C2v, E, C2 (z), v(xz), v(yz). linear functions, rotations. quadratic functions. cubic functions. A1, +1, +1, +1, +1, z, x 2, y 2, z 2, z 3, x 2 z, y 2 z.
Introduction to Character Tables. The Character Table for C2v. Transformation Properties of an s Orbital in C2v. What happens when the E operation is ...
Character table for the symmetry point group C2v as used in quantum chemistry and spectroscopy, with an online form implementing the Reduction Formula for ...
“Representations” Each symmetry operation transforms a molecule to look the same as before (. For example: The z-axis of a C2v molecule remains unchanged for ...
for C2V, C2h and C3V point group, Generators and Cyclic groups. Similarity Transformation, Table of ... Construction of character table: C2V and C3V (only).
Inspection of the C2v character table indicates that all vibrational modes will be Raman active. Since each irreducible representation has a.
#11.
the C2v point group
The C2v Point Group. This point group contains four symmetry operations: E the identity operation. C2 a twofold symmetry axis σv the first mirror plane (xz)
#12.
1 Rz xy 1
Characters of the irreducible representation ... Chem 104A, UC, Berkeley. C. 2v. Character Table. C2v ... C2v symmetry elements grouped into classes.
#13.
3_4 Character tables - Chemistry |
Deriving character tables: Where do all the numbers come from? ... e.g.: Consider an arbitrary reducible representation Γred in C2v symmetry: C2v.
#14.
1.5: Character Tables - Chemistry LibreTexts
Components of a Character Table · The Point Group · The Symmetry Operation · The Mulliken Symbols · The Characters for the Irreducible ...
Traits of a Character Table. 1. order, h is the total number of symmetry operations in the point group ... The Character Table for the C2v Point Group.
#17.
A Point Group Character Tables
trated in Table C.11 which gives the character table for point group C2v (see. Table A.5), but the symmetry operations for the twofold axes can refer to.
#18.
before class - Agapie Group
Note: Use of published character tables is not allowed for this problem set. ... For the C2v point group, the following characters can be obtained from the ...
#19.
Tables for Group Theory - Oxford - UJI
This provides the essential tables (character tables, direct products, ... C2, C3, C6, D3, D6, C2v, C3v, C6v, C2h, C3h, C6h, D3h, D6h, D3d, S6.
#20.
Character table - Wikipedia
In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, ...
#21.
Chem 59-250 Character Tables for Point Groups
that are conveniently listed as a matrix known as a Character Table. As an example, we will look at the character table for the C. 2v point group.
#22.
Group theory in action: molecular vibrations
The water molecule is C2v point group. ... unshifted atoms and the contribution to character. C2v ... 3. μ : character table, x→B1, y→B2, z→A1.
#23.
Point Groups: Likelihood for Molecules - CEM311 - Lecture ...
C2v has 4 irreps. Page 6. Character Tables. There are many sections in a character table:.
#24.
Solved Consider this C2v character table. Indicate the - Chegg
Consider this C2v character table. Indicate the meaning of the numbers appearing in the row labeled A2. And is an electric dipole transition from ...
#25.
Symmetry: Translation and Rotation
Symmetry: Translation and Rotation. The sixth column of the C2v character table indicates the symmetry species for translation along (T) and rotation.
#26.
Chapter 13. Electron Spin Double Groups ( )2J
Two examples of character tables for spin double groups are given below. Table 13-1 – The character table of the C2v M. ( )2 spin double group. C2v M.
#27.
1 EXPERIMENT 5 MOLECULAR SYMMETRY, POINT ...
MOLECULAR SYMMETRY, POINT GROUPS AND CHARACTER TABLES. NOTE: lab write-up consists of submitting ... This is the character table for the C2v point group:.
#28.
Part 2.5: Character Tables - ppt video online download
Review Character table structure Properties of Char. Tables Mulliken symbols ... -no groups for C2v Operations: E, C2, σ, σ' h = = 4 The table is square.
#29.
Answered: cis-C2H2Cl2 belongs to C2v point group ...
Using the C2v character table in the picture, i. Find the reducible representation for the given compound. ii. Determine the symmetry of moIecuIar motions (like ...
#30.
Origin of Character Tables Group Multiplication Tables
The number of elements = Group order (h) here h = 4. C2v. E. C2 σv σv'. E. E. C2 ... makes up the character table for each point group. )( )( RD. R i ii. ∑.
#31.
Applications of molecular symmetry and group theory - e-PG ...
We have to now find irreducible representations for which x, y, z, Rx, Ry, Rz are the basis. Table.3 Character table of C2v point group. C2v.
#32.
Group Theory and Symmetry dj q - Cal State LA
(use the appropriate character table in your text) ... χi is the character of the irreducible representation for the operation, x ... character table. C2v.
#33.
Character Table Hell | Physics Forums
Also how do you assingn z,y,x, Rx,.....etc. to an irreducible representation. For example in the C2v character table why does z go with A1, Rx, ...
#34.
Group Theory - Genesis Tutorials
The character table of C2V point group is given below. In cis-butadiene molecule the. Vibrational modes belonging to A2 irreducible representation are IR ...
#35.
GROUP THEORY AND ITS APPLICATIONS
Area II : Area II of the character table are the characters of the irreducible representation of the point group C2v. Area III : Area III represents the ...
#36.
1 Rz E 2 -1 0 (x
Symmetry, Point Group s and Character Tables. Character Table for C3v ... In any given representation the characters of all matrices.
#37.
Molecular Symmetry
TABLE II: Multiplication Table for the C2v Group ... As another example consider the character table of the C2v symmetry group which is shown in Table IV.
#38.
Chapter 3 – Group Theory – p. 1 - 3. Compact Course
For any group, we can set up a multiplication table, which tabulates the ... the characters and representation matrices for the symmetry group C2V from the ...
#39.
[Solved] The characters of E, C2, σv, and σ'v symmetr
Hence, the table that represents the characters of E, C2, σv, and σ'v symmetry operations, in this order, for valid irreducible representation(s) of the C2v ...
#40.
Point Group C2v - an overview | ScienceDirect Topics
any filled orbital (or set of degenerate orbitals) is totally symmetric (top row of the character table). SAQ 11.1 : Show that, for H2O, the (b1) ...
3 Character Table Group Symbol Irreducible Representations Symmetry Elements ... rotations B1 B2 A1 quadratic functions In the C2v point group px has B1 ...
#43.
Lecture Notes in Physics - ResearchGate
The character tables for each of the 32 crystallographic point groups discussed in ... Table 2.6 Character table for point group C2v. C2v.
#44.
Symmetry and Group Theory - C2v and C3v - Free Video ...
Lecture 30 : Character Tables: C2v and C3v tutorial of Symmetry and Group Theory course by Prof Prof. Anindya Datta of IIT Bombay.
#45.
Resources - Hunt Research Group
combination of the H 1s AOs and the O 2s AO. • water has C2v symmetry or belongs to the C2v point group, so we use the. C2v character table (Figure 13).
#46.
Character table of point group C2V - Big Chemical Encyclopedia
Big Chemical Encyclopedia. Chemical substances, components, reactions, process design ... Articles Figures Tables About · [<< Page.] [Page >>].
#47.
MOLECULAR SYMMETRY - Chemistry Division, Faculty of ...
The entries in a complete character table are derived by using the formal techniques of group theory. • SO2 (px). +. +. +. -. -. -. C2V (E ...
View Notes - 104A Sp09 lecture 6 from CHEM ???? at University of California, Berkeley. C2v Character Table C2v symmetry elements grouped into classes C2v A1 ...
#49.
QUESTION BANK CHP -4102 Section I
5) The character table for C2v point group is given below. In cis butadiene molecule the vibrational modes belonging to A2irreducibla representation are.
#50.
The character table of c point groups is given below in cis ...
The character table of C point groups is given below in ... The remaining IR active modes are C2v E C2 Ov Ov A 1 1 1Z,x,y,z A2 1 -1 -1 R2,Xy ...
#51.
Character Table Point Group - Never Stop Learning
2.8. Derivation of C2v Character Table. 12:50. Group ...
#52.
- - OAK RIDGE NATION - OSTI.GOV
4 THE CHARACTER TABLES OF THE POINT GROUPS ... In the C2v, C4b, and C6V groups, u v should (if possible) pass through more atoms than u; (which is.
#53.
Character Tables - VDOCUMENT
Introduction to Character Tables The Character Table for C2v Character Tables Christopher C. Cummins Massachusetts Institute of Technology ...
#54.
Character Tables for Point Groups - SlideServe
As an example, we will look at the character table for the C2v point group. Point Group Label Symmetry Operations – The Order is the total ...
#55.
How do you create a character table? - QuickAdviser
Introduction to Character Tables The Character Table for C2v Transformation Properties of an s Orbital ...
#56.
Group Theory and Symmetry, Part IV: Great or Grand, We've ...
Figure 2: Character table for the C2v point group. Enter the GOT. The standard way to reduce a reducible representation is to use the Great ...
#57.
无机化学(5.3)Symmetry and Point Groups (Part 3) - 百度文库
1 9/24/2014 Properties of Characters C2V A1 A2 B1 B2 E 1 1 1 1 C2 1 1 ... This means that character tables have the same number of rows and ...
Show that BF2Br belongs to the C2v point group. ... 4.5 Character tables: an introduction While Figure 4.10 provides a point group assignment using certain ...
#59.
MOLECULAR SYMMETRY, GROUP THEORY ...
Example: a matrix representation of the C2v point group (the allyl radical) ... Appendix B – Character tables and direct product tables. Problem sheet ...
#60.
σv σv σv - FIU Faculty Websites
... Cnv, and Cs may have a permanent dipole moment: so, pyridine (C2v) and nitroethane (Cs) may be polar. 3. The C4v character table:.
#61.
3_4 Character tables - DOCOBOOK.COM
Deriving character tables: Where do all the numbers come from? ... e.g.: Consider an arbitrary reducible representation Γred in C2v symmetry: C2v.
#62.
UNIVERSITY OF SWAZILAND FINAL EXAMINATION ... - Library
Decision Tree (Flow chart) for point groups ... The C2h character table is in part: ... Use the accompanying C2v character table to determine possible ...
#63.
Chem 59-250 Character Tables for Point Groups - DOKUMEN ...
As an example, we will look at the character table for the C2v point group. 1-1-11B2. -11-11B1. -1-111A2. 1111A1. v (yz)v (xz)C2EC2V. Representation of B2.
#64.
Irreducible Representation
Part 2.6: Using Character Tables. 1. Using Character Tables. Basis Functions; Representations. Reducible; Irreducible. Red. to Irr. Reps; Examples.
#65.
How to build Character Tables - All 'Bout Chemistry
a character table is a two-dimensional table whose rows correspond to irreducible group representations, and whose columns correspond to ...
#66.
The characters of E, C2, σv, and σ'v symmetry operations, in ...
The character table can be given as follows: ... for valid irreducible representation(s) of the C2v point group is given in the table below: ...
#67.
Quantum Chemistry problem (Symmetry and Character tables)
Formaldehyde (H2CO) is a planar molecule with C2v symmetry. ... He first writes the character table for C2v and then finds the Γ values to ...
#68.
Chemistry 6330 Problem Set 4 Answers
By inspection of the character table, the 2T2 modes are IR active and A1, E, and 2T2 ... Raman active: 3A1 + B1 + 2B2. (e) SF4 see-saw (C2v). C2v.
#69.
Appendix A: Character and Correlation Tables of Graphene
conduction state in graphene is B2,. Along the T-K line the point-group symmetry is lowered. Dhh D3h. D2h. C2v(c2') C2v(c2''). Table A.1: Correlation table ...
#70.
Use of Point Groups - Reciprocal Net
The specific vibrational motion for these three modes can be seen in the infrared spectroscopy section. For Raman, we will refer to the C2v character table:.
#71.
Contents - CiteSeerX
Most applications of group theory to molecular symmetry will involve the use of character tables. A sample character table4 for the group C2v can be seen in ...
#72.
group theory and its applications in molecular spectroscopy
Character Table (C2v. ) The functions to the right are called basis functions. They represent mathematical functions such as orbitals, rotations, etc.
#73.
509 Character Tables notes 1 - Warning: TT: undefined function
The sum of the squares times # of operations = order of the group. ‐Algebra. Classes are grouped. ‐no groups for C2v. The table is square.
#74.
Practical Group Theory and Raman Spectroscopy, Part I
in detail one of the most simple character tables — the. C2v point group, which is shown in Table I. The top row consists of the type and number of symmetry ...
#75.
Character Tables in Chemistry - [PDF Document] - Cupdf
Character Table (C2v). 14. Example: C4v. What are the characters for the z-axis for each symmetry operation ? E 2C4 C2 2 v 2 d.
#76.
Symmetry And Broken Symmetry in Molecules - Encyclopedia ...
The character table of the point group C2v. The xyz axis system is shown in. Figure 3. A couple of technical points need to be raised here. We have said that ...
#77.
E–1402
Or. How the set of elements are classified in different classes in. C3v point group ? 3. Construct a character table for C2v point group. Assign. Mulliken's ...
#78.
chapter 12 - molecular symmetry
C3v character table reveals that NH3, and other molecules of the same symmetry, can have only ... molecule belongs to the symmetry group C2v with a two-fold.
#79.
Lecture Notes: Molecular Symmetry and Optical transitions
These irreducible representations are indicated in the character table, let us call them Γx , Γy , Γz (for example, in the C2v point group, they are B1, B2, ...
#80.
4 Molecular Symmetry - NET
character table of the C2h point group is shown below. ... have the following symmetries: (i) C1; (ii) Cs; (iii) C2; (iv) C2v; (v) S4; (vi) D2.
#81.
Construction of character table - Sarah Tucker College
The group has four irreducible representations. The C2h point group is isomorphic to C2v and D2, and also to the kleenex four-group; The C2h point group is ...
#82.
Symmetry Groups - nmsu.edu is a Web Hosting
D3h. On this page you can see the character tables of most of the groups we use. I will try to update the list as soon as I can. You choose a group from the ...
#83.
If
Character table of C3v point group is given below 1 point 1 point E ... Character table-construction of character tables for C2v, C3v and C4v point groups.
#84.
Mathematical Physics 18KP1P01
Cnv groups, C2v · C3v · C4v · C5v. n group theory, a branch of abstract algebra, a character table is a two- dimensional table whose rows correspond to ...
#85.
What is character table in group theory? - FindAnyAnswer.com
In group theory, a branch of abstract algebra, a character table is a ... C2v is the symmetry point group of H2X (X=O, S, Se), SO2, ...
#86.
Point Group Tables of T d (-43m) - Bilbao Crystallographic ...
Character Table of the group Td(-43m)*. Td(-43m), #, 1, 3, 2100, -4, m110, functions. Mult. -, 1, 8, 3, 6, 6, ·. A1, Γ1, 1, 1, 1, 1, 1, x 2 +y 2 +z 2.
It is C2v and as no center of inversion, so may be both IR and Raman active. In the character table, ov(xz) is out of the molecular plane and ov(yz) is in ...
#89.
Symmetry characterization of electrons and lattice excitations
Character table and common basis functions for the point group C2v(2mm) (taken from [1]). E. C2 v v. A1 x2, y2, z2.
#90.
Point-Group Theory Tables - Theoretical Chemistry
Obtention of the character table for the double group ... tion of the group Cs that appears in the products for D2h and C2v must be.
#91.
C Tables for 3D Space Groups - UFMG
trated in Table C.11 which gives the character table for point group C2v (see. Table A.5), but the symmetry operations for the twofold axes can refer to.
#92.
c9cp03774h1.pdf - Supporting Information
Within the D3h point group (Table S.1) x and y have the E symmetry, while z has A2 . Con- ... Table 0.2 Character table for the C2v point group. C2v.
#93.
From irreducible representations to character tables - CDEEP ...
From irreducible representations to character tables ... Orthogonality of characters of different IRs. 8. [Γi (R)mn] [Γϕ (Ρ)µ ν' ']∗ = ... C2v E C2 σv.
#94.
Group Theory Analysis For Pyridine Vibrations
C2v Symmetry - Pyridine. ORIGIN ... C2v. 1. 1. 1. 1. Contribution per atom, i.e., for each x,y,z. Operation E C(θ) σ S(θ).
#95.
8. Using the C2v character table, a) determine the reducible...
8. Using the C2v character table, a) determine the reducible representations of terminal H's for CIHz (H: 1 Cl: 17) b) determine the ...
#96.
Molecular Symmetry - 第 92 頁 - Google 圖書結果
For the C2v point group, we have already found all the standard labels, ... Table 4.7 shows that the sum of the characters B1 + B2 agrees with the totals ...
#97.
Symmetry and Structure: (Readable Group Theory for Chemists)
In deriving the C2v character table in Chapter 2 it was asserted that there is no other set of characters other than those considered there which ...
6.3 Character tables In the next chapter, we will present various chemical ... As shown in Table 6.3.1, we can see that the C2v character table is divided ...
c2v character table 在 [問題] 群論... - 精華區Chemistry - 批踢踢實業坊 的推薦與評價
C3v │E 2C3 3σv
──┼──────
A1 │1 1 1
A2 │1 -1 1
E │2 -1 0
想問~是如何決定上述的數字壓?
應該是先決定數字才能判斷A1 A2吧...
數字1 -1 2 0再這代表什麼意義壓?
我還是搞不懂...
有迷有人可以告訴我 Q_Q
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: sunev (不知所謂) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Sun Nov 2 22:21:21 2003
※ 引述《vicianose ( )》之銘言：
: C3v │E 2C3 3σv
: ──┼──────
: A1 │1 1 1
: A2 │1 -1 1
1 1 -1
: E │2 -1 0
: 想問~是如何決定上述的數字壓?
就我目前學到的知識
用湊的...^^;;
: 應該是先決定數字才能判斷A1 A2吧...
沒錯...
: 數字1 -1 2 0再這代表什麼意義壓?
: 我還是搞不懂...
: 有迷有人可以告訴我 Q_Q
^^ (u和o有點遠?)
你得先了解什麼是representation
representation正如其名
是一種表達operator的方式
最一般的做法是拿xyz來做成矩陣
可以想像
representation的取法有無限多種
但數學家告訴我們
所有的representation都可以表為少數幾個
irreducible representation的線性組合
而下面的那些數字就是所謂的irreducible repersentation.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 210.85.226.46
> -------------------------------------------------------------------------- <
作者: vicianose ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Sun Nov 2 22:41:55 2003
※ 引述《sunev (不知所謂)》之銘言：
: ※ 引述《vicianose ( )》之銘言：
: : C3v │E 2C3 3σv
: : ──┼──────
: : A1 │1 1 1
: : A2 │1 -1 1
: 1 1 -1
^^^^^^^^^^^
???????????????
: : E │2 -1 0
: : 想問~是如何決定上述的數字壓?
: 就我目前學到的知識
: 用湊的...^^;;
: : 應該是先決定數字才能判斷A1 A2吧...
: 沒錯...
: : 數字1 -1 2 0再這代表什麼意義壓?
: : 我還是搞不懂...
: : 有迷有人可以告訴我 Q_Q
: ^^ (u和o有點遠?)
: 你得先了解什麼是representation
: representation正如其名
: 是一種表達operator的方式
: 最一般的做法是拿xyz來做成矩陣
: 可以想像
: representation的取法有無限多種
: 但數學家告訴我們
: 所有的representation都可以表為少數幾個
: irreducible representation的線性組合
: 而下面的那些數字就是所謂的irreducible repersentation.
我看後面其他的character table
譬如說...S4的character table會出現i
S6的character table會出現ε
簡單的character table可以用湊的，但是複雜的又該如何呢？
C3v │E 2C3 3σv│ │
──┼──────┼───────┼───────────
A1 │1 1 1 │z │x^2+y^2, z^2
A2 │1 -1 1 │Rz │
E │2 -1 0 │(x,y) (Rx,Ry) │ (x^2-y^2,xy) (xy,yz)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
不知這又怎麼出來的~Q__Q~
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: sunev (不知所謂) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Sun Nov 2 23:18:35 2003
※ 引述《vicianose ( )》之銘言：
: ※ 引述《sunev (不知所謂)》之銘言：
: : 1 1 -1
: ^^^^^^^^^^^
: ???????????????
我是用背的...
我記錯了嗎?? ^^;;
: : 但數學家告訴我們
: : 所有的representation都可以表為少數幾個
: : irreducible representation的線性組合
: : 而下面的那些數字就是所謂的irreducible repersentation.
: 我看後面其他的character table
: 譬如說...S4的character table會出現i
: S6的character table會出現ε
ε 和 i其實意謂著同一件事
就是複數的出現
好像可交換群就是會生出這種東西
Cn也是
詳細狀況我也不清楚...:p
: 簡單的character table可以用湊的，但是複雜的又該如何呢？
: C3v │E 2C3 3σv│ │
: ──┼──────┼───────┼───────────
: A1 │1 1 1 │z │x^2+y^2, z^2
: A2 │1 -1 1 │Rz │
: E │2 -1 0 │(x,y) (Rx,Ry) │ (x^2-y^2,xy) (xy,yz)
: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
: 不知這又怎麼出來的~Q__Q~
把後面的函數當成一種representation
去算其代表各operator的
就會發現這個函數的representation
恰好就是這個row的irreducible representation
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 210.85.226.46
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Mon Nov 3 22:45:46 2003
※ 引述《vicianose ( )》之銘言：
: C3v │E 2C3 3σv
: ──┼──────
: A1 │1 1 1
: A2 │1 -1 1
: E │2 -1 0
: 想問~是如何決定上述的數字壓?
: 應該是先決定數字才能判斷A1 A2吧...
: 數字1 -1 2 0再這代表什麼意義壓?
: 我還是搞不懂...
: 有迷有人可以告訴我 Q_Q
一定有個 total symmetric 的representation, 所以 A1 的就不說啦,
假設為 A2 為 a1 a2 a3
E 為 b1 b2 b3
則由 a1^2 + 2*a2^2 + 3*a3^2 = 6 (6為order =1+2+3)
應該不難湊出整數解了, 可以 a1*1 + a2*1 + a3*1 是否等於 0 確認,
a1 a2 a3 是算對;
再由
b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
即可求出 b1 b2 b3
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.118
> -------------------------------------------------------------------------- <
作者: vicianose ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Tue Nov 4 14:16:04 2003
※ 引述《barts ( )》之銘言：
: ※ 引述《vicianose ( )》之銘言：
: : C3v │E 2C3 3σv
: : ──┼──────
: : A1 │1 1 1
: : A2 │1 -1 1
: : E │2 -1 0
: : 想問~是如何決定上述的數字壓?
: : 應該是先決定數字才能判斷A1 A2吧...
: : 數字1 -1 2 0再這代表什麼意義壓?
: : 我還是搞不懂...
: : 有迷有人可以告訴我 Q_Q
: 一定有個 total symmetric 的representation, 所以 A1 的就不說啦,
: 假設為 A2 為 a1 a2 a3
: E 為 b1 b2 b3
: 則由 a1^2 + 2*a2^2 + 3*a3^2 = 6 (6為order =1+2+3)
: 應該不難湊出整數解了, 可以 a1*1 + a2*1 + a3*1 是否等於 0 確認,
: a1 a2 a3 是算對;
: 再由
: b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: 即可求出 b1 b2 b3
你的意思是說 b1 b2 b3各為 2 1 0 嗎??
但是這樣1*b1*1+2*b2*1+3*b3*1就會不=0耶...^^a
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Tue Nov 4 19:16:39 2003
※ 引述《vicianose ( )》之銘言：
: ※ 引述《barts ( )》之銘言：
: : 一定有個 total symmetric 的representation, 所以 A1 的就不說啦,
: : 假設為 A2 為 a1 a2 a3
: : E 為 b1 b2 b3
: : 則由 a1^2 + 2*a2^2 + 3*a3^2 = 6 (6為order =1+2+3)
: : 應該不難湊出整數解了, 可以 a1*1 + a2*1 + a3*1 是否等於 0 確認,
: : a1 a2 a3 是算對;
: : 再由
: : b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: : 即可求出 b1 b2 b3
: 你的意思是說 b1 b2 b3各為 2 1 0 嗎??
: 但是這樣1*b1*1+2*b2*1+3*b3*1就會不=0耶...^^a
所以 2 1 0 是錯的, 2 -1 0 才對
1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.137
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Tue Nov 4 19:26:23 2003
※ 引述《vicianose ( )》之銘言：
: ※ 引述《sunev (不知所謂)》之銘言：
: : 1 1 -1
: ^^^^^^^^^^^
: ???????????????
: : 就我目前學到的知識
: : 用湊的...^^;;
: : 沒錯...
: : ^^ (u和o有點遠?)
: : 你得先了解什麼是representation
: : representation正如其名
: : 是一種表達operator的方式
: : 最一般的做法是拿xyz來做成矩陣
: : 可以想像
: : representation的取法有無限多種
: : 但數學家告訴我們
: : 所有的representation都可以表為少數幾個
: : irreducible representation的線性組合
: : 而下面的那些數字就是所謂的irreducible repersentation.
: 我看後面其他的character table
: 譬如說...S4的character table會出現i
: S6的character table會出現ε
: 簡單的character table可以用湊的，但是複雜的又該如何呢？
: C3v │E 2C3 3σv│ │
: ──┼──────┼───────┼───────────
: A1 │1 1 1 │z │x^2+y^2, z^2
: A2 │1 -1 1 │Rz │
: E │2 -1 0 │(x,y) (Rx,Ry) │ (x^2-y^2,xy) (xy,yz)
: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
: 不知這又怎麼出來的~Q__Q~
沒錯, 簡單可以用湊的, 複雜的(非整數)很難算;
所以一般都不會考太難的, 如 Cnv, Dnh, Td, 考到Td就已經是殘忍了,
如果考 Oh 以上就沒人性啦~~~~~
至於你指的第III, IV區, 還是可以算出來, 不過, 在這很難跟你解釋;
運氣好的話, 無機會提到, 不然要等研究所的高等無機才會教!!
有興趣可參考 F.A. cotton application of group theory (書名快忘了)!!
寫得不錯, 不過第一次念不容易懂唷~~~~
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.137
> -------------------------------------------------------------------------- <
作者: vicianose ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Wed Nov 5 15:27:04 2003
※ 引述《barts ( )》之銘言：
: ※ 引述《vicianose ( )》之銘言：
: : 你的意思是說 b1 b2 b3各為 2 1 0 嗎??
: : 但是這樣1*b1*1+2*b2*1+3*b3*1就會不=0耶...^^a
: 所以 2 1 0 是錯的, 2 -1 0 才對
: 1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
但是~你前面不是說~
b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
若a1 a2 a3 = 1 -1 1
b1 b2 b3 = 2 -1 0
就不會=0了耶 ^^||
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: unamnesia ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Wed Nov 5 20:16:03 2003
※ 引述《vicianose ( )》之銘言：
: ※ 引述《barts ( )》之銘言：
: : 所以 2 1 0 是錯的, 2 -1 0 才對
: : 1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
: 但是~你前面不是說~
: b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: 若a1 a2 a3 = 1 -1 1
: b1 b2 b3 = 2 -1 0
: 就不會=0了耶 ^^||
建議去找書先從 character table 建構的五個基本定理看起，會比較有通盤的了解
我用很直觀的方式概述
1.character table 必然是 n*n 的形式，列數與行數一定恰好相等
2.E 操作的那一列 (最左方那列) 的平方和一定恰等於上頭操作元素的個數
3.同 class (像2C3 這兩個) 擁有同樣的值
4.5. 大正交定理，直列與橫排都必然彼此正交 (橫排甲*橫排乙*上頭係數 = 0)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.109.112.214
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Wed Nov 5 22:26:18 2003
※ 引述《vicianose ( )》之銘言：
: ※ 引述《barts ( )》之銘言：
: : 所以 2 1 0 是錯的, 2 -1 0 才對
: : 1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
: 但是~你前面不是說~
: b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: 若a1 a2 a3 = 1 -1 1
: b1 b2 b3 = 2 -1 0
: 就不會=0了耶 ^^||
沒有錯, 所以我再看了你的原 post;
你的原post中, A2 寫錯了, A2 應該是 1 1 -1,
因為 A2 和 A1 沒有orthorgonal
兩兩相互是 orthorgaonal的;
請再check C2v 的character table!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.137
※ 編輯: barts 來自: 140.112.55.137 (11/05 22:28)
> -------------------------------------------------------------------------- <
作者: satanfh (Satan) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Fri Nov 7 17:09:38 2003
去找個已經懂得同學解釋一次給你聽吧...
這樣最快
^_^
※ 引述《barts ( )》之銘言：
: ※ 引述《vicianose ( )》之銘言：
: : 但是~你前面不是說~
: : b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: : 若a1 a2 a3 = 1 -1 1
: : b1 b2 b3 = 2 -1 0
: : 就不會=0了耶 ^^||
: 沒有錯, 所以我再看了你的原 post;
: 你的原post中, A2 寫錯了, A2 應該是 1 1 -1,
: 因為 A2 和 A1 沒有orthorgonal
: 兩兩相互是 orthorgaonal的;
: 請再check C2v 的character table!!
--
來看看喔～ ^_^
https://oz.nthu.edu.tw/~d927536/yuxin/index.html
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.109.227.150
... <看更多>