first principle study of carbon nanotubes(rahul).pptx

carbon nanotubes are the base for semiconducting industry.

1. First principle study of carbon nanotubes S ubmitted By: Submitted To: Rahul Dr.Sunita Negi M.Sc Physics Associate professor 200130302002 Physics School of En gineering and Sciences, G.D. Goenka University Grurgram , Haryana – 122103, INDIA Correspondence to : [email protected]

2. Objectives To calculate the density of state using first principles. To develop a better understanding of ABINIT and VMD software. To use VMD software for development of simulated model of “CNT” (carbon nanotube) using graphene sheets.

3. Introduction Graphene sheet Graphene sheets are essentially the finest materials in the world. Graphene sheet is a one-atom-thick planar sheet of carbon atoms which are intensively packed in a hexagonal lattice structure. Carbon nanotube A carbon nanotube (CNT) is one of the most important nanomaterial, it is a hollow tube made up of carbon of nanoscale diameter. Nanotubes are formed by folding or rolling two-dimensional graphite into a cylindrical shape structure. Nanotubes are hollow from inside. The diameter of the nanotube is around 1-3 nanometers.

4. What is ABINIT ABINIT is a package whose main program allows to find the total energy, charge density and electronic structure of systems made of electrons and nuclei (molecules and periodic solids) within Density Functional Theory Some possibilities of ABINIT go beyond Density Functional Theory, i.e. the many-body perturbation theory (GW approximation the Bethe- Salpether equation), Time-Dependent Density Functional Theory.

5. . 1. Access to the executable : After compilation, the main code will be present in the package as ~ abinit / src /98_main/ abinit (or perhaps at another place, depending on your installation). 2. An input file : The detailed description of input variables is as follows Basic variables : Are generally used to define the dimensions, types of atoms in a unit cell etc. Ground-state calculation variables : Are used to assign ground state input variables GW variables : These variables provides the description of the name (keywords) of the gw input variables to be used in the input file for the abinit executable and used to assign calculation methods. The main executable: abinit

6. Files handling variables : These variables provides the description of the name (keywords) of the files input variables to be used in the input file for the abinit executable and used to assign Hamiltonian and eigenstates Parallelisation variables : This provides the description of the name (keywords) of the paral input variables to be used in the input file for the abinit executable and used to work in parrel mode with GPU. Density Functional Perturbation Theory variables : This provides the description of the name (keywords) of the dfpt input variables to be used in the input file for the abinit executable and used for liner,non -linear calculations and perturbations. The main executable: abinit

7. The main executable: abinit 3. A pseudopotential input file for each kind of element in the unit cell:   The pseudopotential is an attempt to replace the complicated effects of the motion of the  core  (i.e. non- valence )  electrons  of an  atom  and its nucleus with an effective  potential , or pseudopotential, so that the  Schrödinger equation  contains a modified effective potential term instead of the  Coulombic  potential term for core electrons normally found in the Schrödinger equation. The pseudopotential is an effective potential constructed to replace the atomic all-electron potential (full-potential) such that core states are eliminated and the valence electrons are described by pseudo-wavefunctions with significantly fewer nodes. Motivation: Reduction of basis set size Reduction of number of electrons Inclusion of relativistic and other effects

8. VMD (Visual Molecular Dynamics) VMD is designed for modelling, visualization, and analysis of graphene sheets, carbon nanotubes, biological systems such as proteins, nucleic acids, etc. VMD provides a wide variety of methods for rendering and coloring a molecule: simple points and lines, CPK spheres and cylinders, licorice bonds, backbone tubes and ribbons, cartoon drawings, and others. VMD can be used to animate and analyze the trajectory of a molecular dynamics (MD) simulation. In particular, VMD can act as a graphical front end for an external MD program by displaying and animating a molecule undergoing simulation on a remote computer.

9. VMD files Graphene sheet Carbon nanotube

10. Test Run on Electron Localization Function (ELF) The standard input file used for isolated H-atom acell 3*30 natom 1 nsym 8 tolwfr 1.0d-14 diemac 1.0d0 nband 1 ntypat 1 typat 1 diemix 0.5d0 nkpt 1 occ 1 wtk 1 iscf 3 nline 3 rprim 100 010 001 znucl 1 ixc 20 nsppol 1 symrel 1 0 0 0 1 0 0 0 1 -1 0 0 0 1 0 0 0 1 1 0 0 0-1 0 0 0 1 -1 0 0 0-1 0 0 0 1 1 0 0 0 1 0 0 0-1 -1 0 0 0 1 0 0 0-1 1 0 0 0-1 0 0 0-1 -1 0 0 0-1 0 0 0-1 xred 3*0 kpt 3*0.25 nstep 6 tnons 24*0 prtelf 1

11. . Comparison of ABINIT results with the earlier theoretical data

12. Test Run on an isolated Li atom Since the hydrogen atom is a bit peculiar for test of ELF we have also performed a test with another isolated atom. We use here lithium (Li) because ELF which can be used to show up the shell structure of isolated atoms, is very simple for Li. Actually for Li this is just a single s shell. We use for that an all electron calculation. First with a bare pseudopotential : Then with fhi pseudopotential :

13. ABINIT ELF for an isolated Li atom with a bare pseudo

14. ABINIT ELF for an isolated Li atom with a fhi pseudo

15. Importance of elf ( electron localization function) Electron localization function (ELF) helps in understanding the empirical concept of electron localization. One important characteristic of the ELF is its numerical stability with respect to the theoretical level at which the electron density and the molecular orbitals are calculated. The ELF has emerged as a powerful tool to understand in a qualitative way the behavior of the electrons in a nuclei system. It is possible to explain a great variety of bonding situations ranging from the most standard covalent bond to the metallic bond.

16. Conclusions Developed better understanding of ABINIT and VMD softwares Calculated ELF for isolated H-atom and compared with the analytical graphs Calculated ELF for isolated Li-atom. In future we plan to calculate the DOS of hydrogen and lithium using ABINIT As the input file for CNT are not available in the ABINIT package so we will have to look out for some other methods for creating the same.

17. References http://abinit.github.io/abipy/gallery/plot_ebands_edos.html#sphx-glr-gallery-plot-ebands-edos-py J. W. Mintmire and C. T. White. (1998). Universal Density of States for Carbon Nanotubes. Phys. Rev. Lett. 81, 2506 Pavel V.Avramov , Konstantin N.Kudin , Gustavo E.Scuseria . (2002). Single wall carbon nanotubes density of states: comparison of experiment and theory. Chemical Physics Letters, Volume 370, Issues 5–6. Demichelis , Raffaella & Noel, Yves & d'arco , Philippe & Rérat , Michel & Zicovich -Wilson, Claudio & Dovesi , Roberto. (2011). Properties of Carbon Nanotubes: An ab Initio Study Using Large Gaussian Basis Sets and Various DFT Functionals. The Journal of Physical Chemistry C. 115. 8876-8885. 10.1021/jp110704x Gonze , X. & Beuken , Jean-Michel & Caracas, Razvan & Detraux , F. & Fuchs, M. & Rignanese , G.-M & Sindic , L. & Verstraete , Matthieu & Zerah, G. & Jollet , F. & Torrent, Marc & Roy, A. & Mikami , Masayoshi & Ghosez , Philippe & Raty , Jean-Yves & Allan, D.C.. (2002). First-principles computation of material properties: The ABINIT software project. Computational Materials Science. 25. 478-492. 10.1016/S0927-0256(02)00325-7. https://docs.abinit.org/tutorial/ https://docs.abinit.org/variables/#A Qian Jia,  Zaixiu Yang, Lei Sun,  Kaixiong Gao, Bin Zhang,  Xingkai Zhang,  Junyan Zhang, Catalytic superlubricity via in-situ formation of graphene during sliding friction on Au@a-C:H films, Carbon, 10.1016/j.carbon.2021.10.016,  186 , (180-192), (2022). Stéphane Noury , Xénophon Krokidis , Franck Fuster , Bernard Silvi , Computational tools for the electron localization function topological analysis, Computers & Chemistry, Volume 23, Issue 6, 1999, Pages 597-604, ISSN 0097-8485. Patricio Fuentealba , E. Chamorro, Juan C. Santos, Chapter 5 Understanding and using the electron localization function, Editor(s): Alejandro Toro- Labbé , Theoretical and Computational Chemistry, Elsevier, Volume 19, 2007, Pages 57-85, ISSN 1380-7323, ISBN 9780444527196,

18. Thank you

19. Basic variables Accuracy: Allows to tune the accuracy of a ground-state or DFPT calculation optdriver =0 or 1 , by setting automatically the variables according to the following table : accuracy 1 2 3 4 5 6 ecu E_min E_med E_med E_max E_max E_max pawecutdg ecut ecut 1.2 * ecut 1.5 * ecut 2 * ecut 2 * ecut fband 0.5 0.5 0.5 0.5 0.75 0.75 boxcutmin 1.5 1.8 1.8 2.0 2.0 2.0 bxctmindg 1.5 1.8 1.8 2.0 2.0 2.0 pawxcdev 1 1 1 1 2 2 pawmixdg 1 1 pawovlp 10 7 7 5 5 5 pawnhatxc 1 1 1 1 1 tolvrs 1.0d-3 1.0d-5 1.0d-7 1.0d-9 1.0d-10 1.0d-12 tolmxf 1.0d-3 5.0d-4 1.0d-4 5.0d-5 1.0d-6 1.0d-6 optforces 1 1 2 2 2 2 timopt 1 1 1 1 npulayit 4 7 7 7 15 15 nstep 30 30 30 30 50 50 prteig 1 1 1 1 Prtden 1 1 1 1 accuracy 1 2 3 4 5 6 ecu E_min E_med E_med E_max E_max E_max pawecutdg ecut ecut 1.2 * ecut 1.5 * ecut 2 * ecut 2 * ecut fband 0.5 0.5 0.5 0.5 0.75 0.75 boxcutmin 1.5 1.8 1.8 2.0 2.0 2.0 bxctmindg 1.5 1.8 1.8 2.0 2.0 2.0 pawxcdev 1 1 1 1 2 2 pawmixdg 1 1 pawovlp 10 7 7 5 5 5 pawnhatxc 1 1 1 1 1 tolvrs 1.0d-3 1.0d-5 1.0d-7 1.0d-9 1.0d-10 1.0d-12 tolmxf 1.0d-3 5.0d-4 1.0d-4 5.0d-5 1.0d-6 1.0d-6 optforces 1 1 2 2 2 2 timopt 1 1 1 1 npulayit 4 7 7 7 15 15 nstep 30 30 30 30 50 50 prteig 1 1 1 1 Prtden 1 1 1 1

20. Basic Variables acell : Gives the length scales by which dimensionless primitive translations ( rprim ) are to be multiplied. By default, given in Bohr atomic units (1 Bohr=0.5291772108 Angstroms) e cut : Used to define the kinetic energy cutoff which controls the number of planewaves at given k point. The allowed plane waves are those with kinetic energy lower than  ecut , which translates to the following constraint on the planewave vector G in reciprocal space

21. . ½(2 ) 2 ( k + G ) 2 ‹ ecut All planewaves inside this  basis sphere  centered at k are included in the basis. The cutoff can be specified in Ha units (the default), Ry,eV or Kelvin, since  ecut  has the energy characteristics. (1 Ha = 27.2113845 eV) iscf : Controls the self-consistency algorithm. Positive values correspond to the usual choice for doing the usual ground state (GS) calculations or for structural relaxations, where the potential has to be determined self-consistently while negative values correspond to non-self-consistent calculations.  

22. . k pt : Contains the k points in terms of reciprocal space primitive translations (NOT in cartesian coordinates!). Needed ONLY if  kptopt  = 0, otherwise deduced from other input variables. natom : Gives the total number of atoms in the unit cell. Default is 1 but you will obviously want to input this value explicitly. Note that  natom  refers to all atoms in the unit cell, not only to the irreducible set of atoms in the unit cell n band : Gives number of bands, occupied plus possibly unoccupied, for which wavefunctions are being computed along with eigenvalues.

23. . n kpt : If non-zero,  nkpt  gives the number of k points in the k point array  kpt . These points are used either to sample the Brillouin zone, or to build a band structure along specified lines. n step : Gives the maximum number of cycles (or “iterations”) in a SCF or non-SCF run. n sym : Gives number of space group symmetries to be applied in this problem. Symmetries will be input in array “ symrel ” and ( nonsymmorphic ) translations vectors will be input in array “ tnons ”.

24. . n typat : Gives the number of types of atoms in the unit cell. o ccopt : Controls how input parameters  nband ,  occ , and  wtk  are handled. Possible values are from 0 to 9 r prim : Give the three dimensionless primitive translations in real space, to be rescaled by  acell  and  scalecart . s ymrel : Gives “ nsym ” 3x3 matrices expressing space group symmetries in terms of their action on the direct (or real) space primitive translations.

25. . t ypat : Array giving an integer label to every atom in the unit cell to denote its type. The different types of atoms are constructed from the pseudopotential files. x red : Gives the atomic locations within unit cell in coordinates relative to real space primitive translations 

26. Ground-state calculation variables used to assign ground state input variables some of the gs variables are

27. gw input variables These variables provides the description of the name (keywords) of the gw input variables to be used in the input file for the abinit executable and used to assign calculation methods. Some of the gw variables are awtr cd_customnimfrqs cd_imfrqs ecutwfn bdgw cd_halfway_freq ecutsigx freqspmin freqspmax cd_full_grid ecuteps gw1rdm freqremin cd_frqim_method fftgw gw_nqlwl freqremax cd_subset_freq gw_icutcoul gw_invalid_freq freqim_alpha cd_max_freq gw_frqre_inzgrid gw_frqre_tangrid

28. File handling variables This document lists and provides the description of the name (keywords) of the files input variables to be used in the input file for the abinit executable and used to assign Hamiltonian and eigenstates Some of the parallelisation variables are get1den get1wf getbscoup getbsreso getddb_filepath getbseig getddb getddk getdelfd getdvdb_filepath getden getden_filepath getdkde getdkdk getdvdb getpot_filepath gethaydock getocc getqps getefmas getscr getscr_filepath getsigeph_filepath getsuscep getwfk_filepath getwfkfine_filepath getwfq getwfq_filepath getwfk indata_prefix

29. autoparal use_gpu_cuda max_ncpus nphf use_slk paral_kgb pw_unbal_thresh paral_rf paral_atom npspinor nppert npkpt npimage npfft npband np_slk localrdwf gwpara gpu_linalg_limit gpu_devices Parallelisation variables This document lists and provides the description of the name (keywords) of the paral input variables to be used in the input file for the abinit executable and used to work in parrel mode with GPU. Some of the parallelisation variables are

30. Density Functional Perturbation Theory variables This provides the description of the name (keywords) of the dfpt input variables to be used in the input file for the abinit executable and used for liner,non -linear calculations and perturbations. Some of the dfpt variables are bdeigrf d3e_pert1_atpol d3e_pert2_atpol d3e_pert2_phon d3e_pert3_atpol d3e_pert2_elfd d3e_pert3_dir efmas_dim efmas_deg_tol efmas_deg d3e_pert2_dir efmas_calc_dirs d3e_pert3_elfd efmas_ntheta ixcrot d3e_pert1_phon efmas_bands efmas_dirs frzfermi nonlinear_info d3e_pert1_elfd dfpt_sciss ieig2rf esmear lw_qdrpl d3e_pert1_dir d3e_pert3_phon elph2_imagden efmas_n_dirs lw_flexo