Messages

16

General Questions and Answers / Re: How to explain difference in C-N and C-B interactions?

« on: September 28, 2009, 15:52 »

Yes, according to the eigenstate pictures corresponding to K in the bilayers and trilayers, we frequently see isolated graphene orbitals, in those with a significant band gap.  In the valence band, we tend to see single pi orbitals situated near one set of atoms, while in the conduction band, we see the other set of pi orbitals present in the eigenstate.  In those without this band gap, the energy levels are degenerate and give different-looking eigenstates.  We never get mixing of orbitals at K, because the BN layer bands stay far away from the graphene bands around this point, by as much as 2.5 eV relative to the Fermi energy level.  Thus, this is clearly an indication of doping effects at a long range.  In our models, the layers are kept at 3.34 angstroms apart.  The band gap is easily tuned by interlayer distance, due to exponential decay of the pi orbitals away from the origin.

I have already applied electronegativity differences among these elements in my discussions, so I was looking for other kinds of reasons.  The electron-doping for C...N interactions appears to be stronger than the hole-doping that C...B interactions inflict upon the band gap of graphene.  What influences the strength of the doping effect that a heteroatom has on the orbitals of nearby atoms?

17

General Questions and Answers / How to explain difference in C-N and C-B interactions?

« on: September 27, 2009, 19:54 »

Fellows,
     I have returned with a new challenge regarding my hexagonal boron nitride/graphene composites.  I and my mentor are trying to treat these systems using first-order perturbation theory, by defining interlayer interactions as separable and distinct from each other.  In the unit cells, we have only B...C and N...C interactions.  We also have intrabond interactions, as a primary source for band degeneracy in graphene and polarized bonds in h-BN layers.  Based on our eigenstate pictures for both materials, we found larger orbitals for boron compared to nitrogen.  We focus on the energy levels near K of the Brillouin zone, where the band gap is formed in our composites and Dirac cones exist for graphene.  Basically, we control how far the apexes in the Dirac cones are from each other in these composites.  This produced one of our initial assumptions about the contributions arising from B...C and N...C interactions.

However, when I analyzed the composites by looking at each instance either of these interactions occur in the unit cells, I was able to reproduce observed band gap size trends when the N...C interaction contributes more to energy level perturbations than the B...C interaction does.  Trying the other way, relying on orbital size alone, fails to reproduce the finding that a NB C staggered bilayer has a larger band gap opening (0.0637 eV for a DZDP 40x40x20 LDA grid) than a BN C staggered bilayer (0.0399 eV with the same parameters).  In the NB C staggered bilayer, the N atom is situated above a C atom in the graphene layer, leaving the B atom situated above a hole in the ring.  The BN C staggered bilayer has the opposite situation.  We also encounter problems for trilayer conformers with regards to how large the band gap is, depending on how many of these interactions appear in the unit cell, when we initially assume a B...C interaction is stronger than a N...C interaction.

I have performed electron density contour cuts through a BN C eclipsed bilayer, provided in the post (whose band gap is a sum of both staggered bilayers' band gaps), observing that the N atom expands outwards more than the B atom.  This means that the probability density at nitrogen atoms expands further out than that at boron atoms.  In our first-order perturbation theory treatment, we assume that each N...C interaction pushes the graphene energy level upwards (destabilizes it), while B...C interactions are attractive and move the energy level to lower energies.  Each interaction is kept at the same distance from each other, and these interactions clearly show exponential dependence on distance between layers.  Adding a new layer for trilayer conformers retains the additivity of these interactions, but also introduces cancellation by dipole-dipole opposition.

As each B...C interaction is essentially an empty orbital interacting with a half-occupied orbital (for graphene there is a degenerate pair of orbitals and we are filling them half-way with electrons to simulate its metallic behavior), and a N...C interaction is a lone pair interacting with a half-occupied orbital, there is a difference between these two interactions in terms of electron-electron interactions.  One is an one-electron interaction (indeed attractive but weak), while the other is a three-electron interaction (repulsive and can be strong).

Here is my question for you: Are there reasons as to why I am getting a larger band gap when I allow N...C interactions, compared to B...C interactions?  This will really help me a lot with my dissertation and can help me answer challenges from my mentor and committee alike.  I wanted to discuss this because of the initial assumptions failing to make sense (how can a larger atomic orbital not induce a stronger energy shift compared to a smaller one, unless there are differences between these orbitals in terms of another property?).

18

General Questions and Answers / Re: Unoccupied orbitals with unusual shapes

« on: September 18, 2009, 17:28 »

Thank you for the information.  I found out more about the role of the unit cell in defining the Bloch wavefunction conditions.  It tells that at edges of unit cells or Brillouin zones, discontinuities can exist.  They cannot exist anywhere else, and I noticed that the four-fold coloring of the orbitals arises from four separate discontinuities.  As one of the atoms lies right on the edge of the unit cell (coordinates of that atom are x=0 and y=0, leaving it right on an edge), there are four unit cell replicates it is crossing through.  Perhaps a look straight down at one of these orbitals should help to confirm this.

I have been able to explain this to my mentor and will consider making a picture showing a top-down view of the multi-colored orbitals for the supplemental information.  Graphite is an excellent example of these orbital discontinuities, as it has two atoms on the edge of the unit cell.

19

General Questions and Answers / Re: Unoccupied orbitals with unusual shapes

« on: September 15, 2009, 15:41 »

An update...I found out the composition of the Gamma eigenstate at the conduction band level!  After reading an article on photoelectron spectroscopy with 65 eV photons in Surface Science, vol. 162, year 1985, pages 11-18, the mention of 3s orbitals gave me a clue.  As the Gamma LUMO eigenstates in bilayers or larger systems are two-noded and spherically symmetrical, they are very likely 3s orbitals.  I have a few more orbitals to show, in hopes of getting responses from you.  This time, these are from graphite conformers I tested for the dissertation.  It is another of the challenges from my mentor, so solving it will make the dissertation harder to compromise.

In some of these eigenstates, the phase factors seem quite different from the usual 0 and pi values.  There are also instances of sharp discontinuities between phase=0 and phase=pi in some of the conduction band eigenstates.  Can you explain why this happens?  They do look very much like pi orbitals, despite their strange coloring patterns.

20

General Questions and Answers / Unoccupied orbitals with unusual shapes

« on: September 5, 2009, 23:26 »

Fellows, it is me again.

I am continuing my work on the dissertation, and have received a new challenge from my mentor (we had solved some of the others) regarding the work in it.  He seems to be concerned about the unoccupied eigenstates I plotted for some of the materials I am using in the dissertation.  For the examples I am posting on this topic, I am using monolayer hexagonal boron nitride, whose calculations I performed with a 40x40x20 LDA-PZ grid and DZDP (double zeta double polarized).  I obtained the eigenstates near the Fermi energy level at Gamma, K, and M.  As h-BN is isoelectronic with graphene, both have the same number of eigenstates.  In the case of monolayer h-BN, the occupied eigenstates end with eigenstate #3 (starting from #0), and the unoccupied energies begin with eigenstate #4.  These eigenstates are the solid-state equivalents of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and are used primarily to help my chemistry-oriented committee understand my work.

When I plotted the LUMO eigenstate at Gamma for h-BN, I obtained an orbital that looks quite different.  It is quite easy to figure out which orbitals contribute to the eigenstates that are occupied, but virtual orbitals are challenging in terms of physical meaning.  In h-BN, I do get N-centered orbitals for the occupied eigenstates, as they are electron-rich.  The boron atoms are primarily used for the empty orbitals (unoccupied energy levels), as they are electron-poor. 

Can you find out what orbitals contribute to the Gamma LUMO in h-BN?  I sometimes get the same thing in orbital images using bilayer structures with h-BN in them.  Do you have anything else to tell me about unoccupied orbitals near the Fermi energy level?  They generally arise from mixing of atomic or group orbitals (very useful for molecular orbitals).

21

General Questions and Answers / Re: a question about temperature in two probe calculation

« on: August 27, 2009, 15:24 »

Related to the electron temperature for the Fermi-Dirac distribution function in calculations, is there an explanation for why an electron temperature set to zero K causes failure of the calculation?  In this instance, the distribution is discontinuous at the Fermi energy level, but at other values, it is continuous.  This was one of the challenges I received from my mentor while discussing the methods I used in the thesis.  We can easily generate results using temperatures of 5 K, but never with zero K.

Is there a reason why the discontinuous distribution at 0 K cannot be used, while a continuous distribution at 300 K leads to successful calculations, aside from the difficulty of derivatives being taken from it (such a distribution is well treated in integral calculus)?

22

General Questions and Answers / Definitions of split valence orbitals

« on: August 25, 2009, 19:33 »

Fellows,
      I am continuing to work on my dissertation draft, which features a lot of calculations using this program.  Right now I am encountering some challenges from my mentor.  One of these is the definition of split valence orbitals in my theoretical calculation section of the draft. So I would like to see good illustrations of split valence orbitals.  Split valence orbitals are the basis sets we use in the program, and the type of orbital I routinely use is the double zeta double polarized basis set.  What I am looking for is a clear and concise description of split valence orbitals and how they contribute to an approximation of the Schrodinger equation solutions.  This will help me explain the basis sets I used in my calculations better, and as I am a visual learner, pictures or illustrations help me a lot.

Some questions to consider:

What is the general definition of a split valence orbital?  Why were they originally developed as an approximation to the Schrodinger equation? Based on literature I have found, it is a composite of two wavefunctions represented by their own basis sets.

What advantages do split valence orbitals offer to theoretical calculations?  Compared to Hartree-Fock orbitals, Slater basis sets (STO-3G), and popularly used Gaussian basis sets (like 6-31G, a basis set that uses six primitive orbitals plus a few Gaussian wavefunctions for each atomic orbital)?

Are there good literature sources that I can use to help with definitions of split valence orbitals?

I appreciate your help with this and hope others can learn from these questions.

23

General Questions and Answers / Re: ATKError: bad allocation

« on: July 31, 2009, 23:25 »

I see...I have already repeated the runs using 30x30x10 grids for the normal size unit cells.  They are working now at the moment.  Some of the literature that investigated the same kinds of pi-stacked layer materials have used 36x36 grids in the past, and I was well aware of why larger grids improve results of band structure calculations.  That was in fact the solution to the misaligned bands in graphite relative to the Fermi energy level (one of my posted topics).

24

General Questions and Answers / Re: ATKError: bad allocation

« on: July 31, 2009, 22:20 »

There is basically not much difference between the two systems.  The same six atoms placed in relative positions to each other, yet the boundaries are at different distances from this ensemble of atoms.  I have been using DZDP and a 40x40x10 grid to help obtain high-quality results for my dissertation work.  The mesh cutoff is 150 Rydbergs and I normally use LDA-PZ or GGA-revPBE, one at a time.  The models that worked were the ones having the boundaries far away from the atoms (the c-axis direction in the Brillouin zone is very reduced), while the ones that failed were the ones with a more significant c-axis component in the BZ.

The Brillouin zone pathway I used in the previous experiment was to comply with another article, a 1992 entry in Russian Physics Journal by Grinyaev and Lopatin.  It is A-L-M-Gamma-K-H-A-Gamma or in fractional coordinates: (0,0,1/2) - (0,1/2,1/2) - (0,1/2,0) - (0,0,0) - (1/3,1/3,0) - (1/3,1/3,1/2) - (0,0,1/2) - (0,0,0) in that order.  60 points between each k-point are used to produce the band structure diagrams, which help me a lot with making zooms of the K point for carbon-containing layer models.

I have attached the VNL files that failed to produce output.  The crystal system is hexagonal, so that I can relate with the previous conformers (staggered and eclipsed) of the same layered system.  I have looked at the structures with Nanoscope and found no overlap of atoms, but very well formed hexagonal rings.

25

General Questions and Answers / Re: ATKError: bad allocation

« on: July 31, 2009, 01:54 »

I get this same error with a system known as rhombohedral graphite, which I successfully converted to a hexagonal crystal structure.  The unusual thing is that if I use a large sized unit cell to separate the three layers from their neighboring cells (a supersized cell), I do not encounter this error.  If I use a normal sized unit cell for the structure, I seem to get this error below.

Traceback (most recent call last):
  File "c:/users/christ~1.wel/appdata/local/temp/tmpo_zain.nl", line 213, in ?
    runtime_parameters = runtime_parameters
ATKError: bad allocation
Terminated Abnormally

The normal sized cell has c set at 10.065 angstroms, while the supersized unit cell has it set at 30 angstroms, with the layers still at 3.435 angstroms apart.

I attached a VNL file corresponding to a successful result (the supersized cell).  The error happens almost immediately, before the self-convergence iteration begins, so it does not complete.  I have a dual core PC on Vista.

26

General Questions and Answers / Rhombohedral graphite?

« on: July 8, 2009, 02:20 »

Friends,

I am continuing my research into graphite and hexagonal boron nitride modeling with Virtual NanoLab 2008.10.  When I looked through the default Crystal Cupboard to look for a particular form of graphite, it was not there.

This form is rhombohedral graphite, which is 40% or less of natural graphite.  It has the ABCABC stacking of graphene sheets and a two-atom unit cell.  The dimensions of this cell, according to IUPAC, are a = 256.6 pm and c = 1006.2 pm (in angstroms they are a = 2.566 A and c = 10.006 A).  The space group this crystal belongs to is R(3 bar)m.  The Schoenflies symbol it belongs to is D_3d⁵.  A similar structure can be found at the Naval Research Laboratory crystal structure database.

I want to use this model to make mixed carbon/boron nitride models that mimic the ABCABC stacking structure, and also to calculate band structures of both carbon and boron nitride versions.  I have already used the Bernal and simple hexagonal structures of graphite with both C and BN.  If you know how to make rhombohedral graphite on your program, I would appreciate your help.  I would also like to see coordinates of the atoms in both fractional and Cartesian coordinates, as well as supercells (so I can mix the elements together in them).

Thank you for your help.

27

General Questions and Answers / Re: Fermi energy misalignment in graphene-based models

« on: June 23, 2009, 00:37 »

Yes, I have unit cells with only two to six atoms in them.  I took notice of the grid size effect on the Fermi energy level after testing whether that strategy would help.  I am actually running this program on two dual-core computers and one single-core computer, but they are not parallel with each other.  This allows me to run three independent experiment trials.

The strategy here is to prepare high-quality runs for the same layered models as before, using the finer grid over the coarse grid that I started out with.  That way, I will have publishable band structure pictures that reproduce other works using VASP (theoretical plane-wave) and ARPES (experimental method).  So I basically had run 'crude' tests with the 5x5x5 grid and now am in a position to do the bigger grid runs.

28

General Questions and Answers / Re: Fermi energy misalignment in graphene-based models

« on: June 22, 2009, 21:22 »

That is correct.  I am actually planning on repeating the layer calculations with a grid of 40x40x10 and using a different k-point pathway to expose the Dirac intersection points at K for graphene-containing models.  My original 5x5x5 grid results were good enough to reveal the splitting patterns and is being used towards a grant proposal in the future.

This means if you have a feeling about where the Fermi energy level should be but default grids are not treating it properly, use a finer grid to see if it fixes the energy placement of the individual bands in the calculation.

29

General Questions and Answers / Re: Fermi energy misalignment in graphene-based models

« on: June 22, 2009, 18:59 »

Seems that no one had an answer...

So I went ahead and had an idea that something in the parameters had to do with this quandary.  I noticed that the Brillouin zone integration grid has a very dramatic effect on where the Fermi energy level is for these materials.  I first tried a 10x10x1 grid then another experiment with 15x15x1 (different from the default 5x5x5 grid) on the same graphene model.

I got the K-H line to lie very close to the Fermi energy level with the 15x15x1 grid, so it is the integration grid that was producing the misalignment.  As I was using so few sample points in the grid, overestimation ran rampant in the calculations.  This led to the misalignment, so I plan to repeat the layered material experiments with a different grid.

So if you notice something different with your band structure calculations with the default 5x5x5 grid (even if the k*p behavior is great), try altering your integration grid by adding more points to it.  That will definitely improve accuracy of the calculations significantly, sometimes at little cost of computational time.

30

General Questions and Answers / Fermi energy misalignment in graphene-based models

« on: June 16, 2009, 00:48 »

Fellows,
     I have been investigating layered materials based on graphene and hexagonal boron nitride.  Recently, when using Virtual NanoLab 2008.10, I examined effects of conformation and composition on the band structures of these layered materials.  I created a lattice-matched model for both layer materials to be used in the same unit cell, assuming that they relax to form the interface.  These materials differ by less than 1.8% in their lattice constants, so little strain is expected for the interface formation.  One consistent tendency I found was misalignment of the Fermi energy level of the graphene or carbon band structure.  The individual graphene bands rarely line up with the Fermi energy level at the K and H points of the Brillouin zone (where the Dirac intersection point should be).  Since band structure is calculated relative to the Fermi energy level, the misalignment is quite visible in band structure diagrams, because it is not placing the Dirac intersection point right at zero energy (should be the Fermi energy) of the diagram.  What factors can cause misalignment of the Fermi energy level, as in these examples?

I had found that boron nitride layers were causing the graphene layers to experience loss of degeneracy at the K and H points, turning graphene sheets into indirect band gap conductors.  The misalignment is not making it difficult to understand the K-H line behavior, but is making it tricky to look at carrier concentration in the line.  We do know that a band gap opens in graphene when it is covered with boron nitride layers, regardless of orientation.  This finding seems to be very similar to the discovery that electric fields cause degeneracy lifting in graphene or bilayer graphene (Nature, June 11, 2009), as the boron nitride layers have intrinsic electric fields of their own.  I have included four examples of the misaligned K-H lines, computed at DZDP basis level with LDA for exchange correlation.