careful, detailed statistical arguments which are worth careful reading in the paper.

The paper is also extremely careful in exploring the effects of the assumptions imposed. There will be force mismatches at the region edges, along with the lack of conservative dynamics. However, plausible arguments are made that these should average out for relatively uniform systems. A challenging system such as water, which contains both weak and strong bonds, might well show more significant deviation from these assumptions.

The authors tested the method with an embedded atom method (EAM) for Ag(100) with adatoms, vacancies and steps, and show excellent agreement with normal MD. For rare events, they show that boost of 10^6 are possible and give good agreement with transition state theory, though normally they work on boost factors around 100.

The Conquest developers (of which I am one) have recently performed full DFT molecular dynamics on 32,768 atoms for 2ps, and static calculations on over 1,000,000 atoms; in combination with LHD, we can see that DFT MD should be possible on 100,000+ atoms for nanoseconds and beyond.

[1] Rep. Prog. Phys. 75 036503 (2012) DOI:10.1088/0034-4885/75/3/036503
[2] Rep. Prog. Phys. 71, 126601 (2008) DOI:10.1088/0034-4885/71/12/126601
[3] Phys. Rev. Lett., 78, 3908(1997) DOI:10.1103/PhysRevLett.78.3908
[4] J. Chem. Phys., 139, 144110 (2013) DOI:10.1063/1.4824389