3d orbital after 3p?Why not 4s?

[easwar2641993]

Why Group 15 elements(except Nitrogen) have empty d orbitals while bonding?
Aufbau Principle states that electrons are added in orbitals only in the increasing order of energy of sub-shells.Also Bohr Bury rule adds to the above principle that increasing order of energy depends on the value of n+l where n is the principal quantum number and l is the azimuthal quantum no and according to these rules the increasing order of sub-shells is
1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f…

But my question is when higher p-block elements form compounds,it is said that they form bonds by
promoting the electron of the valence shell to the next available vacant orbital.
Consider the example.For PCl5.For this P in ground state is 1s2 2s2 2p6 3s2 3p3.In excited state ,it is 1s2 2s2 2p6 3s1 3p3 3d1. If the rules are followed correctly,it should be like this 1s2 2s2 2p6 3s1 3p3 4s1 right?I know hybridization but something is missing in my mind.

 

[AGNuke]

Excitation is a different affair than just writing electronic configuration. During excitation, the electron will jump to the next orbital, which is nearer to it (3d). Energy level has no role to play in it.

The Aufbau principle simply tells us the increasing energy levels of sub-shells. So we fill electrons from lower to higher. But when we excite electron, the electron will jump to next sub-shell in terms of distance, rather than in terms of energy level. 3d, being in the same shell(?) as 3p, is nearer than 4s.

 

[rexol]

3d is able to contract more, hence it gets involved in hybridisation.

 

[DrDu]

But my question is when higher p-block elements form compounds,it is said that they form bonds by
promoting the electron of the valence shell to the next available vacant orbital.
Consider the example.For PCl5.For this P in ground state is 1s2 2s2 2p6 3s2 3p3.In excited state ,it is 1s2 2s2 2p6 3s1 3p3 3d1. If the rules are followed correctly,it should be like this 1s2 2s2 2p6 3s1 3p3 4s1 right?I know hybridization but something is missing in my mind.

D-orbitals are not involved in bonding in main group elements. If your book still claims this, it is outdated by about 50 years.

 

[JohnRC]

D-orbitals are not involved in bonding in main group elements. If your book still claims this, it is outdated by about 50 years.

DrDu Bonding is a matter of a chemical caricature. You are going to have an enormous amount of difficulty accounting for the bonding in SF₆ or (NPF₂)₃, both of which are exceptionally stable compounds, without involving d-orbitals in the bonding explanation.

I know that in high level MO calculations that the d-orbitals play only a very minor role as polarization functions in the optimum molecular orbital wavefunctions, but that is not what the game is about -- it is about explanations in terms of the Chemist's familiar bonding calculus.

As far as the original poster is concerned, the issue really is energy. But the relative energy level of 3d and 4s orbitals depends on nuclear charge and inner electron shielding. The inner d-orbital increases in energy relative to the outer s-orbital for increasing inner-electron shielding, but decreases relative to the outer s-orbital energy for increasing effective nuclear charge.

For a transition metal like iron, the 3d electrons are at slightly higher energy than 4s in the neutral atom, but at considerably lower energy for the doubly charged ion. So in going from the lowest energy state of an iron atom to the lowest energy state of an iron ion, it has to be the two 4s electrons that are lost, even though in the atom itself the d-electrons are less tightly bound.

 

[DrDu]

Yes, but I think these d-orbital models are a wrong caricature (btw. I note that you seem to like this word. Do you know the works by Hans Primas?).
In MO theory the situation is quite clear anyhow and many non-theoretical books on main group chemistry give easily accessible descriptions of bonding in hypervalent main group compounds based on qualitative MO pictures.
In VB-theory, hypervalent compounds can easily be explained using resonance of different valence bond structures.
Even Gillespie, the founder of VSEPR concept so beloved by chemistry teachers does not consider d-orbitals to be useful in that context:
http://144.206.159.178/FT/243/73655/1262995.pdf

 

[Einstein Mcfly]

For the OP, don't confuse the Madelung "rule" or the aufbau principal as fundamental concepts. They are only book keeping devices and approximations respectively. They're meant to give an easy way to make sense of a lot of data. Nothing happens "because of" them.

If you're interested in getting a better view of this, try these:
Transition Metal Configurations and Limitations of the Orbital Approximation
J. Chem. Ed. Volume 66 Number 6 June 1989 481
Why Teach the Electron Configuration of the Elements as We Do?
J. Chem. Ed. Volume 59 Number 9 September 1982 757
Demystifying Introductory Chemistry Part 1: Electron Configurations from Experiment
J. Chem. Ed. Volume 73 Number 7 July 1996 617

 

[Einstein Mcfly]

I know that in high level MO calculations that the d-orbitals play only a very minor role as polarization functions in the optimum molecular orbital wavefunctions, but that is not what the game is about -- it is about explanations in terms of the Chemist's familiar bonding calculus.

JohnRC, I've very much enjoyed many of your posts on this forum. Can you please explain a bit more of what you mean by this? Given that orbitals are an approximation within a theoretical construct and "chemical intuition" with regard to orbitals is ultimately referenced to simple examples of this, it seems to me that the role of d-orbitals in a bonding scheme are DEFINED as no more and no less than what the results of high-level calculations specify. Am I misreading your post?

 

[JohnRC]

To partly explain my previous contribution, I would like the well-informed physicist/chemists who post here to specifically consider SF₆. This molecule has, according to the chemist's bonding calculus, six octahedrally arranged single bonds between sulfur and fluorine.

In the O_h symmetry group, these six bonds are, according to the simple bonding calculus that all chemists routinely use, symmetry adapted as A_1g, E_g, and T_2u. So when sulfur gets into the bonding scene, the composition of these bonding orbitals must be mixtures of S(3s) and F(2pz) for A_1g, of S(3p) and F(2pz) for T_2u, but in E_g, F(2pz) must be non-bonding unless S(3dz2) and S(3dx2-y2) are included in the bonding scheme.

This probably does not matter as far as an advanced MO calculation is concerned. The MO calculation will sort it all out, although I note that MO calculations do not provide good results for electron-rich orbital-short fluorine compounds at the Hartree Fock limit. You need electron correlation and a departure from single electron wavefunctions to get satisfactory results.

But as far as a chemist is concerned, it is disastrous for the explanatory framework of the bonding calculus. The implication of this simple symmetry-based argument is that the S-F bonds in SF₆ have a bond order of only 2/3, while the chemical reality is that these are particularly strong bonds in a particularly unreactive substance. Moreover the idea of free fluoride ions in SF₆ argues strongly that even in aqueous media, the isoelectronic SiF₆^2– should decompose into silicon tetrafluoride and 2 fluoride ions -- in complete opposition to the chemically observed facts of the matter.

I will post again when I have a bit more time to reply to Einstein's last question. The essence of it is that d-orbitals and single electron wavefunctions are approximations that are convenient in providing an explanatory framework, but not a totally accurate picture of the way molecular structure really is.

 

[JohnRC]

JohnRC, I've very much enjoyed many of your posts on this forum. Can you please explain a bit more of what you mean by this? Given that orbitals are an approximation within a theoretical construct and "chemical intuition" with regard to orbitals is ultimately referenced to simple examples of this, it seems to me that the role of d-orbitals in a bonding scheme are DEFINED as no more and no less than what the results of high-level calculations specify. Am I misreading your post?

Yes , I will try to explain. Recognising that single electron wavefunctions do not give a good picture of fluorine compound structures anyway, let us persist with Hartree-Fock type calculations. Most "high level" MO calculations are based around "atomic orbitals" -- that is, about functions which are based on the eigenfunctions for spherical fields around each atom in the molecule. So it is customary to talk about "contributions" of F(2pz) or S(3px) to the structure of individual "molecular orbitals" of SF₆, for example. The real "molecular orbitals" simply do not have the form of such a combination; it is merely a strategy for getting at a pretty good approximation.

In the case of E_g symmetry, there are three pairs of occupied orbitals in the *real* Hartree Fock molecular orbitals. Taking a single orbital from each degenerate pair, the component symmetric with respect to C₂(z) rotation, they are
(1) An extremely close approximation to {F2(1s) – F3(1s) + F4(1s) – F5(1s)}
(2) A pretty good approximation to {F2(2s) – F3(2s) + F4(2s) – F5(2s)}
(3) A rather poor approximation to some combination of
{F2(2px) + F3(2py) – F4(2px) – F5(spy)} and {S(3dx2–y2)}

If we take the last of these orbitals as a normal orbital function, optimized for an isolated sulfur atom, we will find that the lowest energy combination of such a mixture involves very little of the latter function; if on the other hand we re-optimise the d function and allow the sulfur orbital to shrink, while retaining its essential form --most calculations use either
(x²-y²)*exp( –alpha * r) , or
{sum from n = 1 to 4} c_n*(x²-y²)*exp( –ζ_n * r²),
Then we will find a larger contribution from S(3d)
It is neither right nor wrong to declare that "3d orbitals are not involved in the bonding structure of SF₆." Rather, it should be said that for some purposes it is helpful, and for other purposes it is unhelpful.

The *real* third molecular orbital of this symmetry in this molecule will have a definite functional form. If, in an ideal world, we could map out that form with total accuracy, we would be able to calculate its overlap integral with the F(2p) symmetry adapted orbital and the S(3d) orbital. My guess is that the answer would be something like 75% F(2p), 15% S(3d), 10% unaccounted for with these two atomic orbitals.

I like the word caricature, because it is very appropriate for the situation that a serious theoretical chemist often finds himself in. A caricature is a cartoon, particularly a political or a humorous cartoon. The depiction of a character is not like a photograph, it is something that makes a character recognisable by one or two of his features, often in exaggerated form. VSEPR insights, Crystal Field insights, Molecular Orbital insights, and Valence Bond insights into molecular structure are all caricatures: They are each designed to get some features of molecular structure correct, while passing over and failing to paint a correct picture of others. A caricature cannot be right or wrong; it is something that provides a decent explanatory basis for some particular features that it emphasises.

A perfect quantum chemical calculation of molecular structure would produce correct values for a number of observables, backed up by reams of numerical output; it would provide little or no basis for a satisfying explanatory framework that could be shifted to other related systems -- it would simply be "this gee whizz calculation has got all of the numbers right for this particular system"

 

[DrDu]

Ok, but bond orders are always little informative once the bonds are highly ionic.
On the other hand, as you already noted, F2 is not even bound in the Hartree Fock limit although it has a bond order of one and even the experimental bond strength is extraordinarily weak.

 

[DrDu]

I would expect there to be a similar admixture of d-orbitals e.g. in the Eg orbitals in CF4.

 

[JohnRC]

I think not; there would be a minute admixture, but certainly not a "similar" one. For CF₄ the symmetry species for the bonding orbitals in the T_d symmetry are A₁ and T₂; the symmetry species of the d orbitals are E and T₂. So the three T₂ symmetry 3d orbitals on carbon would be able to become involved in the bonding of CF₄. The carbon 2p orbitals are clearly the main contributors to the bonding between the orbitals of this symmetry. Moreover there are good reasons to suppose that the d-orbital involvement would be hugely less than in SF₆, and unlike the case with SF₆, d-orbital participation is not required to explain any broad feature of the bonding structure, and in any case 3p orbital involvement would be greater than 3d.

 

[Einstein Mcfly]

To partly explain my previous contribution, I would like the well-informed physicist/chemists who post here to specifically consider SF₆. This molecule has, according to the chemist's bonding calculus, six octahedrally arranged single bonds between sulfur and fluorine.
In the O_h symmetry group, these six bonds are, according to the simple bonding calculus that all chemists routinely use, symmetry adapted as A_1g, E_g, and T_2u. So when sulfur gets into the bonding scene, the composition of these bonding orbitals must be mixtures of S(3s) and F(2pz) for A_1g, of S(3p) and F(2pz) for T_2u, but in E_g, F(2pz) must be non-bonding unless S(3dz2) and S(3dx2-y2) are included in the bonding scheme.
But as far as a chemist is concerned, it is disastrous for the explanatory framework of the bonding calculus. The implication of this simple symmetry-based argument is that the S-F bonds in SF₆ have a bond order of only 2/3, while the chemical reality is that these are particularly strong bonds in a particularly unreactive substance. Moreover the idea of free fluoride ions in SF₆ argues strongly that even in aqueous media, the isoelectronic SiF₆^2– should decompose into silicon tetrafluoride and 2 fluoride ions -- in complete opposition to the chemically observed facts of the matter.
I will post again when I have a bit more time to reply to Einstein's last question. The essence of it is that d-orbitals and single electron wavefunctions are approximations that are convenient in providing an explanatory framework, but not a totally accurate picture of the way molecular structure really is.

I agree with you that more thought needs to be given to explaining why this compound with a formal 2/3 bond order is unreactive and has the bond lengths that it does. However, shoe-horning the reason into involvement of sulfur d-orbitals based on symmetry when they’re both energetically too high and MO calculations confirm their minor involvement doesn’t seem productive.

This probably does not matter as far as an advanced MO calculation is concerned. The MO calculation will sort it all out, although I note that MO calculations do not provide good results for electron-rich orbital-short fluorine compounds at the Hartree Fock limit. You need electron correlation and a departure from single electron wavefunctions to get satisfactory results.

Generally, DFT calculations give orbital symmetries identical to HF calculations with shapes that are very similar if not identical. Would these results be more satisfactory given that they include correlation?
Also, while higher level multi-reference calculations lose the simple “orbital” when multiple determinants are used, I would guess that there is some contribution that can be made to this discussion, right? I have almost no experience with interpreting the output of such high level post-HF calculations, but they do give such properties as the total J and the symmetry of the total wave function, correct?

Yes , I will try to explain. Recognising that single electron wavefunctions do not give a good picture of fluorine compound structures anyway, let us persist with Hartree-Fock type calculations. Most "high level" MO calculations are based around "atomic orbitals" -- that is, about functions which are based on the eigenfunctions for spherical fields around each atom in the molecule. So it is customary to talk about "contributions" of F(2pz) or S(3px) to the structure of individual "molecular orbitals" of SF₆, for example. The real "molecular orbitals" simply do not have the form of such a combination; it is merely a strategy for getting at a pretty good approximation.
In the case of E_g symmetry, there are three pairs of occupied orbitals in the *real* Hartree Fock molecular orbitals. Taking a single orbital from each degenerate pair, the component symmetric with respect to C₂(z) rotation, they are
(1) An extremely close approximation to {F2(1s) – F3(1s) + F4(1s) – F5(1s)}
(2) A pretty good approximation to {F2(2s) – F3(2s) + F4(2s) – F5(2s)}
(3) A rather poor approximation to some combination of
{F2(2px) + F3(2py) – F4(2px) – F5(spy)} and {S(3dx2–y2)}
If we take the last of these orbitals as a normal orbital function, optimized for an isolated sulfur atom, we will find that the lowest energy combination of such a mixture involves very little of the latter function; if on the other hand we re-optimise the d function and allow the sulfur orbital to shrink, while retaining its essential form --most calculations use either
(x²-y²)*exp( –alpha * r) , or
{sum from n = 1 to 4} c_n*(x²-y²)*exp( –ζ_n * r²),
Then we will find a larger contribution from S(3d)
It is neither right nor wrong to declare that "3d orbitals are not involved in the bonding structure of SF₆." Rather, it should be said that for some purposes it is helpful, and for other purposes it is unhelpful.
The *real* third molecular orbital of this symmetry in this molecule will have a definite functional form. If, in an ideal world, we could map out that form with total accuracy, we would be able to calculate its overlap integral with the F(2p) symmetry adapted orbital and the S(3d) orbital. My guess is that the answer would be something like 75% F(2p), 15% S(3d), 10% unaccounted for with these two atomic orbitals.
A perfect quantum chemical calculation of molecular structure would produce correct values for a number of observables, backed up by reams of numerical output; it would provide little or no basis for a satisfying explanatory framework that could be shifted to other related systems -- it would simply be "this gee whizz calculation has got all of the numbers right for this particular system"

I’m not sure what you mean about (forgive me for paraphrasing) “if the S(3d) is allowed to shrink, we’ll find a higher contribution in the final wavefunction”. The use of Gaussian functions should allow sufficient freedom to create a “contracted S(3d) “ orbital if such a contraction will lower the energy.
Also, while I agree that sometimes quantum chemical calculations can simply be a black box from which predicted observables are pulled, there can certainly be cases where insight into simpler pictures can be gained. In this case, I find it a success of the model to exclude an exemplar of the usual symmetry based MO theory so that chemists can move on to look for other reasons for the stability of SF6.

I like the word caricature, because it is very appropriate for the situation that a serious theoretical chemist often finds himself in. A caricature is a cartoon, particularly a political or a humorous cartoon. The depiction of a character is not like a photograph, it is something that makes a character recognisable by one or two of his features, often in exaggerated form. VSEPR insights, Crystal Field insights, Molecular Orbital insights, and Valence Bond insights into molecular structure are all caricatures: They are each designed to get some features of molecular structure correct, while passing over and failing to paint a correct picture of others. A caricature cannot be right or wrong; it is something that provides a decent explanatory basis for some particular features that it emphasises.

This is perhaps my favorite paragraph that I’ve read on this board. I will likely crib this idea from you in discussions and lectures and will try my best to point out that I didn’t come up with it myself.

 

[Einstein Mcfly]

Ok, but bond orders are always little informative once the bonds are highly ionic.
On the other hand, as you already noted, F2 is not even bound in the Hartree Fock limit although it has a bond order of one and even the experimental bond strength is extraordinarily weak.

Is there a larger theoretical construct that can explain such cases?

I would expect there to be a similar admixture of d-orbitals e.g. in the Eg orbitals in CF4.

What is the best way of estimating the energy difference between the S(3d) and the C(3d)?

 

[JohnRC]

From Einstein McFly:

I agree with you that more thought needs to be given to explaining why this compound with a formal 2/3 bond order is unreactive and has the bond lengths that it does. However, shoe-horning the reason into involvement of sulfur d-orbitals based on symmetry when they’re both energetically too high and MO calculations confirm their minor involvement doesn’t seem productive.

But in the chemist's story about bonding, the sulfur 3d orbitals are neither too high in energy nor too large and diffuse to participate in the bonding in this compound, because inductive withdrawal of electron density from sulfur to fluorine in this compound will cause sulfur to have a much higher effective nuclear charge than in a free element context, leading to a large shrinkage and lowering in energy of sulfur 3d orbitals. No shoe-horning is involved.

Again from Einstein McFly:

Generally, DFT calculations give orbital symmetries identical to HF calculations with shapes that are very similar if not identical. Would these results be more satisfactory given that they include correlation?
Also, while higher level multi-reference calculations lose the simple “orbital” when multiple determinants are used, I would guess that there is some contribution that can be made to this discussion, right? I have almost no experience with interpreting the output of such high level post-HF calculations, but they do give such properties as the total J and the symmetry of the total wave function, correct?

I have no personal experience with DFT calculations. I know that they are semi-empirical, with all of the weaknesses that that entails. Presumably there is a received wisdom about how they handle non-metal fluorides, an area where HF theory consistently fails to produce good results.

The total J and the symmetry species of the total wave function does not need any type of calculation for non-metal halides, or indeed for most molecular compounds. For almost any compound not involving transition metals, the J value is zero, and the symmetry representation of the ground state is totally symmetric. So yes, correct, but not really very informative.

More Einstein McFly:

I’m not sure what you mean about (forgive me for paraphrasing) “if the S(3d) is allowed to shrink, we’ll find a higher contribution in the final wavefunction”. The use of Gaussian functions should allow sufficient freedom to create a “contracted S(3d) “ orbital if such a contraction will lower the energy.

The use of Gaussian functions per se will in fact do so; the use of the Gaussian program might not.

There are 3 ways to incorporate Gaussian S(3d) functions into the E_g calculation for SF₆.
Suppose that we are going to use a 4-gaussian approximation to S(3d), that is to use an angular part appropriate to the 3d symmetry with a radial part consisting of the sum of 4 terms like
a_j * r² * exp( –ζ_j * r²)

(1) Optimise all 7 parameters for atomic sulfur, and incorporate them as fixed parameters into the calculation

(2) Regard the 3 independent a parameters as variable parameters that will better accommodate the local context of sulfur in a particular bonding situation.

(3) Regard both a and ζ values as variable parameters in the calculation.

The wavefunction obtained for the one electron molecular orbital will improve in the order (1), (2), (3), and the orbital contribution of S(3d) will also increase in this order.

Now I have not used the Gaussian program much, and certainly not looked into this aspect of its performance, but I suspect that it takes path (2) from the above choices. In any case, this is what I meant when I talked about "shrinkage" of sulfur 3d orbitals in a particular bonding context.

Unlike you, I (clearly) regard this ploy of involving 3d orbitals in the bonding calculus as a valid extension of it rather than sulfur hexafluoride as an exemplar to be excluded from the bonding calculus and individually examined. 3d orbital shrinkage and expansion from a Lewis octet is a well-established concept in chemical discourse, believe it or not. There are three ways of describing sulfuric acid/sulfate ion: dative bond model, formal charge model, and expanded octet model. Several General Chemistry textbooks, and many chemical authorities firmly believe in the last, and insist that the first two are wrong! My point of view is once again pluralistic -- the first two descriptions are really the same: in my classes I used to use the analogy that the difference between dative bond and formal charge is a bit like the difference between "I will buy both of our cinema tickets", and "I will give you the money so that you can buy your own". But there is a far greater difference in the model with S having two single covalent bonds to OH groups and two double covalent bonds to O atoms. I greatly prefer the dative bond model, but I would never say that the double-bond expanded octet model is wrong, because it is required for some aspects of the properties and structure of sulfuric acid/sulfates.

 

[DrDu]

From the abstract of the following article:
Hypercoordinate molecules of second-row elements: d functions or d orbitals?
Eric Magnusson
J. Am. Chem. Soc., 1990, 112 (22), pp 7940–7951
DOI: 10.1021/ja00178a014

"There is no support for the view that diffuse d-orbitals on the central atom take part in bonding after being contracted in the field of electronegative oxygen or fluorine atoms around in the periphery"