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November 6

why is the bond order of water 1.5 for each O-H interaction??

In the MO treatment of water, there are 3 bonding interactions and one non-bonding interaction for a total average bond order of 1.5, 8 electrons in 4 filled orbitals and 2 empty orbitals. While tutoring organic chemistry this evening I could not adequately explain this discrepancy between MO theory and VB theory except to observe that water has a bond-length of 960 pm whereas methane is 1096 pm. I am familiar with MO treatment of pi systems. Usually 1.5 bond orders can be thought of arising from alternate resonance structures or donating into orbitals that are antibonding for one bond pair but bonding for a different pair. Where is this resonance structure for water though? There is no resonance structure where there is a double bond between O and H?? Yanping Nora Soong (talk) 00:57, 6 November 2017 (UTC)[reply]

Well, to get the ball rolling I found the top hit for water molecular orbital at [1], which says "The five occupied and the lowest three unoccupied molecular orbitals of the isolated molecule (1a1)2(2a1)2(1b2)2(3a1)2(1b1)2 were calculated using the Restricted Hartree-Fock wave function (RHF) using the 6-31G** basis set." This is based on data from [2]. I should admit that I know so little about electron momentum spectrometry and Hartree-Fock theory that I haven't even gone hunting for this on Sci-Hub, at least not yet. I am rather surprised by the way that the molecular orbitals as drawn at the first source seem almost oblivious to the hydrogens except as landmarks of orientation; the antibonding orbitals seem to respect them yet are drawn with nodes near the hydrogen nuclei... Wnt (talk) 04:01, 6 November 2017 (UTC)[reply]

Could you (Yanping Nora Soong) state what your MOs actually are? Specifically, what are the filled three bonding ones, and especially the filled non-bonding one (what atomic contributors to each)? We have a Chemical bonding of H2O article that discusses various approaches. DMacks (talk) 05:26, 6 November 2017 (UTC)[reply]

Page 148 of Inorganic Chemistry by Miessler and Tarr has an MO diagram of water which shows the oxygen 2s orbital unhybridized and the three oxygen 2p orbitals split into three different energy levels, the lower two of which hybridize with the hydrogen 1s orbital and are bonding. Both the 2s orbital (lowest energy) and the highest energy 3p orbital are shown as non-bonding, and only associated with the oxygen atom (i.e. the lone pairs). So according to this diagram, it's two bonding orbitals and two non-bonding orbitals.--Wikimedes (talk) 05:47, 6 November 2017 (UTC)[reply]

I think Yanping is refering to the hybridised MO solution as depicted in Molecular orbital diagram#Water and Chemical bonding of H2O#Molecular orbital treatment of H2O. In the hybridised MO solution, there are three filled bonding MOs (2a₁, ~~1b₁~~1b₂, 3a₁), and one filled non-bonding MO (~~1b₂~~1b₁), resulting in the average O-H bond order of 1.5. In the simple MO solution (also depicted in the latter link), the third MO is considered to be non-bonding reducing the bond order to the conventional integer, 1. Treatment of a molecule according to VB theory correlates more with the simple MO solutions. In other words, while water technically has an average O-H bond order of 1.5, VB is black-and-white and simplifies this understanding to eliminate the bonding or anti-bonding interactions which may be considered weak or borderline. According to the MO solution for water, the oxygen atom only has one lone pair of electrons, the second pair is very weakly delocalised over the molecule, residing mostly on the oxygen. Plasmic Physics (talk) 10:07, 6 November 2017 (UTC)[reply]

You see, an MO diagram is very subjective, it is the direct result of how an individual scientist chooses to interpret the solution generated by the MO model they implemented. When you want to put things in nice little boxes of bonding, anti-bonding, and non-bonding, you have to select the contrast so to speak. The thing is that when you analyse the raw data from the model to construct your diagram, you have to decide how much interaction and of what kind equates to which kind of bond. One scientist can look at the data and say that although the interaction between two atoms is additive, it is too weak to be considered a bonding orbital, and labels it instead a non-bonding orbital, another scientist may have chosen a lower interaction limit, and instead insist that it is in fact a bonding orbital. It's all about how complicated you want to make it. You'll realise that when you have a lower interaction limit, you more often than not have to invoke hypervalency to explain bonding in simple molecules, and in the opposite extreme, your molecules end up being very electron-deficient. Plasmic Physics (talk) 11:34, 6 November 2017 (UTC)[reply]

Alright, this is very ignorant (question not answer), but when I try to make sense out of the [3] link above I see 2a1 looks like s bonds to each hydrogen and 1b2 looks like a p bond interacting with both hydrogens. I would think I could, in some sense, hybridize these to sp orbitals and have one of these bonds to each hydrogen. The figure lists 1b1 as a nonbonding, not a bonding orbital, and does not show any hydrogen contribution to it; i.e. it is a plain vanilla p orbital from the oxygen atom, left untouched. That leaves the weird thing, 3a1. There are the two s orbitals in black, and one lobe of a p orbital in black between them. I would assume as with an sp that the thing adds up to something with a smaller negative lobe and a large broad density in the positive lobe that encompasses the oxygen and hydrogens? In any case, there is just one of these for two hydrogens, so I would be prone to guess this is where the extra .5 bond order can be found... however it works. Given that it involves a perpendicular p orbital I assume it is formally some sort of pi bond. Wnt (talk) 14:21, 6 November 2017 (UTC)[reply]

Sorry, I've corrected my typos. Plasmic Physics (talk) 18:31, 6 November 2017 (UTC)[reply]

Frankly speaking, you'd be lucky if the bond orders predicted by VB theory agree precisely with that predicted by MO theory for anything except diatomic species. Plasmic Physics (talk) 23:29, 6 November 2017 (UTC)[reply]

Yes, but when a group of blind men grope an elephant, viewers hope to see a happy ending. Is there any chance that the 3a1 bond here is analogous to a three-center two-electron bond, sort of a reverse instance of something like this? That way you could show a higher bond order in valence theory. Admittedly, this still has the very large issue that the hydrogen has to be part of two different bonds by all appearances, with more than two electrons in its shell, but I would think there's no way around that and still claim a 1.5 bond order. Somehow the oxygen lone pair would need to be donated back to a hydrogen 2s after the 1s has formed its main sigma bond. Is any of that not nuts? Wnt (talk) 03:23, 7 November 2017 (UTC)[reply]

LOL. Yes, it could be considered the reverse. No, there is no way around it, except to sweep it under the rug by using the simplified MO diagram. Fortunately, each hydrogen only has to put up with a small contribution by one extra electron, like the third wheel on a date that spends most of the time at the bar, but still drops by to interupt the romance. Plasmic Physics (talk) 04:05, 7 November 2017 (UTC)[reply]

For what it's worth, as I was saying, just because the diagram in the link shows the 1b₁ MO to be non-bonding does not make it neccesarily so. That is just the interpretation of the scientist who drew it. The oxygen px orbital could in theory interact additively with the anti-sigma bond in the dihydrogen. Plasmic Physics (talk) 10:35, 7 November 2017 (UTC)[reply]

Well, if this way of looking at it is valid, then it seems like the contribution of the 3a1 bond to the hydrogens can't be too minor, because the two "sp orbitals" in the MO diagram produced from a single p will be voting for a 180 degree bond angle, and the apparent p orbital will be abstaining. According to this the affinity of hydrogen for electrons in its second shell should be the only thing pulling it down into range of the oxygen's perpendicular p orbital, which I would think votes for a 0 degree bond angle. Wnt (talk) 12:28, 7 November 2017 (UTC)[reply]

Actually, if we take east to be zero, the 3a₁ is voting for a 0 degree allignment, and the 1b₂ is voting for a 90 degree allignment. They partially cancel each other to get the proper allignment. That's how molecules get their shape, different MOs fighting with each other, until the equilibrium is reache that gives the most stable allignment.

It no so much hydrogen's affinity for the extra electron, as it is the affinity of the p-orbital for hydrogen. Compare how the bond angle changes as you go down group 16. Plasmic Physics (talk) 19:27, 7 November 2017 (UTC)[reply]

Drone (bee)

The article states: "They convert and extend the queen's single unfertilized egg into about 10 million genetically identical male sperm cells." But what exactly does that mean? Does the queen only lay one single egg? And what about these millions of sperm cells – in one egg? What concrete significance do they have for that single egg? Sorry, but I'm a complete layman. Thanks in advance for any assistance. Best wishes--Herfrid (talk) 20:18, 6 November 2017 (UTC)[reply]

The "single unfertilized egg" is the one from which the drone hatched.

The idea is that from that one unfertilized egg, you get (from the drone) millions of sperm cells with the same dna as the drone's mother. ApLundell (talk) 21:15, 6 November 2017 (UTC)[reply]

See haplodiploidy, Parthenogenesis#Insects and Hymenoptera#Sex_determination. Male bees are weird. They have no father, but they do have grandfathers. And they cannot have sons. They also have roughly half the genome of their sisters. This is also why sisters are more related to each other than they are to their mother or father, and is thought to be part of the reason why eusociality evolved in the Hymenoptera.

That's a confusing and poorly sentence you quote, by the way, I will fix it later when I get a chance. SemanticMantis (talk) 22:19, 6 November 2017 (UTC)[reply]

@SemanticMantis: Thanks a lot already! What I still don't quite get is: Does the egg turn into a drone, which after hatching produces these sperms within the egg or how does it work?--Herfrid (talk) 19:39, 10 November 2017 (UTC)[reply]

Hi User:Herfrid, no, that part is not quite so weird. A queen lays an unfertilized egg, it hatches, and must become a male drone, which has only half (16) the chromosomes of any female bee (32). That drone is totally a slacker, all he does is mill about and get free food from his sisters. But, he is otherwise like a normal bee, has four wings and six legs, etc. Inside his body, he has testes, and like in many other male organsisms, they make sperm. However, whereas e.g. human testes must do meiosis to turn there full set of chromosomes into a half set, bee testes do not. When the time is right, the male bees out for a nuptial flight, and if they are lucky inseminate a queen, then die soon after. It is this reason why the sentence you quote is written in a confusing way: it's kind of trying to make a point that a male honey bee does little functional good to the colony, other than convert a single unfertilized egg into bunch of sperm. But that's kind of blurring your eyes and just looking at the function overall. Does that make sense? It really is an interesting and confusing area, so feel free to ask more here, or a new question below. SemanticMantis (talk) 20:54, 10 November 2017 (UTC)[reply]

@SemanticMantis: Thanks once again. However, I'm afraid I still don't feel experienced enough to improve the article myself. Would you recommend to make a corresponding comment there?--Herfrid (talk) 21:25, 10 November 2017 (UTC)[reply]