According to the valuable answer posted from Peter, I am a perplexed answerer when I see your profil and publications. You can find  the theoretical interpretation  in various books and articles.

Please start Google Scholar and NOT Google and give your question in the filter.

On other part, I think that you have access to an uni library. I send you some pages as jpg files  of 2 books

1- Theodor Förster Fluoreszenz Organischer Verbindungen (Try to obtain the English translation.

Peter (dixit):

That is vibrational structure of the emission band. The measurement you are referring to was made at room temp, in condensed phase, using cyclohexane as solvent. The spectral resolution of that measurement in general, and that of the apparatus used to obtain that spectrum, is poor.

Do you know an theoretical interpretation of the emission (fluorescence) spectrum of benzene ? - ResearchGate. Available from: https://www.researchgate.net/post/Do_you_know_an_theoretical_interpretation_of_the_emission_fluorescence_spectrum_of_benzene [accessed Oct 19, 2016].

I agree with the answer of Peter concerning the poor resolution. P.e. between 1922

and 1975 (Birks references, scientists investigated benzene in various states and at temperature between room temp. and 77 K with a better resolution.

Shopl 'skii  E.V published valuable articles too .

Books:

2-Organic molecular photophysics vol.1 and  2      editor j.B. Birks  1975

JRG

Another interesting link :

http://pubs.acs.org/doi/abs/10.1021/j100215a022.

Absorption and emission spectroscopy of benzene in cryogenic solutions. An estimate of the intermolecular potential

F. Li, J. Lee, E. R. Bernstein

J. Phys. Chem., 1982, 86 (18), pp 3606–3611

DOI: 10.1021/j100215a022

Publication Date: September 1982

The fluorescence spectrum of benzene is built up of tens of thousands of lines. Those are the transitions originating from the thousands of energy levels in the excited state populated according to Boltzmann distribution. These are the rotational states of with the excited electronic state from which the fluorescence originates. In addition some low-energy vibrational states are populated with the superimposed rotational states. From those thousands of states transitions occur to the respective ro-vibrational levels in the electronic ground state. Due to the large number of close lying lines they clump to one broad band.

The peaks in the spectrum are the so-called progression bands. They are explained via the Franck-Condon principle (see Google under item vibronic spectroscopy). Those are transitions in which the quantum number of the FC vibration increases, with the associated difference in energy. This is the v2 vibration of the benzene ring

FYI there are high-resolution fluorescence spectra for benzene in the gas-pse at low temperatures at which very few ro-vibrational levels are populated. Those are highly resolved spectra showing rotational fine structure

Just consulted my "bible" and noticed a detailed analysis for the benzene spectrum along the lines I skethed

This bible is Jeffrey Steinfeld

Molecules and Radiation (An introduction to Modern Molecular Spectroscopy)

I could scan in the respective pages in case you are interested

Dear all!

Very good and useful answers.

Thank you very much!

Mr. Dubrovkin,

'Photochemcad' is an experimental database.

The multiple profile of the bands has vibronic character. It is typical to all bands and can be taken into consideration, theoretically, using Franck–Condon and Herzberg-Teller approximations, which account for vibronic coupling states; or by nuclear ensemble method. The coupling of ES by more than one vibration can be accounted computing the Duchinsky's effect.

On the other hand, there is still a problematic task assignment of ES data of benzene. GS shows aromatic character (D6h symmetry), but ES T1 state (1 3B1u), which is not electronically degenerated state of D6h symmetry exhibits a pseudo Jahn-Teller deformation. There are available EPR studies, indicating that the hexagonal conformation of C6H6 is unstable in T1 state and a symmetry transition D6h-to-D2h(*) (Pseudo D2h, because of there is discrepancy towards the data of "pure" D2h symmetry, too) occurs. Furthermore anti-aromatic S1 state of benzene has been also proposed. In this context a theoretical modeling of S1-to-S0 and T1-to-S0 transitions via mentioned above methods involves set geometry changes of benzene skeleton, along with various electronic structures. Thus, it is not predisposed to expecting a parallel between vibronic structures of PL and FS specra.

Although large scale known literature data, it is arguably more effort in theoretical computations of ES of benzene, because of there is frequently discrepancy between theoretical and experimental data, which cannot be regarded as drawback to the corresponding theoretical methods (above) and their inaccuracy.

Dear  Bojidarka B. Ivanova, very interesting question.

Thank you very much

In addition, as I have expected the monograph mentioned by Mr. ten Brink, (J. Steinfeld, Molecules and Radiation, Happer and Row Publishers, 1974, N.Y.) has educational character, and thus it has a mixed monograph-textbook style, as it is written still in the preface (..."more material in the present text can be covered in a single one semester course...Clearly, the book has been designed for use in a graduate-level course"...).

For this reason the description about ''ES'' phenomena of C6H6 strictly follows the logic that..."D6h symmetry is preserved." (page 213). This has been done, because of the text treats the vibrational structure in terms of Franck-Condon factors, assuming perturbation (Not change) of the geometry in GS and ES. As we can read in the next page (page 214), there is shown an only weak rotation. The major reference material is Phil. Trans. Roy Soc. (London) A259, 499 (1966) showing the already well known, but 'absorption' spectrum of benzene. On the other hand still that time (60's-70's) there have been cumulated experimental data about the distortion of the D6h symmetry of the benzene in ES, including problems with the assignment of the vibronic couplings effects, furthermore, such as data can be even found more recently. Therefore in ES the electronic configuration cannot be expressed by a2u, e1g....(D6h), but by b1u, b2g...(if the symmetry is D2h, for example).

In this context the mentioned ref is not suitable to the topic of this discussion.

There is a more recent review-article to the topic of this discussion:

Ref. 1. Chem. Soc. Rev., 2015, 44, 6472--6493

Unfortunatelly, it treats only contributions of computational chemistry, however. There are not included experimental data during these decades.

mrs Ivanova

Indeed I mentioned the textbook as an introduction to molecular spectroscopy

as you say there are publications on second-order deviations in the spectra but here the question was on the basic emission spectrum and why it only has 4 wide overlapped peaks

Dear Bojidarka B. Ivanova and Harry ten Bring, very useful comments.

My another question concerns to "...has 4 wide overlapped peaks".

I found parameters of these peaks mathematically. I need a physical data

about these parameters. I should like to compare my parameters with their theoretical values.

As I wrote above this this is the so-called progression in the v2 mode of benzene (in the ground electronic state) and the distance in the peaks correspond to that frequency

Dear Harry ten Brink. Very useful answers. I will cited all discussion in my future paper.

Next question:

Whether the envelope of the fine structure is (approximately) equal to the contours of these 4 peaks?

Dear Peter Kapusta, very nice answer. I will cite this answer in my presentation in Isranalytica-2017.

Regards, Joseph 

Peter

In this case it is the congestion of the tens of thousands of lines that gives rise to a structureless spectrum with 4 peaks

In jet-cooled benzene gas the rotational lines are resolved and then the spectral resolution of detection and excitation also plays a role

The spectrum of benzene in solution is like a hand with short fingers and the bands can not be fitted with a gaussian

I used asymmetrical functions

Joseph:

but why do you want to fit the spectrum with a mathematical construction?

Only for math! I compare this spectrum with spectra of another compounds which contain

benzene rings.

the structure should not be much different from the "fingerprint" of benzene when the phenyl group is the chromophore

Mr. Dubrovkin,

As Mr. ten Brink has already pointed out, the spectrum is a vibrot one (F. Duschinsky, Acta Physicochim. USSR 7 (1937) 551), like the shown example of H2C=O (attachment, Step 1). It contains a set of lines, which approximation yields to a common profile of such as spectra (Step 2).

The sub-bands can be curve-fitted by Gauss' function as Mr. Kapusta has pointed out, too. The level of confidence is 100 % (Step 3) or r2 = 1, meaning a full (in quantitative terms, not qualitatively) coincidence between both patterns.

So, my questions are: To which of these steps, you should apply new non-linear function; And how you shall improve a confidence level 100 %? (They are 100 % reliable by Gauss' approximation).

Asymmetrical functions gave best fit for my spectrum.

Mr. Dubrovkin,

The new attachment shows experimental vibrot spectra and change of the pattern due to phase transition. The band maximum positions/intensities are shown, too. The application of Gauss' function yields to reliability 99.926-99.937 %. The deviation from 100 % is due to baseline correction (gas-phase spectra, shown) and vibrot contribution to condense-phase spectrum (shown). It is effect of not full compensation during measurements. Furthermore, if you have observed something like broadering/or asymmetry to the gas-phase data, this is associated with the Doppler effect and/or effect of bandpass filters of the spectrometer.

Details about the theory of vibrot spectra can be found in refs 1 and 2.

The spectrum reflects energy profile. It depends on the molecular and electronic structure of the object. Any perturbation/change of geometry/electric redistribution affects the energetics of corresponding molecular system, and thus the spectroscopic profile (curve). Or the spectrum reflects a concrete molecular geometry and its electronic structure. This is the so-called “fingerprint”. Any energy fingerprint corresponds to only one molecular geometry and its electronic structure. Therefore, it is characteristic to individual molecule. This is topic of structural chemistry of molecular systems.

The curve cannot be approximated just a imaginary curve, without knowledge about the origin of the bands, because of, band positions and their intensities, corresponding to given electronic transitions are sensible toward molecular (structural) and environmental (P, T, phase, medium and more) factors. In addition, to factors mentioned above. Furthermore, for correlative analysis of sets of datablocks already have a large scale statistical methods.

Ref. 1. D. McQuarrie, Quantum Chemistry, University Science Books, Oxford University Press, 1983, Mill Valley, CA, pp. 1–517.

Ref. 2. D. Papousek, M. Aliev, Molecular Vibrational-Rotational spectra, 1982, Elsevier Publishing Company, pp. 1 – 323, Amsterdam.

ms Ivanova

please have a look in the link provided in the question

There you see a spectrum that consists of  a few very broad bands with a width of several 100s of cm-1 for benzene. The spectrum is that benzene dissolved in a solvent.

In this case all rovibronic transitions overlap and give rise to a very broad emission spectrum

As for your example: for my PhD I studied and used the spectrum of a molecule that is only slightly more complex than your example formaldehyde viz glyoxal (C2H2O2) . In the dilute gas phase it shows resolved structure but not for the single rotational lines that are clumped into a non-symmetric flag type structure. This is due to the differences in the rotational constant in ground and electronically excited state and this in turn is due to a difference in equilibrium distances of the atoms due to a different configuration of orbitals (very brief description)

Mr. ten Brink,

Let us first focus attention on Photochemcad 2.1 data on C6H6 (attachment). Both spectra (EAs and emission) are in C6H12. Therefore, if the broadening of the signal in the emission spectrum is explained only with a solvent effect; And if the origin of the spectra is one and the same, then this effect should also be observed in the corresponding absorption spectrum (The measurements are at the same conditions (solvent, other parameters, operator) and instrument), accounting for same structure/symmetry in GS and ES.

But they are different from profile. Therefore, the profile of the emission spectrum cannot be associated with the geometry and electronic structure of GS. Such as broadening of the profile is observed in polar protic solvent in EAs. But the measurements inPhotochemcad 2.1 are only in non-polar aprotic solvent C6H12. Thus, the effect of the medium can be associated with the effect of the dielectric constant. There are not specific solute-solvent interactions with non-polars C6H6 and C6H12.

In addition, the bands in ES are not 4 but many more (Attachment). Therefore over range of confidence levels 99.992-99.998 % more then 10 sub-bands can be determined. But definitively, the number of sub-bands are many more then 4.

The well-known scheme of the absorption spectra of benzene as a system with D6h symmetry is not applicable even to real experimental EAs spectra. Because of this, it is within the scope of 'one' electron approximation, which describes the excitation phenomena of only one electron. In the real systems, however, all electrons are excited during irradiation. Further, when the irradiation in ES is polychromatic, transitions from electronic states (Sx, Tx) coinciding with vibration levels are not only from S1 state (fluorescence), but also from vibration levels of T1 (Pl), or even S2/S3 states (Upper ES emission).

Please note the well-known Jablonski's diagram. T1-oscillation states are often energetically arranged to S1-state. It can be experimentally difficult to clearly distinguish emission bands. They can be S1-to-S0 and/or T1-to-S0 transitions. Or an overlapping of the band from S1-S0 to T1-S0 (it can also be about 310 nm for C6H6) can be obtained. Because of in emission processes, an intersystem crossing (S1-T1) is found. The two-photon emission measurements are necessary to evaluate the level of the overlapping effect of S1-S0 and T1-S0 bands since they also have a multiple character.

Therefore, measurements using two-photon emission spectroscopy are needed in combination with quantum chemical calculations on different geometries/electronic structures in ES. Because of how I've written some change in geometry and electronic structure, disrupt/alter the spectrum (below examples).

In addition, you have written, that the effect is only weak rotation in ES, but I have done few fast calculations of the S1 state accounting for 'weak' and 'strong' rotation. It caused a change in the 0-0 band position of 300 cm-1 (Energy units, attachment). The weak rotation does not change the profile. In comparison with the available experimental data, the system correlates well with the experimental pattern (Compare both profiles in the different attachments) with strong ES disturbance. The optimization of the geometry is carried out in C6H12, but at a low theoretical level (Basis set: sto-3g). These preliminary data rather assume that ES is associated with a strong change in the electronic structure, rather a disturbance (or weak rotation). On the other hand, the shown Fs spectra of benzene in Photochemcad 2.1 are at room temperature. Because of the measurements in the solution, but at low temperature show different profiles. An increase in the number of sub-maxima occurs. In addition, I have shown how the change in symmetry affects the profile of the spectrum (Attachment Gauss-3b.gif).

ms Ivanova

It seems/appears that we are addressing different issues

1. The questioner specifically asks for a theoretical basis for the structure of a spectrum as found in the photochemcad data base in which 4 distinct bands are seen

This the spectrum in solution (solvent?) and in emission

2. You deconvolute the spectrum into more subbands but then my question is to what vibronic bands do these belong?

3. In an earlier entry I made it clear that (even) in the gasphase, thus with free rotation, the structure is fully blurred. This is due to the thousands of rotational transitions allowed and indeed schematically but sufficiently described in Steinfeld's book

Due to the abundancy of rotational states thousands are populated ay room temperature according to the Boltzman distribution of energy. From all those states there arethus thousands of  transitions and these do not coincide and therefore there is a broad vibronic band going as far that these overlap.

Mr. ten Brink,

We do not handle different problems, but obviously you did not pay attention to my attachments. You maintain that the bands are 4, but in the attachment Gauss-3a.gif the theoretical pattern is shown using 4-sub maxima. Even qualitative (without further statistical treatment) the curves (experimentally and theoretically) are not mutually complementary. So, once more, the sub-bands are not 4!!!

Your comment, however, assumes that you have not only with emission spectroscopy, but with absorption spectroscopy experience. Both spectroscopies, however, treat one process. It is: The molecules that are in the GS at irradiation are excited at given ESs, where they do not remain permanent. After a short time, the molecules return to the GS (as I wrote, this is the well-known Jablonski's diagram). In particulat, pay attention to the life-times of ES phenomena. The diagram is shown relatively comprehensively, here:

http://images.google.de/imgres?imgurl=http%3A%2F%2Fhome.uni-leipzig.de%2Fpwm%2Fweb%2Fimg%2Fintro_fluorescence_1.png&imgrefurl=http%3A%2F%2Fhome.uni-leipzig.de%2Fpwm%2Fweb%2F%3Fsection%3Dintroduction%26page%3Dfluorescence&h=300&w=450&tbnid=gHR9Vf2gepB7EM%3A&vet=1&docid=R2CVOv6iKgIH-M&ei=oeQkWOaHFImMgAbP_bv4Dg&tbm=isch&iact=rc&uact=3&dur=1851&page=1&start=24&ndsp=29&ved=0ahUKEwim3PqMj5_QAhUJBsAKHc_-Du8QMwhEKCEwIQ&bih=814&biw=1391

The first part of this (one) process is observed by absorption spectroscopy, while the secon one - by emission spectroscopy. Both methods reflect molecular structure and the electronic configuration (population) at GS and the corresponding (more than one) excited states. The profile of the resulting band is expressed by Gaussian (or Lorentzian) function. So, this is one resulting process GS-to-ES-to-GS. The molecules do not remain permanent in ES.

In order to understand the profile of the emission spectrum of C6H6 and to determin the number of sub-components and transition these are needed two-photon emission spectra of C6H6 at different temperatures and solvents; To determin the electronic population of corresponding S1 and T1 excited states.

Please pay attention to a new attechment Gauss 4.gif showing the absorption spectra of C6H6 in the gas phase and solution. The same as character profiles correspond to both S1-to-S0 and T1-to-S0 transitions. In addition, they are overlapped in C6H6 to some extend (Ca. 310-320 nm). Thus it is not possible to distinguish the integral intensity (S1-to-S0) from the spectrum in Photochemcad 2.1, and thus the quantum yield, due to contribution from T1-to-S0 stransition.

Now, concrete to your points:

To item 1:

The theoretical spectrum, which I have uploaded is vibrational resolving emission of C6H6 (a particular state analysis), depending on different models of molecular and electronic structures of C6H6.

To points 2 and 3: The comments are shown in the general part to this posting (above).

I must emphasize that RG is not University! There are many references in the topic to this question, including large scale theoretical treatments and experimental measurements. 

I find it derogatory the way you react. I have 15 years of practical experience in excited state spectroscopy from isolated gas-phase to condensed phase solutions for small molecules to aromatics including extensive studies of relaxation of vibrarot states. So do not teach me spectroscopy

The question here is and was the THEORETICAL basis of the form of the  emission spectrum of benzene in solution as provided in the reference. Fine that you can convolute it in several more subbands than the seemingly 4 main structures. The question then is what are those 12 (?) aubstrutures I presume that the normal modes acitive a s progression in the FC transition but what the are those modes

I mentioned the v2 in an ealier response but the there might be other(s)

In addition low-energy vibrational modes are populated at room temperature. Transitions from those modes to the equivalent mode in S1 will have  shift relative to the 0-0 transition leading to additional vibronic bands. Example is my "own" molecule glyoxal where the v7 and v12 are populated and the transitions 711 is blue shifted. This is due to a stiffening of the bond between the two C atoms in S1. The rotational structure of this overtone band is in between the rotational structure of the 0-0; for a large molecule his leads to a full congestion of the vibronic spectrum, mainly due to the mentioned thousands of rotational transitions in single vibronic "line"

The structure n your last figure shows this rotational STRUCTURE as a flag and it does actually not change much going to a solution solution apart from a solution effect of the absolute 0-0

Dear colleagues, very interesting discussion but:

If one has not any a priori information then from "pure mathematics" there are infinite number of the components. Physicists are always looking for the simplest models. To a first approximation, there are only four bands. It seems unreal to detect the distant badly resolved  trees in a forest in the dense fog by a bad spectroscopic eye.

Regards, Joseph

Joseph

indeed the spectrum does not contain any valuable information as it is. Only in the low temp gas phase the spectrum is dissolved and then the different molecular parameters can be deduced like the rotational moments of the molecule and the energy of some of the normal vibrations

Mr. ten Brik, 

Talking about 'scientific experience', it does not matter how long you hold the academic position, but how much work you have done, holding this employment position. You are co-author of 97 publications (Scopus) and 320 (RG) with a significant number of participations at conferences, however. Results that are reported to conference are frequently not available and they can therefore not be evaluated by independent scientific communities. So, what is the novelty is unknown to a large extend. Your published activity remains up-to-date 100 publications over a period of time from 1978 to 2012. There are more than 2 co-authors. In this respect, to whom I should address ''your'' experience? - You personally and/or your 4-5 co-authors?

Who has more experience? - Someone who has measured and analyzed (More importantly) 7-10 000 spectra (only qualitative analysis, without spectroscopic quantification, which is significantly more as effort) published in 500-600 publications, monographs and patents; Or someone with about 210-500 qualitative spectra in 90 publications? (NB! The values are approximate since the amount depends on the number of data and the total volume of published information, which vary widely).

The discussion of the issue of "quality" of academic/research work and "quality of information for Society"; Labor costs for scientists/researchers by the public budget and individual efforts on chemistry, physics, mathematics, medicine; Criteria for the evaluation and so on, is complex. RG is neither University nor advisory board; Accreditation Bodies/Committees and more, too.

If you have claimed that you have great experience, meaning are an expert, this is valid to your Country/University, It is domestic policy. It does not means that you are expert to the other Countries/Educational Institutions, as well. Within the framework of a conflict of interest, for example, like funding by external funds, your expertness is under great juridical obstruction. And this which I have mentioned above are only scarce details from the available quantitative attestation criteria accounting for the 'quality' of the work of the academic/research staff.

In other words, as academic-researcher your obligations only consist of: (i) Science knowledge generation; (ii) Science knowledge implementation; and (iii) Teaching - knowledge distribution. Your 'expertness' and 'experience' is evaluated by domestic factors in your Country/University. The factors, however, are different to different Countries/Universities and there is not correlation between them from Country to Country and from one University/Educational Institution to another University/Educational Institution even within the framework of your Country.

Within the framework of EU there is only unification of the educational grads using the Bologna Convention.

'Scientific expert', however, is associated with scientific responsibility, and the person concerned is appointed by the Court.

So, can you upload a Decision by the Court (Instance, place, datum, number), which gives you appointment to be 'scientific expert' in your area?

Dear colleagues!

Our discussions are transferred from the scientific area to the ethical field.

This is not the president's election in US.

Regards, Joseph