# Lobachevsky State University of Nizhni Novgorod. Polyhedron. Quick Start Guide

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1 Lobachevsky State Unversty of Nzhn Novgorod Polyhedron Quck Start Gude Nzhn Novgorod 2016

2 Contents Specfcaton of Polyhedron software... 3 Theoretcal background Interface of Polyhedron The calculaton optons The polyhedron buldng optons Man menu Settngs of Polyhedron Selecton of coordnaton polyhedrons Results Analyss of coordnaton polyhedrons Comparson of polyhedrons n the current structure Comparson of arbtrary polyhedrons

3 Specfcaton of Polyhedron software The Polyhedron software s a part of а software package called PseudoSymmetry. General features of Polyhedron are: The analyss of coordnaton polyhedrons n crystal structures; The quanttatve estmaton of the degree of smlarty of polyhedrons wth the pont model usage The quanttatve estmaton of the degree of smlarty of polyhedrons va the electron densty functon System requrements: Wndows 7, 8, 10 (64 bts); PC wth multcore processor; RAM 4 Gb or more; recommended to have CUDA-devce wth RAM 2 Gb or more. For more nformaton contact Dr. Nkolay Somov 3

4 Theoretcal background The degree of smlarty of two polyhedrons Every polyhedron can be represented as a set of vectors; every vector connects the center of the = be the representaton of the orgnal polyhedron, and the polyhedron and vertex. Let the vector set T { t } vector set S = { s } be the representaton of the standard polyhedron. Sets T and S are somorphc. Let the centers of T and S concde. The rotaton of T s descrbed by the β matrx. The scale factor and the deformaton of the standard polyhedron are descrbed by α matrx. The quanttatve estmaton of the degree of smlarty s determned as maxmum of the followng functon: n Φ( T, S ) = max p ( ) exp λ ϑ, (1) α,β = 1 where n s a number of vectors n sets T and S, Parameter ( ) x, x > 0 α s,β t p =, где x 0, x 0 max α s, β t ϑ n (1) s an angle between vectors s and t The value of ( T,S ) =. (2) ( α s,β t ) ( ) 2 ϑ = arccos. (3) α s, β t Φ s the degree of smlarty of polyhedrons T and S. The calculaton of Φ ( T,S ) requres the optmzaton of (1) wth α and β matrces. The electron densty method Let some atomc cluster be corresponded to the coordnaton polyhedron T. Also specfy the standard polyhedron S. Matrces α and β should be obtaned from (1). Electron densty functons can be calculated for these polyhedrons. Each vector s and t corresponds to -atom from the atomc cluster. The r t r α s }. electron densty functon ( ) functonal ρ s bult on { T β } vectors, and ( ) ρ on { S The quanttatve estmaton of the comparson for electron denstes ρ ( r) and ( r) S ρ uses the T where η[ρ T -1 ( r),ρ ( r) ] max K ρ ( r) ρ ( r) dv S = α,β V 2 2 = ρ T ( r) dv = ρ ( r) S V V T S, (4) K dv, (5) 4

5 where V s the volume of the unt cell. As α and β are obtaned by (1), they may not correspond to the maxmum of (4), so the addtonal refnement of (4) s needed. The expresson (5) can be calculated n the recprocal space. In ths case (5) has the next vew ( r),ρ ( r) ] max ( KV ) 1 F ( H) F ( H) η[ρ =. T S T S (6) α,β H The coeffcent К n the recprocal space can be calculated as = V 1 FT H ( ) K. (7) H 2 5

6 1. Interface of Polyhedron parts: The man wndow of the Polyhedron software s presented on fgure 1.1. Ths wndow contans next Man menu contans dfferent optons of the software; Toolbar contans short call of some optons and flters for the polyhedron buldng; Structure navgator contans the lst of atoms for the target structure; Result vewer contans representaton of results and detaled nformaton; Result navgator contans the tree of results; Output the log of the calculaton. Man menu Structure navgator Toolbar Result vewer Result navgator Output Fg Man wndow of Polyhedron 6

7 1.1. The calculaton optons Ths opton allows selectng the type of the calculaton devce: CPU The calculaton carres out on CPU only (OpenMP). CUDA The calculaton carres out on CPU and GPU (NVIDIA CUDA). Ths opton s avalable only for PC wth CUDA 2.0 compatble devces. You may use vdeo cards wth the support of CUDA (NVIDIA GTX 4xx and more) technology or specfc HPC modules (NVIDIA Tesla and etc.) To use ths feature t s necessary to select CUDA n Target devce menu and to select CUDA-devce (f you have more than one). Note: GPU usage allows to accelerate the calculaton substantally. Fg The optons of the target calculaton devce 7

8 1.2. The polyhedron buldng optons These optons allow settng dfferent flters for determnaton of polyhedrons: 1. Determne bonds by (fg a): 1.1 Max. dstance All atoms whch are located closer than the set value belong to the polyhedron. The value of the maxmal nteratomc dstance s entered n the feld Max. dstance. 1.2 Ion rad All atoms whch are located closer than the sum of the on rad belong to the polyhedron (Data Rad ). 1.3 Wan-der-Waals rad All atoms whch are located closer than the sum of the Van-der-Waals rad belong to the polyhedron (Data Rad ). 1.4 Bonds All atoms whch are located closer than specfc dstances belong to the polyhedron. The edtng of the bond length collecton carres out wth the bond length edtor (Data Bonds ). 2. Polyhedron type (fg b): 2.1 Face In ths case the polyhedron descrbed by the set of faces. Cauton: Ths method hasn t been tested enough yet! 2.2 Vertces The polyhedron s descrbed by the set of vertces (default mode). 3. Center n (fg c): 3.1 Atom The polyhedron center s set n the central atom. 3.2 Center of mass In ths case the center of the polyhedron s set n the center of mass of polyhedron. 4. Mn. tems and Max. tems These controls set the maxmum and mnmum number of polyhedron tems (for example, the number of vertces). 5. Target atoms The lst of selected atoms. You can enter labels or types of atom (the separator s the space symbol). a) b) c) Fg Optons for the polyhedron determnaton 8

9 1.3. Man menu 1. Fle (see fg a) 1.1. New project Start a new project Open project Open saved project Import structure Import structure nformaton from CIF-fle Save project as Save the project fle Global settngs The global settngs of PseudoSymmetry package PS:> Command lne of PseudoSymmetry Ext Ext program. 2. Structure (see fg b) 2.1. Rebuld geometry Ths opton starts the process of buldng new geometry of coordnaton polyhedrons wth selected optons (See secton 1.2) Out graph Prnt the structure graph n the output wndow. 3. Data (see fg c) 3.1. Bonds Run the bond collecton edtor Rad Run the atomc rad edtor Atom Informaton Run atom nformaton tool Polyhedra Run the standard polyhedron collecton edtor. 4. Analyss (see fg d) 4.1. Analyss of Polyhedra Start the calculaton of the degree of smlarty of polyhedrons for selected atoms. 4.2.Comparson of polyhedra n the current structure Ths opton allows to compare polyhedrons of the current structure. You should select one polyhedron as standard, others polyhedrons wll be orgnal (target). 4.3.Comparson of optonal polyhedra Ths opton allows to compare some polyhedrons. Orgnal polyhedrons may be mported to polyhedrons collecton from the current structure or load from the external fle. One polyhedron from ths collecton should be selected as a standard. All polyhedrons from polyhedron collecton compare wth the selected standard polyhedron Manual comparatve analyss of polyhedra Ths opton allows to compare the orgnal polyhedrons wth the standard collecton usng addtonal optons. For example, you may exclude some standard polyhedrons from analyss. 4.5.Settngs Settngs wndow of Polyhedron (See secton 1.4). a) b) c) d) Fg Man menu of Polyhedron 9

10 1.4. Settngs of Polyhedron The settngs of Polyhedron contan followng optons (fg ): Refne cycles number The maxmum number of cycles n the refnement procedure. Maxmal bond length The default value of the maxmal nteratomc dstance. Refne precson The precson of the refnement. Map sze Ths value sets the number of nodes of the 3D net. 3D net s used for searchng of the optmal polyhedron orentaton. Wth the ncrease of ths value the accuracy of calculatons also ncreases (default s 60). Delta for dervatve A value of delta n numercal dervatves. Search method The selecton of the method of the polyhedron orentaton search. Drect method of permutaton The method based on permutaton of vertces, and useful for small coordnaton only (less than 10). Fast method The method based on the optmzaton of the specal target functon (default). It requres hgh values of Map sze. Calculate the electron densty for all data Ths opton allows to run the electron densty calculaton for all studed polyhedrons. The electron densty calculaton runs automatcally after optmzaton of the functon n (1). Include central atom Ths opton ncludes the central atom n coordnaton polyhedron for the electron densty calculaton. Resoluton Ths opton sets the maxmal resoluton of data n recprocal space (angstroms). Fg Settngs wndow of Polyhedron 10

11 1.5. Selecton of coordnaton polyhedrons The structure navgator contans the lst of atoms. Each atom has coordnaton nformaton: nteratomc dstances and valence angles (fg ). Select target coordnaton polyhedrons by checkng central atoms. All atoms are checked by default, you may exclude some atoms (uncheck). Fg The structure navgator wndow 11

12 1.6. Results Result navgator wndow has the next structure (fg ): - Project Shows the short report table (fg ); o Atom Shows the full report for the target atom. Standard polyhedrons Shows the report of the refnement for the selected standard polyhedron. Fg The typcal vew of the results tree The short report table contans a detaled nformaton for all polyhedrons (fg ): the central atom Φ T,S values for them. label, the lst of standard polyhedrons and ( ) Fg The short report table Result reports contan dfferent tables of data. In ths part only the most mportant data s descrbed. The refnement nformaton table (fg ) contans next data: Name The label of polyhedron; Symmetry Symmetry group of the standard polyhedron; Type The type of polyhedron (see) Status The refnement flag, whch descrbes the lst of refned parameters; α, β and γ Euler angles for the orgnal polyhedron orentaton. These angles are refned and corresponded to the optmal orentaton of orgnal polyhedron wth respect to the standard polyhedron; 12

13 Scale X, Y and Z Scale factors of the standard polyhedron; Number of tems The number of tems n the standard polyhedron; Φ The value of Φ ( T,S ). If the electron densty method was used, the table would present addtonal nformaton. α, β and γ Euler angles ftted by the electron densty method. The average dstance for the standard polyhedron s a refned parameter. The resoluton of the electron densty s the mnmum of the nterplanar dstance. Also the result of calculaton η[ρ ( r),ρ ( r)] va (6) and other useful data are presented. T S Fg The refnement nformaton table The comparson of tems of the standard polyhedron and the orgnal polyhedron n Comparson of tems table s presented (fg ). In ths table the mnmal angles between standard and orgnal polyhedrons are presented. 13

14 Fg The comparson table Atomc clusters of orgnal and standard polyhedron n the table Atomc clusters for electron densty analyss are presented (fg ). Both clusters are n the same lattce. The center of polyhedrons are the orgn (0, 0, 0). Dstances between the polyhedron center and dedcated atoms are also presented n the table. Fg Atomc clusters 14

15 2. Analyss of coordnaton polyhedrons The step by step nstructon for the analyss of coordnaton polyhedrons s presented. I. Import atomc structure nformaton. Load CIF-fle va Fle Import structure (See secton 1.3). II. Implement flters. Set next optons: - Max. dstance = Polyhedron type = Vertces - Center n = Atom - Mn. Items = 4 - Max. Items = 5 (or more) - Target devce = CPU - Target atoms = (Empty) III. Rebuld structure. Ths operaton updates nformaton of the atomc coordnaton. Use Structure IV. Rebuld geometry menu opton or the toolbar button. Selecton of necessary coordnaton polyhedrons. See secton 1.5. Check the target atoms n the structure navgator. V. Run the calculaton. Use Analyss Analyss polyhedra menu opton or the toolbar button. VI. Vew results. See secton 1.6. VII. The electron densty method. Some polyhedrons could be analyzed by the electron densty method. Use Convoluton of Electron Densty opton of the context menu at the result navgator. 15

16 3. Comparson of polyhedrons n the current structure The Polyhedron allows to compare polyhedrons wth the same coordnaton n the current structure. One polyhedron s set to the standard polyhedron and others are set to target. In ths case we compare target polyhedrons wth the standard polyhedron whch belongs to current structure. I. IV same secton 2. Select the lst of polyhedrons wth the same coordnaton. V. Select the standard polyhedron. You may select the target atom n the atom lst and press the button Set standard atom or clck on t twce(fg. 3.1). VI. Select target polyhedrons. Select target atoms n the atom lst and press the button Add target atoms. VII. Run the calculaton by Analyss button. Fg The comparson wndow 16

17 4. Comparson of arbtrary polyhedrons The Polyhedron allows to compare arbtrary polyhedrons. The lst of polyhedrons can be formed n dfferent ways. You may mport selected polyhedrons by the context menu opton (fg. 4.1). Also you may load polyhedrons from external fles. Form the polyhedron lst by context menu optons. Select one polyhedron as standard. Run the calculaton by Analyss button. Note: In ths method the standard polyhedron Is compared wth all polyhedrons from the lst (ncludng standard). Fg The comparson wndow 17

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