User's Guide for the PHonon package
Contents
1. Rove Wscr setki sar Mikl arlVikta 1 qv The phonon linewidth Yq is defined by 2ra Idar k i 1 8 eas er Cras er 2 while the electron phonon coupling constant Ag for mode v at wavevector q is defined as Yav a u 3 rq TAN ep w2 3 where N ep is the DOS at the Fermi level The spectral function is defined as Sow So 4 ae wav 1 a F w IN er The electron phonon mass enhancement parameter can also be defined as the first reciprocal momentum of the spectral function 2 F N Ydq 2 A a 5 qu Wl Note that a factor M is hidden in the definition of normal modes as used in the code McMillan j 7 1 1 T a D exp 0 T 6 1 45 A 1 0 62u po or better 1 04 1 T S exp 04 1 A 1 2 A 1 0 62u4 u where 2 f dw Wiog XP k i 2a F ulows 82. and in particular the physics and the methods of PHonon PHonon has the following directory structure contained in a subdirectory PHonon of the main QUANTUM ESPRESSO tree The Doc contains the user_guide and input data description examples some running examples PH source files for phonon calculations and analysis Gamma source files for Gamma only phonon calculation D3 source files for third order derivative calculations codes available in the PHonon package can perform the following types of calculations phonon frequencies and eigenvectors at a generic wave vector using Density Functional Perturbation Theory effective charges and dielectric tensors electron phonon interaction coefficients for metals interatomic force constants in real space third order anharmonic phonon lifetimes Infrared and Raman nonresonant cross section Phonons can be plotted using the PlotPhon package Calculations of the vibrational free energy in the Quasi Harmonic approximations can be performed using the QHA package 2 The People PHonon package was originally developed by Stefano Baroni Stefano de Gironcoli Andrea Dal Corso SISSA Paolo Giannozzi Univ Udine and many others We quote in particular Michele Lazzeri Univ Paris VI for the 2n 1 code and Raman cross section calculation with 2nd order response Andrea Dal Corso for the implementation of Ultrasoft PAW noncolinear spin orbit extensions to PH
3. directory produces the following codes e PH ph x Calculates phonon frequencies and displacement patterns dielectric tensors effective charges uses data produced by pw x e PH dynmat x applies various kinds of Acoustic Sum Rule ASR calculates LO TO splitting at q 0 in insulators IR and Raman cross sections if the coefficients have been properly calculated from the dynamical matrix produced by ph x e PH g2r x calculates Interatomic Force Constants IFC in real space from dynamical matrices produced by ph x on a regular q grid e PH matdyn x produces phonon frequencies at a generic wave vector using the IFC file calculated by q2r x may also calculate phonon DOS the electron phonon coefficient A the function a F w e PH lambda x also calculates and a F w plus T for superconductivity using the McMillan formula e PH fgha x a simple code to calculate vibrational entropy with the quasi harmonic ap proximation e D3 d3 x calculates anharmonic phonon lifetimes third order derivatives of the energy using data produced by pw x and ph x USPP and PAW not supported e Gamma phcg x a version of ph x that calculates phonons at q 0 using conjugate gradient minimization of the density functional expanded to second order Only the T k 0 point is used for Brillouin zone integration It is faster and takes less memory than ph x but does not support USPP and PAW Links to the main QUANTUM ESPRESSO bin directory a
4. up to a distance that depends on the size of the grid of q vectors Input documentation in the header of PHonon PH q2r 90 Program matdyn x may be used to produce phonon modes and frequencies at any q us ing the Interatomic Force Constants file as input Input documentation in the header of PHonon PH matdyn 90 See Example 02 for a complete calculation of phonon dispersions in AlAs 4 3 Calculation of electron phonon interaction coefficients Since v 5 0 there are two ways of calculating electron phonon coefficients distinguished accord ing to the value of variable electron_phonon The following holds for the case electron_phonon interpolated see also Example 03 The calculation of electron phonon coefficients in metals is made difficult by the slow conver gence of the sum at the Fermi energy It is convenient to use a coarse k point grid to calculate phonons on a suitable wavevector grid a dense k point grid to calculate the sum at the Fermi energy The calculation proceeds in this way 1 a scf calculation for the dense k point grid or a scf calculation followed by a non scf one on the dense k point grid specify option la2f true to pw x in order to save a file with the eigenvalues on the dense k point grid The latter MUST contain all k and k q grid points used in the subsequent electron phonon calculation All grids MUST be unshifted i e include k 0 2 anormal scf phonon dispersion calculation on the coars
5. Omen DEMOCRITOS DEmocritos MOdeling Center for Research In aTOmistic Simulation IOM User s Guide for the PHonon package version 5 1 2 Contents 1 Introduction 1 2 People 2 3 Installation 2 3 1 Compilation s se scs a ee ok we eb Oe eb eee ee a See eb See 2 Using PHonon 4 1 Single q calculation o 2a d4 4 oo9 4 6 4 nm Oba wo ee wade es 4 4 2 Calculation of interatomic force constants in real space 4 4 3 Calculation of electron phonon interaction coefficients 5 Parallelism 5 3 wo l er Troubleshooting A Appendix Electron phonon coefficients T 1 Introduction This guide covers the usage of the PHonon package a part of the QUANTUM ESPRESSO distribution Further documentation beyond what is provided in this guide can be found in the directory PHonon Doc containing a copy of this guide This guide assumes that you know the contents of the general User s Guide for QUANTUM ESPRESSO and of the User s Guide for PWscf It also assumes that you have already installed QUANTUM ESPRESSO PHonon is not a stand alone package it requires PWscf to be compiled and used If not please locate the general User s Guide in directory Doc two levels above the one containing this guide and the User s Guide for PWscf in PW Doc or consult the web site http www quantum espresso org It is also assumed that you know the physics behind QUANTUM ESPRESSO the methods it implements
6. e k point grid specifying option electron _phonon interpolated and the file name where the self consistent first order variation of the potential is to be stored variable fildvscf The electron phonon coeff cients are calculated using several values of Gaussian broadening see PHonon PH elphon f90 because this quickly shows whether results are converged or not with respect to the k point grid and Gaussian broadening 3 Finally you can use matdyn x and lambda x input documentation in the header of PHonon PH lambda f90 to get the a F w function the electron phonon coefficient A and an estimate of the critical temperature Ty See the appendix for the relevant formulae Important notice the q 0 limit of the con tribution to the electron phonon coefficient diverges for optical modes please be very careful consult the relevant literature 5 Parallelism We refer to the corresponding section of the PWscf guide for an explanation of how parallelism works ph x may take advantage of MPI parallelization on images plane waves PW and on k points pools Currently all other MPI and explicit OpenMP parallelizations have very limited to nonexistent implementation phcg x implements only PW parallelization All other codes may be launched in parallel but will execute on a single processor In image parallelization processors can be divided into different images corresponding to one or more than one ir
7. ng in insulators Moreover no Acoustic Sum Rule ASR is applied In order to have the complete dynamical matrix at q 0 including the non analytic terms you need to calculate effective charges by specifying option epsil true to ph x This is however not possible because not physical for metals i e any system subject to a broadening At q 0 use program dynmat x to calculate the correct LO TO splitting IR cross sections and to impose various forms of ASR If ph x was instructed to calculate Raman coefficients dynmat x will also calculate Raman cross sections for a typical experimental setup Input documentation in the header of PHonon PH dynmat 90 See Example 01 for a simple phonon calculations in Si Example 06 for fully relativistic calculations LDA on Pt Example 07 for fully relativistic GGA calculations 4 2 Calculation of interatomic force constants in real space First dynamical matrices are calculated and saved for a suitable uniform grid of q vectors only those in the Irreducible Brillouin Zone of the crystal are needed Although this can be done one q vector at the time a simpler procedure is to specify variable ldisp true and to set variables ng1 nq2 nq3 to some suitable Monkhorst Pack grid that will be automatically generated centered at q 0 Second code q2r x reads the dynamical matrices produced in the preceding step and Fourier transform them writing a file of Interatomic Force Constants in real space
8. onon The PlotPhon and QHA packages were contribute by the late Prof Eyvaz Isaev Other contributors include Lorenzo Paulatto Univ Paris VI for PAW 2n 1 code William Parker Argonne for phonon terms in dielectric tensor We shall greatly appreciate if scientific work done using this code will contain an explicit acknowledgment and the following reference P Giannozzi S Baroni N Bonini M Calandra R Car C Cavazzoni D Ceresoli G L Chiarotti M Cococcioni I Dabo A Dal Corso S Fabris G Fratesi S de Gironcoli R Gebauer U Gerstmann C Gougoussis A Kokalj M Lazzeri L Martin Samos N Marzari F Mauri R Mazzarello S Paolini A Pasquarello L Paulatto C Sbraccia S Scandolo G Sclauzero A P Seitsonen A Smo gunov P Umari R M Wentzcovitch J Phys Condens Matter 21 395502 2009 http arxiv org abs 0906 2569 3 Installation PHonon is a package tightly bound to QUANTUM ESPRESSO For instruction on how to down load and compile QUANTUM ESPRESSO please refer to the general Users Guide available in file Doc user_guide pdf under the main QUANTUM ESPRESSO directory or in web site http www quantum espresso org Once QUANTUM ESPRESSO is correctly configured PHonon can be automatically down loaded unpacked and compiled by just typing make ph from the main QUANTUM ESPRESSO directory 3 1 Compilation Typing make ph from the root QUANTUM ESPRESSO directory or make from the PHonon
9. re automatically generated 4 Using PHonon Phonon calculation is presently a two step process First you have to find the ground state atomic and electronic configuration Second you can calculate phonons using Density Functional Perturbation Theory Further processing to calculate Interatomic Force Constants 3 to add macroscopic electric field and impose Acoustic Sum Rules at q 0 may be needed In the following we will indicate by q the phonon wavevectors while k will indicate Bloch vectors used for summing over the Brillouin Zone The main code ph x can be used whenever PWscf can be used with the exceptions of DFT U semiempirical VdW corrections nonlocal vdW and hybrid functionals external elec tric fields constraints on magnetization nonperiodic boundary conditions USPP and PAW are not implemented for higher order response calculations See the header of file PHonon PH phonon 90 for a complete and updated list of what PHonon can and cannot do Since version 4 0 it is possible to safely stop execution of ph x code using the same mecha nism of the pw x code i e by creating a file prefix EXIT in the working directory Execution can be resumed by setting recover true in the subsequent input data Moreover the exe cution can be cleanly stopped after a given time is elapsed using variable max_seconds See example Recover_example 4 1 Single q calculation The phonon code ph x calculates normal modes at a given q vec
10. rep or q vectors Images are loosely coupled processors com municate between different images only once in a while so image parallelization is suitable for cheap communication hardware e g Gigabit Ethernet Image parallelization is activated by specifying the option nimage N to ph x Inside an image PW and k point parallelization can be performed for instance mpirun np 64 ph x ni 8 nk 2 will run 8 images on 8 processors each subdivided into 2 pools of 4 processors for k point parallelization In order to run the ph x code with these flags the pw x run has to be run with mpirun np 8 pw x nk 2 without any nimage flag After the phonon calculation with images the dynmical matrices of q vectors calculated in different images are not present in the working directory To obtain them you need to run ph x again with mpirun np 8 ph x nk 2 and the recover true flag This scheme is quite automatic and does not require any additional work by the user but it wastes some CPU time because all images stops when the image that requires the largest amount of time finishes the calculation Load balancing between images is still at an experimental stage You can look into the routine image_q_irr inside PHonon PH check_initial_status to see the present algorithm for work distribution and modify it if you think that you can improve the load balancing A different paradigm is the usage of the GRID concept instead of MPI to achie
11. that should have w 0 Acoustic Sum Rule violation see the item before this one e wrong data file read e wrong atomic masses given in input will yield wrong frequencies but the content of file fildyn should be valid since the force constants not the dynamical matrix are written to file e convergence threshold for either SCF conv_thr or phonon calculation tr2_ph too large try to reduce them e maybe your system does have negative or strange phonon frequencies with the approx imations you used A negative frequency signals a mechanical instability of the chosen structure Check that the structure is reasonable and check the following parameters The cutoff for wavefunctions ecutwfc For USPP and PAW the cutoff for the charge density ecutrho The k point grid especially for metallic systems Note that negative frequencies are actually imaginary the negative sign flags eigenvalues of the dynamical matrix for which w lt 0 Wrong degeneracy error in star_q Verify the q vector for which you are calculating phonons In order to check whether a symmetry operation belongs to the small group of q the code compares q and the rotated q with an acceptance tolerance of 10 set in routine PW eqvect 90 You may run into trouble if your q vector differs from a high symmetry point by an amount in that order of magnitude A Appendix Electron phonon coefficients The electron phonon coefficients g are defined as
12. tly verified because the system is never exactly translationally invariant as it should be The calculated frequency of the acoustic mode is typically less than 10 cm but in some cases it may be much higher up to 100 cm t The ultimate test is to diagonalize the dynamical matrix with program dynmat x imposing the ASR If you obtain an acoustic mode with a much smaller w let us say lt 1cm t with all other modes virtually unchanged you can trust your results The problem is in the fact that the XC energy is computed in real space on a discrete grid and hence the total energy is invariant only for translation in the FFT grid Increasing the charge density cutoff increases the grid density thus making the integral more exact thus reducing the problem unfortunately rather slowly This problem is usually more severe for GGA than with LDA because the GGA functionals have functional forms that vary more strongly with the position particularly so for isolated molecules or system with significant portions of vacuum because in the exponential tail of the charge density a the finite cutoff hence there is an effect due to cutoff induces oscillations in rho and b the reduced gradient is diverging info by Stefano de Gironcoli June 2008 ph x yields really lousy phonons with bad or negative frequencies or wrong symmetries or gross ASR violations Possible reasons e if this happens only for acoustic modes at q 0
13. tor starting from data files produced by pw x with a simple SCF calculation NOTE the alternative procedure in which a band structure calculation with calculation phonon was performed as an intermediate step is no longer implemented since version 4 1 It is also no longer needed to specify Inscf true for q 0 The output data files appear in the directory specified by the variable outdir with names specified by the variable prefix After the output file s has been produced do not remove any of the files unless you know which are used and which are not you can run ph x The first input line of ph x is a job identifier At the second line the namelist amp INPUTPH starts The meaning of the variables in the namelist most of them having a default value is described in file Doc INPUT_PH Variables outdir and prefix must be the same as in the input data of pw x Presently you can specify amass i a real variable the atomic mass of atomic type 7 or you can use the default one deduced from the periodic table on the basis of the element name If amass i is not given as input of ph x the one given as input in pw x is used When this is 0 the default one is used After the namelist you must specify the q vector of the phonon mode in Cartesian coordi nates and in units of 27 a Notice that the dynamical matrix calculated by ph x at q 0 does not contain the non analytic term occurring in polar materials i e there is no LO TO splitti
14. ve paral lelization over irreps and q vectors Complete phonon dispersion calculation can be quite long and expensive but it can be split into a number of semi independent calculations using options start_q last_q start_irr last_irr An example on how to distribute the calculations and collect the results can be found in examples GRID_example Reference Calculation of Phonon Dispersions on the GRID using Quantum ESPRESSO R di Meo A Dal Corso P Giannozzi and S Cozzini in Chemistry and Material Science Applications on Grid Infrastructures editors S Cozzini A Lagana ICTP Lecture Notes Series Vol 24 pp 165 183 2009 6 Troubleshooting ph x stops with error reading file The data file produced by pw x is bad or incomplete or produced by an incompatible version of the code In parallel execution if you did not set wf_collect true the number of processors and pools for the phonon run should be the same as for the self consistent run all files must be visible to all processors ph x mumbles something like cannot recover or error reading recover file You have a bad restart file from a preceding failed execution Remove all files recover in outdir ph x says occupation numbers probably wrong and continues You have a metallic or spin polarized system but occupations are not set to smearing ph x does not yield acoustic modes with zero frequency at q 0 This may not be an error the Acoustic Sum Rule ASR is never exac
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