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钙钛矿结构材料Sr-%2c8-CaRe-%2c3-Cu-%2c4-O-%2c24-压力效应地研究.pdf
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文档介绍：--------------------------Page1------------------------------2008年磺士论文．李圣爱摘要虽然钙钛矿结构氧化物RI。A。№幻3(其中R是稀土金属离子，A是碱土金属离子)的研究历史已经超过了半个世纪，但这系列化合物仍然是凝聚态物理中的一个重要方向．作为强关联电子系统(SCEM)，一方面钙钛矿结构化合物是理解电荷，自旋，轨道和晶格自由度间复杂相互作用而产生的丰富物理现象的理想材料；另一方面这系列化合物拥有极丰富的相图，各种电学和磁学性质对外界条件相当敏感．使它们将成为研制量子调控器件的极好材料。今年的诺贝尔物理学奖颁给了法国科学家阿尔贝·费尔和德国科学家彼得骼林贝格尔，以表彰他们对。巨磁电阻”效应领域的巨大贡献．巨磁电阻是钙钛矿材料的一个重要电磁特性，广泛应用在存储电子元件上，极大地推进了现代文明的发展。同时外界对基础科学的肯定极大地也激发了研究工作者的热情．钙钛矿材料中一个最基本的研究对象当属kh缸m，它是研究钙钛矿结构材料的最好电子系统。所以我们首先以LaMn03为研究对象，研究了它的J1r畸变，磁性结构和电子．电子互作用之间的关系及对其电磁性质所起的作用。并且进一步考虑到这种材料在不同压力下的各种物理参数和结构变化所引起的新效应。另外，2003年由几位日本科学家通过高温高压合成了额型钙钛矿材搴孚SrsCaR隅，它的特别之处在于它不但表现出较强的磁性，而且还有很高的居里相变温度(Tc)，众所周知，铜氧化物中既有铁磁性又有很高Tc的材料很少见，所以SrsCaRe3Cu‘Ou是很好的研究自旋电子材料，很可能具有非常广泛的应用前景。理论方面：2∞5年，XG．Wan等人运用密度泛函理论和格林函数方法研究了该材料的电子结构和磁性性质。研究表明这种材料是绝缘体，每个元胞有1．OlIB的磁矩，所得结果和实验一致。本人延续前人的之前介绍到如何去计算声子谱,计算完成后,可以去分析声子谱 工具/原料 VASP phonopy 方法/步骤 之前小编给大家介绍了怎样去计算声子谱,在14节有介绍,没有看到的小伙伴可以去看一下 注意INCAR里不要多加入一些没用的参数设置,这样容易出错,只要必须的参数设置就可以了,如小编上一节介绍的 计算完成后结果如图所
这里小编介绍如何计算磁性体系的磁性耦合态 方法/步骤 计算磁性体系,首先要知道它的稳定态是什么,一般第一步要进行优化 分两步来看,
INCAR是计算的参数,也就是告诉软件如何执行任务去计算,这里小编告诉大家如何来写一个简单的INCAR 工具/原料 INCAR 方法/步骤 INCAR格式如下 SYSTEM name of Syste
应力对材料的性质有重要影响,比如随着应力的不同,磁性材料的基态可能会发生变化 对应力进行扫描计算,可以找到最稳定的晶格常数 工具/
这一节小编给示范计算态密度的过程 工具/原料 VASP,P4v.exe 方法/步骤 先讲一下DOS,就是态密度,也就是每个轨道的电
好久不见了,这一节小编给大家介绍怎样计算电极化,born有效电荷. 参照manual,这里使用NaF作为例子 工具/原料 vasp
syml文件的写入和能带的计算 工具/原料 VASP,syml,band.x 方法/步骤 这里继续上一节内容,就是关于syml的内
这一节介绍分子动力学的计算方法 工具/原料 VASP 方法/步骤 首先,做分子动力学的模型要原子足够多,可以建立超胞来处理 比如小
这一节继续介绍P4v.exe软件调处态密度DOS 工具/原料 VASP P4v.exe 方法/步骤 打开P4v.exe,如下图 打开计算得到的vasprun.xml 如图,点击DOS+Band 或者左边图标也可以看到,下图也可以看到DOS 计算PDOS可以这样:Local DOS + Band Control,调出如下
U用于处理电子之间强的库伦相互作用. Hubbard U 工具/原料 VASP 方法/步骤 上一节说倒磁性计算,先给小伙伴看下小编
声子谱是看体系能否稳定存在的一个重要指标,所以在计算中,声子谱也是常用的一个计算 工具/原料 VASP phonopy 方法/步骤 声子谱是一个重要参数,可以鉴定和预测体系是否稳定存在 安装phonopy,这里小编就不具体讲了,不会的小伙伴等小编以后补上相关软件的安装就可以了,安装好以后会出现如下界面 建立好POSCA
这一节介绍如何计算能带 工具/原料 需要几个脚本:gk.x 和 band.x 以及syml文件 方法/步骤 能带跟DOS是对应的,
这一节一起来看一下VASP计算完成后的输出文件吧 工具/原料 VASP 方法/步骤 VASP的主要输出文件如下: 这里先讲一下主要
这一节介绍wannier接口VASP的计算实例.wannier用于计算能带等信息有着较高的精度和准确度,配合vasp计算能够更好地
本系列将全面介绍VASP的使用和实例.小伙伴给赞就是小编的最大动力!!! 本节主要讲如何写POSCAR,如何用MS里建立的模型转成
这里补充一下POSCAR的写法,怕有的小伙伴看不懂 工具/原料 VASP MS 方法/步骤 上一节讲到怎样生成.cell 文件,就
这一节给大家一个简单的实例,这里就选择优化CrI3 工具/原料 VASP 方法/步骤 做一个非磁的优化 第一步,写入INCAR: ISTART=0 ICHARG=2 IBRION=2 NSW =60 NELM=40 EDIFF=1E-4 EDIFFG=-0.01 ISMEAR=0 SIGMA=0.02 ISIF=3 E
今天教大家写脚本处理态密度! 工具/原料 vasp 方法/步骤 首先要知道态密度数据是在DOSCAR中的,让我们先看一下里面的结构 从第六行开始, 前两个数据是能量范围,第三个是NEDOS数,第四个是费米能级 我们的目标是把前两列提取出来,而且提取的列数=NEDOS的值(INCAR中的参数)比如我的INCAR中的NEDOS=601,这里我就要提取601列. 如下图,从第六行开始,我这里INCAR中的NEDOS=601,所以我要取到第607行 也就是要提取第7~NEDOS+6 行的数据,最后一步要做能量修正
这一节讲一下DOSCAR文件,OSICAR等 方法/步骤 DOSCAR文件内容如下 具体参数和意义如下 CHG和CHGCAR 这两
这一节讲一下态密度的问题 方法/步骤 态密度:电子在对应能量的数量比,比如下图,在-23eV左右有一个峰值,意味着这里有较多的电子
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第一原理电子结构计算程序：VASP? 程序原理 ? 输入文件 ? 输出文件 ? 应用输入文件POTCAR KPOINTS POSCAR INCARpseudopotentail file Brillouin zone sampling structural data steering parametersChoosing POTCAR file LDA GGA PAW_LDA PAW_GGA PAW_PBE(VASP4.5)Check following line in POTCAR LEXCH= CA or 91 GGA= LPAW= T基本任务? 计算电子态密度,能带,电荷密度 ? 优化晶体参数 ? 内部自由度弛豫 ? 结构弛豫INCAR输入文件: 程序控制参数System =diamond Si ISTART = 0 ENCUT = 150.0 NELM= 200 EDIFF = 1E-04 EDIFFG = -0.02 GGA=91 NPAR=4 NSW=100 IBRION = 2 ISIF=2 ISYM = 1 LWAVE = F LCHARG = FPOSCAR输入文件: 原胞中的原子位置Diamond Si 3.9 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 1 Direct 0.0 0.0 0.0基矢的公因子 基矢a1 基矢a2 基矢a3 原胞中的原子个数 坐标系选为基矢构成的坐标系 基矢坐标系下原子的位置ρ ρ ρ 1 a1 = a ( j + k ) 2 ρ 1 ρ ρ a 2 = a (i + k ) 2 ρ 1 ρ ρ a3 = a (i + j ) 2KPOINTS输入文件: 控制K-点的选取方式K-Points 0 Monkhorst Pack 11 11 11 0 0 0POTCAR输入文件: 赝势文件US Si 4.00000 parameters from PSCTR are: VRHFIN =Si: s2p2 LEXCH = CA EATOM = 115.7612 eV, 8.5082 Ry GGA = -1.8 .0293 -.9884 eV TITEL = US Si LULTRA = T use ultrasoft PP ? IUNSCR = 1 unscreen: 0-lin 1-nonlin 2-no RPACOR = 1.580 partial core radius POMASS = 28.085; ZVAL = 4.000 mass and valenz RCORE = 2.480 outmost cutoff radius RWIGS = 2.480; RWIGS = 1.312 wigner-seitz radius (au A) ENMAX = 150.544; ENMIN = 112.908 eV EAUG = 241.945 …………输出文件OUTCAR CONTCAR CHGCAR CHG WAVECAR DOSCAR EIGENVAL OSZICAR LOCPOT PROOOUT示例1: 用VASP求硅的电子态密度和能带分如下几步:(1). 生成4个输入文件: POSCAR POTCAR INCAR KPOINTS (2). 优化晶格参数,求出能量最低所对应的晶格参数 (3). 固定晶格参数, 求出能态密度(DOSCAR), 确定费米能量 (4). 修改KPOINTS和INCAR输入文件,固定电荷密度,做非自洽 计算,得到输出文件EIGENVAL (5). 提取数据,画图(1). 生成4个输入文件: POSCAR POTCAR INCAR KPOINTSSystem =diamond Si ISTART = 0 ENCUT = 150.0 NELM= 200 EDIFF = 1E-04 EDIFFG = -0.02 NPAR=4 NSW=1 IBRION = 2 ISIF=2 ISYM = 1Diamond Si 5.5 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 2 Direct 0.0 0.0 0.0 0.25 0.25 0.25VASP提供 各种POTCARK-Points 0 Monkhorst Pack 21 21 21 0 0 0(2). 优化晶格参数,求出能量最低所对应的晶格参数运行VASP程序, 查看SUMMARY.fcc输出文件:(3). 固定晶格参数, 求出能态密度(DOSCAR), 确定费米能量(i)找到平衡晶格常数后, 把该值写入到POSCAR文件中,并增加K点数 作一个离子步自洽计算(NSW = 0, IBRION = -1) .(ii) 从DOSCAR输出文件中读出态密度和费米能级,费米 费米能级也可从OUTCAR中读出.(4). 做非自洽计算, 求电子结构? 修改INCAR文件: 将参数ICHARG设为 11 ? 修改KPOINTS输入文件 ? 运行VASP程序,从输出文件EIGENVAL中提出电子结构画出电荷密度? VASP输出电荷密度文件CHGCAR ? 采用免费程序LEV00处理数据文件CHGCAR www.cmmp.ucl.ac.uk/lev10(?)-10 0 .0 7 0 .1 4 0 .2 1 0 .2 8 0 .3 4 0 .4 1 0 .4 8 0 .5 5-2-3 -3 -2 -1 0 1 2 3(? )示例2: 用VASP求Mg的电子态密度和能带分如下几步:(1). 生成4个输入文件: POSCAR POTCAR INCAR KPOINTS (2). 优化晶格参数,求出能量最低所对应的晶格参数 (3). 固定晶格参数, 求出能态密度(DOSCAR), 确定费米能量 (4). 修改KPOINTS和INCAR输入文件,固定电荷密度,做非自洽 计算,得到输出文件EIGENVAL (5). 提取数据,画图(1). 生成4个输入文件: POSCAR POTCAR INCAR KPOINTSHcp-Mg 3.208 0.5 -0.866 0 0.5 0.866 0 0.0 0.0 1.6 2 Direct 0.0 0.0 0.0 0.33 0.5VASP提供 各种POTCARK-Points 0 Monkhorst Pack 21 21 21 0 0 0System =hcp Mg ISTART = 0 ENCUT = 150.0 NELM= 200 EDIFF = 1E-04 EDIFFG = -0.02 NPAR=4 NSW=1 IBRION = 2 ISIF=2 ISYM = 1c/aρ 1ρ 3 ρ a1 = a( i ? j ) 2 2 ρ 1ρ 3 ρ a2 = a( i + j ) 2 2 ρ ρ a3 = ck(2). 优化晶格参数,求出能量最低所对应的晶格参数hcp结构晶体含有一个内部自由度, 晶格参数优化过程要比立方 结构费时Mg: a=3.208, c/a=1.6(3). 固定晶格参数, 求出能态密度(DOSCAR), 确定费米能量(i)找到平衡晶格常数后, 把该值写入到POSCAR文件中,并增加K点数 作一个离子步自洽计算(NSW = 0, IBRION = -1) .(ii) 从DOSCAR输出文件中读出态密度和费米能级,费米 费米能级也可从OUTCAR中读出.0.60.5DOS0.40.30.20.1 -6 -4 -2 0 2 4 6 8 10Energy(4). 做非自洽计算, 求电子结构? 修改INCAR文件: 将参数ICHARG设为 11 ? 修改KPOINTS输入文件? 运行VASP程序,从输出文件EIGENVAL中提出电子结构ρ 1ρ a1 = a( i ? 2 ρ 1ρ a2 = a ( i + 2 ρ ρ a3 = ck3ρ j) 2 3ρ j) 2ρ 2π ρ b1 = (i ? a ρ 2π ρ b2 = (i + a ρ 2π ρ b3 = k c3 3 3 3ρ j) ρ j)ρ ρ ρ Γ = 0b1 + 0b2 + 0b3 = (0,0,0) 1 ρ ρ 1 1 K = (b1 + b2 ) = ( , ,0) 3 ρ 3 3 M = 0.5b1 = (0.5,0,0) ρ A = 0.5b3 = (0,0,0.5) ρ ρ ρ H = 0.5b1 + 0.5b2 + 0.5b3 = (0.5,0.5,0.5) ρ ρ ρ L = 0.5b1 + 0b2 + 0.5b3 = (0.5,0,0.5)KPOINTS文件:k-points along high symmetry lines 100 ! 100 intersections Line mode rec 0 0 0 ! gama 0.3 0 ! K 0.3 0 !K 0.5 0.0 0.0 ! M 0.5 0.0 0.0 ! M 0 0 0 ! gama 0 0 0 ! gama 0 0 0.5 ! A 0 0 0.5 ! A 0.3 0.5 ! H 0.3 0.5 ! H 0.5 0.0 0.5 ! L 0.5 0.0 0.5 ! L 0 0 0.5 ! A电荷密度Be(112 0)Be(0001)示例3: 用VASP求铅锌矿结构CoO的电子结构设CoO呈铁磁性,故需做自旋极化计算(1). 生成4个输入文件: POSCAR POTCAR INCAR KPOINTS (2). 优化晶格参数,求出能量最低所对应的晶格参数 (3). 固定晶格参数, 求出能态密度(DOSCAR), 确定费米能量 (4). 修改KPOINTS和INCAR输入文件,固定电荷密度,做非自洽 计算,得到输出文件EIGENVAL (5). 提取数据,画图(1). 生成4个输入文件: POSCAR POTCAR INCAR KPOINTS2.98 0.5 -0.866 0.5 0.0 2 2 Direct 0.0 0.0 0.0 0.33 0.5 0.33 0. 0.0 0.6337ρ 1ρ 3 ρ a1 = a( i ? j ) 2 2 ρ 1ρ 3 ρ a2 = a( i + j ) 2 2 ρ ρ a3 = ck0.0 0.0 1.735 VASP提供 各种POTCAR K-Points 0 Monkhorst Pack 21 21 21 0 0 0 System =hcp Mg ISTART = 0 ENCUT = 150.0 NELM= 200 EDIFF = 1E-04 EDIFFG = -0.02 ISPIN = 2 NPAR=4 NSW=1 IBRION = 2 ISIF=2 ISYM = 10.866 0.0B A B A(2). 优化晶格参数,求出能量最低所对应的晶格参数wurtzite晶体含有两个内部自由度, 晶格参数优化过程要比立方 结构费时CoO: a=2.98, c/a=1.735, u=0.3678844E (eV)00-4-4-8-8-24ALMΓAHKΓ-24ALMΓAHKΓDENSITY OF STATES50-5-20-100 ENERGY (eV)1020固体材料表面的第一原理计算介绍? VASP程序 ? 构造超原胞 ? 计算表面性质 ? 应用Building surfaces (1)asymmetric setup(2)symmetric setupunit cell coordinates are optimized Fixed layers (bulk)vacuum示例1: 用VASP求1*1Mg(0001)的表面性质分如下几步:(1). 生成4个输入文件: POSCAR POTCAR INCAR KPOINTS (2). 优化晶格参数,求出体Mg的晶格参数 (3). Mg(0001)的原子层数,构造超原胞的POSCAR (4). 计算表面性质 (5). 提取数据,画图POSCARMg(0001): 3..5 0.5 0.0 6 Direct 0.0 0..0 0..0 0.6666667-0...00.0 0.0 10.224410.0 0..0 0..0 0.33333330......6951212表面性质Surface energyσ = 1 ( Esurf ? N atom × Ebulk ) 2Geometry getting relaxed structure from CONTCAR Relaxation of surface layers :d i ? d idea ×100% d ideaHeat of formation of overlayers of A on substrate BH n ( A) =E slab( B ) + 2n ( A) ? ( E slab( B ) + 2nEbulk ( A) ) 2(Should use the same energy cutoff for each calculation)Local Density of states INCAR: RWIGS = γ ? (works only for NPAR = 1 or serial version) LORBIT = 11 (only for PAW) ISMEAR = -5 (use tetrahedron for DOS calculations) NPAR = 1 Output file : DOSCAR (energy, s-dos, p-dos, d-dos for each atom) PROCAR (dos for each band and k-point)Work function INCAR: LVTOT = .TRUE. Output file : LOCPOT (same format as CHGCAR)WRITE(IU,FORM) (((V(NX,NY,NZ),NX=1,NGX),NY=1,NGY),NZ=1,NGZ)LOCPOT only contain electrostatic part of potential, if exchange correlation potential is to be included, change one line in main.F :! comment out the following line to add exchange correlation ! INFO%LEXCHG=-11. Search “E-fermi” in OUTCAR to get fermi-level 2. Analyze and plot data in LOCPOTEnergy (eV)Energy (eV)DOSCoulomb potential (eV) Coulomb potential (eV)Coulomb potentialΦFermi energyW(100)W(110)(eV)Z-axis(?)Coulomb potentialZ-axis(?)W(111)W(211)(eV)Z-axis(?)Z-axis(?)Mg(0001)的表面性质10 8 6 4 2 0 -2 -4 -6ΓMLAΓL2 1 0 -1 -2Γ(a)(c)MLAΓL ΓMLAΓL(b)(d)-6-4-202468 -6-4-2Energy (eV)0 2 4 Energy (eV)68
示例2: 原子氢在Mg(0001)表面的吸附性质POSCARMg(0001)+H: 3..5 0.5 0.0 6 2 Direct 0.0 0..0 0..0 0..3333333-0...00.0 0.0 10.224410.0 0..0 0..0 0..66666670.......721
示例3: 原子氢在表面的吸附性质最佳吸附位置
示例4: Mg在Si(111)表面的吸附性质
形成能 (formation energy)Si(111)/Mg系统的电子结构性质Clean Si(111)0.25ML0.5ML1ML3-0.040 -0.0222-0.005 0.0131Mg0.030 0.048 0.065 0.083(?)00.100-1SiSi-2-3 -3 -2 -1 0 1 2 33(?)-0.040 -0.0222-0.005 0.013 0.0301Mg0.048 0.065 0.083(?)00.100-1SiSi-2-3 -3 -2 -1 0 1 2 3(?)3-0.017 -0.0102-0.003 0.004 0.0111Mg0.018 0.026 0.033(?)00.040Si-1Si-2-3 -3 -2 -1 0 1 2 3(?)示例5: ZnO在MgO(111)表面上的极向生长Formation energy:吸附能O-O 反相层
高压相变弹性系数熔化曲线,第一原理分子动力学金属钼的熔化曲线扩散系数和粘性系数的计算结果V 15.48 10.98 T(K) 00 00
D(10-9m2/s) 1.460 5.116 0.189 0.192 6.669 0.885 1.324 (mPa?s) 16.35 5.158 259.2 222.6 8.028 62.751 35.6949.84Hands on Session I:Georg KRESSE¨ Institut fur Materialphysik and Center for Computational Material Science Universit¨ t Wien, Sensengasse 8, A-1090 Wien, Austria ab-initioackage ienna imulationG. K RESSE , H ANDSON(I):ATOMS AND MOLECULESPage 1Overviewdiscussion of the required ?les lot’s of examples C O atom C O2 dimer C CO C H2 O tasks C relaxation C vibrational frequencies C MDG. K RESSE , H ANDSON(I):ATOMS AND MOLECULESPage 2The very ?rst step: a single atom?les required to do all calculations presented in this session can be found in ?vw/1_1_description_of_job1 ?vw/1_2_description_of_job2 ?rst digit corresponds to the number of the hands on session, second one to the example required ?les INCAR, KPOINTS, POSCAR, POTCAR C POTCAR pseudopotential ?le generated by concatenation of individual POTCAR ?les from the data-base C KPOINTS Brillouin zone sampling describes which k-points are used C POSCAR structural data basis vectors and positions C INCAR steering the calculationsG. K RESSE , H ANDSON(I):ATOMS AND MOLECULESPage 3The POTCAR ?lein this course, you can copy the POTCAR ?les from ?vw/potpaw_PBE/element_name/POTCAR ?vw/potpaw_PBE/O/POTCAR or simply type makepaw_PBE O or copy all input ?les from?vw/1 1 Oatom mkdir O cd O cp ?vw/1_1_Oatom/* . what information can be found in the POTCAR ?le: C pseudopotential description C data that is required to regenerate the potential C number of valence electrons C atomic mass C required energy cutoffG. K RESSE , H ANDSON(I): 11 OatomPage 4The KPOINTS ?ledetermines how many k-points are used to sample the Brillouin zone for molecules or atoms only a single k-point is required KPOINTS ?le: Gamma-point 1 ! rec ! 0 0 0 1 ! only one k-point in units of the reciprocal lattice vector 3 coordinates and weightfor atoms and molecules the Bloch theorem does not apply, hence there is no need to use more then one single k-point when more k-points are used, only the interaction between the atoms (which should be zero) is described more accuratelyG. K RESSE , H ANDSON(I): 11 OatomPage 5The POSCAR and INCAR ?lesdetermines the lattice vectors (Bravais lattice) and the coordinates (position of the atoms) a single atom POSCAR ?le: O atom in a box 1.0 ! 8.0 0.0 0.0 ! 0.0 8.0 0.0 ! 0.0 0.0 8.0 ! 1 ! cart ! 0 0 0 universal scaling parameters lattice vector a(1) lattice vector a(2) lattice vector a(3) number of atoms positions in cartesian coordinatesINCAR steers the calculations: SYSTEM = O atom in a box ISMEAR = 0G. K RESSE , H ANDSON(I): 11 OatomPage 6Running vasptype: vasp vasp.4.6.2 07Jul02 POSCAR found : 1 types and 1 ions LDA part: xc-table for Pade appr. of Perdew POSCAR, INCAR and KPOINTS ok, starting setup WARNING: wrap around errors must be expected entering main loop N E dE d eps ncg rms DAV: 1 0.3.3.9 0.335E+0 DAV: 2 0.3.3.3 0.480E+0 DAV: 3 -0.1.4.3 0.376E+0 DAV: 4 -0.3.1.1 0.660E+0 DAV: 5 -0.3.2.2 0.907E-0 DAV: 6 -0.3.8.1 0.397E-0 DAV: 7 -0.3.1.2 0.149E-0 DAV: 8 -0.3.5.2 0.469E-0 1 F= -. E0= -. d E =-. writing wavefunctionsG. K RESSE , H ANDSONrms(c)0.286E-01 0.142E-01 0.480E-02(I): 11 OatomPage 7OSZICAR and stdout ?leinitial charge corresponds to the charge of isolated overlapping atoms (POTCAR) for 4 steps the charge remains ?xed, then the charge is updated (rms(c) column) N E dE d eps ncg rms rms(c) iteration count total energy change of total energy change of the eigenvalues (?xed potential) number of optimisation steps Hψ total residual vector ∑nk wk fnk H charge density residual vector εnk ψnkG. K RESSE , H ANDSON(I): 11 OatomPage 8OUTCAR ?leindividual parts are separated by lines ---------------------------------------------------------?rst part: reading INCAR, POTCAR, POSCAR nearest neighbor distances and analysis of symmetry information on what was parsed from INCAR verbose job information information on lattice, k-points and positions information on the basis set (number of plane waves) non local pseudopotential information information for each electronic step (one line in OSZICAR)G. K RESSE , H ANDS (I): 1ON1 OatomPage 9POTLOK: VPU time 0.93: CPU time 0.93 SETDIJ: VPU time 0.01: CPU time 0.01 EDDAV : VPU time 0.82: CPU time 0.83 DOS : VPU time 0.00: CPU time 0.00 -----------------------------------------LOOP: VPU time 1.76: CPU time 1.76 eigenvalue-minimisations : 14 total energy-change (2. order) : 0. number of electron 6.0000000 magnetization augmentation part 6.0000000 magnetization(-0.)Free energy of the ion-electron system (eV) --------------------------------------------------alpha Z PSCENC = 0. Ewald energy TEWEN = -91./2 Hartree DENC = -281. -V(xc)+E(xc) XCENC = 26. PAW double counting = 245.7. entropy T*S EENTRO = -0. eigenvalues EBANDS = -43. atomic energy EATOM = 432. --------------------------------------------------free energy TOTEN = 39. eV energy without entropy = 39. energy(sigma-&0) =ON39.Page 10G. K RESSE , H ANDS(I): 11 Oatomeigenvaluesk-point 1 : 0.0 0.0000 band No. band energies occupation 1 -23.00 2 -8.33 3 -8.33 4 -8.33 5 -0.00 6 1.00 7 1.00information on charge + some more timing informationssoft charge-density along one line, spin component 0 1 2 3 4 x 5.5 4.1 2. 1....3290G. K RESSE , H ANDSON(I): 11 OatomPage 11information on the energy and stress tensorFREE ENERGIE OF THE ION-ELECTRON SYSTEM (eV) --------------------------------------------------free energy TOTEN = -0.314276 eV energy without entropy= -0.005752 energy(sigma-&0) = -0.160014FORCE on cell =-STRESS in cart. coord. units (eV/reduce length): Direction X Y Z XY YZ ZX -------------------------------------------------------------------------------------Alpha Z 0.27 0.27 0.27 Ewald -30.64 -30.64 -30.64 0.00 0.00 0.00 Hartree 93.89 93.89 93.89 0.00 0.00 0.00 E(xc) -27.94 -27.94 -27.94 0.00 0.00 0.00 Local -147.85 -147.85 -147.85 0.00 0.00 0.00 n-local -20.54 -20.54 -20.54 0.00 0.00 0.00 augment 5.55 5.55 5.55 0.00 0.00 0.00 Kinetic 126.50 126.50 126.50 0.00 0.00 0.00 ------------------------------------------------------------------------------------Total -0.77 -0.77 -0.77 0.00 0.00 0.00 in kB -2.41 -2.41 -2.41 0.00 0.00 0.00 external pressure = -2.41 kB Pullay stress = 0.00 kB?nal timing informationG. K RESSE , H ANDSON(I): 11 OatomPage 12Some comments on this particular runthe relevant energy for molecules and atoms is energy without entropyenergy without entropy= -0.005752 energy(sigma-&0) = -0.160014three degenerate p orbitals are occupied by 2/3 electrons causing a unphysical electronic entropyentropy T*S EENTRO = -0.a tiny value for SIGMA=0.01 would reduce the entropy but might slow convergence (default is SIGMA=0.2) SIGMA controls the electronic temperature, which is not a very meaningful quantity for molecules and atoms the total energy is found to be essentially zero VASP subtracts from any calculated energy the energy of the atom in the con?guration for which the pseudopotential was generated all pseudopotentials were generated using non spin polarized reference atomsG. K RESSE , H ANDSON(I): 11 OatomPage 13Restart vasp in same directoryvasp.4.6.2 07Jul02 POSCAR found : 1 types and 1 ions LDA part: xc-table for Pade appr. of Perdew found WAVECAR, reading the header POSCAR, INCAR and KPOINTS ok, starting setup WARNING: wrap around errors must be expected the WAVECAR file was read sucessfully initial charge from wavefunction entering main loop N E dE d eps ncg rms DAV: 1 -0. -0.3.1 0.899E-03 DAV: 2 -0. 0.6.1 0.353E-03 1 F= -. E0= -. d E =-. writing wavefunctionsrms(c) 0.157E-03when vasp is restarted the WAVECAR ?le is read and the run is continued from the previous wavefunctions (converging rapidly)G. K RESSE , H ANDS (I): 1ON1 OatomPage 14Spin polarized calculationthe O atom is an open shell system with 2 unpaired electrons add ISPIN=2 to the INCAR ?le remove WAVECAR and restart vasp (alternatively copy all input ?les from?vw/1 2 Oatomspin)vasp.4.6.2 07Jul02 POSCAR found : 1 types and 1 ions ... entering main loop N E dE DAV: 1 0. 0.38975E+02 DAV: 2 0. -0.35796E+02 DAV: 3 -0. -0.43697E+01 DAV: 4 -0. -0.71103E-01 DAV: 5 -0. -0.85968E-03 ... DAV: 11 -0. 0.1 F= -. E0= -. writing wavefunctionsG. K RESSE , H ANDSONd eps -0.1.3.3.6.85961E-03ncg 32 64 32 32 48rms 0.259E+02 0.438E+01 0.327E+01 0.508E+00 0.504E-01rms(c)0.653E+00-0.4 0.131E-01 d E =-. mag= 1.9986(I): 12 OatomspinPage 15Spin polarized calculationk-point 1 : 0.0 0.0000 band No. band energies occupation 1 -25.00 2 -10.00 3 -10.00 4 -10.00 5 -0.00 6 1.00 7 1.00 8 1.00 spin component 2 k-point 1 : 0.0 0.0000 band No. band energies occupation 1 -21.00 2 -7.33 3 -7.33 4 -7.33 5 -0.00 6 1.00 7 1.00 8 1.00(I): 1eigenstates for spin up and spin down are calculated “separately” in LSDA they interact only via the effective local potential spin-up and spin-down potential in the OUTCAR ?le, one can see two spin components the spin component 1 has 2 more electrons corresponding the a magnetization of 2 ?BG. K RESSE , H ANDSON2 OatomspinPage 16Symmetry broken O atomin the GGA, most atoms are characterized by a symmetry broken solution VASP however symmetrizes the charge-density according to the determined symmetry of the cell check the OUTCAR ?le, which symmetry is VASP using to lower the symmetry simply change the lattice parameters to 7.0 8.0 and 9.0 in the POSCAR ?le (alternatively copy all input ?les from?vw/1 3 Oatomspinlow):7.0 0.0 0.0 0.0 7.5 0.0 0.0 0.0 8.0 ! lattice vector ! lattice vector ! lattice vector a(1) a(2) a(3)and reduce SIGMA to SIGMA=0.01 (INCAR ?le) rerunning VASP you will ?nd a much lower energyvasp.4.6.2 07Jul02 ... DAV: 17 -0.E+01 -0.5.3 1 F= -. E0= -. d E =-. mag=0.128E-02 1.9997G. K RESSE , H ANDS ON (I): 13 OatomspinlowPage 17Let’s add another atom: the O2 dimercopy the required ?les and start VASP (see footnote) POSCAR:O atom in a box 1.0 ! 8.0 0.0 0.0 ! 0.0 8.0 0.0 ! 0.0 0.0 8.0 ! 2 ! cart ! 0 0 0 ! 0 0 1.22 ! universal scaling parameters lattice vector a(1) lattice vector a(2) lattice vector a(3) number of atoms positions in cartesian coordinates first atom second atomINCAR:SYSTEM = ISMEAR = ISPIN = NSW = 5 IBRION = O2 dimer in a box 0 ! Gaussian smearing 2 ! spin polarized calculation ! 5 ionic steps 2 ! use the conjugate gradient algorithmG. K RESSE , H ANDSON(I): 14 OdimerPage 18Relaxing the O2 dimerwe have inserted that geometry relaxation should be performed: in this case 5 ionic steps (NSW = 5) should be done at most for the relaxation a conjugate gradient algorithm is used IBRION = 2 CG requires a line minimizations along the search directionx0 x0 x1 x1 xtrial 2 xtrial 1this is done using a variant of Brent’s algorithm C trial step along search direction (gradient scaled by POTIM) C quadratic or cubic interpolation using energies and forces at x0 and x1 allows to determine the approximate minimum C continue minimization, if app. minimum is not accurate enoughG. K RESSE , H ANDSON(I): 14 OdimerPage 19Relaxing the O2 dimerDAV: 1 0.E+02 0.5.3 0.528E+02 ... DAV: 11 -0.E+01 -0.8.5 0.746E-02 1 F= -. E0= -. d E =-. mag= 2.0000 curvature: 0.00 expect dE= 0.000E+00 dE for cont linesearch 0.000E+00 trial: gam= 0.00000 g(F)= 0.111E+00 g(S)= 0.000E+00 ort = 0.000E+00 (trialstep = 0.100E+01) search vector abs. value= 0.111E+00 bond charge predicted ... 2 F= -. E0= -. d E =0. mag= 2.0000 trial-energy change: 0. .order 0...484030 step: 0.1406(harm= 0.1859) dis= 0.00726 next Energy= -9.862210 (dE=-0.767E-02) bond charge predicted ... 3 F= -. E0= -. d E =-. mag= 2.0000 curvature: -0.09 expect dE=-0.448E-05 dE for cont linesearch -0.448E-05 trial: gam= 0.00000 g(F)= 0.484E-04 g(S)= 0.000E+00 ort =-0.231E-02 (trialstep = 0.828E+00) search vector abs. value= 0.484E-04 reached required accuracy - stopping structural energy minimisationG. K RESSE , H ANDSON(I): 14 OdimerPage 20CG: What does all this mean?the quantity trial-energy change is the change of the energy in the trial step the ?rst value after 1.order is the expected energy change calculated from the forces ((F start F trial 2 change of positions) central difference second and third value corresponds to F start change of positions change of positions and F trialthe value step: is the estimated size of the step leading to a line minimization along the current search direction harm is the optimal step using a second order (or harmonic) interpolation the trial step size can be controlled by the parameter POTIM the value step: times the present POTIM is usually optimal the ?nal positions after the optimisation are stored in CONTCAR you can copy CONTCAR to POSCAR and continue the relaxationG. K RESSE , H ANDSON(I): 14 OdimerPage 21Let’s add another species: the CO moleculescopy required ?les and start VASP POSCAR:... 1 1 cart 0 0 0 0 0 1.12 ! ! ! ! number of atoms for each species positions in cartesian coordinates first atom second atomPOTCAR is created by the concatenation of two individual POTCAR ?les corresponding to O and C; e.g.: cat ?vw/potpaw_PBE/O/POTCAR ?vw/potpaw_PBE/C/POTCAR &POTCARa similar relaxation as in the previous case is performed but in this case more steps are required, since the ?rst estimate for the minimum is not very accurate the trial steps are much too long (POTIM parameter)G. K RESSE , H ANDSON(I): 15 COPage 22Relaxing the CO dimer1 F= -. E0= -. d E =-. curvature: 0.00 expect dE= 0.000E+00 dE for cont linesearch 0.000E+00 trial: gam= 0.00000 g(F)= 0.822E+00 g(S)= 0.000E+00 ort = 0.000E+00 (trialstep = 0.100E+01) search vector abs. value= 0.822E+00 ... 2 F= -. E0= -. d E =0. trial-energy change: 2. .order 1...446784 step: 0.1925(harm= 0.1925) dis= 0.02710 next Energy= -14.843291 (dE=-0.791E-01) ... 3 F= -. E0= -. d E =0. curvature: -0.10 expect dE=-0.909E-01 dE for cont linesearch -0.909E-01 ZBRENT: interpolating opt : 0.0929 next Energy= -14.802370 (dE=-0.382E-01) ... 4 F= -. E0= -. d E =-. curvature: -0.04 expect dE=-0.341E-03 dE for cont linesearch -0.341E-03 trial: gam= 0.00000 g(F)= 0.844E-02 g(S)= 0.000E+00 ort =-0.833E-01 (trialstep = 0.819E+00) search vector abs. value= 0.844E-02 reached required accuracy - stopping structural energy minimisationG. K RESSE , H ANDSON(I): 15 COPage 23Vibrational frequencies of the CO dimerSYSTEM = CO dimer in a box ISMEAR = 0 ! Gaussian smearing IBRION = 5 ! vibrational spectrum NFREE = 2 ! use central differences POTIM = 0.02 ! 0.02 stepwidth NSW = 1 ! ionic steps must be larger 0 (that’s all)POSCAR:sel cart 0 0 0 0 0 1.143 ! ! F F F F selective degrees of freedom are changed positions in cartesian coordinates T ! first atom T ! second atomthe selected degrees of freedom are displaced once in the direction x and once ? ? 0.02 Ax by ?in the present case this makes 4 displacements plus the equilibrium positions (i.e. a total of ?ve ionic con?gurations)G. K RESSE , H ANDSON(I): 16 COvibPage 24SECOND DERIVATIVES (NOT SYMMETRIZED) -----------------------------------1Z 2Z 1Z -114..Z 114.4.305971 Eigenvectors and eigenvalues of the dynamical matrix ---------------------------------------------------1 f = 63.876494 THz 401.PiTHz
cm-1 264.172038 meV X Y Z dx dy dz 0... 0 -0.... 0 0. f/i= 0.074763 THz 0.PiTHz 2.493841 cm-1 0.309197 meV X Y Z dx dy dz 0... 0 -0.... 0 -0.655709 Eigenvectors after division by SQRT(mass) Eigenvectors and eigenvalues of the dynamical matrix ---------------------------------------------------1 f = 63.876494 THz 401.PiTHz
cm-1 264.172038 meV X Y Z dx dy dz 0... 0 -0.... 0 0. f/i= 0.074763 THz 0.PiTHz 2.493841 cm-1 0.309197 meV X Y Z dx dy dz ...G. K RESSE , H ANDSON(I): 16 COvibPage 25H2 O moleculesPOSCARH2O _2 0.52918 ! scaling parameter 15 0 0 0 15 0 0 0 15 1 2 select cart 0.00 0.00 0.00 F F F 1.10 -1.43 0.00 T T F 1.10 1.43 0.00 T T Fall coordinates are scaled by the factor 0.529 INCAR:PREC = Normal ! ENMAX = 400 ! ISMEAR = 0 ; SIGMA IBRION = 1 ! NFREE = 2 ! NSW = 10 ! EDIFFG = -0.02 ! standard precision cutoff should be set manually = 0.1 use DIIS algorithm to converge 2 independent degrees of freedom 10 ionic steps forces smaller 0.02 A/eVG. K RESSE , H ANDS ON (I): 17 H2OPage 26H2 O molecules: commentsPREC = Normal should be used in vasp.4.6 sightly more balanced setup than the default PREC = Medium I strongly urge to set the energy cutoffs manually in the INCAR ?le , as it gives you more control over the calculations for the ionic optimisation the DIIS algorithm is used this algorithm builds an approximation of the Hessian matrix and converges usually faster than the conjugate gradient algorithm it is however recommended to set the independent degrees of freedom manually EDIFFG determines when to terminate relaxation positive values: energy change between steps must be less than EDIFFG negative values: Fi i 1 NionsG. K RESSE , H ANDS ON (I): 17 H2OPage 27Interpreting the eigenstates of COthe PROCAR ?le gives valuable information of the character of the one electron states LORBIT LORBIT 10 11 DOSCAR and l decomposed PROCAR ?le DOSCAR and lm decomposed PROCAR ?lewe use LORBIT=11 to distinguish px and pz states copy the required input ?les, and check them using an editor execute vasp againG. K RESSE , H ANDSON(I): 19 COstatesPage 28PROCAR ?le:band ion 1 2 tot band ion 1 2 tot band ion 1 2 tot 3 # energy s 0.000 0.000 0.000 py 0.546 0.157 0.703 -11. # occ. pz 0.000 0.000 0.000 px 0.000 0.000 0.000 dxy 0.000 0.000 0.000 2. dyz 0.000 0.000 0.000 dz2 0.000 0.000 0.000 dxz 0.000 0.000 0.000 dx2 0.000 0.000 0.000 tot 0.546 0.157 0.7034 # energy s 0.000 0.000 0.000 py 0.000 0.000 0.000-11. # occ. pz 0.000 0.000 0.000 px 0.546 0.157 0.703 dxy 0.000 0.000 0.0002. dyz 0.000 0.000 0.000 dz2 0.000 0.000 0.000 dxz 0.000 0.000 0.000 dx2 0.000 0.000 0.000 tot 0.546 0.157 0.7035 # energy s 0.001 0.172 0.173 py 0.000 0.000 0.000-8. # occ. pz 0.135 0.261 0.396 px 0.000 0.000 0.000 dxy 0.000 0.000 0.0002. dyz 0.000 0.000 0.000 dz2 0.000 0.000 0.000 dxz 0.000 0.000 0.000 dx2 0.000 0.000 0.000 tot 0.136 0.433 0.569G. K RESSE , H ANDSON(I): 19 COstatesPage 29Let’s do some a MD for H2 OINCAR:PREC = Normal ! standard precision ENMAX = 400 ! cutoff should be set manually ISMEAR = 0 ; SIGMA = 0.1 IBRION = 0 NSW = 100 POTIM = 1.0 ! molecular dynamics ! 100 steps ! timestep 1 fsSMASS = -3 ! micro-canonical ensemble TEBEG = 2000 ; TEEND = 2000 ! temperaturetime step for this system should be around 0.5-0.7 fs POSCAR: to save time the box size is reduced to 12 a.u. OSZICAR:1 2 3 4 5 T= T= T= T= T= . . 1307. E= E= E= E= E= -. -. -. -. -. F= F= F= F= F= -. -. -. -. -.G. K RESSE , H ANDSONE0=.. E0=.. E0=.. E0=.. E0=..(I): 1EK= EK= EK= EK= EK=0.5.5.3.2.33778E+00SP= SP= SP= SP= SP=0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00SK= SK= SK= SK= SK=0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00Page 3010 H2OmdEnergy conservation-13 e(pot) 1fs e(total) 1fs e(pot) 0.5fs e(total) 0.5 fs-13.5-14-14.5-15vi020406080100G. K RESSE , H ANDSON(I): 110 H2OmdPage 31ExcersisesHow does the energy change when you decrease SIGMA to 0.01 in the INCAR ?le starting from?vw/1 1 Oatom ? Why ? Try to copy CONTCAR to POSCAR after running the example?vw/1 4 Odimer. Why is the calculation so fast ? Try to play with the parameter POTIM for the example?vw/1 4 Odimer. What is the optimal value ? What is the reason for the imaginary frequency in the example?vw/1 6 COvib. Does the behavior improve when the step width (smaller or larger) is changed. Also try to improve the precession to which the groundstate is converged (EDIFF=1E-5). What happens if the accuracy of the calculations is improved (PREC=Accurate). Try to use the conjugate gradient algorithm to the H2 O molecule (example ?vw/1 7 H2O). Calculate the vibrational frequencies of the H2 O molecule (example?vw/1 7 H2O) after relaxation (example?vw/1 8 H2Ovib). Why does one ?nd 3 modes that haveG. K RESSE , H ANDSON(I): 110 H2OmdPage 32small frequencies. EDIFF=1E-5 gives much improved results than EDIFF=1E-4, can you reproduce this behavior.G. K RESSE , H ANDSON(I): 110 H2OmdPage 33The following participants have to share one terminal: M¨ ller and Sahli (ETH Z¨ rich) u u Koza and Poehlmann (Univ. Montpellier) Mok and Soon (Univ. Singapore) Calatyyud and Mguig (Univ. P.and M. Curie)possibly, if we encounter troubles: Hobbs and Milazzo (Kings College, London) Garcia-Vergniory and Rodriguez (Univ. Bilbao, Spain) Cordente and Ricardo Chavez (Univ. Toulouse)G. K RESSE , H ANDSON(I): 110 H2OmdPage 34Hands on Session II:Robert LORENZ¨ Institut fur Materialphysik and Center for Computational Material Science Universit¨ t Wien, Strudlhofgasse 4, A-1090 Wien, Austria ab-initioackage ienna imulationR. L ORENZ , “C RYSTAL S TRUCTURE O PTIMIZATIONANDBAND - STRUCTURE C ALCULATIONS ”Page 1OutlineKPOINTS ?le (DOS and Bandstructure) searching the optimal lattice parameter interpreting the OUTCAR ?le electronic density of states and bandCstructure relaxing the structure relaxing internal degrees of freedomR. L ORENZ , “C RYSTAL S TRUCTURE O PTIMIZATIONANDBAND - STRUCTURE C ALCULATIONS ”Page 2Getting Startedtodays worklist: Si C setup bulk calculation for different crystal structures C ?nd the optimal volume / lattice parameter (automated volume scan) C DOS and Bandstructure C Crystal Structure Optimization Ni C setup fcc Ni (spinpolarized) C determine optimal lattice parameter C DOS ?les required for this session can be found in ?vw/2_1_description_of_job1 ?vw/2_2_description_of_job2R. L ORENZ , “C RYSTAL S TRUCTURE O PTIMIZATIONANDBAND - STRUCTURE C ALCULATIONS ”Page 3BasicsPOTCAR all calculations use GGA PotentialC?le POTCAR from ?vw/potpaw_GGA/Si ( ?vw/potpaw_PBE/Ni) from the vasp potential database Si PAW PBE Si 05Jan2001 Si: s2p2, ENMAX = 245.345; EAUG = 322.069 Ni PAW PBE Ni 06Sep2000 Ni: ENMAX = 269.533; EAUG = 544.565R. L ORENZ , H ANDS ON (III):Page 4insulators: fcc SiINCAR initial charge-density from overlapping atoms energy cut-off: 240 eV (from POTCAR) KPOINTS equally spaced mesh odd centered on Γgeneral: System = fcc Si ISTART = 0 ; ICHARG=2 ENCUT = 240 ISMEAR = 0; SIGMA = 0.1;K-Points 0 Monkhorst Pack 11 11 11 0 0 0results in 56 k-points in IBZR. L ORENZ , H ANDS ON (III): 21 fccSi (fcc Si)Page 5insulators: fcc Si continuedPOSCAR ? fcc Si lattice constant 3.9 A 1 atom in cell groundstate volume ? calculate energy for different lattice parameters ?t to some equation of states to obtain the equilibrium volumefcc Si: 3.9 0.5 0.5 0.0 0.0 0.5 0.5 0.5 0.0 0.5 1 cartesian 0 0 0?les used in this example: POTCAR KPOINTS INCAR POSCARR. L ORENZ , H ANDS ON (III): 21 fccSi (fcc Si)Page 6automated volume scansearching the optimal lattice parameter automated batch job: write a script store energy vs lattice parameter (Volume) very fast use one of those famous visualization tools like Mma to ?nd optimum lattice parameterR. L ORENZ , H ANDS ON (III): 21 fccSi (fcc Si)Page 7#! /bin/bash BIN=?vw/bin/vasp.4.6 rm WAVECAR for i in 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 ; do cat &POSCAR &&! fcc: $i 0.5 0.5 0.0 0.0 0.5 0.5 0.5 0.0 0.5 1 cartesian 0 0 0 ! echo &a= $i& ; $BIN E=‘tail -1 OSZICAR‘ ; echo $i $E &&SUMMARY.fcc done cat SUMMARY.fccloop.sh Unix bash script use lattice parameters from ? 3 5 to 4 3 A Result in SUMMARY.fccR. L ORENZ , H ANDS ON (III): 21 fccSi (fcc Si)Page 8automated volume scan (continued)SUMMARY.fcc Energy vs. lattice parameter3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.41 1 1 1 1 1 1 1 1 1 1F= F= F= F= F= F= F= F= F= F= F=-. -. -. -. -. -. -. -. -. -. -.E0= E0= E0= E0= E0= E0= E0= E0= E0= E0= E0=-. -. -. -. -. -. -. -. -. -. -.d d d d d d d d d d dE E E E E E E E E E E=-. =-. =-. =-. =-. =-. =-. =-. =-. =-. =-.R. L ORENZ , H ANDS ON (III): 21 fccSi (fcc Si)Page 9DOS (fcc Si)perform a static (NSW=0, IBRION=-1) self-consistent calculation DOSCAR large system 1. convergence with a small number of kpointsDOS in2. for DOS; increase the number of kpoints and set ICHARG=11, chargeCdensity (CHGCAR) from the last self-consistent run C ICHARG=11 treats all k-points independently C charge density and the potential ?xed C BandstructureR. L ORENZ , H ANDSON(III): 22 fccSi dos (fcc Si density of states)Page 10DOS (fcc Si)INCAR read CHGCAR from previous run set smearing to ?t the problem KPOINTS2general: System = fcc Si ICHARG=11 #charge read file ENCUT = 240 ISMEAR = -5 #tetrahedron K-Points 0 Monkhorst Pack 21 21 21 0 0 01.5DOS10.50 -20-100 E-EF (eV)1020R. L ORENZ , H ANDSON(III): 22 fccSi dos (fcc Si density of states)Page 11Bandstructure (fcc Si)KPOINTS ? k-points along line L 10 points per line keyword line to generate bandstructure0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1 1 1 1 1 1kpoints from kgen kpoints for bandstructure L-G-X-U K-G 10 line reciprocal 0.00 0..00 0.00000 1? Γ? X? ? UK? Γin reciprocal coordinates all points with weight 10-10-20-30LGXKR. L ORENZ , H ANDS ON (III): 23 fccSi band (fcc Si bandstructure)Page 12insulators: diamond Sicubic diamond 5.5 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 2 Direct -0.125 -0.125 -0.125 0.125 0.125 0.125POSCAR ? diamond Si lattice constant 5.5 A fcc cell 2 atoms in cell calculate energy vs. lattice parameter C execute ?vw/2_4_diamondSi/loopR. L ORENZ , H ANDS ON (III): 24 diamondSi (diamond Si)Page 13insulators: diamond Si (continued)SUMMARY.diamond Energy vs. lattice parameter ? a 5 465 A for DOS and bandstructure rounded to ? a 55A5.1 5.2 5.3 5.4 5.5 5.6 5.71 1 1 1 1 1 1F= F= F= F= F= F= F=-. -. -. -. -. -. -.E0= E0= E0= E0= E0= E0= E0=-. -. -. -. -. -. -.d d d d d d dE E E E E E E=-. =-. =-. =-. =-. =-. =-.R. L ORENZ , H ANDS ON (III): 24 diamondSi (diamond Si)Page 14Density of StatesSi diamond a=5.5A2.0BandstructureBandstructure Si diamond5 0 -51.5DOS1.0-10 -15 -200.0 -15 -10 -5 E-EF (eV) 0 5 100.5LGX UKGR. L ORENZ , H ANDS ON (III): 24 diamondSi (diamond Si)Page 15relaxing the structure?t the energy over a certain volume range to an equation of states (see last pages) relaxing the structure with vasp C IBRION=2 conjugate-gradient algorithm C ISIF=3 change internal parameters & shape & volumeSystem = diamond Si ISMEAR = 0; SIGMA = 0.1; ENMAX = 240 IBRION=2; ISIF=3 ; NSW=15 EDIFF = 0.1E-04 EDIFFG = -0.01NSW=15 15 steps of ionic relaxation increase accuracy of electronic steps ? forces on ions smaller than 0 01 eV/AR. L ORENZ , H ANDS ON (III): 24 diamondSi vol rex (diamond Si)Page 16relaxing the structure (cont)------------------------------------------------------------------------------------Total 0.00 0.00 0.00 0.00 0.00 0.00 in kB 0.05 0.05 0.05 0.00 0.00 0.00 external pressure = 0.05 kB Pullay stress = 0.00 kB VOLUME and BASIS-vectors are now : ----------------------------------------------------------------------------energy-cutoff : 240.00 volume of cell : 40.81from equation of state a relaxing the structure a? 5 488 A(volume scan) ? 5 465 Adifference is is due to the Pulay stress C increase the plane wave cutoff by 30% (ENMAX) C use small EDIFFR. L ORENZ , H ANDS ON (III): 24 diamondSi vol rex (diamond Si)Page 17Crystal Structure Optimization (Summary)calculation of the equilibrium volume C ?t the energy over a certain volume range to an equation of states C when internal degrees of freedom exist (e.g. c/a), the structure must be optimized IBRION = 2 at each volume NSW = 10 ISIF=4 conjugate-gradient algorithm e.g. 10 ionic steps change internal parameters & shapesimpler but less reliable: relaxing all degrees of freedom including volume C to relax all degrees of freedom use: ISIF=3 change internal parameters & shape & volume C mind Pulay stress problem (details in Section Accuracy) increase cutoff by 25-30% when the volume is allowed to change (e.g. Si ENMAX = 300)R. L ORENZ , H ANDS ON (III): 24 diamondSi vol rex (diamond Si)Page 18Crystal Structure Optimization (cont.)?les to watch during relaxations C STDOUT (Terminal), each electronic step is written to the terminal C OSZICAR a copy of the Terminal output C OUTCAR more detailed information on every electronic and ionic step other important ?les C CONTCAR holds the structure of the last ionic step, the structural result (also very important for restarting a relaxation) C STOPCAR stops a relaxationR. L ORENZ , H ANDS ON (III): 24 diamondSi vol rex (diamond Si)Page 19diamond Si - relaxing internal degrees of freedomINCAR NSW = 5 ionic relaxation, 5 steps IBRION = 2: rithm conjugate-gradient algo-general: System = diamond Si START = 0 ; ICHARG=2 ENCUT = 240 ISMEAR = 0; SIGMA = 0.1; NSW = 5; IBRION = 2 ISIF = 2ISIF=2 relax internal parametersR. L ORENZ , H ANDS ON (III): 26 diamond relax Si (diamond Si)Page 20diamond Si - relaxing internal degrees of freedomPOSCAR0.5 0.0 0.5 0.5 0.5 0.0fcc: 5.5 0.0 0.5 0.5 2 Direct -0.125 0.125standard diamond structure break symmetry change z position from 0 125 0 130-0.125 -0.125 0.125 0.130after 1 step:POSITION TOTAL-FORCE (eV/Angst) ----------------------------------------------------------------------------------4.50 4.830 0...25 0.6830 -0..005889 ----------------------------------------------------------------------------------total drift: -0...000001R. L ORENZ , H ANDSON(III): 26 diamondSi relax Si (diamond Si)Page 21insulators: beta-tin Sibeta Sn 4.0 1.0 0.0 0.0 0.0 1.0 0.0 0.5 0.5 0.26 2 Direct -0.125 -0.375 0.25 0.125 0.375 -0.25POSCAR ? beta-tin Si lattice constant A 2 atoms in cell use loop and determine groundstate volume 1 internal parameter, use relaxation method to determine c aR. L ORENZ , H ANDSON(III): 25 beta-tinSi (beta-tin Si)Page 22metals: fcc NiINCAR initial charge-density from overlapping atoms energy cut-off: 270 eV (default) MP-smearing (metal!) spinpolarized calculation initial moments of 1 static calculation KPOINTS equally spaced mesh, 56 kpoints odd centered at Γgeneral: SYSTEM = fcc Ni ISTART = 0 ; ICHARG=2 ENCUT = 270 ISMEAR = 1 ; SIGMA = 0.2 spin: ISPIN=2 MAGMOM = 1 K-Points 0 Monkhorst-Pack 11 11 11 0 0 0R. L ORENZ , H ANDS ON (III): 27 fccNi fcc NiPage 23metals: fcc Ni continuedPOSCAR once again the fcc structure for a the groundstate lattice ? parameter of 3.53 A usually it is a good idea to start from the experimental volume.fcc: 3.53 0.5 0.5 0.0 0.0 0.5 0.5 0.5 0.0 0.5 1 cartesian 0 0 0R. L ORENZ , H ANDS ON (III): 27 fccNi fcc NiPage 24start vasp result:... N E dE d eps ncg ... DAV: 9 -0.E+01 0.3.64 DAV: 10 -0.E+01 0.7.38 1 F= -. E0= -. d E =0. mag=fcc Ni3rms 0.646E-01 0.758E-02 0.5683rms(c) 0.891E-0221DOS0-1-2-3 -10.0-8.0-6.0-4.0 E-EF (eV)-2.00.02.0R. L ORENZ , H ANDS ON (III): 27 fccNi fcc NiPage 25metals: fcc Ni continuedloop.sh our script to scan the volume#! /bin/bash BIN=?/bin/vasp.4.6 rm WAVECAR for i in 3.0 3.1 ... .... ISMEAR = -5 RWIGS = 1.4INCAR tetrahedron method m=0.5704?B ? Wigner-Seitz radius of 1.4 AR. L ORENZ , H ANDS ON (III): 27 fccNi fcc NiPage 26SummarizeImportant: before starting any further analyses or relaxations: perform a static (NSW=0, IBRION=-1) self-consistent calculation using a few k-points save the CHGCAR ?le from this run for the further steps the charge density and the effective potential converge rapidly with increasing number of k-points. important parameter: ICHARG=11 all k-points can be treated independently, there is no coupling between them, because the charge density and the potential are kept ?xedR. L ORENZ , H ANDS ON (III): 27 fccNi fcc NiPage 27Hands on Session IIIAndreas EICHLER¨ Institut fur Materialphysik and Center for Computational Materials Science Universit¨ t Wien, Sensengasse 8, A-1090 Wien, Austria ab-initioackage ienna imulationG. E ICHLER , H ANDSON(III):SURFACESPage 1OverviewNi(100) C surface relaxation C surface energy C LDOS C surface band-structure Ni(111) C clean surface C CO adsorption C adsorption-energy C LDOS C work-function (change) C frequenciesG. E ICHLER , H ANDSON(III):SURFACESPage 2Ni(100) - surface relaxationfcc (100) surface 3.53 .5 -.5 .0 5 Selective Dynamics Cartesian .0 .0 .0 .0 .0POSCAR? Ni lattice constant 3.53 A.0 5.000001 atom per layer 5 nickel layersp11 cell?rst two layers (of one side) relaxed 3 3 53.0 1.00 2.00000 F F F T T F F F T T F F F T T? 10 59A vacuumPOTCAR PAW-GGA potential for NiA. E ICHLER , H ANDSON(III): 31 Ni 100clean relPage 3general: SYSTEM = clean Ni(100) surface ISTART = 0 ; ICHARG=2 ENCUT = 270 ISMEAR = 2 ; SIGMA = 0.2 spin: ISPIN=2 MAGMOM = 5*1 dynamic: IBRION = 1 NSW = 100 POTIM = 0.2 K-Points 0 Monkhorst-Pack 9 9 1 0 0 0INCAR initial charge-density from overlapping atoms energy cut-off: 270 eV (default) MP-smearing (metal!) spinpolarized calculation initial moments of 1 ionic relaxation KPOINTS equally spaced mesh odd centered on Γresults in 15 k-points in IBZ 1 in z-direction !A. E ICHLER , H ANDSON(III): 31 Ni 100clean relPage 4the relaxation runforces in the ?rst and last step (in OUTCAR)POSITION TOTAL-FORCE (eV/Angst) ----------------------------------------------------------------------------------0.00 0.000 0...00 1.000 0...00 3.000 0...00 5.000 0...00 7.000 0..396197 ----------------------------------------------------------------------------------total drift: 0...000485 . POSITION TOTAL-FORCE (eV/Angst) ----------------------------------------------------------------------------------0.00 0.000 0...00 1.000 0...00 3.000 0...00 5.000 0...00 7.000 0..069316 ----------------------------------------------------------------------------------total drift: 0...007076A. E ICHLER , H ANDSON(III): 31 Ni 100clean relPage 5surface energyEnergy convergenceEnergy (eV) ?25.56?25.562energy changes during relaxation from -25.560 to -25.575 eV relaxation energy E rel 15 meV surface energy of (unrelaxed) surface according σ1 2?25.564?25.566?25.568?25.57Esurf1 2Natoms Ebulk 25 560 5 5 457 0 86 eV?25.572σunrel0.2 0.4 0.6 0.8 1.0 1.2 1.4 Step 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0?25.574 0.0σσunrelE rel0 71 eVA. E ICHLER , H ANDSON(III): 31 Ni 100clean relPage 6geometryfrom CONTCAR (or OUTCAR) ?lePhonons - (100)-direction 3.00 0.0 0.0 0.0 0.0 5.0000 5 Selective dynamics Direct 0.0 0.0000 F F 0.0 0.0014 F F 0.0 0.0028 F F 0.0 0.4291 T T 0.0 0.0696 T TF F F T Tinward relaxation of surface layers Δd12 0 9 0 1 Δd12 0 0 0 14 1% 1 9%A. E ICHLER , H ANDSON(III): 31 Ni 100clean relPage 7Ni(100) - local density of statesgeneral: SYSTEM = clean (100) Ni surface ISMEAR = -5 ALGO=V spin: ISPIN=2 MAGMOM = 5*1 NPAR = 1 RWIGS = 1.4INCARtetrahedron method ? Wigner-Seitz radius of 1.4 A NPAR=1 necessary for parallel run POSCAR copy CONTCAR (optimized!) to POSCARA. E ICHLER , H ANDSON(III): 32 Ni100clean LDOSPage 8total charge # of ion s p d tot ---------------------------------------1 0.522 0.390 8.449 9.361 2 0.551 0.577 8.463 9.591 3 0.551 0.571 8.464 9.586 4 0.559 0.595 8.470 9.624 5 0.535 0.415 8.461 9.411 ----------------------------------------tot 2.72 2.55 42.31 47.57 magnetization (x) # of ion s p d tot ---------------------------------------1 -0.003 -0.023 0.715 0.689 2 -0.008 -0.028 0.618 0.582 3 -0.008 -0.029 0.618 0.582 4 -0.008 -0.028 0.621 0.585 5 -0.004 -0.024 0.705 0.678 ----------------------------------------tot -0.03 -0.13 3.28 3.12partial charge - magnetizationat the end of the OUTCAR ?le information on local charge and magnetization is given by changing RWIGS the total number of electrons within the spheres could be adapted (nickel pseudo-potential has a valence of 10) enhancement of the magnetic moment at the surface in the center “bulk likeA. E ICHLER , H ANDSON(III): 32 Ni100clean LDOSPage 9LDOSprojection onto surface layer and bulk layer each spin component is plotted separately band narrowing at surface exchange splitting larger at surfaceA. E ICHLER , H ANDSON(III): 32 Ni100clean LDOSPage 10Ni(100) - band structureICHARG general: SYSTEM ENMAX ISMEAR ALGO=V = 11 = clean (100) nickel surface = 270 = 2 ; SIGMA = 0.2INCARread in charge density (1) and do not upnon-selfconsistent run! date it (+10) set FFT grid parameters manually to same values, to make sure that CHGCAR ?le is read properlyspin: ISPIN=2 MAGMOM = 5*1 NPAR=1 RWIGS = 1.4 for consistency with parallel run: NGX = 10 ; NGY = 10 ; NGZ = 72 NGXF= 18 ; NGYF= 18 ; NGZF= 140A. E ICHLER , H ANDSON(III): 33 Ni100clean BANDPage 11kpoints for 13 reziprok .0 .2 .5 .5 .5 .2 .00000band-structure G-X-M-GKPOINTS ? 13 k-points along line Γ ? X ? M ? Γ.0 .0 .0 .2 .5 .2 .00000.0 .0 .0 .0 .0 .0 .000001 1 1 1 1 1 1 1 1 1 1 1 1in reciprocal coordinates all points with weight 1A. E ICHLER , H ANDSON(III): 33 Ni100clean BANDPage 12surface bandstructure... Static calculation charge density remains constant during run spin polarized calculation ...Bandstructure (projected)in OUTCAR status message on actual job non-selfconsistent calculationbandstructure consists mainly out of bulklike bands dots mark localization at surface layer0.00.20.40.60.81.01.21.41.6A. E ICHLER , H ANDSON(III): 33 Ni100clean BANDPage 13Ni(111) - surface relaxationgeneral: ISTART SYSTEM ENMAX ISMEAR ALGO=VINCAR= 0; ICHARG = 2 = clean (111) surface = 270 = 2 ; SIGMA = 0.2same INCAR ?le as previously for (100) surface spin-polarization neglecteddynamic: NSW=100 POTIM = 0.2 IBRION = 1A. E ICHLER , H ANDSON(III): 34 Ni111clean relPage 14Ni - (111) 3.53 .0 -0.. .. selective dynamics direct .000000 F .111111 F .222222 F .333333 T .444444 TPOSCAR similar setup as for (100) surface again 5 layers, 2 relaxed 1 444 5 196 3 53 ? 10 2A of vacuumF F F T TF F F T TA. E ICHLER , H ANDSON(III): 34 Ni111clean relPage 15surface energy - geometryPOSITION TOTAL-FORCE (eV/Angst) ----------------------------------------------------------------------------------0.00 0.000 0...12 2.000 0...56 4.000 0...00 6.000 0...12 8.000 0..174199 ----------------------------------------------------------------------------------total drift: -0...004855forces already at the beginning rather small small relaxations for compact surfaces for surface energy non-spin-polarized bulk nickel as reference ! σunrel 1 25 729 5 5 406 0 65 eV 2 (111) surface more stable than (100) surfaceA. E ICHLER , H ANDSON(III): 34 Ni111clean relPage 16Ni(111) - CO adsorptionNi - (111) 3.53 .0 -0.. .. 1 1 selective dynamics direct .000000 F .111111 F .222222 F .333333 T .444444 T .029062 T .298866 TPOSCARtwo additional types (C+O) POTCAR! CO molecule put above surface atom on-topF F F T T T T F F F T T T TzC540 ? 1 76A444 5 196 3 53 540 5 196 3 53dCO 603 ? 1 16A POTCARappend carbon and oxygen potentialsA. E ICHLER , H ANDS ON (III): 35 COonNi111 relPage 17geometryPOSITION TOTAL-FORCE (eV/Angst) ----------------------------------------------------------------------------------0.00 0.000 0...12 2.000 0...56 4.000 0...00 6.000 0...12 8.000 0...12 9.000 0...12 11.000 0..022250 ----------------------------------------------------------------------------------total drift: -0...014065small outward relaxation of surface due to adsorption Δd12 8 154 6 109 2 038 0 4% CO geometry dCO 11 063 9 909 ? 1 155A; zC 9 909 8 154 ? 1 755A.Page 18A. E ICHLER , H ANDS ON (III): 35 COonNi111 relNi(111) - 400 eV(for adsorption energy)potentials for oxygen and carbon require an energy cut-off of 400 eV. previous calculation for clean cannot be used as reference recalculate with same energy cut-off INCARENMAX = 400 general: SYSTEM = Ni(100) ISTART = 0 ICHARG = 2 ISMEAR = 2 SIGMA = 0.2 ALGO=V special: LVTOT = .TRUE.change of cut-off lowers total energy C25.730 eV (270 eV) C25.741 eV at 400 eV becomes more important for larger cells! Eads Eads Etotal Eclean ECO 14 833 0 256 eV40 83025 741we use this run also to calculate the work-function of Ni(111)A. E ICHLER , H ANDSON(III): 36 Ni111clean 400eVPage 19work-function8.0 6.0usage of simple utility vtotav gives planar average of the potential vacuum-potential E vac 5 46 eV4.0 2.0E [eV]ON0.0 ?2.0 ?4.0 ?6.0 ?8.0Fermi-level εF 0 225 eV (from OUTCAR) Φ E vac εF 5 24 eV?10.0 0 50 100 150 200 250 z(III): 3A. E ICHLER , H ANDS6 Ni111clean 400eVPage 20LDOS, workfunctiongeneral: ENMAX = 400 SYSTEM = CO adsorption on Ni(100) ISMEAR = -5 ALGO=V LDOS: LORBIT = 1 ; NPAR RWIGS = 1.40 1.29 workfunction: IDIPOL=3 LDIPOL= .TRUE. LVTOT = .TRUE.INCARfor DOS calculation ISMEAR=-5 two additional WS-radii LVTOT writes LOCPOT ?le local potential into= 1 1.11IDIPOL enables dipole correction in direction 3 active dipole corrections to potential (=dipole layer) POSCAR copy CONTCAR (optimized!) to POSCARA. E ICHLER , H ANDS ON (III): 37 COonNi111 LDOSPage 21LDOSlm-decomposed DOS helps to analyze the bonding CO 5σ,1π,2π from comparison LDOS with substrater2C hybridization with Ni-d3z2 C no interaction with dxy from symmetryA. E ICHLER , H ANDS ON (III): 37 COonNi111 LDOSPage 22workfunction8.0 6.0 4.0εF 1 66 eV (from OUTCAR)2.0vacuum-potential at 8.15 / 6.76 eV ΦCO 6 49 Φclean 5 10 eV too small result for clean surface due to too small vacuum ...E [eV]0.0 ?2.0 ?4.0 ?6.0 ?8.0?10.0 0 50 100 150 200 250 zA. E ICHLER , H ANDS ON (III): 37 COonNi111 LDOSPage 23frequenciesSYSTEM= CO on Ni111 - frequencies general: ENMAX ISMEAR ALGO EDIFFINCARthe very usual settings ... smaller termination criterion EDIFF= 400 = 2 = V = 1E-6; SIGMA = 0.2automatic frequency calculation ? (displacement 0.04 A)dynamic: NSW=100 POTIM = 0.04 IBRION = 5 NFREE = 2A. E ICHLER , H ANDS ON (III): 38 COonNi111 freqPage 24Ni - (111) + CO ontop 3.00 0......... 1 1 Selective dynamics Direct 0...0000000 F F 0...1111111 F F 0...2222222 F F 0...3314564 F F 0...4453762 F F 0...5177755 F F 0...5815997 F FPOSCAR take CONTCAR from relaxed calculation frequencies only for CO molecule and zdirection (z- and (x,y) are independent!)F F F F F T TA. E ICHLER , H ANDS ON (III): 38 COonNi111 freqPage 25frequenciesAdditional output in OUTCAR ?le for frequency calculation via ?nite difference:Finite differences progress: Degree of freedom: 1/ 2 Displacement: 1/ 2 Total: 1/ 4After the ?rst calculation for the equilibrium geometry, NFREE displacements ( POTIM) are performed for ea from these displacements the dynamical matrix is set up and diagonalized at the end of the OUTCAR ?le the C forces, C the dynamical matrix and ?nally C the eigenfrequencies and C eigenvectors (?rst normalized and then mass-weighted) are listedA. E ICHLER , H ANDS ON (III): 38 COonNi111 freqPage 26Eigenvectors and eigenvalues of the dynamical matrix ---------------------------------------------------1 f = 64.112970 THz 402.PiTHz
cm-1 265.150026 meV X Y Z dx dy dz 0... 0 0 0... 0 0 1... 0 0 0... 0 0 0... 0 0 0... 0 -0.... 0 0. f 12.362230 THz 77.PiTHz 412.359599 cm-1 51.126093 meV X Y Z dx dy dz 0... 0 0 0... 0 0 1... 0 0 0... 0 0 0... 0 0 0... 0 -0.... 0 -0.195303 =CO stretchCO-metalA. E ICHLER , H ANDS ON (III): 38 COonNi111 freqPage 27Hands on Session IVMartijn MARSMAN¨ Institut fur Materialphysik and Center for Computational Material Science Universit¨ t Wien, Sensengasse 8/12, A-1090 Wien, Austria ab-initioackage ienna imulationM. M ARSMAN , H ANDS ON (4):MAGNETISMPage 1Overviewfcc Ni, an elementary ferromagnetic metal NiO, antiferromagnetic coupling LSDA+U (Dudarev’s approach) SOI: freestanding fcc Fe and Ni (100) monolayers Constraining magnetic moments What to do about convergence problems?M. M ARSMAN , H ANDS ON (4):MAGNETISMPage 2fcc NiPOSCAR ? Volume set to 10.93 A fcc primitive cell KPOINTS 11 11 11 Γ-centered Monkhorst-Pack grid POTCAR makepaw_GGA Ni (a PAW-GGA PW91 potential)fcc: -10.93 0.5 0.5 0.0 0.0 0.5 0.5 0.5 0.0 0.5 1 Cartesian 0 0 0k-points 0 Gamma 11 11 11 0 0 0M. M ARSMAN , H ANDS ON (4): 4 1 N IPage 3SYSTEM ISTART ISPIN MAGMOM ISMEAR VOSKOWN LORBIT= = = = = = =Ni fcc bulk 0 2 1.0 -5 1 11INCAR Spin polarized calculation (collinear) Initial magnetic moment: 1 ?B Interpolation of the correlation part of the exchange-correlation functional according to: S. H. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58, ). k-mesh integration: tetrahedron method with Bl¨ chl’s correco tions Orbital resolved DOS and calculation of local magnetic momentOr copy the ?les from: ?vw/4_1_NiM. M ARSMAN , H ANDS ON (4): 4 1 N IPage 4The magnetic momentIn OSZICAR (total magnetic moment):N E dE d eps ncg DAV: 1 0.E+02 0.1.38 DAV: 2 -0.E+01 -0.2.12 DAV: 3 -0.E+01 -0.2.16 DAV: 4 -0.E+01 -0.2.24 DAV: 5 -0.E+01 -0.3.32 ... DAV: 9 -0.E+01 0.4.96 DAV: 10 -0.E+01 0.6.74 1 F= -. E0= -. d E =0. mag= rms 0.828E+02 0.123E+02 0.140E+01 0.459E-01 0.173E-02 0.839E-01 0.126E-01 0.5781 rms(c)0.793E+00 0.847E-02in OUTCAR (integration of magnetic moment in the PAW sphere):magnetization (x) # of ion s p d tot ---------------------------------------1 -0.007 -0.026 0.625 0.591M. M ARSMAN , H ANDS ON (4): 4 1 N IPage 5DOSfcc Ni n(E) (states/eV atom) 3 2 1 0 ?1 ?2 ?3 ?4 ?2 0 2 4 6 E(eV)Exchange splitting0.5 eVPage 6M. M ARSMAN , H ANDS ON (4): 4 1 N IProper initialization of magnetic momentToo small initial moment will/may lead to a nonmagnetic solution (the previous example with MAGMOM = 0.0)... DAV: 9 -0.E+01 0.3.31 DAV: 10 -0.E+01 -0.7.49 1 F= -. E0= -. d E =0. mag= 0.339E-01 0.106E-01 0.E-02Badly initialized calculations take longer to converge Coexistence of low- and high spin solutionsM. M ARSMAN , H ANDS ON (4): 4 1 N IPage 7Noncollinear magnetismReplace ISPIN = 2 and MAGMOM = 1.0 by:LNONCOLLINEAR = .TRUE. MAGMOM = 0.0 0.0 1.0leads toDAV: 9 -0.E+01 0.4.42 0.330E-01 0.695E-02 DAV: 10 -0.E+01 0.5.58 0.446E-02 1 F= -. E0= -. d E =0. mag= 0.0 0.5792or with MAGMOM = 1.0 0.0 0.0DAV: 9 -0.E+01 0.4.58 0.330E-01 0.692E-02 DAV: 10 -0.E+01 0.6.58 0.432E-02 1 F= -. E0= -. d E =0. mag= 0.0 0.0000idem for MAGMOM = 0.0 1.0 0.0DAV: 9 -0.E+01 0.4.52 0.330E-01 0.692E-02 DAV: 10 -0.E+01 0.6.52 0.434E-02 1 F= -. E0= -. d E =0. mag= 0.2 0.0000M. M ARSMAN , H ANDS ON (4): 4 1 N IPage 8NiORocksalt structure AFM ordering of Ni (111) planesM. M ARSMAN , H ANDS ON (4): 4 2 N I OPage 9NiO AFM 4.17 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 2 2 Cartesian 0.0 0.0 0.0 1.0 1.0 1.0 0.5 0.5 0.5 1.5 1.5 1.5 k-points 0 Gamma 4 4 4 0 0 0POSCAR AFM coupling: 4 atoms in the basis (instead of 2) KPOINTS 4 4 4 Γ-centered Monkhorst-Pack grid POTCAR makepaw Ni O_s (PAW-LDA potentials)M. M ARSMAN , H ANDS ON (4): 4 2 N I OPage 10SYSTEM ISPIN MAGMOM ENMAX EDIFF ISMEAR AMIX BMIX AMIX_MAG BMIX_MAG LORBIT= NiO = 2 = 2.0 -2.0 2*0 = 250 = 1E-3 = -5INCAR Initial magnetic moment: 2 ?B (Ni), 0 ?B (O) AMIX=0.2 and AMIX MAG=0.8 (default) BMIX and BMIX MAG practically zero, i.e. linear mixing Or copy the ?les from:= = = =0.2 0. 0.00001?vw/4_2_NiO= 11M. M ARSMAN , H ANDS ON (4): 4 2 N I OPage 11The magnetic momentIn OSZICAR (total magnetic moment = 0!):N E dE d eps ncg rms 0.298E-01 0.107E-01 0.0000 rms(c) 0.169E-02 ... DAV: 13 -0.E+02 0.1.1 DAV: 14 -0.E+02 -0.1.2 1 F= -. E0= -. d E =0. mag=in OUTCAR (integration of magnetic moment in the PAW sphere):magnetization (x) # of ion s p d tot ---------------------------------------1 -0.012 -0.014 1.245 1.219 2 0.012 0.014 -1.242 -1.216 3 0.000 -0.001 0.000 -0.001 4 0.000 -0.001 0.000 -0.001 -----------------------------------------------tot 0.000 -0.003 0.003 0.000M. M ARSMAN , H ANDS ON (4): 4 2 N I OPage 12Total DOS, and LDOS Ni d-orbitalsDOS n(E) (states/eV atom) n(E) (states/eV atom) 8 6 4 2 0 ?2 ?4 ?6 ?8 ?4 ?2 0 2 4 E(eV) 6 8 10 4 2 0 ?2 ?4 ?4 ?2 0 2 4 E(eV) 6 8 10 Ni d?LDOS t2g egmNi = 1.21 ?B (exp. 1.70 ?B )Egap = 0.44 eV (exp. 4.0 eV)M. M ARSMAN , H ANDS ON (4): 4 2 N I OPage 13LSDA+U; Dudarev’s approach... LDAU LDAUTYPE LDAUL LDAUU LDAUJ LDAUPRINTaddition to INCAR of NiO calc.= = = = = = .TRUE. 2 2 -1 8 00 0.00 0.95 0.00 2Switch on L(S)DA+U Select Dudarev’s approach (LSDA+U Type 2) L quantum number for which on site interaction is added (-1 = no on site interaction) U parameter J parameter Print occupation matrices in OUTCAR L,U, and J must be speci?ed for all atomic types!Or copy the ?les from: ?vw/4_3_NiO_LSDA+UM. M ARSMAN , H ANDSON(4): 4 3 N I O LSDA+UPage 14On site occupancies (see OUTCAR)atom = 1 type = 1 l = 2onsite density matrix ... ... occupancies and eigenvectors o o o o o o o o o o = = = = = = = = = = 0.6 0.0 0.3 0.3 1.8 v v v v v v v v v v = 0.0 0.0 0.0000 = 0.0 0.0 0.0000 = 0.0 0.0 0.0000 = 0.0 0.0 0.0000 = 0.0 0.0 0.0000 = -0.6 0.2 -0.0039 = 0.4 -0.9 -0.0001 = 0.4 0.4 0.0000 = -0.6 -1.6 0.0000 = 0.7 0.7 1.3 0.7 0.4 0.0 0.0 0.6 -0.7 -0.1 -0.1 0.6 0.0 0.2 0.6 -0.4 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0000dxydyzdz2r2dxz dx2y2dxydyz dz2r2dxz dx2y2M. M ARSMAN , H ANDSON(4): 4 3 N I O LSDA+UPage 15For comparison: when U=0 and J=0 (i.e. just LSDA) the on site occupancies are as follows:o o o o o o o o o o = = = = = = = = = = 0.2 0.5 0.7 0.8 0.9 v v v v v v v v v v = 0.0 0.0000 = 0.0 0.0000 = 0.0 0.0000 = 0.0 0.0000 = 0.0 0.0000 = 0.6 0.9974 = 0.3 0.0420 = 0.4 0.0000 = -0.7 0.0085 = 0.5 -0.0 0.8 0.1 0.6 0.0 0.9 -0.4 -0.0 0.4 0.0 0.0 0.0 -0.7 -0.9 0.0 0.4 -0.9 -0.4 -0.0 0.0 0.0 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.1 -0.0 0.0 0.0 -0.5 0.0 0.0 0.0000dxydyzdz2r2dxz dx2y2dxydyz dz2r2dxz dx2y2M. M ARSMAN , H ANDSON(4): 4 3 N I O LSDA+UPage 16The Ni d-LDOS and local magnetic momentLSDA n(E) (states/eV atom) n(E) (states/eV atom) 4 2 0 ?2 ?4 ?4 ?2 0 2 4 E(eV) 6 8 10 t2g eg 4 2 0 ?2 ?4 ?4 ?2 0 2 4 E(eV) 6 8 10 Dudarev U=8 J=0.95 t2g egmagnetization (x) # of ion s p d tot ---------------------------------------1 -0.003 -0.006 1.721 1.711 2 0.003 0.006 -1.719 -1.710 3 0.000 -0.001 0.000 -0.001 4 0.000 -0.001 0.000 -0.001 -----------------------------------------------tot 0.000 -0.002 0.002 0.000M. M ARSMAN , H ANDSON(4): 4 3 N I O LSDA+UPage 17Total EnergyOn site occupancy matrix is NOT idempotent Total energy contains penalty contribution!... DAV: 15 -0.E+02 -0.1.5 DAV: 16 -0.E+02 -0.2.1 1 F= -. E0= -. d E =0. mag= 0.104E-01 0.492E-02 0.E-02The total energy for U J (just LSDA, see below):0 is in that case always higher than for UJ0... DAV: 13 -0.E+02 0.1.1 DAV: 14 -0.E+02 -0.1.2 1 F= -. E0= -. d E =0. mag=0.298E-01 0.107E-01 0.00000.169E-02Comparing the total energies from calculations with different UJ is meaningless!M. M ARSMAN , H ANDSON(4): 4 3 N I O LSDA+UPage 18SOI: freestanding fcc Fe and Ni (100) monolayersPOSCAR Lattice constant for bulk fcc Ni ? (for Fe take a0 3