Mr. Ramirez,

Such as information can be obtained by NBO analysis. You could check is VASP allows it.

Dear Maximo Ramirez,

before I can can answer your question you should more precisely describe what do you mean by charge/electron transfer:

1) The transfer of charges to the electrode of a battery cell?

2) A charge transfer between Li ions and the spinel structure?

3) or other situations?

In principle, adding charges to specific atoms is not possible in DFT calculations. One can only add charges to the whole system. Where these charges are spatially located is one of the results of the DFT calculations.  

Regards,

Roman

hey, i can help you if you use quantum espresso.

but I do believe that it is similar.

try to get mesh files with 3D charge values then substract them from each other the way you want to describe the charge differences then you will end up with a file storing that difference you want to check

check more details in: http://dx.doi.org/10.1039/C5NR06038A 

and https://doi.org/10.1109/ESSDERC.2016.7599645 

let me know if you need further help.

Dear Karim Elgammal,

I apreciate your help. I have been tried to use Quantum Espresso, but unfortunately I couldn't optimize my unit cell.

An extra question, I have LiMn2O4, you suggest me that I should calculate the chanrge density for Li, Mn2O4 and LiMn2O4, and for calculate the different of charge density substract:

LiMn2O4 - Mn2O4 - Li or LiMn2O4 - Mn2O4?

According to the comments by Mr. Leitsmann, if we describe a system HCN with total change '0' and multiplicity '0'; and perform a DFT optimization, despite the initial charge distribution there should be obtained one and the same final state corresponding to the PES minimum (i.e. absence of negative frequencies), because of there is a net charge '0'. This final state should be NCH (N-C triple bond).

Now, let us describe the following two systems NCH (N-C triple bond) and N(-)=C(+)-H (Attachment). Presumably the latter system should yield to the former one according to the discussed concept. The results, however, show two NCH final systems with N-C triple bond with absence of negative frequencies in both cases. But the differences of the IR modes are within 7-4 cm-1 (The geometry parameters are also shown). Taking into consideration that the accuracy of DFTs is within 2-1 cm-1 computing stretching vibrations between heavy atoms, the DFTs, therefore, distinguish, two states on the base on their different electronic initial states, both corresponding to the minimum of PES of the system HCN. Furthermore, we are talking here for a completely simple as electronic and molecular structures examples of molecules (3 atoms and one complex bond).

A third system, {[NCH]0}, but with the following initial charge distribution state: N(+)=C(-)-H can be examined, as well. Presumably, it can be regarded as a model of an ensemble of {N(+)-C...H-} species, where C-N+ has a higher order bond (attachment). A completely different final state, again corresponding to the minimum PES (i.e. without negative frequencies, attachment), is obtained. Same is valid to the IR data and the NBO analyses (Attachment).

These examples are very particularly illustrative about the DFTs' capability and sensibility to distinguish charge localization/delocalization (i.e. fine electronic effects), in fact.

As attachments are also given the input *.gjfs.

According to the comments by Bojidarka B. Ivanova, of course it is possible to define different initial electronic configurations in DFT calculation. In this one can obviously obtain different final states (within different local minima). 

My point was that in complex bulk system an additional charge cannot easily be added to specific spatial regions, because the electronic states are usually delocalized. 

If one is now interested in the calculation of e.g. reduction reactions at battery electrodes (Mn2O4 is a common electrode material) one has to take into account the charge transfer of electrons provided by the electrical potential of the electrode. A correct description of the dynamics of this process is quite complicated with DFT methods (but of course not impossible).

Therefore, I have asked in which kind of charge transfer Maximo Ramirez is interested.  

According to the comment of Karim Elgammal, the same is also possible in VASP.

The CHGCAR file contains the calculated 3D charge density.  

see: https://cms.mpi.univie.ac.at/vasp/vasp/CHGCAR_file.html

Dear,

I refer to charge around of Mn and O atoms.

I don't want to add extra charge to the initial structure.

CHGCAR file contains total charge density multiplied by the volume.

Here you can read the article in question, especially the electronic section: http://everest.iphy.ac.cn/papers/prb67.115130.pdf

Let us, first, summarize briefly what means the term 'periodic boundary condition'. The connotation is: Description of properties of bulk/crystalline materials within the framework of the unit cell content. Or the theoretical treatment expresses the properties of a (whole) bulk system, in fact. Because of the properties of the bulk are periodic function from a unit cell to the next one. This common approach is used in describing properties of bulk independently of the methodology (DFT, ab initio, etc.).

Now, in this context according to the comments by Mr. Leitsmann, within the framework of a total charge value, there should be obtained equal distribution over the given type atoms within the framework of a unit cell using DFT.

Let us focus attention to the following examples (Attachment). The first system is {[Fe3O]6+}. It can be regarded as {[(Fe3+)2.(Fe2+)O]6+}. The second example describes {[Fe3O]7+} (Oxidation state only Fe3+). There are obtained different local (non-equal) charges over the three Fe3+ ions. The CT effects can be evaluated using the so - called 'stabilization energy' (Equation and data, attachment page 1).

For redox analysis it is useful to apply a model of DFT computations in anisotropic medium. We could assume that applying a voltage there are affected the polarization properties of the medium. There are shown examples of computations of {[Fe3O]6+} in isotropic and anisotropic media (Anisotropic: ex = ey = 0.1, ez = 100) (Attachment, page 2). If there is important to account the effect of the ionic strength (Often it is!) the corresponding computations in page 3 (See data in page 2 (right-column) and page 3) account for both anisotropic medium and the ionic strength effect (mu = 1.0 mol.dm-1, for example).

So, the evaluation of the natural electronic configurations, bond-nature and CT effects allows to study in detail the chemistry of any redox process by the DFT.

It goes without saying that such analyses are very far from complex ones. These results are a direct great argumentation with respect to the capability of the shown approaches to provide detail data about the chemistry of redox processes of complex (furthermore mixed valence) objects.

In addition, the natural charges correlate well to the Bader's topological treatment of the electron density. Given that, by two different methods as methodologies and philosophies, there are obtained comparable information about the charge localization/delocalization.

The essential computations of a redox potential (quantities) is more than clear, and well known, as equations and methodologies as well.

The the Nernst's equation is a textbooks' knowledge.

When activity a = 1, the standard electrode potential is E0 = E.

But: DG = -nFE (Where DG - Gibbs free energy; F - Faraday's cost. (96485 C.mol-1)).

On the other hand DG = DG0 + RT ln(ared/aox).

Or there are needed only the energies of the red and ox, but they are derivated directly via the shown computations.

By definition of charge density in an extended system, charge transfer is ill defined in principle. Further, more often than not, processes entailing charge transfer near the Fermi level are generally compensated by other population backflows from one species to another in the electronic structure. You cannot make quantitative statements except in very rare instances, and then only approximately and not unambiguously.

That said, we all resort to and rely on the charge transfer concept in a way or another. Ways to estimate charge population on each species in a condensed phase that are sometimes useful include the Bader decomposition (a postprocessing tool doing that for VASP exists) or the Mulliken population analysis, as well as, of course, DOS projection on atomic orbitals. In some computational methods such as self-interaction corrected DFT there are atom- and orbital-resolved occupation numbers that, empirically, look fairly reasonable too.

Mr. Ramirez,

According your new comments, there is a question about what your analysis presents, in fact?! The interactions in a model system {Li0 + 2xMn0 + 4xO0} does not seem to be what is happening as interactions in the ionic-covalent compound {[LiMn2O4]0}.

There should be distinguished between different oxidation states of the interacting atoms in order to obtain meaningful information, nevertheless of the methodology.

You could pay attention to a new attachment, in this context. It reflects, how different initial oxidation states (electronic configurations of the atoms in the models) reflects on orbital population, energetics and other parameters/properties.

It is also shown (Attachment, page 2) an example of 2D cubic unit cell of 4C-atoms (a = 5 A). Your methodology is also illustrated as a comparative analysis.

Even within the framework of identical ensembles of 4C atoms in a 2D structure, there is a difference of the energies at about 0.0279 a.u. (ca. 17.5 kcal.mol-1) depending on the positions of C+/C- centers.

If you would like to predict any CT effect, you should take into consideration the proper oxidation states of the ionic species in your compound. Otherwise, you present a theoretical model of interacting atoms in their atomistic electronic configurations (Or this system: {Li0 + 2xMn0 + 4xO0}).

Simply speaking, you do not add and/or remove charges over the atoms. You fix the initial electronic configurations corresponding to the chemically bonded/interacting species (below).

Of course, the comments stated above do not exclude CT effects between species in their elemental state. But, it should be noted, here, that the latter model cannot be regarded as a plausible one of the real chemical compound {[LiMn2O4]0}. There are overridded the energetics and processes associated with bonds formation and different types inter-ionic interactions; and mechanisms of the reaction(s) of Mn2O4- anion, as well.

The latter statement, means that, the isolated chemical compound {[LiMn2O4]0} does not represent a '7 “particles”-problem', because of the synthetic mechanism includes more than one reaction step.

Toward: ...."we all resort to and rely on the charge transfer concept in a way or another" (A comment by Mr. Fiorentini): The terms 'CT effect' and 'oxidation state' have different connotations. There is explicitly shown that CTs (but negligible effect to C-atoms) could be found even when the particles have oxidation state '0' (elemental state) and a general p-character. But, the energetics and the electronic population on the orbitals are different, and depend on the oxidation states (meaning electronic configuration). A completely different situation is CT effect from C0 (el. conf.: 1s22s22p2) and {C-] (el. conf.: 1s22s22p3), minimum, because of in the former case there is a JT effect, too (Attachments pages 1 and 2).

On the other hand, we do not talk here about theoretical concepts in the chemistry. We reflect chemical reactivity and structural analysis of Mn2O4- anion (Experimental properties of evidences). It has significant degree of covalency. So, the anion is not an ensemble of {[2xMn + 4xO]-} interacting 6 neutral spheres and one free electron between them. Therefore, how a negative charge is distributed over the atoms in the initial state of a model of a complex ion affects significantly to the energetics, orbital population, nature of the bond, etc., and thus to the chemical properties.

Dear Ivanova,

I suppose that you reffer to NBO code from the Schmidt Group [http://schmidt.chem.wisc.edu/nbosoftware].

In theory, my configuration should be {Li+1 + 2xMn+? + 4xO-2}, where "? symbol" should be half of 3 and the other half of 4, for oxidation state or valence, but at this point I don't know how I can reproduce the expected oxidation state in DFT calculation, expecially in VASP.

According to your comments the objetive is distinguish between different oxidation states, but the question is how?

About the paragraph before the last one, is acceptable generate pseudo potentials (POTCAR in the vasp context) for especific one electronic configuration? By example, one for Mn+3 and other to Mn+4?

Well, you expect either a metal or an insulating mixed-valence system (in the latter one Mn is "+3" and the other "+4"). the latter case is standard fare in magnetite Fe3O4, for example, which is well described in semilocal DFT. you do not need to -in fact, you emphatically should not- nudge the DFT code to do something in particular. just use the pseudos provided by vasp: the simplest is Mn and has valence 7, i.e. all of the d and s outher shells. more complex ones are Mn_pv (or Mn_sv) which have semicore p (or p+s) states. such calculations will certainly tell you something useful, unless of course correlations beyond whatever functional you use (I suppose it may be PBE or so) plays an important role, in which case +U or SIC or hybrid methods should be applied.

Dear Fiorentini,

Thanks for the clarification of atoms valence in DFT codes.

Exactly the object LiMn2O4 is an example of crystal structure with mixed oxidation states of Mnn+ ions. Please find as an attachment a figure of the unit cell, using known cif (Ref. 1).

As the authors have written, Mnn+ ions are with oxidation states 3+ and +4, randomly distributed within the framework of the unit cell [Ref.1]. The cif can be downloaded. The synthesis of this compound has been shown in ref. 1 as well.

In this context, Mr. Ramirez,, should perform similar computations like those of Fe3O in my postings of a set of systems using the attached unit cell content within the framework of randomly distributed MnIII/MnIV ions balancing the total charge, which should be '0'.

The energetics should be treated in statistically, in order to determine the correspondence between electronic structure (oxidation state)-energy and, thus, redox potentials.

The computations in my postings were carried out by Gaussian (www.gaussian.com). But NBO can be found as a separate program-package.

Ref. 1. LiMn2O4: a spinel-related low-temperature modification, K. Tateishi, K. Suda,

D. du Boulay, N. Ishizawa, S. Oishi, Acta Cryst. (2004). E60, i18-i21.

Dear Ivanova,

If you didn't add extra charge before de DFT calculation, how can you do calculation for {[Fe3O]6+} and {[Fe3O]7+}, while these compound have differents total charge?

In the Ref. 1 cif file the structure presented is an slice of non-cubic LiMn2O4, with about 700 atoms.

When you write about "The energetics should be treated in statistically", what specific treatement do you refer? Monte Carlo, maybe?

On the other hand, I couldn't install NBO, I don't have neither ifort nor mkl libraries.

Finally, I have been done Bader analysis of charge density and found that there are atoms of Mn with differernt charge, but also O atoms have different charge values.

May be we should state that there are some differences between a plane wave code (VASP) and a code with localized atomic orbitals (NBO). In the latter it is possible to force certain initial charge distributions which correspond to certain oxidation states. In a plane wave code this is not possible! In VASP you can define only the amount of total charge of the system, the total spin of the system, and you can force a certain occupation of the Kohn-Sham level during the calculation. BUT a certain initial spatial charge distribution cannot be given!

Mr. Ramirez ,

The unit cell content is 228 atoms (LiMn2O4, ref.1). As I have written all solid-state computations are within the framework of PBC.

In my examples in Prasentation1-4c.pdf, there are shown different charge redistribution within the framework of the total charge const. These computations you should reproduce using DFT.

'Statistically' means that you should place initial charges 3+ or 4+ of Mnn+ at different positions over the atoms in the unit cell of LiMn2O4. Given that, you should receive a set of different energies, corresponding to a concrete distribution of 3+/4+ charges. (The latter analysis does not include Monte Carlo computations).

For example, your unit cell contains the following 2D distribution of the atoms in the unit cell:

Mn(1)....O(1).....Mn(2)....Li(1)

Li(2)....Mn(3)....O(2).....Mn(4)

You should perform a combination of computations where Mn(2) or Mn with number (2) should have oxidation state +3 or +4. Same is valid to all other Mn(n) atoms. The total charge should be '0'.

'Different initial charges' corresponds to different initial electron density distribution over the concrete atoms in the 3D unit cell content.

But as I have written the correlation is: Electronic configuration (meaning ordital distribution and orbital energies)-total energy (or any other energy term).

Natural Bond Orbital (NBO) population analysis has available in Gaussian (www.gaussian.com) (I have mentioned). Or it is available in Gamess-US (http://www.msg.ameslab.gov/gamess/). The latter program-package is free of charge.

Dear Ivanova,

Firstly, thanks for the the Gamess-US link for the NBO calculation.

I'm confused, as mentioned Mr. Leitsmann "In DFT, like VASP, is not possible to add initial charges to atoms". Is there another alternative for simulating the Mn3+/Mn4+?

Mr. Ramirez ,

The alternatives, which I know are already mentioned.

Tmportance of initial charge localization on your computational output data could be illustrated computing Mn3+, Mn4+ and Mn0 ions/atom (attachment).

There are used NBO and AIM analyses. There is significant change of the energy, natural populations and quadrupole moments together with intra-ionic CT effect.

So, you cannot neglect all these effects within the framework of a many-atomic system with a random distribution of Mn3+ and Mn4+ in the 3D space. They affect the energy significantly, which means that they affect the redox potentials studying LiMn2O4 crystal uner different conditions.

In other words, without to take into consideration the initial electronic configurations of the Mnn+ ions you cannot produce meaningful DFT (or any other, including AIM analysis as it is shown) quantum chemical analysis of the chemical compound LiMn2O4. Furthermore, I have written that the degree of covalency of Mn-O bond is relatively high.

You could perform DDEC6 analysis to compute the net atomic charges and bond orders. The net atomic charges quantify the charge transfer between atoms in the material. (The net atomic charges for LiMn2O4 are studied in Table 1 of paper # 2 below.) This method has a lot of useful properties. See the following papers for details:

(1) T. A. Manz and N. Gabaldon Limas, “Introducing DDEC6 atomic population analysis: part 1. Charge partitioning theory and methodology,” RSC Advances, 6 (2016) 47771-47801 (http://dx.doi.org/10.1039/C6RA04656H).

(2) N. Gabaldon Limas and T. A. Manz, “Introducing DDEC6 atomic population analysis: part 2. Computed results for a wide range of periodic and nonperiodic materials,” RSC Advances, 6 (2016) 45727-45747 (http://dx.doi.org/10.1039/C6RA05507A).

(3) T. A. Manz, "Introducing DDEC6 atomic population analysis: part 3. Comprehensive method to compute bond orders," RSC Advances, 7 (2017) 45552-45581 (http://dx.doi.org/10.1039/C7RA07400J ). (open access)

The DDEC6 method is available in the free Chargemol program (http://ddec.sourceforge.net) which can analyze the outputs of VASP, Gaussian, and other quantum chemistry programs.

For VASP, follow these steps:

(1) Get your desired geometry from either experiments or geometry optimization or any other method of your choice.

(2) Prepare an INCAR file with the following keywords: NSW = 0 (don't change geometry), Prec = Accurate (use an accurate integration grid), ENCUT = value greater than or equal to 400 eV, LAECHG = .TRUE. (generate the AECCAR0 and AECCAR2 files), and LCHARG = .TRUE. (generate the CHGCAR file), and any other keywords appropriate to your particular material calculation.

(3) In the KPOINTS file, set up your k-point grid so that the product of number of k-points along each lattice direction times the length of that lattice vector is at least 16 angstroms. For example, if your lattice vector lengths are 2.54 angstroms, 5.8 angstroms, and 17.2 angstroms, you could use a 7 (or 8) x 3 x 1 kpoint mesh. Usually the auto Monkhorst-Pack scheme works well; however, use Gamma point if k-point mesh is 1 x 1 x 1.

(4) Place the AECCAR0, AECCAR2, CHGCAR, and POTCAR file into a directory and add the job_control.txt file. (See above program manual for how to set up and use the job_control.txt file.)

(5) Run the Chargemol program to produce the output files containing the net atomic charges, atomic spin moments (for magnetic materials), atomic dipoles and quadrupoles, bond orders, overlap populations, etc.