Hi Anex Jose,

Thank you for your email. I have done all this stuff. The things that you have mentioned are quite straightforward and I have already performed. But I am interested with some promolecular properties like deformation density comparison between experimental and theoretical results. I am particular interested in calculating the theoretical structure factors (hkl) in same space group using Gaussian. I know it is possible to get using Crystal 09. But I want to calculate using Gaussian.

Hi Arshad

you ca use the program denprop, availble from Anatoliy Volkov (MTSU), that calculates structure factors from wfn files from Gaussian or games.

As an alternative the program tonto from Dylan Jayatilaka is also doing that (calculating the wave function and the structure factors)

Dear Dr. Piero Macchi,

It is no doubt an honor me that you replied. I am working on Experimental Charge density and I have been following your cutting-edge research articles since the start of my PhD.

Thank you very much for your reply. Finally I got reply from an expert of field. So I dare to ask one more question. Can I use the theoretical structure factor file for Multipolar Refinement? Because, as per my knowledge, Gaussian is not much specific to space group symmetry. So can I calculate the deformation density theoretically using these theoretical structure factor obtained from Gaussian wavefunction using denprop or tonto? And can I use these theoretical structure factor for multipolar refinement using MoPro?

Thank you very much again.

Kind Regards,

Dear Arshad

it is a pleasure for me to answer these questions. Gaussian is of course not a program for solid state, despite the tentative periodic option which is in my view not so useful.

Of course you can use the theoretical structure factors for a multipole refinement with XD or MoPro. However if your purpose is studying the theoretical deformation density, there is no need to do a multipolar expansion. Tonto can printout a promolecule density and you could use it for your purposes. Alternatively denprop should also be able to do so, as far as I remember

best regards

Piero

Mr. Mehmood,

Theoretical structural factor compared to what? Structural factor as definition indicates the reliability of a theoretical model to experimental e-densities. It is a statistical parameter. gaussian has not such as option. You can obtain the geometry as commented by participants in this discusion, and you should compare the reliability of this model with given experimental set of data or between theoretical models separately.   

The structure factor is not a statistical parameters. It is the Fourier transformation of a quantum mechanical observable (the electron density) into reciprocal space.

I understand that Mehmood is interested in computing the structure factors from ab initio wave functions in order to test the flexibility of a (multipolar) model, not the correctness of the experimental observations. I understand that he would like to check if the model he uses is able to properly reconstruct the theoretical electron density, If so then the experimental model may be more reliable. If I understood correctly Mehmood's intention, then comments concerning the geometry optimization are misleading because that would not be the point.

Dear Dr. Piero Macchi and  Bojidarka B. Ivanova,

Dr. Piero Macchi has rightly understand my problem. I want to calculate the structure factors from ab initio wave functions which are also called static theoretical structure factors and then to perform the Multipolar Refinement on these static structure factors as I have done on experimental data (structure factors). My intentions are to compare the experimental deformation density, bond paths, Laplacian, atomic basins and other stuff with the calculated one after multipolar refinement of theoretical structure factors. Simply,

"I want to use Gaussian/denprop/tonto as theoretical SC-XRD where I want to give ab initio wave function as input (instead of a single crystal that is used in SC-XRD) and want to get the theoretical diffraction data".

For reference, I am attaching a paper.

I have been trying to use denprop and tonto (as recommended by Dr. Piero Macchi)  by inputting the wave function file obtained from Gaussian. But unfortunately, denprop is rejecting my wavefunction (I don't know why) and tonto is very difficult to use, highly user unfriendly. I tried VESTA and was successful to get hkl, Fcal, d, and 2theta. But obtained hkl file is not being read by any structure refinement software. (My bad luck).

Best Regards,

unless I am mistaken, VESTA does not produce theoretically calculated structure factors (as it could be from gaussian wave function) but structure factors calculated with the independent atom model (thus equal to shelx). This would not be particularly useful for your purposes, Mehmood, I am afraid

Let us first clarify the question about is F(hkl) (structural factor) statistical parameter or not relating the comments by Mr. Macchi.

F(hkl) for a unit cell is given by F(hkl) = f(fr and phir), where fr is atomic scattering factor (ASF) of a rth atom in a unit cell, while phir is phase factor. The ASF, however, is given by f0=f(U(r)), where U(r) is probability to find e- between r and r+dr from a centre of atom. This f0 is for isolated atom. Integration U(r) from 0-to "infinite" yields Z to each atom. The process of scattering is consider to be unpolarized, however, during scattering there is a partial polarization and this polarization depends on angle of scattering. Or intensity, this which we have measured experimentally varies with the angle. Also vibrations of unpolarized beam is included in the amplitude. As far as the intensity is proportional to amplitude square, the intensity equation has involved a polarization factor. Furthermore ASFs are calculated for atoms at rest, but accounting for thermal motion we have fluctuation due to displacement of atoms from their mean positions. For this reasons when we have determined atomic positions by X-ray experiments we have talken about structural factor probabilities, because of calculating the scattering factors and comparing with experimental f0 we make assumption about distribution of electrons in the atoms. Thus e-density is a sum of expected densities to each of atoms in the unit cell, which is a probability weighted sum of all possible positions. Or the e-density map (Patterson map) has r.m.s error, which can be large, due to stated above reasons. Solving the structure we have placed the atoms towards an electron density map on positions where the density is relatively high, meaning relatively high intensity. Those atoms, thereby, have relative positions. Please pay attention to attachment where is shown example of experimental crystallographic data, Fourier map and quantum chemical data of same crystal. The structural factor is Fourier transform of electron density. FT, in fact, minimizes the mentioned r.m.s error in electron density map giving a common pictire of a structure from a (single crystal) crystallographic experiment (attachment).

In other words when electron density is probability-weighted sum of set of possible positions, the structural factor is also probability parameter, or it is a statistical parameter. Or when we are speaking about structural factor, in all the time we are spacing, in fact, about probability statistics.

If I am properly understood, Mr. Mehmood would like to find structural factor F(h,k,l) from quantum chemical electron density data of an optimized structure (crystal) (attachment). Or this essencially is vise versa problem of a crystallographic structural solution. Here however stays the question which I have already written in my previous posting, i.e. with what this sructural factor shall be compared? Because of F(h,k,l) contains information about atomic scatering factor and phase of rth atom. It shall be used as a quantitative value comparing applicability of various theoretical approaches - only as a parameter, or it shall be used to account for total energy reflected by (h,k,l) plane, for example?

Its involvement as a parameter evaluating between theoretical reliabilities of two structural optimizations, generally, has not sence, because of the validation of theoretically predicted structures is carried out towards experimental crystallographic data. Furthermore, It is well known that largest part of theoretical quantum chemical approaches operate with set of parameters taken from various experimental methods.

If it shall be used to account for total energy reflected, that how shall be taken into consideration polarization factor? If a quantum chemically predicted F(h,k,l) shall be used to predict intensity of a Ihkl reflection, meaning to use quantum chemistry of model of crystal to predict I(h,k,l) remains the problem about the polarization factor, which, however, cannot be solved theoretically.

In other words, with quantum chemical methods or other mathematical tools, including available theoretical approaches, you cannot redict the picture of a crystallographic experiment. And thus you cannot use the quantum chemistry to verify experimental crystallographic data sets (or 'to predict diffraction data').

Please pay attention to the stated below books (1-4), they are useful to the topic of this discussion.

In summary, why you cannot predict the diffraction data and how the polarization factor makes the crystallographic data set unique? By contrast to many other methods, where the experimental data can be deduced or even reproduced at a high level of probability using quantum chemistry, the crystallography operates with a unique set to each measurements of experimental I(hkl) versus scattering anges (it is involved in the polarization factor). This set of data is different within the frame of independent measurements of one and the same crystal as well as within the frame of measurements of different crystal of one and the same compound. In other words, despite that the structure solution of each of those measurements has yielded to one and the same crystal structure, those solutions have different statistical probability, accounted for the R1-factor.

On this base even if you have extracted a quantum chemical F(hkl) factor you cannot compute the intensities, without to know the relationship I(hkl)=f(scattering anges), coming from the experiment however and depends of series factors some of them briefly mentioned above. If you have decided to take I(hkl)=f(scattering anges) from an exeriment to concrete structure and to use it within the frame of quantum chemically determined F(hkl) you do not do nothing different than the crystallographic structure solution. Furthermore this not sense also because of when you have the structure from X-ray experiments, there is not need it theoretical prediction. The single crystal X-ray diffraction as method, provides absolute determination of the structure of the matter.

Even if you have decided to use experimental I(hkl)=f(scattering anges) set from powder XRD exeriments and to combine with the quentum chemistry as an effort to predict the structure, please bear in mind that by contrast to the single crystal XRD, the powder XRD is not absolute method. Meaning that to two different set of experimental I(hkl)=f(scattering anges) powder XRD data you can have a set of two isomorphic structures, having however different chemical content; or there may have spontaneous co-crystallization of two polymorphs of one and the same compound in the matter solution. In the last cases you have in fact two different compounds and structures from chemical and, respective, crystallographic points of view.

In the last topic please pay attention to a discussion and relating attachments:

Why_do_I_get_a_the_same_XRD_spectrum_after_crystallization (https://www.researchgate.net/post/Why_do_I_get_a_the_same_XRD_spectrum_after_crystallization)

There are presented examples of such as systems.

NB! The shown as attachment, herein, total charge density from quantum chemical data is not realistic picture, because of crystallographic data are used as input, but the geometry otimization is at semi-empirical theoretical level and this it has only illustrative character.

[1] D. Cruickshank, H. Juretschke, N. Kato (Eds.) P.P. Edwald and his Dynamic Theory of X-ray Difraction, International Union of Crystallography, Oxford Science Publishing, 1992, pp. 1-161

[2] J. Glusker, K. Trueblood, Crystal Structure Analysis, Oxford University Press, 1985, pp. 1-266

[3] W. Clegg, Crystal Structure analysis, International Union of Crystallography, Oxford Science Publications, pp. 1-261, 2001

[4] P. Mueller, Crystal Structure refinment, A crystallographer's guide to SHELXL, International Union of Crystallography, Oxford Science Publications, 2006, 1-212 (+ CD)

Once again, I stress that Arshad wrote he is not interested in using theoretical calculations to check the correctness of the structure factors extracted from experimental measurement (even more of the actually measured intensities) nor the correctness of a structure optimization. He seems to be interested to see how approximate is the model that he uses (multipolar model) to fit the experimental data. Because the exact electron density is not known, he wants to use the same model to fit a theoretical electron density after transformation in reciprocal space, mimicking what normally done with measured structure factors. By doing so, he expects to estimate how much inaccurate is the multipolar procedure used to fit the experimental data.

Having said that, I take also the liberty to comment on other statements.

There is a lot of research (for more than 20 years) dedicated to fitting theoretical wave functions or density matrices to experimentally measured Bragg structure factors or even intensities, as well as to experimental Compton scattering profiles. Saying that this is impossible, means neglecting a huge part of the research in this field. Atomic displacements can also be calculated with molecular dynamics and therefore properly taken into account in a computation of theoretical structure factors (for example this is now possible with CRYSTAL14). This is not what Arshad plans to do, but it is doable.

In conclusion, the experiment of diffraction by a crystal can be modelled by first principles in all its aspects, once of course all details of the experimental setup are known (which includes the polarization of the radiation, the energy, the response of the detector etc.). At this stage, it is not particularly useful or practical, bu doable for sure.