NF - mysteries of a small molecule

Nitrogen fluoride (NF) seems like a very simple molecule and you would think it would very well understood, particularly as it is small enough that it is accessible to high level quantum chemistry calculations. However, the molecule exhibits some subtle properties that present a theoretical challenge. There is limited experimental data because the molecule is only found as an intermediate in some chemical reactions.

Just like oxygen (O2), to which it is isoelectronic, the ground state is a triplet due to Hund's rule, as discussed for O2 here.

I just read a nice paper
A Valence Bond Study of the Low-Lying States of the NF Molecule 
Peifeng Su, Wei Wu, Sason Shaik, and Philippe C. Hiberty

Given that F is more electronegative than N one might expect the ground state to have a large electric dipole moment and this to increase as the molecule is stretched.
However, the ground state has only a small moment, it has the opposite direction to that expected from the electronegativity, and the direction changes sign when the bond is stretched.

Furthermore, unlike most molecules, the bond length is shorter and the dissociation energy larger in the low-lying excited states [which are singlets] than in the ground state.

The ground state has one sigma bond and six electrons in two pi orbitals.

The latter form three-electron bonds, which in the Valence Bond picture, involve exchange in position of an electron pair and an unpaired electron, where one goes from T1 above to the configurations shown below.

The authors consider 9 valence bond structures for the triplet ground state and 12 singlet VB structures for the two lowest singlet states. Their calculations lead to the following picture in terms of Lewis structures.

What insights are gained by the VB approach? Key is the idea of back donation or back bonding.

In a nutshell, the three lowest-lying states of NF can be considered as primarily bonded by a polar two-electron σ bond, complemented by π-bonding contributions of the three-electron bonding type for the ground state, and of the classical two-electron type for the excited states. In all three cases, the π-bonding contributions correspond to charge transfer from F to N, thus counterbalancing the σ polarization by back-donation. The tendencies of the bond lengths in the various electronic states comply with this simple model. Thus, all the computations and experimental measurements show that the bond length decreases consistently from the ³Σ⁻ state to ¹Δ, and from ¹Δ to ¹Σ⁺. This counterintuitive tendency, which implies that the more excited the molecule is, the more strongly it is bonded, is easily explained by the weights of the π-bonding Lewis structures, that sum up to 19 % in ³Σ⁻ state, to 28 % in the ¹Δ state, and to 37 % in the ¹Σ⁺ one (Figure 1 and Table 1 and Table 3). The same increase in the π-bonding contribution accounts again for the unusual fact that the bonding energy is far larger in the first excited state than in the ground state (96.4 vs 72.0 kcal mol⁻¹ at the VBCISD level). On the other hand, the bonding energy of the second excited state is now smaller than that of the first, as expected, since both excited states dissociate to the same products.

The tendencies in the dipole moment values of the various states are also readily rationalized by the simple VB model. The polar σ bond tends to tip the electron density towards the fluorine atom, and thus to favour negative values of the dipole moment (in the direction N⁺F⁻), while backdonation from the π systems has the opposite effect. The two effects compensate for each other in the ground state, where backdonation is moderate (19 % of π charge transfer). In the ¹Δ state, as the π charge transfer is increased relative to the ground state (28 % vs 19 %), backdonation wins over σ polarization, leading to a significant positive dipole moment, in the direction F⁺N⁻. The effect is further reinforced in the ¹Σ⁺ state, in which the π-charge transfer Lewis structure has such a large weight (37 %) that it completely overwhelms the σ polarization, ending up at a positive dipole moment of 0.728 D at the BOVB level.

I would like to see a basic description of these essential features in terms of a polarised two site Hubbard model with multiple orbitals and Hund's rule coupling, generalising the unpolarised two-orbital model here.

I got interested in this paper because of thinking about improper hydrogen (and halogen) bonds and wondering whether there is an "excited" diabatic state that has a shorter and stronger X-H bond than in the ground state. A general "ionic" (X^-H+) state will not have this property but if there is the option of back donation maybe something can happen....

Justifying pure science research: Discovery

How do you convince politicians to fund basic research?

On The West Wing there is an episode Dead Irish Writers in which many things are happening simultaneously. One is that Sam Seaborn [White House Deputy Communications Director] is meeting with a Princeton Physics Professor, Dr. Millgate who is dying of cancer but trying to secure funding for the Superconducting Super Collider. It features the following excellent dialogue.

Sam Seaborn: Okay. I said I'd do this, but it's likely he's gonna say this is an unaffordable luxury. 

Millgate: We're losing the race for discovery, Sam. For discovery. Tonight, it's just me and you. 

Sam Seaborn: That doesn't really sound like enough. 

Millgate: No.

Then in a later scene

Senator Enlow: If only we could only say what benefit this thing has, but no one's been able to do that. 

Dr. Millgate: That's because great achievement has no road map. The X-ray's pretty good. So is penicillin. Neither were discovered with a practical objective in mind. I mean, when the electron was discovered in 1897, it was useless. And now, we have an entire world run by electronics. Haydn and Mozart never studied the classics. They couldn't. They invented them. 

Sam Seaborn: Discovery. 

Dr. Millgate: What? 

Sam Seaborn: That's the thing that you were... Discovery is what. That's what this is used for. It's for discovery.

Is this why in Australia the main source of research grants for people like me are "Discovery Grants"?

John Nash (1928 - 2015): a founder of game theory

John Nash and his wife, Alicia, tragically died in a car crash on the weekend. There is a New York Times obituary He was a brilliant young pure mathematician who laid foundations for game theory in a 27 page Ph.D thesis. Nash became widely known outside academia through the movie A Beautiful Mind, that tells his life story, focusing on his struggle with severe mental illness. It is based on an excellent biography by Sylvia Nasar. It is less sanitised than the Hollywood version.

Tragically Nash's life also illustrates the importance of mental health issues in academia, and so I mention him in talks I give about mental health for scientists.

I have a strange personal connection with Nash. When I was a graduate student at Princeton I often saw a middle aged man reading Scientific American in the Maths/Physics library. He was often there and I wondered why he was there. Didn't he have a job? Yet I don't remember ever asking anyone about him. Also, sometimes in the Physics building there were strange scribblings all over the chalk boards.

One day in 1994 I got a shock when I received a copy of The Princeton Alumni Weekly. There on the cover was a photo of the man I often saw in the library with the headline "John Nash wins Nobel Prize in Economics". Finally I found out who he was and learnt his story.

Advice for undergrads giving research talks

At UQ all physics honours students (4th year undergrad) have to give two 15 minute talks about their year long research project. The first is a progress report at the end of the first semester and the second at the end of the project. No grades are given for these presentations but they are attended by the 3 thesis examiners [supervisor, expert, and non-expert] and so may influence the grade for the thesis.

I think these presentations are very challenging for the students and I am sometimes impressed at the quality of the talks. This is a great opportunity for students to develop and improve their communication skills. When I was an undergrad we never had opportunities like this. Most of us also had very little public speaking experience. Students today are quite different and much more confident and polished.

Here is my advice to students.

First, review general material on giving scientific talks such as Garland's Advice to Beginning Physics Speakers or Wilkins' one page or Geroch's suggestions or Mermin's. Don't think you know better than these old timers.

Second, decide on your audience [your friends, other students, faculty, your research group, the examiners?]. I hate to say it but the examiners is the correct answer.
Taylor the talk accordingly.

Third, decide on your real goal [impress others, show how much work you have done, show off how much jargon you have learnt, be entertaining, talk about how great your research field is, make excuses for your lack of results....?].
Taylor the talk accordingly.

The goals of the progress seminar are simple.
Show you have a well defined and realistic project.
Show you have a clear plan.
Show you have started to make some progress.

The goal of the final seminar is simple.
Show you have achieved something concrete and worthwhile.
Anything else is subsidiary.

Be realistic about how much you can achieve in 15 minutes.
Some background is crucial but don't let it dominate your talk.
Don't spend more than a minute about why the research field is important and interesting.
Don't spend more than a minute on the history of the field.
Don't think you can explain how Shor's algorithm works, the subtleties of the quantum measurement problem, or the microscopic basis for Landau's Fermi liquid theory, ...
Most of the talk should be about what you have done and why it is significant.
Yet, if you can teach people one small thing they will be very appreciative.

Clearly distinguish between the contributions of founders of the field, those of your supervisor, and yourself.
Include relevant references on your slides.

Avoid irritants: being late, having problems with the technology, small fonts, endless jargon, hype, lavish Powerpoint animations, .....

Practise. Practise. Practise.
Consider writing out explicitly what you are going to say.

Start preparations early. Get feedback.

How you answer the questions is important.
Listen carefully. Don't cut off the questioner.
Don't bluff an answer. Saying you don't know is o.k.

Relax. The audience knows that this is a stressful experience, particularly for the inexperienced, and does not expect a perfect talk.

A unified picture of weak chemical bonds: hydrogen, halogen, carbon...

Previously I posted about improper hydrogen bonds. These are weak hydrogen bonds that have the unusual property that in the X-H...Y system H-bonding leads to a shortening and hardening (blue shift) of the X-H bond. In contrast, for "proper" bonds, X-H lengthens and softens (red shift).

The past few years has seen a rapid increase in interest in an even broader class of weak bonds such as "halogen bonds",  denoted X-Z...Y where Z can now be not just H but a halogen (F, Cl, Br), chalcogen (O, S, Se, Te), or pnictogen (N, P, As, ..)....

There is an interesting paper that contains the helpful summary figure below
Negative hyperconjugation and red-, blue or zero-shift in X-Z---Y complexes
Jyothish Joy, Eluvathingal D. Jemmis and Kaipanchery Vidya

In trying to understand the paper I found reading the following older paper helpful
Electronic Basis of Improper Hydrogen Bonding:  A Subtle Balance of Hyperconjugation and Rehybridization
Igor V. Alabugin, Mariappan Manoharan, Scott Peabody, and Frank Weinhold

[Aside: note the senior author is Weinhold who has featured in some previous posts]

The basic idea is that there are two competing interactions. "Hyperconjugation" is Weinhold's view of proper H-bonds, via the Natural Bond Orbital donor-acceptor picture where the H-bond arises due to charge transfer from the lone pair orbital on Y to the σ* (anti-bonding) orbital associated with X-H. This lengthens and hardens X-H.
When this interaction is weak there is “X-H bond shortening” due to increase in the s-character (rehybridisation of the atomic orbital on X) and polarization of the X−H bond. This is associated with a shorter and harder X-H bond.

Bent's rule is central. It is one of the most general rules governing structure of organic molecules.

atoms tend to maximize the amount of s-character in hybrid orbitals aimed toward electropositive substituents and direct hybrid orbitals with the larger amount of p-character toward more electronegative substituents.

Increasing s-character generally leads to shorter bonds.
As the donor acceptor distance (X-Y) decreases the X-Z bond becomes more polarised and the s-character increases.
The authors note it should be possible to test predicted trends since the amount of s character in the X-Z bond can be measured from the relevant NMR coupling constant.

My question is whether this subtle competition can be captured by generalising my simple 2 diabatic state model for H-bonds to a 3 state model that includes the ionic character of the X-Z bond.

Measuring the viscosity of the electron fluid in a metal

Previously I posted about the theoretical issue of the viscosity of the electron fluid in strongly correlated metals. This interest is partly motivated by claims from string theory techniques [AdS-CFT] that there is a universal lower bound for the viscosity.  A recent experimental paper estimated the viscosity in the cuprates by an indirect method from ARPES data.

I only became aware recently that there is a somewhat direct way to measure the viscosity of the electron fluid in a metallic crystal. This has a long history going back to Mason and Pippard who in 1955 related the viscosity to the attenuation of sound. A more sophisticated and general theory was developed by Kahn and Allen.

The connection between shear viscosity and ultrasound attenuation can be loosely motivated as follows. In a viscous fluid the attenuation of a shear wave is given by Stokes law

where  is the shear viscosity of the fluid,  is the sound's frequency,  is the fluid density, and  is the speed of sound in the medium.

This equation has been used to determine the shear viscosity as a function of temperature for helium three [a correlated neutral fermion fluid]. Extensive experimental data is reviewed here.

In a metal, provided the wavelength of sound is much larger than the electronic mean free path, then one is in the hydrodynamic limit, and the attenuation is given by a similar expression to that above (with appropriate indices for crystal axes), with  the solid density (not the electron fluid).

One can show from the Boltzmann equation that in a simple free electron model that the electronic viscosity is proportional to the scattering time, just like the conductivity. Hence, the ultrasound attenuation should scale with the conductivity.

Indirect evidence for this idea is from the data below that shows the temperature dependence of ultrasound attenuation of aluminium (taken from here).

In clean metals, such as for the data shown above, the attenuation [and viscosity] becomes very large at low temperatures, making it easier to measure.
Also, for high frequency ultrasound, one can reach the "quantum regime" where the mean free path becomes comparable to the sound wavelength. Pippard worked out a general theory describing the crossover from the hydrodynamic regime to this quantum regime.

In bad metals could one experimentally see the small viscosity, of the order of n hbar [where n is the density]? First, the small mean free path, characteristic of bad metals, means one will always be in the hydrodynamic regime. However, the small viscosity means that the sound attenuation due to the electron fluid will be small and possibly dominated by other sources of attenuation such as crystal dislocations. A rough estimate for an electron viscosity of order of n hbar and a sound frequency of 1 GHz gives an attenuation of less than 0.1 cm-1, of the order of typical sensitivity, such as in these measurements for heavy fermion compounds.

What is real scientific integrity?

According to the Oxford English Dictionary Integrity = "The quality of being honest and having strong moral principles".

When people talk about scientific integrity and misconduct they mostly have a narrow definition which means "don't make up data."

However, I think we need to consider a broader definition of integrity that relates to all communications and messages.

Scientists talk about their research in a wide range of forums:

• private discussions
• articles in luxury journals
• articles in professional society journals (PRA, JCP etc)
• grant applications and job applications
• seminars at universities and conference presentations
• press releases and interviews
• public lectures and popular books

Yet it seems it has now become quite acceptable to have different messages (claims and conclusions) in different forums. This post was stimulated by a perceptive comment by Steve W on a previous post.

My finding is if you talk to the authors of luxury papers with controversial or sexy explanations, that they will be the first to admit their own skepticism regarding their explanations of the data. But somehow this skepticism is not conferred to the text, because the luxury journals like clear, concise, authoritative explanations. Most of the details get hashed out later in less prominent, but longer form journals, and these are only followed closely by those within the specific community. 

For a concrete example see a recent post by Peter Woit about the basic question, "Is string theory experimentally testable?" He highlights a significant inconsistency between the answers in a preprint, the published version in PRL, a press release, and a public talk by Amanda Peet.