User’s manual
Version 2017.03.03
Code name: BlueSKY

NAKANISHI, Hiroshi
National Institute of Technology, Akashi College, Japan
Graduate School of Engineering, Osaka University0You may not give, sell, rent, lease, export or disclose the Naniwa
software or any copy of them and this document without permission.
Participants of CMD® workshop can use them only for academic research.
In your future publications of academic work performed using NANIWA,
the use of the software shall be properly acknowledged, e.g. in the form:''The calculations have been performed using the NANIWA codes developedat Osaka University & National Institute of Technology, Akashi College,
Japan [1,2].”[1] Hiroshi Nakanishi, 2016. Ch.6 Quantum adsorption states of small
mass atoms on solid surfaces. In: H. Kasai, M. C. S. Escaño, ed. Physics ofSurface, Interface and Cluster Catalysis. Bristol, UK, IOP Publishing.
[2] Hiroshi Nakanishi, Quantum States of the Hydrogen Isotope in Solid
Materials and on Their Surfaces", J. Comput. Chem. Jpn., Vol. 15, No. 5,
pp. 124–135 (2016).
Copyright © 2013 Osaka University. All rights reserved.
Naniwa programs are protected by Japanese Patent 4774523 & 5902495
and US Patent 8,140,467. Additional patents may be pending in Japan andelsewhere.

1

Contents
1. INTRODUCTION

4

1.1 Naniwa formulation

4

2. SYSTEM REQUIREMENTS

8

3. HOW TO INSTALL

9

4. PROGRAM CODES AND FILES

13

4.1 Programs

13(1) naniwaSS_run

13(2) Tools for getting potential energy surface for atom motion

13(3) Tools for visualization of results

13

4.2 files

14

4.2.1 List of important files

14

4.2.2 INSET

14(0) Comment lines

14(1) Calculation mode in the 5th line

14(2) Mass of the target quantum particle, which unit is that of a proton.

15(3) Number of nodes for the 3D Gaussian functions (No1 x No2 x No3) in th 8 th line

15(4) Gaussian decay factor (SigmaX, SigmaY SigmaZ) in the 10th lines

15(5) Number of output eigen states in the 12th line

15(6) Correction by crystal structure symmetry

15

4.2.3 POTENG

20

4.2.4 LOG

21

44.2.5. EIGEN

23

4.2.6 stateXXXXX

23

5.1

Making 3D-potential energy surface for quantum particle in material.

25

5.2

Making the simulation setting

25

5.3 Executing the simulation program.

25

5.4 Check simulation results

252

5.4.1 How to see the Eigenenergies as a function of quantum number.

25

5.4.2 How to see the Wave functions

26

5.4.2.1 OpenDX case26

5.4.2.2 XcrySDen case30

5.4.2.3 VESTA case

36

REFERENCES

40

APPENDIX

41

A Porting

41

B

Making 3D-potential energy surface by VASP

43

C

Required parameters for convergence45

C.1 Number of nodes for the 3D Gaussian functions

45

C.2 Gaussian decay factor (SigmaX, SigmaY SigmaZ)

45

3

1. Introduction
The first principles calculation based on the density functional theory is one of the most successful
and powerful methods in the materials physics. And also the first principles molecular dynamics
methods have been used for various dynamical behaviors which are from vibrational motions tochemical or biochemical reactions. In the case of small mass atoms like hydrogen atoms, we should
treat their nuclei in a quantum-mechanical manner, in addition to the electrons. The quantum
behaviors of the nuclei have crucial roles to play in the materials related to today’s energy technology:
fuel cell and lithium-ion rechargeable battery, and also various catalytic reactions to producehydrogen fuel, not only from their academic interests.
We have been developing the quantum simulation code for the small mass atoms motion inmaterials, “Naniwa” [1-15].
“NANIWA” series codes are computational codes for performing first principles quantum
mechanical calculations, which were developed at Kasai laboratory (-2015) in Osaka University andhave been developed at Nakanishi laboratory in NITAC (2016-). This document describes about the

Naniwa-K [3,4], which is a nucleus version of the first principles quantum state calculations [5-15].
You can solve the eigenvalue problem and obtain the eigenstates and their eigenenergies for atom
(nuclear) motion in the materials by this code.

1.1 Naniwa formulation
We consider that kinds of particles which construct the material are electron and nucleus. If weknow how these particles behave, we can know the material properties.

Total Hamiltonian of the electrons and nuclei in material is given by4N nc.
  2  2 ne   2  2 
i  V (r , R)
 I    H    
2M I 2me I 1 
i 1 

(1)

where M I and me are masses of electron and nucleus I , and  is the Dirac constant. Numbers of
nucleus and electron are N nc. and ne. .

Potential energy is given by the coulomb interaction

between all particles;
ne N nc.
N nc. I 1
Z Z e2
 Z e 2 ne i1 e 2V (r ,R)    I         J I i 1 I 1 ri  RI
i 1 j 1 r j  ri
I 1 J 1 RJ  RI

(2)

where Z I is atomic number of nucleus I , and e is elementary charge.
The positions of the electrons and nuclei are indicated by    r  r1 , r2 , r3 ,, ri ,rne ,







(3.1)



(3.2)

   R  R1 , R2 , R3 ,, RI ,, RN nc. .

Total Schrödinger equation is  H  ( r , R)  E  ( r , R) ,(4)

where E and Ψ are the total energy and wave function describing the state of this material system.
Within the adiabatic approximation, we can divide the wave function Ψ into two parts; n, (r , R)   n;R (r )   ;n ( R) ,(5)


Where  n; R (r ) is the n-th electron wave function in the case of the fixed nucleus position R and ;n ( R) is the 𝜔-th nucleus motion wave function in the case of the electron staten.

Then, we can divide the total Schrödinger equation into two equations. One is for electrons, ne   2  2  i  V (r , R)  n;R (r )  U n ( R)  n;R (r )  2me 
 i 1 (6)Another is for nuclei
(7)




 N nc .   2  2
 I  U n ( R)  ; n ( R)  E ; n ; n ( R).
    I 1  2M I From Schrödinger equation for electron system with fixed R, we can obtain the eigenenergies andeigenstates with the aid of the conventional first principles (electron states) calculation. Theeigenenergies, U n (R) of electron state as a function of R can be considered as the adiabatic potential
energy surface for nucleus motion. Eigenenergy of nuclei corresponds to the total energy, E, appearedin the Schrödinger equation for total system. Naniwa series codes solve this equation.

5

Naniwa-SKY code solves the Schrödinger equation for a single atom motion in the material.; 2  2

2
2 

  U 0 ( X , Y , Z )  ;0 ( X , Y , Z )  E ,0 ;0 ( X , Y , Z ).



2
2
2 
2
M

X

Y

Z





(8)

The wave function for atom motion in the material has rather position localized character. Then we
described it by linear combination of the 3D-Gauss functions located at grid points,NG ( X , Y , Z )   C ,G ( X , Y , Z ) ,

(9)

1



where G ( X , Y , Z ) is the ℓ-th 3D-Gauss function located at the ℓ-th grid point R  X  , Y , Z   , 8   222G ( X , Y , Z )   X 3Y Z  exp   X  X  X     Y Y  Y    Z Z  Z   ,



1

4

Factors  X , Y , Z indicate the decays of Gauss function along the X, Y, Z directions  8    1422
2
G ( X , Y , Z ; k )   X 3Y Z  exp   X  X  X    ik X X  Y Y  Y   ikY Y   Z Z  Z    ikZ Z The nearest neighbor 3D-Gauss functions have to be overlapped.

6

(10)

Naniwa code use the variation method with the trial function (9) to solve the Schrödinger equation(8). And Naniwa code solves the following equation instead of eq (8).

 H




 E ,0 S   C ,  0(11.0)(11.1)H   K   U    


 

K     G  ( X , Y , Z ) 
 2  G  ( X , Y , Z )dXdYdZ,
2
2

Y
Z 
 2M  X
2

2

2

2

(11.2)

U     G ( X , Y , Z )U 0 ( X , Y , Z ) G ( X , Y , Z )dXdYdZ(11.3)



S    G ( X , Y , Z ) G ( X , Y , Z )dXdYdZ(11.4)



Here, we can integrate K and S, analytically. On Naniwa-K code, the special routines are installed
to integrate U in an efficient way [Japanese Paten No.5902495]. From eq.11.0, secular equation is
written byH11  E S11
H 21  E S 21
H NG 1  E S NG 1

H12  E S12
H 22  E S 22
H NG 2  E S NG 2

 H1N G  E S1N G
 H 2 NG  E S2 NG
0 H NG NG  E S NG NG

.

(12)

We solve the secure eq.(12) and obtain eigenenergy 𝐸𝜔,0 , 𝜔 = 0,1,2 ⋯. Then, we can solve eq.(11.0)
for all obtained 𝐸𝜔,0 , and get the corresponding eigenvectors (𝐶𝜔,1 , 𝐶𝜔,2 , 𝐶𝜔,3 , ⋯ , 𝐶𝜔,𝑁𝐺 ).
You should check the convergence of these numerical results by the some trial runs for various
Gaussian decay factors  X , Y , Z and number of grid point, 𝑁𝐺 .

The expectation value of an observable, O, at 𝜔th state is given byO    * ( X , Y , Z )Oˆ  ( X , Y , Z ) dXdYdZNG NG  C* , q C , q  Gq ( X , Y , Z ) Oˆ Gq ( X , Y , Z ) dXdYdZ
q 1 q  1.

It is easy to calculate 〈𝑂〉𝜔 from obtained eigenvectors(𝐶𝜔,1 , 𝐶𝜔,2 , 𝐶𝜔,3 , ⋯ , 𝐶𝜔,𝑁𝐺 ).

7

(13)

2. System Requirements
Hardware
Recommended
Computer Processor: 3.0GHz Intel Core i7 or better
Computer Memory:

8 GB/core or more

Operating System: 64-bit Linux distribution
Software(1) Naniwa package file：NaniwaSKYXXXXXXXX.tar.gz
XXXXXXXX is version number. (ex. NaniwaSKY20160817.tar.gz)(2) ab initio electronic state calculation package
For install(1) Compiler:Intel® Fortran compiler [16](2) Math library: Intel ® Math Kernel Library (MKL) [17]For use(1) Text editor: vi , mule … (as you like)(2) C shell: csh or tcsh
(When you use other Unix shell, you must rewrite the script files by yourself.)(3) Visualization tool: gnuplot and OpenDX, XCrySDen, or VESTA.
“gnuplot” is a command-line program that can make 2- and/or 3-dimensional plots offunctions and data. [18]“OpenDX” is IBM Visualization Data Explorer program. [19]“XCrySDen” is a crystalline and molecular structure visualization program. [20]“VESTA” is a Visualization program for Electronic and STructural Analysis.

8

3. How to install(1) Copy the package file “NaniwaSkyXXXXXXXX.tar.gz” to your home directory.
XXXXXXXX is version number. (ex. NaniwaSky20160817.tar.gz)(2) Decompress the package file.
Type following command lines:
gzip

-d

NaniwaSkyXXXXXXXX.tar.gz [Enter]

tar

xvf

NaniwaSkyXXXXXXXX.tar[Enter]You can get following directory on your home directory.

Installed directory structure~-+ : your home directory|-- naniwa -+|-- doc: documents|-- SRC :source codes|-- bin: : you will install the execution programs into this directory|-- work:working directory|-- qs : script for Grid Engine (Job scheduler)|-- etc -+|-- OpenDX:

files for Visualization software OpenDX®

|-- charge:

files for BADER CHARGE ANALYSIS|-- potential:

files for making potential data|-- example:

input data examples|-- results:

some simulation results(3) Move to SRC directory
Type :

cd./naniwa/SRC[Enter](4)Compile the source codes
Type :

make all [Enter]
The compilation must finish without errors, although warnings may be possible.
If you get error message, you must modify following values in “Makefile” file under SRC directory.
(A) Error message
make: ifort: Command not found
make: *** [naniwa] Error 127

Please ask to your system administrator to install Intel Fortran.
9

If you use older Intel Fortran, please change the compiler namein ” Makefile”

From
FC = ifort
To
FC = ifc(B) Error message:/tmp/ifortzvGoSf.o: In function `MAIN__':
NaniwaSYMk.f:(.text+0x40fb): undefined reference to `dfti_create_descriptor_highd'
NaniwaSYMk.f:(.text+0x410f): undefined reference to `dfti_set_value_intval'
NaniwaSYMk.f:(.text+0x4123): undefined reference to `dfti_set_value_intval'
NaniwaSYMk.f:(.text+0x4137): undefined reference to `dfti_set_value_intvec'
NaniwaSYMk.f:(.text+0x414b): undefined reference to `dfti_set_value_intvec'
NaniwaSYMk.f:(.text+0x4155): undefined reference to `dfti_commit_descriptor_external'
NaniwaSYMk.f:(.text+0x416d): undefined reference to `dfti_compute_forward_zz'
NaniwaSYMk.f:(.text+0x41a0): undefined reference to `dfti_free_descriptor_external'
NaniwaSYMk.f:(.text+0x6fb2): undefined reference to `zhegv_'
make: *** [naniwa] Error 1

If you see the above-mentioned errors, you must change the path of Intel MKL installed
directory in Makefile
From
LIB = /opt/intel/mkl /lib/intel64
INC= -I/opt/intel/mkl/includeTo
LIB = /opt/intel/mkl /lib/em64t
INC= -I/opt/intel/mkl/includeor
LIB = /opt/intel/mkl/XXXXXX/lib/em64t
INC = -I/opt/intel/mkl/XXXXXX/include
here, XXXXXXX is version of the Intel MKL installed on your computer.
(C) Error message:
fastDFT3D_MKL.f(5): error #7002: Error in opening the compiled module file.

Check INCLUDE paths.

[MKL_DFTI]Use MKL_DFTI----------^
fastDFT3D_MKL.f(10): error #6457: This derived type name has not been declared.

[DFTI_DESCRIPTOR]

type(DFTI_DESCRIPTOR), POINTER :: hand-----------^
compilation aborted for fastDFT3D_MKL.f (code 1)
make: *** [naniwa] Error 1

If you see the above-mentioned errors, you should ask to your system administrator tocompile mkl_dfti.f90.
Please do followings as root (super user).
10

cd /opt/intel/mkl/include
ifort –c mkl_dfti.f90* You can find some hints to solve your problem in Makefile.
(5) Move the execution file to binary directoryType:make all-install [Enter]
Check the execution files under bin directory
Type :

ls../bin[Enter]You can see following files:
BandStructure cellexpander chkPOTENG
BHGCAR2DX

ChargeState

makeBHGCAR naniwaSS_run state2dx

eigen2spec makePOTENG poteng2dx(6) test run.
Move to work directory.

cd [Enter]cd ./naniwa/work[Enter]Copy the test data.

cp -r../etc/example/test./[Enter]cd ./test [Enter]If necessary, change the “LD_LIBRARY_PATH” value in “run.csh” file by text editor :setenv LD_LIBRARY_PATH LD_LIBRARY_PATH:'/opt/intel/mkl/lib/em64t'.
orsetenv LD_LIBRARY_PATH LD_LIBRARY_PATH:'/opt/intel/mkl/ XXXXXXX /lib/em64t'.
here, XXXXXXX

is version of the Intel MKL installed on your computer.

Execute the programcsh./run.csh [Enter]machine nameJob start date & time
Naniwa start date & timefinish naniwa

Naniwa terminate date & time
Check output filesls [Enter]11

state2xsf

INSETkpoint0000

LOG

POTENG

run.cshIf successful, you can get the following LOG file:*****************************************
Naniwa code******************************************
NaniwaSky Version 2012.11.22
created by NAKANISHI, Hiroshi
OSAKA UNIVERSITY----------------------------------------INSET title :*Calculaton mode :0*** Full calculation----------------------------------------Atomic Mass = 1.00000000000000(proton)wave00005.xsf was created.
= 1.672621637000000E-027 (kg)WAVE function----------------------------------------Max value= 1.68540114820597
Number of node index (No1,No2,No3)
Min value= -1.84336513692804
999probability= 0.999869835826559
Gaussian decay factors (1/Angstrom Angstrom)
SigmaX= 5.00000000000000
SigmaY= 5.00000000000000
wave00006.xsf was created.
SigmaZ= 5.00000000000000
WAVE function----------------------------------------Max value= 1.93274716286747** No correction by symmetry.
Min value= -1.03123097291435--------------------------------------probability= 0.999869796584020- Lattice vector (A)3.00000000000000
0.000000000000000E+000
0.000000000000000E+000
wave00007.xsf was created.
0.000000000000000E+000
3.00000000000000
WAVE function
0.000000000000000E+000
Max value= 1.72099225797871
0.000000000000000E+000
0.000000000000000E+000
Min value= -1.72768364358320
3.00000000000000
probability= 1.00175769772228- Lattice unit volume (A^3)
27.0000000000000--------------------------------------wave00008.xsf was created.
Reciprocal lattice vector (/A)
WAVE function
2.09439510239320
0.000000000000000E+000
Max value= 1.00317921937198
0.000000000000000E+000
Min value= -1.96774733538390
0.000000000000000E+000
2.09439510239320
probability= 1.00175785191399
0.000000000000000E+000
0.000000000000000E+000
0.000000000000000E+000
2.09439510239320
wave00009.xsf was created.
Reciprocal lattice unit volume (/A^3)
WAVE function
9.18704494231106
Max value= 0.825426714232840--------------------------------------Min value= -2.44372845893816
MSG: reading POTENG
probability= 1.00175785169862
MSG: finish reading POTENG
MSG: start FFT of POTENG data
MSG: finish FFT
wave00010.xsf was created.
I cannot find KPOINTS file.
WAVE function
I will set single k-point calculation.
Max value= 1.64599264710982
Min value= -1.54178274285677
probability= 0.999839014572012

12

4. Program codes and files
4.1 Programs(1) naniwaSS_run :main simulation execution file to calculate eigenstates and eigenenergies

Input files: INSET : simulation setting information
POTENG : Potential energy surface for atom motion
KPOINTS (option): for dispersion [Under construction, Coming soon]
Output files: LOG : run time information
EIGEN: Eigenenergy for atom motion
stateXXXXX: information about eigenstate for atom motion(2) Tools for getting potential energy surface for atom motion(2.1) auto.csh: automatic launcher for ab initio electronic state calculation VASP
(2.2) collect.csh:

to make POTDAT from many OSZICAR files of VASP

(2.3) makePOTENG: to make POTENG from POTDAT and POTDAT.cfg(2.4) chkPOTENG: checking the max and min values in POTENG file.
(3) Tools for visualization of results(3.1) poteng2dx: to make input file for WaveViewer3D in order to see the potential energy surface
input file: POTENG, POTDAT.cfg (option)
output file: PES.dat, PES3D.general(3.2) state2dx: to make input file for WaveViewer3D in order to see the wave function
input files: stateXXXXX,POTDAT.cfg (option)

output files: waveXXXX.dat, waveXXXX.generalusage : state2dx [start state number] [end state number]example: state2dx 1 10 [Enter](3.3) WaveViewer3D_XXX (Visual program for OpenDX (http://www.opendx.org/)
WaveViewer3D_XXX.cfg, WaveViewer3D_XXX.net(3.4) state2xsf: to make input file for XcrySDen in order to see the wave function
input files: stateXXXXX,POTDAT.cfg (option)

output files: waveXXXX.xsf
usage : state2xsf [start state number] [end state number]example: state2xsf 1 10 [Enter](4) Band structure builder(4.1) BandStructure: [Under construction, coming soon]

13

4.2 files
4.2.1 List of important files
INPUT files:
INSET

:

Calculation setting about basis function and particle mass, etc.

POTENG:

Super cell geometry and potential energy surface

KPOINTS:[Under construction, coming soon]:

calculation information

OUTPUT files:
LOG

under the directory of “kpoint0000”
EIGEN

:

Eigenenergy set

state00000:

Eigenstate information of the ground state

stateXXXXX:

Eigenstate information of the XXXXXX th excited state

4.2.2 INSET
Example* Naniwa Sky test / Hydrogen* Calculation mode
* 0: full calculation, 1: parameter-check only
(1)
*
0
(2)
* Mass of your quantum particle (/proton mass)* 0:muon, 1:proton, 2: deuterium, 3: tritium,4: quadrium, n: Hydrogen-n
1
c Number of nodes for the 3D Gaussian functions (No1 x No2 x No3)(3)
9 9 35c Gaussian decay factor (SigmaX, SigmaY SigmaZ) (1/Angstrom Angstrom)
10.18 10.18 10.6
(4)c number of output eigen states
20c correction by Symmetry: E, C3v, C4v
(5)
C3v
(6)

Contents(0) Comment lines
The lines that begin with with a "c" or “*” (asterisk) are comment line. In
comment lines, you can write something as you like in these lines, but don’tchange the number of all comment lines and their positions in INSET.
(1) Calculation mode in the 5th line
0; full calculation mode.
14

1:parameter check mode.

( no calculation )(2) Mass of the target quantum particle, which unit is that of a proton.
1: proton, 2: deuterium, 3: tritium,4: quadrium, n: Hydrogen-n
if you input 0, program will replace it by the mass value of the (Anti)muon.

(3) Number of nodes for the 3D Gaussian functions (No1 x No2 x No3) in th 8thline
Please input 3 positive integer numbers which are numbers of nodes for 3D
Gaussian functions, No1, No2, No3. They correspond to the numbers ofpartitions of primitive vectors: 𝐿𝑎⃗⃗⃗⃗1 , ⃗⃗⃗⃗⃗⃗
𝐿𝑎2 , 𝐿𝑎⃗⃗⃗⃗3 (See next section 4.2.3)(4) Gaussian decay factor (SigmaX, SigmaY SigmaZ) in the 10th lines
Please input 3 positive floating-point type data which are Gaussian decay
factors along the directions of x, y and z-axis, σx, σy, σz. Their unit is1/(Angstrom･Angstrom). ( If you put 0, 0, 0, then these values areautomatically reset by default values.)(5) Number of output eigen states in the 12th line
Please input a positive integer number of output eigen states which you
request.
(6) Correction by crystal structure symmetry(6)-1. Correction by rotational symmetry around z-axis
Please input one rotational symmetry symbol.
Supported symbols: C1, C3v, C4v(Schönflies notation)
for surfaces perpendicular to Z-axis(6)-2. Correction by Crystal structure symmetry
Supported symbols: Oh, Td^2, Oh^7 (Schönflies notation)
graphene (special)--------------

15

Supported symmetry symbols.
(i)SymbolE

Symmetry

1-fold rotation

Requirement non(ii)
Symbol

C3v

Symmetry

3-fold rotation symmetry with 3 mirror planes containing thez-axis (vertical planes).
⃗⃗⃗⃗⃗⃗2 |, 2𝑎Requirement No1=No2, |𝐿𝑎⃗⃗⃗⃗1 | = |𝐿𝑎⃗⃗⃗⃗1 ∙ ⃗⃗⃗⃗
𝑎2 = |𝑎⃗⃗⃗⃗2 |2, σ𝑥 = σ𝑦(iii)
Symbol

C4v

Symmetry

4-fold rotation symmetry with 4 mirror planes containing thez-axis (vertical planes).
⃗⃗⃗⃗⃗⃗2 |, √2 ⃗⃗⃗⃗
Requirement No1=No2, |𝐿𝑎⃗⃗⃗⃗1 | = |𝐿𝑎𝑎1 ∙ ⃗⃗⃗⃗
𝑎2 = |𝑎⃗⃗⃗⃗2 |2, σ𝑥 = σ𝑦

16

(iv)
SymbolOh

Symmetry

The rotation axes of an octahedron or cube (three 4-fold axes,
four 3-fold axes, and 6 diagonal 2-fold axes) with a mirror plane
perpendicular to the z-axis (horizontal plane).
⃗⃗⃗⃗⃗⃗2 | = |𝐿𝑎⃗⃗⃗⃗⃗⃗3 |,Requirement No1=No2=No3, |𝐿𝑎⃗⃗⃗⃗1 | = |𝐿𝑎𝑎1 ∙ ⃗⃗⃗⃗
𝑎2 = √2 ⃗⃗⃗⃗
𝑎1 ∙ ⃗⃗⃗⃗
𝑎3 = √2 ⃗⃗⃗⃗
𝑎2 ∙ ⃗⃗⃗⃗
𝑎3 = |𝑎⃗⃗⃗⃗2 |2 ,√2 ⃗⃗⃗⃗
σ𝑥 = σ𝑦 = σ𝑧(v)
SymbolTd^2, F -4 3m, 216

Symmetry

Zinc Blend crystal structure.
⃗⃗⃗⃗⃗⃗2 | = |𝐿𝑎⃗⃗⃗⃗⃗⃗3 |,Requirement No1=No2=No3, |𝐿𝑎⃗⃗⃗⃗1 | = |𝐿𝑎
2 ⃗⃗⃗⃗
𝑎1 ∙ ⃗⃗⃗⃗
𝑎2 = 2 ⃗⃗⃗⃗
𝑎1 ∙ ⃗⃗⃗⃗
𝑎3 = 2 ⃗⃗⃗⃗
𝑎2 ∙ ⃗⃗⃗⃗
𝑎3 = |𝑎⃗⃗⃗⃗1 |2, σ𝑥 = σ𝑦 = σ𝑧(vi)
SymbolOh^7, F d -3 m, 227

Symmetry

Diamond crystal structure.
⃗⃗⃗⃗⃗⃗2 | = |𝐿𝑎⃗⃗⃗⃗⃗⃗3 |,Requirement No1=No2=No3, |𝐿𝑎⃗⃗⃗⃗1 | = |𝐿𝑎
2 ⃗⃗⃗⃗
𝑎1 ∙ ⃗⃗⃗⃗
𝑎2 = 2 ⃗⃗⃗⃗
𝑎1 ∙ ⃗⃗⃗⃗
𝑎3 = 2 ⃗⃗⃗⃗
𝑎2 ∙ ⃗⃗⃗⃗
𝑎3 = |𝑎⃗⃗⃗⃗1 |2,σ𝑥 = σ𝑦 = σ𝑧
No1 mod 4 = 0

17

When you use this function, you can get accurate degenerate eigen values.
In the case of hydrogen atom in Pd(001), which has C4v symmetry, you can get
following eigenvalues:

And in the case of hydrogen atom in Pt(111), which has C3v symmetry, you can get
following eigenvalues:

Green: no correction

18

and their wave functions:
E (no use)

C3v

the ground state

the 1st excited state

the 2nd excited state

the 3rd excited state

the 4th excited state

the 5th excited state

the 6th excited state
19the 7th excited state
4.2.3 POTENG

The first line is a comment line. The second line provides a universal scaling factor 𝐿(Angstrome), which is used to scale the primitive vectors in the simulation system. On
the following three lines, the three primitive vectors, 𝐿𝑎⃗⃗⃗⃗1 , 𝐿𝑎⃗⃗⃗⃗2 , 𝐿𝑎⃗⃗⃗⃗3,defining thesupercell of the simulation material system are given . Each line has the x, y, z
components of Cartesian coordinate system, whose unit is 𝐿. The sixth line supplies
the numbers, 𝑁1 , 𝑁2 , 𝑁3 , of the potential energy calculation point along the primitive
vectors, ⃗⃗⃗⃗
𝑎1 , ⃗⃗⃗⃗
𝑎2 , ⃗⃗⃗⃗
𝑎3 . The lines from seventh provide the potential energy values (eV)and its particle positions. Each line has n1 , n2 , n3 , 𝑈(𝑅n1 ,n2 ,n3 ) .
n

n

n3

𝑁1

𝑁2

𝑁3

Here, 𝑅n1,n2,n3 = 𝐿 ( 1 𝑎⃗⃗⃗⃗1 + 2 ⃗⃗⃗⃗
𝑎2 +
where

𝑎3 ),
⃗⃗⃗⃗

n1  0,1,2,  , N 1  1
n2  0,1,2,  , N 2  1
n3  0,1,2,  , N 3  1

20.

* POTENG: POTENTIAL ENERGY for H on Pd(111)2.820295
1.000000
0.0000000E+00 0.0000000E+00
0.5000000
0.8660254
0.0000000E+00
0.0000000E+00 0.0000000E+00 3.81165754909725
12
12
44
1
1
1 -8.7710377E-04
2
1
1 -6.4631744E-04
31
1 -3.8508927E-03
41
1 -1.8527496E-03
51
1 -2.3826952E-03
61
1 -4.5110146E-03
71
1 -6.5468652E-03
~
~
~
~
11
12
1
2
3
4
5
6
2
3
4
5
6
7
8
9
10
11
12
* END of POTENG

~
2
2
3
3
3
3
3
3
12
12
12
12
12
12
12
12
12
12
12

~
1 -1.1861493E-03
1 -6.4631744E-04
1 -3.8508927E-03
1 -1.2586723E-03
1 -1.6357267E-03
1 -2.8395073E-03
1 -5.4807067E-03
1 -8.3559640E-03
44 -1.732900
44 -0.2266000
44 1.000000
44 1.000000
44 1.000000
44 1.000000
44 1.000000
44 1.000000
44 1.000000
44 1.000000
44 -0.2266000

4.2.4 LOG
It gives you the information about your simulation situation.
When the simulation is executing, you can check it by following command.

tail -f LOG [Enter]
Following is the example of LOG file.
******************************************
Naniwa code******************************************
mode: NaniwaSSk Version 2012.02.10
created by NAKANISHI, Hiroshi
OSAKA UNIVERSITY----------------------------------------Calculaton mode :0*** Full calculation-----------------------------------------

21

Atomic Mass =1.00000000000000(proton)= 1.672621637000000E-027 (kg)----------------------------------------Number of node index (No1,No2,No3)9
935
Gaussian decay factors (1/Angstrom Angstrom)
SigmaX=
5.09173682192627
SigmaY=5.09173682192627
SigmaZ=
8.55607353478694------------------------------------------------------------------------------- Lattice vector (A)
3.98849944000000
0.000000000000000E+000 0.000000000000000E+000
0.000000000000000E+000
3.98849944000000
0.000000000000000E+000
0.000000000000000E+000 0.000000000000000E+000
11.9654983200000- Lattice unit volume (A^3)
190.348676260400--------------------------------------Reciprocal lattice vector (/A)
1.57532565230225
0.000000000000000E+000 0.000000000000000E+000
0.000000000000000E+000
1.57532565230225
0.000000000000000E+000
0.000000000000000E+000 0.000000000000000E+000 0.525108550767416
Reciprocal lattice unit volume (/A^3)
1.30313611328161----------------------------------------------------------------------------MSG: reading POTENG
MSG: finish reading POTENG
MSG: start FFT of POTENG data
MSG: finish FFT
I cannot find KPOINTS file.
I will set single k-point calculation.
--------------------------------------------------K-sampling point information.
Number of K-points:
1***# fractional of reciprocal lattice vector(unit : b1/2, b2/2, b3/2)
1 : 0.0000000E+00 0.0000000E+00 0.0000000E+00***# kx,ky,kz vector (/A)
1 : 0.0000000E+00 0.0000000E+00 0.0000000E+00---------------------------------------------------MSG: start k-loop+++++++++++++++++++++++++++++++++++++++++++++++
MSG: k-loop:
1
MSG: POTMTX file is created----------------------------------------MSG: start diagonalization----------------------------------------MSG: end diagonalization
MSG: info from ZHEGV =------------------------------------------------------------------------------Eigen energy value (eV)
0 -2.738340
1 -2.705202
2 -2.647121
3 -2.643604
4 -2.624361
5 -2.624101
6 -2.622245

022

7 -2.603370
8 -2.585140
9 -2.583143
10 -2.579886
11 -2.563037
12 -2.553304
13 -2.549820
14 -2.521095
15 -2.514894
16 -2.509215
17 -2.488150
18 -2.482372
19 -2.474471--------------------------------------MSG:checking the probality of each eigenstates
All k-point calculation, which you requested,are done.

********************************* Naniwa code is terminated *********************************-----------------------------------------

44.2.5. EIGEN
It gives you the information about quantum number and eigenenergies (eV)
0
1
2
3
4
5
6
7
8
9
10
11
~
~
2828
2829
2830
2831
2832
2833
2834

-2.738340-2.705202-2.647118-2.643600-2.624484-2.624043-2.622192-2.603305-2.585474-2.583032-2.579732-2.562970~~
1.397943
1.401005
1.405767
1.427601
1.433854
1.451622
1.454133

4.2.6 stateXXXXX
It gives you the information about the XXXXXth eigenstate.

23

stateXXXXX
0-2.73834024018558
2.82029500000000
0.000000000000000E+000 0.000000000000000E+000
1.41014750000000
2.44244710549300
0.000000000000000E+000
0.000000000000000E+000 0.000000000000000E+000 10.7499987274312
993510.1834736495052
10.1834736495052
10.6003270094309
000(-1.777456224903666E-006,-4.974294848068331E-007)
1
0
0(7.765809220410138E-007,4.430627433556088E-007)200(1.439251475885052E-006,-2.545852331603858E-007)
~
~
~
~
~
~
(-5.370729930410416E-006,5.895488939631636E-007)
58
34(-5.362392471165102E-006,2.837122256840745E-007)
68
34(3.192389365300413E-006,-2.070464429167339E-007)78
34(-2.748703204133705E-006,1.452834001927643E-007)8834(2.221894867527162E-006,0.000000000000000E+000)
state file namequantum number, 𝜔eigenenergies (eV)⃗⃗⃗⃗⃗⃗1 ) (𝐿𝑎⃗⃗⃗⃗⃗⃗1 ) (𝐿𝑎⃗⃗⃗⃗⃗⃗1 ) (Å)
(𝐿𝑎
𝑥
𝑦
𝑧
⃗⃗⃗⃗⃗⃗⃗2 ) (𝐿𝑎⃗⃗⃗⃗⃗⃗⃗2 ) (𝐿𝑎⃗⃗⃗⃗⃗⃗⃗2 ) (Å)
(𝐿𝑎
𝑥
𝑦
𝑧
⃗⃗⃗⃗⃗⃗⃗3 ) (𝐿𝑎⃗⃗⃗⃗⃗⃗⃗3 ) (𝐿𝑎⃗⃗⃗⃗⃗⃗⃗3 ) (Å)
(𝐿𝑎
𝑥
𝑦
𝑧
𝑛𝑔1 𝑛𝑔2 𝑛𝑔3 : Numbers of Gaussian grid alog ⃗⃗⃗⃗
𝑎1 , ⃗⃗⃗⃗
𝑎2 , ⃗⃗⃗⃗
𝑎3 , where 𝑛𝑔1 × 𝑛𝑔2 × 𝑛𝑔3 = 𝑁𝐺σ𝑥 σ𝑦 σ𝑧1
𝑖𝑔1

: Gaussian decay factors

1
1
𝑖𝑔2
𝑖𝑔3
: 1st grid point indicators alog ⃗⃗⃗⃗
𝑎1 , ⃗⃗⃗⃗
𝑎2 , ⃗⃗⃗⃗𝑎3 .

(Re 𝐶𝜔,1 , Im 𝐶𝜔,1 ): corresponding coefficient of eigenvector
2
𝑖𝑔1

2
2
𝑖𝑔2
𝑖𝑔3
:2nd grid point indicators alog ⃗⃗⃗⃗
𝑎1 , ⃗⃗⃗⃗
𝑎2 , ⃗⃗⃗⃗𝑎3 .

(Re 𝐶𝜔,2 , Im 𝐶𝜔,2 ): corresponding coefficient of eigenvector
⋮
𝑁
𝑖𝑔1𝐺

𝑖𝑔2𝐺 𝑖𝑔3𝐺 :NG-th grid point indicators alog ⃗⃗⃗⃗
𝑎1 , ⃗⃗⃗⃗
𝑎2 , ⃗⃗⃗⃗
𝑎3 .
𝑁

𝑁

(Re 𝐶𝜔,𝑁𝐺 , Im 𝐶𝜔,𝑁𝐺 ): corresponding coefficient of eigenvector24

5. How to use (minimum)
5.1 Making 3D-potential energy surface for quantum particle in material.
You must make the potential energy surface for your quantum particle motion in materials by
ab initio electron state calculation.
Calculate the total energy : 𝐸(𝑋, 𝑌, 𝑍) of electron system as a function of quantum particle
position (𝑋, 𝑌, 𝑍). Use it as adiabatic potential energy: 𝑈(𝑋, 𝑌, 𝑍).
Save these potential energy information into POTENG file. (See the section 4.2 files section)
5.2 Making the simulation setting
Make the setting file: INSET (See the section 4.2 files section).
Copy the input file: INSET, POTENG on your working directory.
5.3 Executing the simulation program.
Type following command line on your working directory.

~/naniwa/bin/naniwaSS_run [Enter]
If successful, you can obtain the LOG file and the kpoint0000 directory.
Please check the contents in the LOG files.
You can find the simulation results under the kpoint0000 directory.
If “Oracle Grid Engine” is installed on your computer, you can submit your simulation byfollowing command line:

qsub run.csh [Enter]
qstat [Enter]
5.4 Check simulation results
Move to sub-directory: “kpoint0000”

cd ./kpoint0000 [Enter]ls [Enter]
cat

EIGEN [Enter]

5.4.1 How to see the Eigenenergies as a function of quantum number.

gnuplot [Enter]
GNUPLOT
Version 4.0 patchlevel 0….
….
Send bugs, suggestions and mods to<gnuplot-bugs@lists.sourceforge.net>
Terminal type set to 'x11'
gnuplot>

gnuplot> plot "EIGEN" [Enter]25

gnuplot> set xrange [0:50][Enter]gnuplot> replot [Enter]

Quit the gnuplot
gnuplot> quit [Enter]

5.4.2 How to see the Wave functions
5.4.2.1 OpenDX caseNaniwa package includes the “WaveViewer3D”, which is Visual Program running on the OpenDX.
(1) Convert the eigenstate data for OpenDX
Make the OpenDX data from the groud state to 10th excited state.
26

cp ../INSET./ [Enter]../../../bin/state2dx

010[Enter]stat2dx
I create the files for Opendx from0 to-------------------------I got the following data from INSET file.
(n1,n2,n3)=999I set (n1,n2,n3)=27
2727-------------------------=================================POTDAT.cfg is not found.
Position origine is reset to
0.0000000E+00 0.0000000E+00 0.0000000E+00=================================
wave00000.dat was created.
WAVE function
Max value= 2.219193
Min value= -4.8887818E-03
probability= 0.9999163

10

wave00000.general was created.gnuplot>…
wave00010.dat was created.
WAVE function
Max value= 1.522613
Min value= -1.618646
probability= 0.9998179
wave00010.general was created.

(2) Convert the potential energy surface (PES) data for OpenDX

cp ../POTENG./[Enter]../../../bin/poteng2dx [Enter]=================================POTDAT.cfg is not found.
Position origine is reset to
0.0000000E+00 0.0000000E+00 0.0000000E+00================================="PES3D.dat" file was created.
Umax= 1.393875
Umin= 0.0000000E+00"PES3D.general" file was created.

(3) Execute the OpenDX

cp../../../etc/OpenDX/WaveViwer3D_405B*

dx [Enter]

27./[Enter]Click “Run Visual Programs”(4) Select the “WaveViewer3D_405B.net in right hand winodw.
28

Click “OK” button.
(5) Operate the “WaveViewer3D”,
You can control it from Control panel.

(6) See the visualized results
You can see the 3-dimensional model in 4 Visualization windows;
top view, bird view, side view and bottom view.

29

(7) Quit the OpenDX

Click “Quit” button.

5.4.2.2 XcrySDen caseNaniwa package includes the Output file converter for XCrySDen.
30

(1) Convert the eigenstate data for XCrySDen.
Make the XCrySDen data from the groud state to 10th excited state.
cd ~/naniwa/work/test/kpoint0000 [Enter]../../../bin/state2xsf

010[Enter]stat2xsf
I create the files for XCrySDen from0 to-------------------------ERROR no INSET file :reset
n1 = 30
n2 = 30
n3 = 90-------------------------=================================POTDAT.cfg is not found.
Position origine is reset to
0.0000000E+00 0.0000000E+00 0.0000000E+00=================================
wave00000.xsf was created.
WAVE function
Max value= 2.18718407153673
Min value= -4.841641351593371E-003
probability= 0.999931342158014

10

wave00001.xsf was created.
WAVE function
Max value= 2.02312748202589
Min value= -1.86989237272753
probability= 0.999900567109712

wave00002.xsf was created.
WAVE function
Max value= 1.94090713382515
Min value= -1.94489431345728
probability= 0.999900392093716(2) Convert the potential enrgy surface (PES) data for XCrySDen
cp ../POTENG./[Enter]cp ../INSET ./ [Enter]../../../bin/poteng2xsf [Enter]***********************************PES data converter for XCrySDen***********************************"PES3D.xsf" file was created.
Umax=

1.393875

Umin=

0.0000000E+00(3) Execute the XCrySDen
xcrysden [Enter]31

(4) Open the file wave00000.xsf① Click “File” ② Click “Open Structure” ③ Click “Open XSF (XCrySDen
Structure file)”32

(④Drag down the thumb in 2nd vertical scrollbar.

⑤Select the file “wave00000.xsf”⑥Click “OK”
5) Set the view status.
33

⑦Click “Tools”

Click⑧Click “Data Grid””OK” button.

Then, you can see this “Isosurface/Property-plane Controls”(6)Set adequate Isovalue ⑨and click “Submit” botton ⑩. You can see its isosurface,34

(7) Select “Plane #1” ⑪ and choose select color basis ⑫ . And check boxes of display colorplane⑬ and display isolines ⑭. Click submit botton ⑮ and you can see the isoline on a crosssection, which can be moved by arrows ⑯.

“wave00000.xsf” case(8) You can also see the excited states whose wave function has node.
35

“wave00001.xsf” case(6) You can also see the potential energy surface“PES3D.xsf” case(7) Quit the XCrySDen
Click “File” and “Exit”
And click “Yes”
5.4.2.3 VESTA case
VESTA can read xsf files to show the wavefunctions36

(1) Make xsf files.
Do the same procedures from (1) to (2) in section 5.4.2.2.
(2) Execute the VESTAVESTA [Enter](3)

Open the file wave00000.xsf① Click “File”②

Click “Open”③ Select the file “wave00000.xsf”. ④Click “OK”

(4) You can see the ground state wave function.

37

(5) You can control the setting of isosurface.
④

Click “Object” ⑤

Select “Property” ⑥ Click “Isosurface…”⑦You can change the level of isosurface and⑧ add the other levels.

(6) You can also see the excited states whose wave function has node.
38

“wave00001.xsf” case(7) Quit the VESTA⑨ Click “File” and ⑩“Exit”

39

References[1] Hideaki Kasai and Ayao Okiji, Progress in Surface Science, Vol. 44, No. 2, pp. 101-183 (1993).
[2] Wilson Agerico Diño, Hideaki Kasai and Ayao Okiji, Progress in Surface Science, Vol. 63, No. 3-5,
pp. 63-134 (2000).
[3] Japanese Patent No. 4774523.
[4] Japanese patent application 2012-16133.
[5] Kunihiro Nobuhara, Hiroshi Nakanishi, Hideaki Kasai and Ayao Okiji, Surface Science, Vol. 493,
No. 1-3, pp. 271-277 (2001).
[6] Kunihiro Nobuhara, Hiroshi Nakanishi, Hideaki Kasai and Ayao Okiji, Surface Science, Vol. 493,
No. 1-3, pp. 271-277 (2001).
[7] Kunihiro Nobuhara, Hideaki Kasai, Hiroshi Nakanishi and Ayao Okiji, Surface Science, Vol. 507510, pp. 82-86 (2002).
[8] Kunihiro Nobuhara, Hideaki Kasai, Hiroshi Nakanishi and Ayao Okiji, Journal of Applied Physics
Vol. 92, No. 10, pp. 5704-5706 (2002).
[9] Kunihiro Nobuhara, Hideaki Kasai, Hiroshi Nakanishi and Wilson Agerico Diño, Journal ofApplied Physics Vol. 96, No. 9, pp. 5020-5025 (2004).
[10] Nobuki Ozawa, Tanglaw Abat Roman, Hiroshi Nakanishi, Hideaki Kasai, Surface Science, Vol.
600, No. 18, pp. 3550-3554 (2006).
[11] Tanglaw Roman, Wilson Agerico Diño, Hiroshi Nakanishi, Hideaki Kasai, e-Journal of Surface
Science and Nanotechnology, Vol. 4, pp. 619-623 (2006).
[12] Nobuki Ozawa, Tanglaw Roman, Hiroshi Nakanishi, Wilson Agerico Diño, Hideaki
Kasai ,Physical Review B Vol.75, No.11, pp. 115421 (2007).
[13] Nobuki Ozawa, Tanglaw Roman, Nelson Buntimil Arboleda Jr., Wilson Agerico Diño, Hiroshi
Nakanishi, Hideaki Kasai, Journal of Physics: Condensed Matter, Vol. 19, No. 48, pp. 365214(2007).
[14] Nobuki Ozawa, Nelson Buntimil Arboleda Jr., Hiroshi Nakanishi, Hideaki Kasai, Surface Science,Vol. 602, No. 4, pp. 859-863 (2008).
[15] Nobuki Ozawa, Nelson Buntimil Arboleda Jr., Hiroshi Nakanishi, Nobuaki, Shimoji, Hideaki
Kasai, Surface and Interface Analysis, Vol. 40, Issue 6-7, pp. 1108-1112 (2008).
[16] https://software.intel.com/en-us/intel-parallel-studio-xe[17] https://software.intel.com/en-us/intel-mkl
Intel-MKL is included in Intel-Composer-XE [16][18] http://www.gnuplot.info/[19] http://www.opendx.org/ (dead link)[20] http://www.xcrysden.org/[21] http://jp-minerals.org/vesta/en/40

Appendix
A PortingNaniwa standard version uses the following system-dependent subroutines.
(1) Intel Fortran built-in subroutine: SYSTEM(2) Lapack subroutine: ZHEGV(3) Intel MKL procedure: MKL_DFTI
If you want to port Nanwia to other system, you must replace these routines. Please rewrite the(1) UNIXcommand_intel.f, (2) diagonalize_lapack.f and (3) fastDFT3D_MKL.f in SRC directory.
And also you must replace Fortran compiler name and its options.
These are defined in Makefile#*
for intel FORTRAN & MKL#*#
ASR = diagonalize_lapack.f
UNIXcommand_intel.f
LIB = /opt/intel/mkl/lib/intel64
INC = -I/opt/intel/mkl/include

fastDFT3D_MKL.f#*Compiler name and option
FC = ifort
OPT = -O3 -mkl -lpthread

A-1. Porting to Hitachi SR16000 with optimized FORTRAN90, MATRIX/MPP and LAPACK
We provide the necessary interface to Hitachi SR16000. You only have to modify the following
parts in Makefile.
Comment out part:#*for intel FORTRAN & MKL#*##ASR = diagonalize_lapack.f
UNIXcommand_intel.f#LIB = /opt/intel/mkl/lib/intel64#INC = -I/opt/intel/mkl/include#*Compiler name and option#FC = ifort#OPT = -O3 -mkl -lpthread

Please insert mentioned-above red # in Makefile.
Uncommented part:

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fastDFT3D_MKL.f

#*
for Hitachi Optimizing FORTRAN90#*
LAPACK & MATRIX/MPP#*#*KEK SYSTEM A#*#ASR = diagonalize_lapack.f UNIXcommand_hitachi.f fastDFT3D_MPP.f#LIB = /opt/hitachi/matmpp/lib -lmatmpp -L/srhome/.tools/lib -llapack_sc -lblas_sc#INC =#*Compiler name and option#FC = f90
#OPT = -Os -64 -model=M1 -parallel

Please remove the mentioned-above blue # in Makefile.
These procedure replaces SYSTEM and MKL_DFTI to HF_SH and HZFT6M. Later subroutine

restricts the value of n1 , n2 , n3 in POTENG. These integer values must be not less than
8 and power of 2.

Please see the naniwa/etc/example/testSR.

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B Making 3D-potential energy surface by VASP
example: H in Si bulk
See the directory: ~/naniwa/etc/potentials/SiBulk
under ~/naniwa/etc/potentials/SiBulk
host :

getting the total energy of host material without hydrogen atom

particle: getting the total energy of hydrogen atom without host material
scan:getting the total energy in the case of hydrogen atom in host material as a function ofhydrogen atom position(1) cd~/naniwa/etc/potentials/SiBulk/host/qsub

run.cshAfter the calculation, getting the energy E_host from last Eo value in OSZCAR(2) cd~/naniwa/etc/potentials/SiBulk/particle/

qsub

run.cshAfter the calculation, getting the energy E_partcile from last Eo value in OSZCAR(3) cdcsh~/naniwa/etc/potentials/SiBulk/scan/./auto.csh

After all calculations, ..
csh./collect.csh

cp POTDAT ./ POTDAT2POTENG
cd./ POTDAT2POTENG

ifort makePOTENG.fvi-omakePOTENG

POTDAT.cfg
Edit the configuration file: POTDAT.cfg
input the value of E_host and E_partcile into this file*title: Potential energy for H in Si bulk
*lattice information
3.83958982184
1.00000000000 0.0
0.0
0.50000000000 0.86602540378 0.0
0.50000000000 0.28867513459 0.81649658092* data mesh numbers
20 20 20*origine of positioni (fractional)
0.00000000 0.00000000 0.00000000*isolated particle energy (eV)-.11089857E+01*isolated slab (host) energy (eV)-.86414775E+02*cut of energy (eV)2.00./makePOTENG
Then you can obtain the POTENG file43For checking the POTENG file.
ifort POTENG2DX.f-o

POTENG2DX

dx
Click “Run Visual Programs”
Select the “PES3D.net in right hand winodw.
Click “OK” button.

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C Required parameters for convergence
In order to get the reliable results, you should try the various parameters and check the convergenceof their results.
C.1 Number of nodes for the 3D Gaussian functions
Here we show the Eigenenergy convergency as a function of the number of nodes for the 3D
Gaussian functions. When only the number of the nodes are changed in the test program:naniwa/etc/example/Harmonic3D, you can see the following dependences in the figure.

As the numbers of the grid increase, the eigen energies converge and you can get reliable results.
C.2 Gaussian decay factor (SigmaX, SigmaY SigmaZ)
Here we show the Eigenenergy convergency as a function of the decay factor of basis Gaussianfunctions. When only the decay factors are changed in the test program:naniwa/etc/example/Harmonic3D with fixed numbers of the grids: 10x10x10, you can see thefollowing dependences in the figure.

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As the decay factors decrease, the calculated Eigen energies converge, and you can get reliable results.
But the decay factors decrease less than certain value, the calculations are suddenly broken. You must also checktheir wave function shapes.

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Nakanishi Laboratory
National Institute of Technology, Akashi College, Japan
Phone & Facsimile: +81-78-946-6229
Lab. WEB: http://www.akashi.ac.jp/~nakanishi/
E-mail: nakanishi@akashi.ac.jp

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