A search of the protein databank (PDB) as http://www.rcsb.org/pdb/search/advSearch.do?search=new reveals 39 systems described by the term trefoil!

]]>This collection DOI: 10.14469/hpc/1053 summarises our implementation of the Mpublish project. It includes an article recently published which goes into a little more detail about the implementation.

]]>Here is another take on playing with *variational* methods (DFT methods cannot be included in this game):

The total variational energies are obtained at the Def2-TZVPP basis set level:

1. CASSCF(2,5) -1.0440685

2. CASSCF(2,8) -1.0441268

3. CCSD(T) -1.0469931

4. CASSCF(2,5)/MP2 = -1.053945 Hartree.

The last of these, which includes both static and perturbational dynamic correlation energies, is clearly the lowest variationally. One more method, the *multireference coupled cluster* procedure, should give an even lower energy. I don’t have access to such code, but if anyone does, can they report that energy?

An alternate way of calculating frequencies is by numerical differentiation and numerical second derivatives, which uses (in part) different code. Using this procedure one gets:

CASSCF(2,5)/Def2-TZVPP (DOI: 10.14469/hpc/2208) ν -307*i*, 1446, 1818 cm-1

CASSCF(2,8)/Def2-TZVPP (DOI: 10.14469/hpc/2208) ν -306*i*, 1446, 1818 cm-1

This compares with -320i, 1460, 1835 cm-1 obtained at the CCSD(T) level and same basis set. The initial conclusion is that the numerical set of results is more consistent with other methods than the analytical. The analytical frequency code is currently being inspected to try to identify the reason for the discrepancy.

There are in fact other anomalies. In any method which calculates the total energy of a system, one basic requirement is *rotational invariance*, which means that the energy must be identical no matter how the system is oriented for the calculation. One way of checking this invariance is to inspect the values of the six normal modes that represent the translations and rotations in a 3N second derivative matrix. For the numerical derivatives, these emerge as -32.6872 -32.5605 -32.3707 0.1435 0.2795 0.8246 cm-1, which is acceptable for this procedure. For the analytical version these are -0.0002 -0.0002 0.0002 515.2515 518.6620 518.8967 cm-1, with the last three clearly not being close to zero.

The various Hamiltonians do seem to be converging to the conclusion that this species is not a minimum, but a three-fold degenerate transition state for extrusion of H_{2} and two protons.

Yet another Hamiltonian method, the CASSCF (complete active space self-consistent-field) procedure, which variationally optimises all the Slater determinants built from an active orbital space. The previous CCSD and DFT methods were based on just a single variational determinant.

CASSCF(2,5)/Def2-TZVPP (DOI: 10.14469/hpc/2203) ν ~+750, 1472, 1870 cm^{-1}

CASSCF(2,8)/Def2-TZVPP (DOI: 10.14469/hpc/2205) ν ~+600, 1437, 1806 cm^{-1}

This latter constructs 36 determinants based on 2 electrons and an active orbital space of 8, including 7 unoccupied orbitals. This recovers much of the so-called static correlation energy, but less of the dynamic version recovered by e.g. MP2 and CCSD methods. I will investigate these aspects next.

]]>Here is a recollection of the *ChemSoc Dinner*. In 1968, university dinners were on their way out; I think only the physics and chemistry departments held them for what was then called “freshers” (first year students). The arrangement was that each first year was paired as the guest of a second year student. Dinner was at a wooden table arranged in a large square, seating perhaps 120 people, with each fresher flanked by two second years.

The food itself itself was unmemorable; the only part I recollect was the final toasts. The most important of these was offered by the *ChemSoc President*, who was probably a final year student. The ceremony consisted of a large cup brought in, containing several litres of beer. It was passed around the table, and each student was invited to take a gulp of the contents before passing it on to the next person. Of course as a fresher, one consulted the 2nd year sitting next to you for advice. They, very conspiratorially, would tell you to pretend to take a sip. They had heard that tradition was that prior to the cup being brought into the hall, the ChemSoc president would take the opportunity to urinate into it first. So, as the cup was passed around, the first few freshers would take a large gulp of liquid, but as the message spread, the gulps seemed to become more and more hesitant, accompanied by many titters from the second year students. Just before it reached the president, no-one seemed to be drinking! He (it tended to be a he in those days, only about 10% of freshers were female) finally received the flagon and of course proceed to take a vast refreshing drink of the contents as their reward. Invariably all the freshers wondered what on earth was going on.

To which I might add that the dinner was probably followed by a visit to the student union bar. This had an impressive large yard of ale displayed behind the bar. Freshers were not allowed to drink from it; one might normally try by about one’s final year. It contains 1.4 litres of beer when filled, which has to be drunk in a single long gulp. Usually, only a proportion of the beer actually enters the mouth.

Yes, if you are wondering that much student social life centred around alcohol, you are probably not wrong. Perhaps this was unique to the chemists? There are many other alcohol related stories that could be told, but I am not sure it would be wise to do so!

]]>One more basis: ωB97XD/aug-cc-pv6z (a 6-ζ level, DOI: 10.14469/hpc/2188) has ν 97, 1465 and 1780. So the CBS limit using this functional it probably is a real minimum.

I would add this is probably the largest basis set I have ever used in anger! I am also intrigued that the CBS limit is so difficult to reach!

]]>1. Def2-TZVPP (DOI: 10.14469/hpc/2181 ), ν +303, 1462, 1784.

2. Def2-QZVPP (DOI: 10.14469/hpc/2182), ν +173, 1466, 1779.

So probably at the CBS (complete basis set) limit, its probably a true minimum, but still worth testing!

But what about the Hamiltonian? The definitive test is CCSD(T).

3. CCSD(T)/Def2-TZVPP (DOI: 10.14469/hpc/2183), ν ~ -320*i*, 1460, 1835

4. CCSD(T)/Def2-QZVPP (DOI: 10.14469/hpc/2186), ν -325*i*, 1459, 1822.

So it seems its not the basis set but the Hamiltonian method that is sensitive. Such a big difference is a bit of a surprise; you would think that with just two electrons, a standard DFT method should not disagree so much with a coupled cluster method?

My purpose anyway was to explore unusual topologies in electron densities, and less to probe whether H_{4}^{2+} was a minimum or not.

http://onlinelibrary.wiley.com/doi/10.1002/jcc.540140305/full

(Popular basis sets using the standard p exponent suggest (erroneously) that the Td geometry is a minimum) ]]>

M.N. Glukhovtsev, P.v.R. Schleyer, K. Lammertsma, “Can the H2+4 dication exist?” Chem. Phys. Lett., 1993, 209, 207-210. DOI: 10.1016/0009-2614(93)80094-6

(Answer: No) ]]>

To complete the series, here is IF_{3}. This brings however a new variable, which is the now more significant contribution from relativistic core electrons on iodine.

The below is the non-relativistic solution (DOI: 10.14469/hpc/2161), derived from a full-electron basis set for I (6-311G(d,p) as obtained from https://bse.pnl.gov/bse/portal).

Basins 8 and 9 have 2.21e each and subtend an angle of 168° at the central iodine. The other difference is that basins 10 and 15 for BrF_{3} (the anomeric anti-periplanar effect to one Br-F bond) are not apparent for IF_{3}.

A wavefunction where the all-electron basis set is replaced by one with a effective-core for the relativistic component (thus the relativistic contraction is absorbed into this calculation, Def2-TZVPP, DOI: 10.14469/hpc/2162) gives the 8/9 basin populations as 2.36e, which is more consistent with the trend Cl => Br => I and an angle subtended at I of 153°.

]]>Just a note that the AIMALL program locates 767 critical points, 152 more than multiFN.

]]>1. All nuclear positions

2. All nuclear mid points

3. All centroids from three nuclei

4. All pyramid centres from four nuclei.

Using just 1 gives 60 critical points of type (3,-3), which are the Na and He nuclei. Using 1-4 gives 615 critical points of which 76 are type (3,-3). The additional 16 are the non-nuclear attractors, shown in white below. These correspond to the ELF basins in the diagram above. I would add however that the Poincare-Hopf relationship is NOT satisfied, which is another indication that the boundaries of this non-periodic model have artefacts.

(3,-3): 76, (3,-1): 290, (3,+1): 185, (3,+3): 64

Poincare-Hopf relationship verification: 76 – 290 + 185 – 64 = -93

A quick comment about the speed of the program. MultiWFN finds all the critical points in about 3 minutes on an 8-processor computer.

]]>Shant: I thought I might answer your question about email in a roundabout sort of way. You might notice my ORCID identifier is appended to all posts and comments (although this latter is not 100% reliable). With the ORCID, you should be able to get my email. Unfortunately when I checked, I noticed that the default privacy setting for this property was (unintentionally) private. It is now public, and so you can now get it there!

Oh, in responding to a comment in WordPress, you have to provide your own email. This is private by default, but the WordPress blog goes off and checks if there is an ORCID account associated with that address. If there is, it (mostly) adds the ORCID at the start of the comment. So perhaps if, before posting your next comment, you register an ORCID for yourself, it should appear here.

I also appreciate that providing one’s genuine identity to social media used to be considered bad form. But that seems to be changing, and now it is more common to appear using one’s real identity (or one of them). With a world where *alternate facts* seems in some circles to be acceptable, I feel in science we should only deal with one set of facts (with of course multiple interpretations always possible), and those facts should ideally include one’s identity.